Modeling and Simulation of Ion ChannelsChristopher Maffeo Swati Bhattacharya Jejoong Yoo David Wells and Aleksei Aksimentiev

Department of Physics University of Illinois 1110 W Green Street Urbana Illinois 61801 United States

CONTENTS

1 Introduction A2 Early Phenomenological Models B3 Most Common Targets of Computer Modeling D

31 Gramicidin A F32 Potassium Channels F33 Mechanosensitive Channels G34 Porins G35 Other Channels H

4 Most Common Simulation Methods H41 Continuum Models I

411 Electrostatics of Ion Channels I412 Ion Transport J

42 Brownian Dynamics K421 General Formulation of the BD Method K422 BD Simulations of Ion Channels K

43 All-Atom Molecular Dynamics L431 General Formulation of the All-Atom

MD Method L432 Ion Channels in Native Environment M433 Homology Modeling M434 Free-Energy Methods M435 Ionization States of Titratable Groups N436 Accelerated Molecular Dynamics Simu-

lations on a Special-Purpose Machine O44 Polarizable Models O

5 Typical Questions of Interest P51 Ion-Binding Sites and Permeation Pathways P

511 Potassium-Selective Channels P512 Gramicidin A Q513 Others Channels Q

52 Ion Conductance R521 Potassium Channels R522 Mechanosensitive Channels R523 α-Hemolysin S524 Outer-Membrane Porins S

53 Selective Permeability S531 Potassium Channels T532 Outer-Membrane Porins T

54 Ion-Channel Gating and Blockages U541 Mechanical Gating U542 Potassium Channels V543 Blockades V

55 Biosensing with Channels V551 α-Hemolysin W552 MspA X553 Other Nanopore Systems X

6 Outlook YAuthor Information Y

Corresponding Author YNotes YBiographies Y

Acknowledgments ZReferences Z

1 INTRODUCTION

Transport of ions through pores in membranes is a process offundamental importance to cell biology In living organismssuch transport is facilitated by ion channels that utilize the ionicflux to perform diverse biological functions such as cellminuscellcommunication and signaling osmotic stress response musclecontraction etc The action of ion channels is responsible formost of what we (humans) perceive as reality in the form ofsound smell sight taste and touch and forms the physiologicalbasis for thought Biomimetic ion channels are ubiquitous inengineering with application ranging from water desalinationto fuel cellsSince the discovery of excitable ionic membranes modeling

and simulation have been an integral part of the developmentof the field From the early studies of Hodgkin and Huxley tothe most recent fully atomistic simulations of ion conductancethe key challenge in this area remains the prediction ofelectrical response of a membrane incorporating ion channelsto external stimuli such as transmembrane voltage chemicalligands tension etc The ever-increasing complexity of thecomputational models of ion channels reflects the dramaticadvances of our experimental knowledge about these systemsmost importantly fully atomistic structures of several ionchannels1minus3 and direct experimental observations of a singlechannelrsquos action4minus7 with more discoveries yet to comeHere we review efforts to model and simulate ion channels

that occurred within the past 10 years First we briefly describeearly phenomenological models of excitable membranes andbriefly review recent developments in this area Next wedescribe several membrane channel systems that have been

Special Issue 2012 Ion Channels and Disease

Received June 29 2012

Review

pubsacsorgCR

copy XXXX American Chemical Society A dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXX

studied extensively by various computational approaches Ourselection of systems is based solely on their popularity amongmodelers and is neither intended to provide a representativeoverview of the evolutionary development of ion channels norpresented in any particular historical order Next we describethe most common computational methods used to study ionchannels Table 1 links the systems and methods by providingexplicit references to the studies of specific systems performedusing specific methods The second half of the review isorganized according to the most typical questions of interestion binding and permeation pathways ion conductanceselectivity and gating The last section summarizes recentdevelopment in the field of stochastic sensorsbiomimetic ionchannels with promising applications in biomedical diagnosticsAt the end of this review we briefly describe our perspective onthe development of the field within the next 10 years

2 EARLY PHENOMENOLOGICAL MODELSEarly work on phenomenological modeling of ion channelsactually occurred well before the existence of ion channels hadbeen established or even surmised395 Rather researchers wereattempting to understand the mechanism of signal propagationin nerve cells Nerve cells at rest maintain an action potentialdefined as the electrical potential of the nerve interior relativeto the exterior Rest action potentials are negative and generallyin the range of minus40 to minus95 mV395 Interestingly the axons ofnerve cells support the transmission of a pulse of slightlypositive action potential which carries the signals used forcommunication in a neural network The technique used byHodgkin and Huxley called a voltage clamp is illustratedschematically in Figure 1a In a voltage clamp experiment thetransmembrane voltage is held constant and the resultingcurrent is measured Such experiments determine themembrane permeability as a function of voltage and timeEarly models described the axon as a ldquocablerdquo with a

conductive core surrounded by a less conductive capacitivesheath later identified as a membrane This model correspondsto the circuit diagram shown in Figure 1b Further experimentsshowed that during excitation the membrane permeabilityincreases dramatically Additionally it was found that assigninga variable electromotive force or emf to the membrane provideda better fit to the experimental data yielding the circuit diagramshown in Figure 1c Finally the brilliant experiments and

insight of Hodgkin and Huxley396 established that the currentsassociated with action potential changes were in fact carried bymultiple ion species primarily K+ and Na+ This conceptual leapremoved the need for a variable emf in the equivalent circuitdiagram instead assigning separate emfs and resistances fortransport of K+ and Na+ species They also found a small so-called ldquoleakagerdquo current associated with a constant resistanceThe final circuit model is shown in Figure 1dThe realization that changes in the action potential were

manifested through multiple ion species was a major advanceExperiments isolating the K+ and Na+ permeability of themembrane revealed a fascinating twist under an externallyapplied potential K+ resistance drops and stays low while Na+

Table 1 Modeling and Simulation Studies in the General Area of Ion Channels Organized According to the System Type andComputational Models Employed

methods

system continuumimplicit solvent

MD all-atom MD hybrid CGothers(QM)

gramicidins 8minus15 16 17 18minus51 52 53 54outer-membrane porins 55minus61 55 62minus64 55 65minus87 55α-hemolysin 88minus93 88 90 94 95 90 93 96minus99 90 93 100minus102K+ channels 103minus109 110minus117 29 88 111minus113116minus197 425 595 596

602minus604107 198minus202 203minus206 207minus211

nAChR 212minus220MscLMscS 221minus228 229 225 230minus248 248minus257 258 225 222 258anion channels (VDACClC)

259 260minus264 265minus268

aquaporins 269minus274NH4

+ transporters 275minus278other channels 279minus310 311minus318 299 312 319minus348 302 330 337

349minus356357 358

synthetic nanopores 359minus370 371minus374 375minus391 350 382 383 392 393 394

Figure 1 Evolution of the equivalent circuit diagrams of nerve axonmodels (a) Schematic representation of an axon Conductanceexperiments are performed by maintaining a given transmembranevoltage and measuring the resulting ionic current (b) Cable model ofthe axon (c) Refined model including a (variable) membrane emf andvariable membrane resistance (d) HodgkinminusHuxley model whichdescribes the emfs and conductivities of potassium and sodiumseparately and also includes a small leakage current

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resistance drops initially but then returns to its previous levelFigure 2 shows the conductance of squid axon to sodium andpotassiumThe HodgkinminusHuxley or HH model describes the behavior

of the two independent ionic resistances introduced in Figure1d For convenience we restate these quantities as theirinverses the ionic conductances gK and gNa In the model gKand gNa vary between zero and maximum values gK and gNarespectively In other words

= g x gK K K

= g x gNa Na Na

The goal of the HH model is to describe the behavior of thecoefficients xK and xNa In the model xK and xNa are onlydependent on time and voltageWe first describe how the potassium coefficient xK is

represented in the HH model To best fit the experimental datathe HH model supposes that four independent particles controlthe potassium conductance Although Hodgkin and Huxley didnot know of the existence of ion channels here we will assumethat the particles control a potassium channel Figure 3aschematically shows a potassium channel and the controllingparticles Each particle may be in one of two states active orinactive In order for the channel to conduct all four particlesmust be active Following Hodgkin and Huxley let us say thatthe probability of a particle being active is n The probability ofthe channel being conductive is then n4 The average current isthen

ε= minusI n g V( )K4

K K (1)

where V is the applied voltage and εK is the emf of thepotassium channel The emf originates in the ion concentrationgradient across the membrane which is driven by ion pumpssuch as Na+minusK+ ATPase398

In the HH model the switching of a particle between activeand inactive states is described by f irst-order kinetics Because ofthis we may describe the behavior of n in terms of two valuesthe steady-state value ninfin which is the value that n approachesgiven enough time and a time constant τn which describes howquickly n approaches ninfin Mathematically the value of n obeysthe following differential equation

τ=

minusinfinnt

n ndd n (2)

Importantly ninfin and τn are functions of the applied voltage Thebehavior of ninfin and τn under a change of voltage is schematicallyshown in Figure 3c Notice that the probability of the channelbeing in a conducting state (n4) rises with increasingtransmembrane biasActivation of sodium channels in the HH model is similar to

that of potassium channels with one essential differenceinstead of four identical controlling particles sodium channelsare controlled by three identical particles and a fourth particleof a different type Let us say the probability of each of thethree particles being active is m while this probability for thefourth particle is h It is the action of this fourth particle thatcontrols deactivation of the channel under an external voltageFigure 3b shows a schematic representation of a sodiumchannel The average current through a sodium channel is then

ε= minusI h mg V( )Na3

Na Na (3)

Figure 2 Conductance of squid axon membrane to sodium (a) and potassium (b) at various applied voltages Voltage was held at the rest value ofminus65 mV then increased to the displayed value at t = 0 While potassium conductance rises and saturates under an applied potential sodiumconductance initially rises but subsequently returns to zero Adapted with permission from ref 397 Copyright 1952 Wiley

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where εNa is the emf of the sodium channel Analogously to nfor the potassium channel the behavior of h and m aredescribed by steady-state values hinfin and minfin and time constantsτh and τm obeying the differential equations

τ=

minusinfinht

h hdd h (4)

τ=

minusinfinmt

m mdd m (5)

The behavior of hinfin τh minfin and τm under a change of voltage isshown in Figure 3d The time constant τh is much higher thanτm meaning that the deactivating particle reacts much moreslowly to a change of external potential than the activatingparticles Thus we see how the conductance traces shown inFigure 2a are explained upon switching from the normalpolarized potential value (low V in Figure 3c d) to highervalues the activating particles quickly switch on due to theirlow time constant τm because of the relatively high value of τhthe inactivating particle is slow to react and continues to allowconduction eventually the inactivating particle does indeedswitch the channel back off and the conductance dropsFinally we would be remiss if we did not mention a related

theory the GoldmanminusHodgkinminusKatz (GHK) theory The GHK

theory relates voltage current and ionic permeabilities395 Oneform of the theory is the GHK voltage equation

=+ ++ +

VRTF

P P PP P P

ln[K] [Na] [Cl][K] [Na] [Cl]0

K o Na o Cl i

K i Na i Cl o (6)

Here V0 is the zero-current voltage R is the gas constant F isthe Faraday constant PX is the permeability of ion species Xand [X]o and [X]i are the concentrations of ion species X onthe outside and inside of the axon respectively Thepermeability PX describes how easily ions cross the membrane

equiv minus ΔP M cX X X (7)

where MX is the flux of X across the membrane and cX is theconcentration difference Among other things the GHK voltageequation may be used to find the action potential givenconcentrations and permeability ratios of potassium sodiumand chloride ions Interested readers are directed to Hille395 fora more thorough treatmentThe HH model was a great leap forward in our under-

standing of nerve cells and excitable membranes in general andcontinues to influence research work in the field Recent studieson expanding the HH model include incorporation of the HHmodel into finite element frameworks399400 adding noise tothe HH model401minus403 and the modeling of coupled neurons404

Wong et al400 proposed a model of cardiomyocytes thatdescribed concerted action of various types of ion channelsRowat401 examined the mechanisms behind the interspikefrequency of a stochastic HH model with applications toirregular neural spiking Tuckwell and Jost402 performed adetailed analysis of the first- and second-order moments ofvoltage and n m and h in a stochastic HH model Linaro etal403 developed a technique for mapping HH-derived Markovmodels of explicit channel activationminusdeactivation events to acomputationally more tractable form for more efficientsimulation Finally Che et al404 described behavior of neuronsexposed to a low-frequency electric field The power andsimplicity of the HH model will no doubt continue to influenceresearch for another 50 years

3 MOST COMMON TARGETS OF COMPUTERMODELING

Sustained unidirectional transport of ions across a biologicalmembrane requires energy input According to the type ofenergy sources ion transport can be assigned to one of thefollowing broad categories Passive transport is driven by theion-motive force or emf which combines the gradient of theelectrostatic potential with the concentration difference across amembrane In a typical biological setting the differencebetween cis and trans ion concentrations creates the trans-membrane gradient of the electrostatic potential In alaboratory setting the electrostatic gradient is most commonlyimposed by applying an external voltage source Theconcentration gradient across the membrane can act along oragainst the electrostatic gradient Despite being passive thetransport can still be selective and gated by voltage tensionand chemical stimuli The focus of this review is primarily onmembrane channels that facilitate passive transport of ionsOver the course of evolution nature has developed

numerous ways to transport ions against the ion-motiveforce The most prominent examples are ion pumps thatutilize the energy of ATP hydrolysis to transport ions across themembrane against the concentration gradient Some of these

Figure 3 (a and b) Schematics of potassium (a) and sodium (b)channels considered in the HodgkinminusHuxley model In the HHmodel the conductance of a potassium channel is controlled by fouractivating particles (black circles) whereas the conductance of asodium channel is controlled by three activating particles and oneinactivating particle (gray circle) (c and d) Behavior of the HH modelvariables describing potassium (c) and sodium (d) conductance as afunction of applied potential

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pumps can work in reverse synthesizing ATP by transportingions along the concentration gradient In so-called antiportersand cotransporters transport of one ion species is coupled totransport of the other Some membrane channels can coupletransport of ions to transport of larger uncharged solutes andor protons In turn proton transport can be coupled to electrontransport for example in respiratory chain proteins Thus theinner and outer membranes of a living cell are full of variousion-transporting entities whose concerted action and synchron-ized response to external stimuli keep the cell alive Interestedreaders are directed to the book by Alberts et al398 for a

complete overview of the field to a paper by Khalili-Araghi etal333 for a recent review of modeling efforts in the field ofactive transport and to a study by Beard405 for an example ofmodeling a system of ion channels in an organelleAt present modeling and simulations of ion channels are

generally limited by the experimental knowledge about themAlthough the HH theory is a beautiful example to the contrarymore often than not a theoretical study of an ion channelrequires some knowledge of the channelrsquos structure ideally atatomic resolution Whereas the ldquono structureno studyrdquo rule isadopted by the majority of researchers working in the field of

Figure 4 Molecular graphics images of membrane channels listed in Table 1 The channels shown are (a) gramicidin A (gA) 1JNO406 (b)mechanosensitive channel of large conductance (MscL) 2OAR407 (c) mechanosensitive channel of small conductance (MscS) 2OAU408 (d)ammonium transporter (AmtB) 2NUU409 (e) K+ channel (KcsA) 3EFF410 (f) voltage-gated K+ channel (Kv) 2R9R411 (g) aquaporin 0 (AQP0)2B6O412 (h) nicotinic acetylcholine receptors (nAchR) 2BG9413414 (i) bacterial outer-membrane porin (OmpF) 2OMF415 (j) bacterial chloridechannel (ClC) 1OTS416 (k) bacterial toxin (α-hemolysin) 7AHL417

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computer modeling of ions channels there are notableexceptions418419 that deduce the structural architecture of thechannel from its ion-conductance propertiesPredicting the structure of a membrane channel from its

sequence is a formidable task Hence development ofcomputational models of ion channels was in a way led bycrystallographers and their ability to solve atomic structures ofion channels Membrane channels are notoriously difficult tocrystallize and are often too large for the NMR method towork Therefore atomic-resolution structures have beenobtained for only a very limited number of ion channels andhence many studies have focused on the same systems Belowwe briefly review the ion channels of known structures that arethe most common targets of computational studies

31 Gramicidin A

Gramicidins are small bacteria-produced antibiotics that whendimerized in a head-to-head fashion (Figure 4a) are able totransport a monovalent cation across a membrane once aboutevery 100 ns39 Gramicidin works by eliminating the iongradient across the membrane of Gram-positive bacteriaGramicidin was the first clinical antibiotic in use and is stillused today in conjunction with other antibioticsAll-atom molecular dynamics simulations (MD) have been

instrumental in the interpretation and refinement of NMRresults28 Gramicidin A was the subject of the first MDsimulation of an ion channel almost 30 years ago420 Advancesin the availability of computational resources have permitted farmore realistic models including lipid bilayers and full solvent tobe simulated for significant durations Gramicidin A now servesas a model system and test bed for new techniques21

32 Potassium Channels

Potassium ion channels are key constituents of electricalsignaling networks in the nervous system When openpotassium channels conduct K+ ions at rates remarkably closeto the diffusion limit (about 108 ions per second)421 and displayincredible sensitivity to the size and valency of ions Thus K+

channels can quickly release ions from within the cell inresponse to appropriate stimulus affecting the action potentialBecause some K+ channels are voltage-sensitive this can resultin a cascade of channel activations that propagates through anaxon K+ channels have been the target of prospectivetreatments for an array of disorders including multiplesclerosis422423

Taken from Gram-positive bacterium Streptomyces lividansthe K+ channel KcsA is similar in sequence to vertebratevoltage-dependent K+ channels but is easily expressed inEscherichia coli making it the prototypical K+ channel forlaboratory studies Like all K+ channels the sequence of KcsAcontains a completely conserved motif that is crucial for its K+

specificity Depicted in Figure 5 the first atomic-resolutionstructure of a K+ channel revealed a tetrameric transmembranepore with an intracellular passage leading to a large (10 Aringdiameter) cavity with a hydrophobic lining followed by anatomically narrow sim4 Aring long selectivity filter that leads to theextracellular side of the membrane1 A more complete structureof this channel was recently resolved410 featuring longcytoplasmic helices that appear to stabilize the closedconformation of KcsA at high pH In contrast to the poreregion the arrangement of cytoplasmic helices in KcsA is not auniversal structural element of K+ channelsIn the selectivity filter four rings each featuring four

negatively charged carbonyl-oxygen atoms hold two K+ ions

that are separated by a single water molecule The ions presentin the selectivity filter are mostly desolvated which carries anenormous free energy penalty that is offset by interactions withthe negatively charged surface of the filter Thus the largeforces experienced by translocating ions balance delicately toallow a smooth free energy landscape that permits rapidpermeation through the pore The balance of these forces mustbe carefully tuned to select K+ over other monovalent ions suchas Na+ Although the latter carries the same charge as K+ and isonly 04 Aring smaller experiments suggest that K+ channels bindK+ with as much as 1 000 times greater affinity than Na+1

The selectivity filter can become occupied by divalent ionswhich generally block the current through the channel The Kiror inward rectifying family of potassium channels uses thismechanism to impede K+ ions moving out of the cell Moregenerally potassium channels are regulated through a variety ofother means that include modification through ligand bindingand voltage- and pH-dependent gating Many biologicallyproduced toxins target K+ channels to interfere with a victimrsquosnervous systemBecause of the biological importance of K+ channels and the

fact that the pore domain of bacterial KcsA is homologous tothat of eukaryotic K+ channels the seminal structure of KcsA1

motivated many computational and theoretical studies148 Theformal analogy between electric current in man-made circuitsand ion conductance through the channels424 led researchers todevelop and apply continuum electrostatics theories of ionchannels103minus109 The availability of high-resolution crystalstructures stimulated development of new atomistic simulationtechniques for studying selectivity conductance and gatingbehaviors of K+ channels using either implicit110minus117 orexplicit2988111minus113116minus197 solvent models Ligand dockingcoupled with free energy calculations was recently used tostudy methods to enhance the specificity of naturally occurringneurotoxins for Kv13 which can suppress chronically activated

Figure 5 Pore region of the KcsA K+ ion channel embedded in a lipidbilayer membrane The image shows the first crystallographicallydetermined structure of a K+ channel1 which did not include the longcytoplasmic helices depicted in Figure 4 e One of the four subunits ofthe KcsA tetramer is not shown to provide a clear view of theselectivity filter The lipid bilayer is depicted as gray van der Waalsspheres

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memory T cells implicated in autoimmune disorders includingmultiple sclerosis422425 To overcome the time and length scalelimitations of the all-atom approaches several multiscalemethods have been developed107198minus202 using K+ channelsas target application systems

33 Mechanosensitive Channels

All living creatures have mechanosensors426427 For examplewe can hear sound because our auditory sensory cells candetect ciliary vibrations caused by acoustic waves We can feelthe pressure on our skin and blood vessels and feel full whenwe eat food because of tension sensors in cell membranesPlants which are immobile and less responsive also havemechanosensors a representative example is the gravity sensorwhich allow roots and shoots to grow in opposite directionsInterested readers are referred to a recent review by Kung andco-workers426427 for more detailed informationA breakthrough in the biophysical study of mechanosensa-

tion was the cloning428429 and structural characterizationof simple prokaryotic mechanosensit ive channels(MSCs)407408430431 When the concentration of osmolytes ina bacterial cell is significantly higher than the concentration ofosmolytes in the environment the gradient of osmolyteconcentration across the cell membrane can cause huge turgorpressure inside the bacterial cell If left to develop fully suchosmotic stress can easily rupture the cell wall killing thebacterium To prevent this from happening bacteria haveevolved ldquosafety valvesrdquothe MSCsthat open when thesurface tension in the membrane exceeds a threshold valuemaking the membrane permeable to most small solutes andwater molecules432 Most importantly the channels return to aclosed state when tension drops Thus MSCs are essential forthe survival of bacteriaIn 1998 Chang et al reported the first high-resolution

structure of MSC of large conductance (MscL) fromMycobacterium tuberculosis in a closed conformation407 MscLis a homopentamer with each subunit having two trans-membrane (TM) helices TM1 and TM2 see Figure 4b In theclosed conformation five TM1 helices form a pore and TM2helices surround the inner TM1 helices Recently Liu et alreported a crystal structure of tetrameric MscL from Staph-ylococcus aureus in an expanded intermediate state431 So fartwo crystal structures of the Escherichia coli MSC of smallconductance (MscS) have been reported one in a non-conductive conformation408 and the other in an openconformation430 Those high-resolution structures show thatthe MscS is a homoheptamer with three TM helices persubunit see Figure 4c Seven TM3 helices form a channel withdiameters of 5 and 13 Aring in closed and open conformationsrespectively see Figure 6430

Despite the fact that mechanosensation is universal andessential for all living creatures427 its mechanism is significantlyless understood if compared to the mechanisms of other sensessuch as vision smell and taste427 Since the first MSC wasdiscovered in 1987432 and the first crystal structures of MscLand MscS were revealed in 1998 and 2002407408 both MscLand MscS have served as model systems for the computationalstudies of mechanical gating Because of its very nature thisproblem has attracted the attention of investigators fromvarious disciplines including traditional MD simulationshomology modeling continuum mechanics and coarse-grainedMD simulations see sections 522 and 541 for more detailsThe computational methods developed for studies of MscL and

MscS will surely be of great value in future studies of morecomplex mechanisms of mechanosensation34 Porins

Outer-membrane porins (OMPs) of Gram-negative bacteria aretransmembrane proteins that allow the bacterial cells to interactwith their environment through passive diffusion of water ionsand small hydrophilic molecules (lt600 Da) across their outermembranes Wide channels such as OMPs and toxins facilitatethe permeation of metabolites rather than merely small ionsHowever often they exhibit interesting behavior such asselectivity toward certain ions and serve as model systems totest computational models of ion transport they are thereforeof interest in this reviewOMPs are β-barrel structures usually forming homotrimeric

water-filled pores The porin channel is partially blocked by aloop (L3) that is folded inside the β-barrel forming aconstriction region that determines the size of the solutesthat can traverse the channel Several crystal structures ofporins have been determined at high resolution415433minus437

Some porins exhibit moderate ion selectivity eg Escherichiacoli OmpF (shown in Figure 4i) and OmpC are two cation-selective porins whereas the Pseudomonas aeruginosa OprP438 isa phosphate-selective porin The cation selectivity is known todepend on the salt concentration and the valence of the ionsGram-negative bacteria that lack porins have other substrate-specific channels that allow the passage of small molecules Forinstance the OccK1 an archetype of the outer-membranecarboxylate channel family from Pseudomonas aeruginosa(previously named OpdK) is a monomeric β-barrel with akidney-shaped central pore as revealed by the X-raystructure439 The members of the OccK subfamily of channelsare believed to facilitate the uptake of basic amino acids440 Adetailed examination of the conductance characteristics ofseveral members of the OccK subfamily of channels by Liu andco-workers441 revealed diverse single-channel electrical signa-tures nonohmic voltage dependent conductance and transientgating behavior Single-molecule electrophysiology analysisalong with rational protein design have revealed discrete gatingdynamics involving both enthalpy- and entropy-driven currenttransitions442443

Studies of porins are relevant to the development ofantibiotics To affect bacteria antibiotics must first pass

Figure 6 Comparison of the pores formed by seven TM3 helices ofMscS in nonconducting408 (a) and open430 (b) conformations viewedfrom the periplasm (top) and from within the membrane (bottom)

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through their outer wall which is a process facilitated by porinsPorin alteration has been implicated in antibiotic resistance444

In addition engineered porins such as the OmpG havepotential for use as stochastic sensors77

Functionally related to porins α-hemolysina toxinproduced by Staphylococcus aureusis secreted as a monomerbut assembles on target cell membranes to form ahomoheptameric channel which leads to an uncontrolledpermeation of ions and small molecules and causes cell lysisThe X-ray structure of α-hemolysin445 revealed a mushroom-like shape with a β-barrel stem protruding from its cap domainsee Figure 4k Its ability to self-assemble in biological orsynthetic membranes and its structural stability over a widerange of ion concentrations temperatures and pHs make α-hemolysin an excellent platform for stochastic sensingapplications446 including detection of DNA sequence bymeasuring the ionic current447 An interesting feature is therectification behavior of the channel which has been exploredby both implicit solvent88 as well as all-atom MDsimulations9093

Another large water-filled biological nanopore is MspAthemajor outer-membrane porin of Mycobacterium smegmatis thatallows the uptake of hydrophilic nutrients from the environ-ment The crystal structure of MspA448 revealed a homo-octameric goblet-like structure with a central channel Theporin has a constriction that is lined by two belts of aspartateresidues (Asp90 and Asp91) that diminish the permeability ofnonpolar solutes Genetically modified variants of the MspAchannel may enable practical nanopore DNA sequencing449450

as they provide superior ionic current signals for nucleic aciddetection if compared with α-hemolysin451

35 Other Channels

The voltage-dependent anion channel (VDAC) residing in themitochondrial outer membrane serves as a conduit formetabolites and electrolytes VDACs mediate the passage ofions such as K+ Clminus and Ca2+ and small hydrophilic moleculessuch as ATP between the cytosol and the mitochondria andregulate the release of apoptotic proteins The pore has avoltage-dependent conductance with an anion-selective high-conductance state at low transmembrane potential and aslightly cation-selective low-conductance state at high poten-tial452 Several NMR and X-ray structures of human as well asmouse VDACs453minus455 have become available Initially thesignificance of these structures was questioned on account of anapparent conflict with biochemical and functional data456

However additional NMR457458 and theoretical stud-ies259262268 have shed light on the structureminusfunction relationreaffirming the biological relevance of the structuresThe ClC chloride channels found in both prokaryotic and

eukaryotic cells control the selective flow of Clminus ions and arebelieved to play an important role in regulation of bloodpressure pH and membrane excitability These channelsconduct not just Clminus but also other anions such as HCO3

minusSCNminus and NOminus Unlike cation channels they do notdiscriminate strongly between different species of anionsDefects in these channels are implicated in several diseasessuch as myotonia congenita Bartterrsquos syndrome andepilepsy459 In the past decade structures of ClC orthologuesfrom two bacterial species Salmonella serovar typhimurium andEscherichia coli have become available460 The X-ray structuresreveal the ClC channels to be homodimers with two identicalbut independent pores see Figure 4j Some prokaryotic

members of the ClC family of channels are now believed tobe ion transporters although the line between ion channels andtransporters is getting blurred461 There have been a fewsimulation studies of the permeation pathways260261 of the ClCchannelsThe nicotinic acetylcholine receptor (nAChR) belongs to a

superfamily of Cys-loop ligand-gated ion channels It couples acationic transmembrane ion channel with binding sites for theneurotransmitter acetylcholine (ACh) so that the gating of thechannel is linked to the binding of ACh The nAChR owes itsname to the ability of nicotine to mimic the effects of ACh inopening up the pore The nAChR is composed of a ring of fiveprotein subunits with three domains a large N-terminalextracellular ligand binding domain (LBD) a transmembranedomain (TM) and a small intracellular domain see Figure 4hThere are two ACh binding sites in the ligand-binding domainthe pore opens when both are occupied414 Although thecomplete high-resolution structure of the nAChR is absent atpresent X-ray and electron microscopy structures of some of itscomponents are available413414 The nAChR plays a critical rolein neuronal communication converting neurotransmitter bind-ing into membrane electric depolarization The channel isfound in high concentrations at the nerveminusmuscle synapsenAChR is implicated in a variety of diseases of the centralnervous system including Alzheimerrsquos disease Parkinsonrsquosdisease schizophrenia and epilepsy462 It is also believed toplay a critical role in mediating nicotine reward andaddiction463 Although detailed study of the gating mechanismis precluded by the lack of a complete structure of the nAChRas well as the time scales involved there have been severalstudies on the TM domain215212 and the LBD218

AmtB is a representative bacterial ammonium transporterwhich belongs to AmtMEP family464 Some bacteria andplants use ammonium as a nitrogen source and have variousforms of transporters for the uptake of ammonium464465 At thesame time ammonium is also a toxic metabolic waste whichshould be removed quickly by transporters usually formammals466 There exist several high-resolution crystalstructures of bacterial AmtB409467minus470 The Escherichia colicrystal structure (Figure 4d) has become the paradigm for thestudy of the transport mechanism of ammonium409 UsuallyAmtB proteins are crystallized as a homotrimer Each monomerconsists of 11 transmembrane helices that form a channel forammonium The channel is highly hydrophobic raising thepossibility that ammonium passes the channel in a deproto-nated form (ammonia)

4 MOST COMMON SIMULATION METHODSAmong a large number of computational approaches proposedand employed for studies of ion channels most fall within thefollowing three categories all-atom molecular dynamics (MD)which is a fully microscopic description with all atoms treatedexplicitly Brownian dynamics (BD) in which only the ions aretreated explicitly while the solvent and the protein and lipidsare represented implicitly and approaches based on PoissonminusNernstminusPlanck (PNP) theory in which the ionic concentrationis treated as a continuum Each of the three approaches haslimitations and advantages The MD method is considered themost computationally expensive but also the most accurateThe PNP and BD approaches are in general less computa-tionally expensive but also provide less detail At the same timethe MD method has the smallest temporal and spatial rangefollowed by BD methods followed by PNP approaches Figure

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dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXH

7 schematically illustrates typical setups for the three modelingapproaches applied to the same systemThe above classification however is rather approximate and

can be misleading Thus the level of computational complexityoften depends on the desired level of detail whereas theaccuracy depends on the assumptions made in deriving theparameters of the model Even the most sophisticated MDsimulations rely on the MD force field which is a classicalmodel that may or may not be adequate for describing a certainphenomenon In this respect full quantum or combinedquantum mechanicsclassical mechanics approaches (QMMM) can in principle provide the highest degree of accuracyHowever the time scale accessible to these methods is severelylimiting Interested readers are directed to reviews of QMMMapproaches for simulations of biomolecules471472 and to arecent review of computational approaches to ion transport innanopores473 On the other hand it is possible to incorporateatomic-level details in BD and even PNP approaches see forexample recent work by Comer Carr and co-workers371373

Other considerations often neglected when evaluating theldquocomputational costrdquo of a certain approach are the qualificationsand ambitions of the researcher performing the modeling tasksand the availability of well-documented and ready-to-use codesFor example it is always possible to increase the computationalcomplexity of the problem by including an exorbitant amountof water in an all-atom simulation or using very fine mesh sizein continuum calculations One could also easily spend severalmonths writing debugging or porting a computationallyefficient code while the same time could have been used torun a more computationally intensive but ready-to-use andtested code Thus there are no simple rules in choosing anoptimal simulation method and researchers new to the field areurged to seek expert advice for their particular problem

41 Continuum Models

Ion channels are complex systems with many degrees offreedom and hence are challenging to model in atomisticdetail Continuum theories based on PoissonminusBoltzmann (PB)and PoissonminusNernstminusPlanck (PNP) equations are powerfultools that make simulation of such systems tractable The mainidea is to employ a continuum description for all componentsof the system ie the solvent the ions and the ion channelThe water the membrane and the channel are represented asfixed structureless dielectrics while the ions are described byspecifying the local density throughout the system Figure 7aschematically illustrates a PNP model of α-hemolysin

411 Electrostatics of Ion Channels The PB equation isthe most popular theoretical model for describing theelectrostatics around a charged biomolecule in ionic solutionIn a system of interacting mobile charged particles theelectrostatic potential arises due to the combined effect of thecharged biomolecules ions and dielectric properties of theenvironment The PB model assumes that the distribution ofcharges in the system is related to the electrostatic potentialaccording to Boltzmann statistics For the purpose of describingelectrostatics of a single biomolecule the PB equation whichwas first introduced independently by Gouy (1910) andChapman (1913) and later generalized by Debye and Huckel(1923) is most frequently written as

sumε ψ πρ π

ψλ

nablamiddot nabla = minus minus

minus

infin

⎛⎝⎜

⎞⎠⎟

c z q

z qk T

r r r

rr

( ( ) ( )) 4 ( ) 4

exp( )

( )

ii i

i

f

B (8)

where ε(r) is the position-dependent dielectric constant ψ(r) isthe electrostatic potential ρf(r) is the fixed charge density ofthe biomolecule ci

infin represents the concentration of ion speciesi at infinite distance from the biomolecule zi is the valency ofion species i q is the proton charge kB is the Boltzmannconstant T is the temperature and λ(r) describes theaccessibility of position r to ions (for example it is oftenassumed to be zero inside the biomolecule) A solution to thePB equation gives the electrostatic potential and equilibriumdensity of ions throughout the space The PB equation invokesa mean-field approximation that neglects nonelectrostatic ionminusion interactions (eg van der Waals or water-mediated) thedielectric response of the system to each ion and effects due tocorrelations in the instantaneous distribution of ions Becauseof these the PB equation fails to describe the electrostatics ofhighly charged objects such as DNA in high-concentration ionsolutions with quantitative accuracy474 In the context of ionchannels which rarely carry such a high charge density the PBtheory has been widely used to calculate the free energy cost oftransferring a charge from bulk solution to the interior of thechannel105287 (see Table 1) to characterize ion-channelinteractions88294 and to compute the distribution of thetransmembrane electrostatic potential103104294299 Such con-tinuum electrostatic calculations have also been used toestimate the relative stability of protonated and unprotonatedstates of ionizable residues in an ion channel (discussed in refs

Figure 7 Schematic illustrations of the PNP (a) BD (b) and all-atom MD (c) modeling methods applied to the same systeman α-hemolysinchannel embedded in a lipid bilayer membrane and surrounded by an electrolyte solution In panel (a) the ions are described as continuous densitywhereas the water protein and membrane are treated as continuum dielectric media In the BD model (panel b) only ions are represented explicitlywhereas all other components are either implicitly modeled or approximated by continuum media All atoms are treated explicitly in the all-atom MDmethod (panel c)

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dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXI

61 and 475) DelPhi476 and APBS477 are two popular computercodes for numerically solving the PB equation412 Ion Transport Although the PB model provides

insights into the equilibrium energetics of an ion channelmodeling of the ion flux requires a nonequilibrium approach Inmost ion channels the time scale of ion permeation rangesfrom tens of nanoseconds (porins) to microseconds and evenmilliseconds (in active transport) Thus observing a statisticallysignificant number of ion-permeation events requires longtrajectories that are still rather expensive to obtain using an all-atom approach The PoissonminusNernstminusPlanck model givesaccess to long time scales albeit at lower temporal and spatialresolutions As in the PB model the lipid protein and watermolecules are approximated as dielectric continua while ionsare described as continuous density distributions The currentdensity is obtained from the NernstminusPlanck (NP) theorywhich is widely used in studies of electrolyte transport In theNP theory ion fluxes arise from two sources the gradient ofion concentration and the gradient of the electrostatic potentialTraditional NernstminusPlanck equations do not describe ion-channel interactions However the classical NernstminusPlanckequations may be modified to include the ion-channelinteractions via an effective potential Thus the flux of ionspecies i Ji is written as

= minus nabla + nabla⎛⎝⎜

⎞⎠⎟t D c t

c tk T

J r r rr

r( ) ( ) ( )( )

( )i i ii

iB

eff

(9)

where Di and ci are the diffusion constant and the numberdensity of ion species i respectively and r( )i

eff is theeffective potential that usually combines the electrostaticpotential ϕ(r) and a core-repulsive potential UCore(r) withthe latter describing interactions between ions and the proteinchannel and not between the ions themselvesThe concentration and the flux of each ionic species obey the

continuity equation

partpart

+ nablamiddot =c t

tt

rJ r

( )( ) 0i

i (10)

Under steady-state conditions the concentration and the fluxdo not vary with time and nablamiddotJi(r) = 0 The electrostaticpotential is calculated from the Poisson equation

sumε ϕ π ρnablamiddot nabla = minus +r q cr r r( ( ) (( ))) 4 ( ( ) ( ))i

i if

(11)

where ε(r) is the dielectric constant qi is the ion charge andρf(r) is again the (fixed) charge density due to the proteinThe above coupled partial differential equations constitute

the PNP equations and may be solved by a variety of methodsin one or three dimensions Typically the NP and the Poissonequations are solved self-consistently to simultaneously obtainthe electrostatic potential ϕ(r) and the ionic concentration ci(r)under appropriate boundary conditionsModeling ion channels within the PNP framework is

computationally inexpensive compared to MD and BDsimulations because the problem of many-body interactions isavoided through a mean-field approximation An undesirableside-effect is that some important physics is neglected by thisapproximation Below we discuss some of the shortcomings ofthe PNP equations in the context of ion channels as well asextensions to the equations that address these shortcomings

Interested readers are directed to comprehensive reviews onthis subject12299307310478

Prior to the surge of popularity of the all-atom MD methodcontinuum electrodiffusion theories played a major role indevelopment of our understanding of ion fluxes in nano-channels81255 Early attempts to use the electrodiffusion theoryto describe ion flux through nanochannels279minus281286 led to thedevelopment of simplified models based on a self-consistentcombination of the Poisson equation and the NernstminusPlanckequations that were subsequently applied to various channelsystems282minus284 Most of the early studies dealt with either one-dimensional models or simplified geometries that lacked adetailed description of the protein structure and static chargedistribution These studies connected qualitative features of thecurrentminusvoltageminusconcentration relationship to structural andphysical features of the models For example the PNP theorywas used to demonstrate how charges at the channel openingscan produce current rectification285479 as well as how achannel with ion-specific binding sites can exhibit lowerconductance in a mixture of two ion types than in a puresolution of either type480 A lattice-relaxation algorithm able tosolve the PNP equations for a 3D model was developed byKurnikova and co-workers8 in later years This procedure allowsthe protein and the membrane to be mapped onto a 3D cubiclattice with defined dielectric boundaries fixed chargedistribution and a flow region for the ionsLike the PB equation the system of PNP equations

constitutes a mean-field theory that neglects the finite size ofthe ions the dielectric response of the system to an ion andionminusion correlations In fact the PNP equations reduce to thePB equation for systems with zero flux everywhere The validityof a continuum dielectric description and mean-fieldapproaches in the context of narrow pores has been thesubject of much debate For example Chung and co-workersobserved considerable differences between the conductancethrough idealized pores using the BD and PNP ap-proaches287294 The authors argued that the mean-fieldapproximation breaks down in narrow ion channels due to anoverestimation of the screening effect by counterions within thepore Larger channels like porins at physiological or lower ionconcentrations are described quite accurately by the PNPequations However the currents computed based on the PNPmodels can be considerably higher (by 50 for OmpF) than inequivalent BD simulations55

When a charge in a high dielectric medium is brought near alow dielectric medium a repulsive surface charge is induced atthe dielectric boundary In continuum descriptions such as PBand PNP the induced charge density includes (usually)canceling components from both positive and negative averagecharge densities The interaction energy between a charge andits induced charge density is often called the dielectric self-energy The dielectric self-energy due to the average chargedensity and the average induced charge density at the dielectricboundary is in general smaller than the interaction energybetween point charges and corresponding induced chargeaveraged over all configurations Put another way a pointcharge approaching a low dielectric medium is strongly repelledby its induced image charge and this repulsion is largely lost bythe implicit averaging in mean-field descriptionsThe PB and PNP equations have been modified to include

the interaction of an ion with the charge density itinduces11294296 Although the corrections account for theinteraction of an ion with its induced dielectric charge they do

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not account for the interaction of the induced charge with asecond nearby ion Similarly the mean-field approximationinherently ignores effects involving correlations in theinstantaneous ion distribution For example the narrowestportion of the potassium channels almost always contains twoions that move in a concerted fashion (see section 511) whichcannot be properly treated by continuum theories Never-theless it was concluded that the dielectric self-energy accountsfor most of the discrepancy between PNP and BD results in thecase of narrow channels294

Although early electrodiffusion studies of Levitt consideredhard-sphere repulsion between ions by iteratively correcting theion concentration279 many studies have since ignored suchfinite-size effects Recently the PNP equations have beenadapted to incorporate finite-size effects using classical densityfunctional theory to describe many-body hard sphereinteractions between ions and solvent290291300481 Unfortu-nately these approaches often yield cumbersome integro-differential equations Finite-size effects can be included in thePNP equations by introducing an entropic term thatdiscourages solvent crowding by ions309 The latter approachyields a tractable set of corrected PNP equations Both the PNPand BD methods usually ignore thermal fluctuations of theprotein and lipid bilayer However these can be effectivelycaptured by combining results from MD or Monte Carlosimulations with 3-D PNP calculations92

The PNP approach continues to play a major role inimproving our understanding of the physics of ion channelsThe computational efficiency of the PNP model is unparallelledfor studies of ion conductance in a low ion concentrationregime where the PNP method is expected to be the mostaccurate The method is highly efficient at predicting the effectof a channelrsquos geometry on the currentminusvoltage dependence atphysiological voltages and can be used to screen for mutationsthat affect conductance of a channel The calculation of currentscan be quite accurate in the case of larger channels such asporins PNP is perhaps the only method that can presentlysimulate the interplay of ion conductances in an ensemble ofion channels (such as in a realistic biological membrane)explicitly taking the structural features of the channels intoaccount Finally the PNP approach is rather flexible to includedescriptions of additional physical effects for examplehydrodynamic interactions354364369370 or the effect of asemiconductor membrane on the ionic current361382383

42 Brownian Dynamics

The BD method allows for simulations of explicit ionpermeations on the microsecond-to-millisecond time scale bytreating solvent molecules implicitly In a way the BD methodoffers a good compromise between all-atom MD andcontinuum electrodiffusion approaches Computational effi-ciency is achieved by reducing the number of degrees offreedom Typically a moderate number of atoms of interest(usually the ions) are simulated explicitly while the solvent isaccounted for via friction and stochastic random forces that actin addition to the electrostatic and steric forces arising fromother ions the protein and the lipid bilayer For the calculationof electrostatic forces the water the membrane and the proteinchannel are usually treated as continuous dielectric media Thechannel is treated as a rigid structure and thermal fluctuationsare typically ignored Figure 7b schematically illustrates a BDmodel of α-hemolysin

421 General Formulation of the BD Method In theBrownian dynamics method a stochastic equation is integratedforward in time to create trajectories of atoms Theldquouninterestingrdquo degrees of motion usually corresponding tofast-moving solvent molecules are projected out in order todevelop a dynamic equation for the evolution of the ldquorelevantrdquodegrees of freedom The motion of the particles is described bya generalized Langevin equation

int = minus prime minus prime prime +m t dt M t t t tr r f( ) ( ) ( ) ( )i i i

t

i i i0 (12)

The force on the ith particle i is obtained from an effectivepotential = minusnabla r( )i i iThe potential function is a many-body potential of mean

force (PMF) that corresponds to the reversible thermodynamicwork function to assemble the relevant particles in a particularconformation while averaging out the remaining degrees offreedom ie the effect of all other atoms is implicitly present in

r( )i The second term on the right-hand side is thedamping force representing the frictional effect of theenvironment and finally fi(t) is a Gaussian fluctuating forcearising from random collisions The frictional force depends onprevious velocities through the memory kernel Mi(tminustprime) Thefirst and second moments of the random force are given by⟨fi(t)⟩ = 0 and ⟨fi(t)middotfj(0)⟩ = 3kBTMi(t)δij where kB is theBoltzmann constant and T is the temperature Both the dragforce and the stochastic force incorporate the effect of thesolvent In the Markovian limit the memory kernel is a Diracdelta function that leads to the traditional Langevin equation

γ = minus +m t t tr r f( ) ( ) ( )i i i i i i (13)

The friction coefficient γi is related to underlying molecularprocesses via the fluctuationminusdissipation theoremIn the overdamped regime (which applies to the motion of

an ion in water) the inertial term can be ignored so that theLangevin equation is reduced to

ζ = +tD

k Ttr( ) ( )i

ii i

B (14)

where Di = kBTγi is the diffusion coefficient of the ith particleand ζi(t) is a Gaussian random noise with a second momentgiven as ⟨ζi(t)middotζi(0)⟩ = 6Diδ(t)

422 BD Simulations of Ion Channels A Browniandynamics simulation requires two basic ingredients adescription of the forces applied to each ion and the diffusioncoefficient for each ion The diffusion coefficient for the ionsshould be in general position-dependent and can be obtainedfrom all-atom MD simulations373482483 or estimated usinganalytical techniques88484 However in most cases a singleposition-independent diffusion constant is used for all ions ofthe same speciesEach ion experiences a force that depends on its position as

well as the positions of all the other ions in the system Thepotential corresponding to the forces on the ions is the multi-ion PMF which is the multidimensional free energy surfacethat is usually broken into an ionminusion PMF and a PMF due tothe pore the solution and other biomolecules373 The PMFscan be calculated from all-atom MD or even quantumchemistry simulations but such calculations are computation-ally expensive

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXK

A more typical approach was presented by Roux and co-workers which we summarize here556263299 The multi-ionPMF can be written as

sum sum sum

sum ϕ ϕ

= | minus | +

+ +

αα γ α

α γ α γα

α

αα α α

neu U

q

r r r r

r r

( ) ( ) ( )

[ ( ) ( )]

core

sf rf(15)

where uαγ(r) is the ionminusion interaction Ucore is a repulsivepotential preventing the ions from entering the ion-inaccessibleregions ϕsf is the electrostatic potential arising from thepermanent protein charge distribution and ϕrf is the reactionfield potential arising from the electrostatic polarization of thevarious dielectric boundaries The static field may be computedfrom an atomic model of the pore using the PBequations556263485 Any externally imposed transmembranebias may be included in the calculation of the electrostaticpotential Usually the ionminusion interaction includes van derWaals and Coulomb terms

εσ σ

ε= minus +α γ α γ

α γ α γ α γ⎜ ⎟ ⎜ ⎟⎡⎣⎢⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎤⎦⎥u r

r r

q q

r( ) 4

12

6

bulk

where εαγ and σαγ are the parameters for the 6minus12 Lennard-Jones potential qα and qγ are the charges of the ions and εbulk isthe dielectric constant of bulk water The local dielectricconstant of the water in the interior of the pore may beextracted from atomistic simulations but it is usually assumedto have the bulk value of 80 Solvation effects can beapproximately described by including a short-range solvationpotential55287486 but that is rarely done in practice Web-basedinterface for GCMCBD simulations of ion channels hasrecently become available268

Early BD studies were performed using one-dimensionalrepresentations of channels487 Later these were extended tomore realistic three-dimensional geometries although theseoften lacked atomic detail63486 However the X-ray structure ofan ion channel can be used to create a more realistic model ofthe channel by computing electrostatic and core repulsionpotential maps from the all-atom structure Brownian dynamicssimulations have been applied to several biological channelsincluding OmpF5562minus64 K+ channels110minus115117 α-hemoly-sin8895 VDAC268 and gramicidin1617 Roux and co-workershave developed a grand canonical Monte CarloBrowniandynamics method (GCMCBD)6263103 to allow for fluctua-tions in the total number of ions in the system and asymmetricion concentration conditions For detailed treatment of thesubject interested readers are directed to a review of thecomputational methods299473

Recently Comer and Aksimentiev373 used all-atom MD todetermine full three-dimensional PMF maps at atomicresolution for ionminusion and ionminusbiomolecule interactionsthereby fully accounting for short-range effects associationwith solvation of ions and biomolecules Using such full 3-DPMFs in BD simulations of ion flow through a model nanoporecontaining DNA basepair triplets yielded ionic currents in closeagreement with the results of all-atom MD but at a fraction ofthe computational cost The authors indicate that such anatomic-resolution BD method can be developed further toincorporate the conformational flexibility of the pore and DNAby altering the PMF maps on-the-fly

43 All-Atom Molecular Dynamics

The all-atom MD method can provide unparalleled insight intothe physical mechanisms underlying the biological function ofbiomacromolecules By explicitly describing all the atoms of thesystem of interest and the majority of interatomic interactionsthis method has the potential to compete with the experimentin completeness and accuracy of the description of microscopicphenomena In the case of an ion channel one can in principledirectly observe ion conductance and gating at the spatialresolution of a hydrogen atom and the temporal resolution ofsingle femtoseconds Critical to the above statement is theassumption that the all-atom MD method is equipped with acorrect description of interatomic interactions and enoughcomputational power is available Despite ever-increasingavailability of massive parallel computing platforms makingquantitative predictions using MD remains challenging in partdue to imperfections of the interatom interaction modelsBelow we briefly review the formulations of the all-atom MDmethod and describe recent advances in the field

431 General Formulation of the All-Atom MDMethod In the MD simulations of biomacromoleculesatoms are represented as point particles and the connectivity(or covalent bonds) among those atom are given a prioriCovalently bonded atoms interact with each other throughbonded potentials while the other atom pairs interact throughnonbonded potentials

= +U U Ur r r( ) ( ) ( )N N Nbonded nonbonded (16)

where rN denotes the coordinates of N atoms in a systemBonded interactions model quantum mechanical behavior ofcovalently connected atoms by means of harmonic bond angleand improper dihedral angle restraints and periodic dihedralangle potentials

sum sum

sum

sum

θ θ

χ δ

ϕ ϕ

= minus + minus

+ + minus

+ minus

θ

χ

ϕ

U K b b K

K n

K

( ) ( )

1 cos( )

( )

bbondedbonds

02

angles0

2

torsions

impropers0

2

(17)

where Kb and b0 are the bond force constant and theequilibrium distance respectively Kθ and θ0 are the angleforce constant and the equilibrium angle respectively Kχ nand δ are the dihedral force constant the multiplicity and thephase angle respectively and Kϕ and ϕ0 are the improper forceconstant and the equilibrium improper angle488 The non-bonded potential usually consists of the Lennard-Jones (LJ)potential for van der Waals interactions and the Coulombpotential for electrostatic interactions

sum εσ σ

ε= minus +

⎧⎨⎪⎩⎪

⎡

⎣⎢⎢⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤

⎦⎥⎥

⎫⎬⎪⎭⎪

Ur r

q q

r4 ij

ij

ij

ij

ij

i j

ijnonbonded

nonbond

12 6

(18)

where εij is the well depth σij is the finite distance at which theLJ potential is zero rij is the interatomic distance and qij areatomic charges The bonded parameters are empiricallycalibrated based on the quantum mechanical calculations ofsmall molecules whereas the nonbonded parameters are mainlyderived from quantum chemistry calculations (eg partial

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXL

charges) and empirical matching of thermodynamic data (eghydration free energy)A biomolecular force field is a set of bonded and nonbonded

parameters defined in eqs 17 and 18 Presently severalbiomolecular force fields exist The force fields can becategorized into types based on whether all the atoms areexplicitly treated or not All-atom force fields which includeCHARMM489 AMBER490491 and OPLS-AA492493 treat allatoms explicitly In the united-atom force fields (egGROMOS494495) some nonpolar hydrogen atoms areneglectedFor the simulations of channel proteins a lipid force field is

as important as a protein force field because the channels areembedded in lipid bilayers Among the all-atom force fields theCHARMM force field includes parameters for lipids the latestupdate at the time of writing this review is CHARMM36496

Together with the AMBER force field for the protein thegeneral all-atom AMBER force field (GAFF) can be used todescribe the lipid bilayer497498 Officially OPLS does notinclude lipid parameters Among the united-atom force fieldsGROMOS comes with lipid parameters499 Berger et alreported improved GROMOS-based lipid parameters basedon the condensed-phase properties of pentadecane500 Thislipid force field has been widely used in combination with otherprotein force fields such as AMBER OPLS and GROMOS501

For an in-depth review of various force fields we referinterested readers to a comprehensive review by Mackerell488

432 Ion Channels in Native Environment Unlikesoluble proteins that are surrounded only by water ion-channelproteins are embedded in a lipid bilayer and therefore are incontact with both water and lipids Because of the drasticallydifferent chemical and electrostatic properties of lipid andwater proper descriptions of proteinminuslipid and proteinminuswaterinteractions are key for the successful simulation of amembrane channel To model ion conduction through arelatively rigid channel (eg gA or KcsA channel) it is possibleto use an implicit solvent model of the channelrsquos environmentin which the volume occupied by lipid and water is treated ascontinuum media of dielectric constants 2 and 78 respec-tively299 However when interactions between a channel and alipid membrane are significant (eg in mechanosensitivechannels) explicit modeling of lipid molecules is essentialThe tails of lipids are long and equilibrate slowly making it

significantly more difficult to assemble a model of a channelembedded in an explicit lipid bilayer than a model of a fullysoluble protein Usually the system setup involves thefollowing steps Starting from a pre-equilibrated and solvatedlipid bilayer membrane one makes a pore in the bilayer bydeleting a minimal number of lipid molecules so that theprotein can fit Next an all-atom model of the protein is placedin the pore which is followed by energy minimization andequilibration of the system using the MD method having thechannelrsquos coordinates restrained to their crystallographic valuesFinally when the proteinminuslipid interface is well equilibratedone can perform a production run without applying restraintson the channel For detailed step-by-step instructions forbuilding atomic-scale models of ion channels in lipid bilayerenvironment interested readers are directed to a tutorial onMD simulations of membrane proteins502 Even though a fullyautomated procedure is not yet available several programs canassist a beginner in building a new system VMD503 containsthe Membrane Builder plugin Jo et al have a web-based

service CHARMM GUI Membrane Builder (httpwwwcharmm-guiorgmembrane)504505

An alternative method for creating an all-atom model of anion channel in its native environment is to first carry out self-assembly simulations using a coarse-grained (CG) MDmethod74165379 The main difference between the CG andall-atom MD methods is the level of detail used to describe thecomponents of the system Typically one CG bead representsabout 5minus10 atoms Being much more computationally efficient(and lower resolution) the CG model allows millisecond-time-scale simulations to be performed on commodity computersInterested readers are directed toward recent reviews on thissubject506minus508

In the CG simulations of self-assembly CG models of lipidssolvent and a membrane protein are placed with randompositions in desired proportions During the course of CGMDsimulations the lipid molecules spontaneously form a lipidbilayer around a protein After obtaining a stable model the CGmodel can be reverse-coarse-grained into a fully atomisticmodel (see for example a study by Maffeo and Aksimen-tiev330) A great advantage of this approach is that it requiresno a priori knowledge of the position of the membranechannels relative to the membrane An obvious disadvantage isthat one has to have a reasonable CG model to carry out theself-assembly simulations and a reliable procedure to recoverthe all-atom details from the final CG model Currently it isnot possible to use a CG approach to model ion conductancethrough large membrane channels due to inaccurate treatmentsof the membrane and water electrostatics in most CG modelsHowever work to improve CG methods is ongoing509510 andsuch simulations should become possible in the near future

433 Homology Modeling Usually an all-atom MDsimulation of a channel protein can be performed only when anatomic-resolution structure of the channel is available Thisrequirement severely limits application of the MD methodFortunately membrane channels of different organisms oftenhave similar amino-acid sequences The sequence similarity canbe used to build an all-atom model of the channel that does nothave an experimentally determined structure through aprocedure called homology modeling511 Briefly homologymodeling proceeds as follows First a sequence alignmentbetween a target sequence and a homologous sequenceforwhich a structure is knownis performed Second thesecondary structures (eg α-helices and β-sheets) of the targetsequence from the homologous sequence are built Finallyloops connecting the secondary structures are modeled and theoverall structure is refined There exist many tools for thehomology modeling (eg Modeler by Sali and Blundell511)The homology modeling method has been successfully used

for building initial structures of several ion channels forsubsequent all-atom MD simulations Capener et al512 built aninward rectifier potassium channel (Kir) based on a high-resolution structure of KcsA1 Sukharev et al used the crystalstructure of Mycobacterium tuberculosis MscL407 to modelclosed intermediate and open structures of Escherichia coliMscL231232 Law et al combined the crystal structure of theLymnea stagnalis acetylcholine binding protein and the electronmicroscopy (EM) structure of the transmembrane domain ofthe torpedo electric ray nicotinic channel to build an entirehuman nicotinic acetylcholine receptor213

434 Free-Energy Methods Perhaps the greatestdisadvantage of the MD method is that simulations are costlyand are currently limited to the microsecond time scalea

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXM

resistance drops initially but then returns to its previous levelFigure 2 shows the conductance of squid axon to sodium andpotassiumThe HodgkinminusHuxley or HH model describes the behavior

of the two independent ionic resistances introduced in Figure1d For convenience we restate these quantities as theirinverses the ionic conductances gK and gNa In the model gKand gNa vary between zero and maximum values gK and gNarespectively In other words

= g x gK K K

= g x gNa Na Na

The goal of the HH model is to describe the behavior of thecoefficients xK and xNa In the model xK and xNa are onlydependent on time and voltageWe first describe how the potassium coefficient xK is

represented in the HH model To best fit the experimental datathe HH model supposes that four independent particles controlthe potassium conductance Although Hodgkin and Huxley didnot know of the existence of ion channels here we will assumethat the particles control a potassium channel Figure 3aschematically shows a potassium channel and the controllingparticles Each particle may be in one of two states active orinactive In order for the channel to conduct all four particlesmust be active Following Hodgkin and Huxley let us say thatthe probability of a particle being active is n The probability ofthe channel being conductive is then n4 The average current isthen

ε= minusI n g V( )K4

K K (1)

where V is the applied voltage and εK is the emf of thepotassium channel The emf originates in the ion concentrationgradient across the membrane which is driven by ion pumpssuch as Na+minusK+ ATPase398

In the HH model the switching of a particle between activeand inactive states is described by f irst-order kinetics Because ofthis we may describe the behavior of n in terms of two valuesthe steady-state value ninfin which is the value that n approachesgiven enough time and a time constant τn which describes howquickly n approaches ninfin Mathematically the value of n obeysthe following differential equation

τ=

minusinfinnt

n ndd n (2)

Importantly ninfin and τn are functions of the applied voltage Thebehavior of ninfin and τn under a change of voltage is schematicallyshown in Figure 3c Notice that the probability of the channelbeing in a conducting state (n4) rises with increasingtransmembrane biasActivation of sodium channels in the HH model is similar to

that of potassium channels with one essential differenceinstead of four identical controlling particles sodium channelsare controlled by three identical particles and a fourth particleof a different type Let us say the probability of each of thethree particles being active is m while this probability for thefourth particle is h It is the action of this fourth particle thatcontrols deactivation of the channel under an external voltageFigure 3b shows a schematic representation of a sodiumchannel The average current through a sodium channel is then

ε= minusI h mg V( )Na3

Na Na (3)

Figure 2 Conductance of squid axon membrane to sodium (a) and potassium (b) at various applied voltages Voltage was held at the rest value ofminus65 mV then increased to the displayed value at t = 0 While potassium conductance rises and saturates under an applied potential sodiumconductance initially rises but subsequently returns to zero Adapted with permission from ref 397 Copyright 1952 Wiley

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXC

where εNa is the emf of the sodium channel Analogously to nfor the potassium channel the behavior of h and m aredescribed by steady-state values hinfin and minfin and time constantsτh and τm obeying the differential equations

τ=

minusinfinht

h hdd h (4)

τ=

minusinfinmt

m mdd m (5)

The behavior of hinfin τh minfin and τm under a change of voltage isshown in Figure 3d The time constant τh is much higher thanτm meaning that the deactivating particle reacts much moreslowly to a change of external potential than the activatingparticles Thus we see how the conductance traces shown inFigure 2a are explained upon switching from the normalpolarized potential value (low V in Figure 3c d) to highervalues the activating particles quickly switch on due to theirlow time constant τm because of the relatively high value of τhthe inactivating particle is slow to react and continues to allowconduction eventually the inactivating particle does indeedswitch the channel back off and the conductance dropsFinally we would be remiss if we did not mention a related

theory the GoldmanminusHodgkinminusKatz (GHK) theory The GHK

theory relates voltage current and ionic permeabilities395 Oneform of the theory is the GHK voltage equation

=+ ++ +

VRTF

P P PP P P

ln[K] [Na] [Cl][K] [Na] [Cl]0

K o Na o Cl i

K i Na i Cl o (6)

Here V0 is the zero-current voltage R is the gas constant F isthe Faraday constant PX is the permeability of ion species Xand [X]o and [X]i are the concentrations of ion species X onthe outside and inside of the axon respectively Thepermeability PX describes how easily ions cross the membrane

equiv minus ΔP M cX X X (7)

where MX is the flux of X across the membrane and cX is theconcentration difference Among other things the GHK voltageequation may be used to find the action potential givenconcentrations and permeability ratios of potassium sodiumand chloride ions Interested readers are directed to Hille395 fora more thorough treatmentThe HH model was a great leap forward in our under-

standing of nerve cells and excitable membranes in general andcontinues to influence research work in the field Recent studieson expanding the HH model include incorporation of the HHmodel into finite element frameworks399400 adding noise tothe HH model401minus403 and the modeling of coupled neurons404

Wong et al400 proposed a model of cardiomyocytes thatdescribed concerted action of various types of ion channelsRowat401 examined the mechanisms behind the interspikefrequency of a stochastic HH model with applications toirregular neural spiking Tuckwell and Jost402 performed adetailed analysis of the first- and second-order moments ofvoltage and n m and h in a stochastic HH model Linaro etal403 developed a technique for mapping HH-derived Markovmodels of explicit channel activationminusdeactivation events to acomputationally more tractable form for more efficientsimulation Finally Che et al404 described behavior of neuronsexposed to a low-frequency electric field The power andsimplicity of the HH model will no doubt continue to influenceresearch for another 50 years

3 MOST COMMON TARGETS OF COMPUTERMODELING

Sustained unidirectional transport of ions across a biologicalmembrane requires energy input According to the type ofenergy sources ion transport can be assigned to one of thefollowing broad categories Passive transport is driven by theion-motive force or emf which combines the gradient of theelectrostatic potential with the concentration difference across amembrane In a typical biological setting the differencebetween cis and trans ion concentrations creates the trans-membrane gradient of the electrostatic potential In alaboratory setting the electrostatic gradient is most commonlyimposed by applying an external voltage source Theconcentration gradient across the membrane can act along oragainst the electrostatic gradient Despite being passive thetransport can still be selective and gated by voltage tensionand chemical stimuli The focus of this review is primarily onmembrane channels that facilitate passive transport of ionsOver the course of evolution nature has developed

numerous ways to transport ions against the ion-motiveforce The most prominent examples are ion pumps thatutilize the energy of ATP hydrolysis to transport ions across themembrane against the concentration gradient Some of these

Figure 3 (a and b) Schematics of potassium (a) and sodium (b)channels considered in the HodgkinminusHuxley model In the HHmodel the conductance of a potassium channel is controlled by fouractivating particles (black circles) whereas the conductance of asodium channel is controlled by three activating particles and oneinactivating particle (gray circle) (c and d) Behavior of the HH modelvariables describing potassium (c) and sodium (d) conductance as afunction of applied potential

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pumps can work in reverse synthesizing ATP by transportingions along the concentration gradient In so-called antiportersand cotransporters transport of one ion species is coupled totransport of the other Some membrane channels can coupletransport of ions to transport of larger uncharged solutes andor protons In turn proton transport can be coupled to electrontransport for example in respiratory chain proteins Thus theinner and outer membranes of a living cell are full of variousion-transporting entities whose concerted action and synchron-ized response to external stimuli keep the cell alive Interestedreaders are directed to the book by Alberts et al398 for a

complete overview of the field to a paper by Khalili-Araghi etal333 for a recent review of modeling efforts in the field ofactive transport and to a study by Beard405 for an example ofmodeling a system of ion channels in an organelleAt present modeling and simulations of ion channels are

generally limited by the experimental knowledge about themAlthough the HH theory is a beautiful example to the contrarymore often than not a theoretical study of an ion channelrequires some knowledge of the channelrsquos structure ideally atatomic resolution Whereas the ldquono structureno studyrdquo rule isadopted by the majority of researchers working in the field of

Figure 4 Molecular graphics images of membrane channels listed in Table 1 The channels shown are (a) gramicidin A (gA) 1JNO406 (b)mechanosensitive channel of large conductance (MscL) 2OAR407 (c) mechanosensitive channel of small conductance (MscS) 2OAU408 (d)ammonium transporter (AmtB) 2NUU409 (e) K+ channel (KcsA) 3EFF410 (f) voltage-gated K+ channel (Kv) 2R9R411 (g) aquaporin 0 (AQP0)2B6O412 (h) nicotinic acetylcholine receptors (nAchR) 2BG9413414 (i) bacterial outer-membrane porin (OmpF) 2OMF415 (j) bacterial chloridechannel (ClC) 1OTS416 (k) bacterial toxin (α-hemolysin) 7AHL417

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computer modeling of ions channels there are notableexceptions418419 that deduce the structural architecture of thechannel from its ion-conductance propertiesPredicting the structure of a membrane channel from its

sequence is a formidable task Hence development ofcomputational models of ion channels was in a way led bycrystallographers and their ability to solve atomic structures ofion channels Membrane channels are notoriously difficult tocrystallize and are often too large for the NMR method towork Therefore atomic-resolution structures have beenobtained for only a very limited number of ion channels andhence many studies have focused on the same systems Belowwe briefly review the ion channels of known structures that arethe most common targets of computational studies

31 Gramicidin A

Gramicidins are small bacteria-produced antibiotics that whendimerized in a head-to-head fashion (Figure 4a) are able totransport a monovalent cation across a membrane once aboutevery 100 ns39 Gramicidin works by eliminating the iongradient across the membrane of Gram-positive bacteriaGramicidin was the first clinical antibiotic in use and is stillused today in conjunction with other antibioticsAll-atom molecular dynamics simulations (MD) have been

instrumental in the interpretation and refinement of NMRresults28 Gramicidin A was the subject of the first MDsimulation of an ion channel almost 30 years ago420 Advancesin the availability of computational resources have permitted farmore realistic models including lipid bilayers and full solvent tobe simulated for significant durations Gramicidin A now servesas a model system and test bed for new techniques21

32 Potassium Channels

Potassium ion channels are key constituents of electricalsignaling networks in the nervous system When openpotassium channels conduct K+ ions at rates remarkably closeto the diffusion limit (about 108 ions per second)421 and displayincredible sensitivity to the size and valency of ions Thus K+

channels can quickly release ions from within the cell inresponse to appropriate stimulus affecting the action potentialBecause some K+ channels are voltage-sensitive this can resultin a cascade of channel activations that propagates through anaxon K+ channels have been the target of prospectivetreatments for an array of disorders including multiplesclerosis422423

Taken from Gram-positive bacterium Streptomyces lividansthe K+ channel KcsA is similar in sequence to vertebratevoltage-dependent K+ channels but is easily expressed inEscherichia coli making it the prototypical K+ channel forlaboratory studies Like all K+ channels the sequence of KcsAcontains a completely conserved motif that is crucial for its K+

specificity Depicted in Figure 5 the first atomic-resolutionstructure of a K+ channel revealed a tetrameric transmembranepore with an intracellular passage leading to a large (10 Aringdiameter) cavity with a hydrophobic lining followed by anatomically narrow sim4 Aring long selectivity filter that leads to theextracellular side of the membrane1 A more complete structureof this channel was recently resolved410 featuring longcytoplasmic helices that appear to stabilize the closedconformation of KcsA at high pH In contrast to the poreregion the arrangement of cytoplasmic helices in KcsA is not auniversal structural element of K+ channelsIn the selectivity filter four rings each featuring four

negatively charged carbonyl-oxygen atoms hold two K+ ions

that are separated by a single water molecule The ions presentin the selectivity filter are mostly desolvated which carries anenormous free energy penalty that is offset by interactions withthe negatively charged surface of the filter Thus the largeforces experienced by translocating ions balance delicately toallow a smooth free energy landscape that permits rapidpermeation through the pore The balance of these forces mustbe carefully tuned to select K+ over other monovalent ions suchas Na+ Although the latter carries the same charge as K+ and isonly 04 Aring smaller experiments suggest that K+ channels bindK+ with as much as 1 000 times greater affinity than Na+1

The selectivity filter can become occupied by divalent ionswhich generally block the current through the channel The Kiror inward rectifying family of potassium channels uses thismechanism to impede K+ ions moving out of the cell Moregenerally potassium channels are regulated through a variety ofother means that include modification through ligand bindingand voltage- and pH-dependent gating Many biologicallyproduced toxins target K+ channels to interfere with a victimrsquosnervous systemBecause of the biological importance of K+ channels and the

fact that the pore domain of bacterial KcsA is homologous tothat of eukaryotic K+ channels the seminal structure of KcsA1

motivated many computational and theoretical studies148 Theformal analogy between electric current in man-made circuitsand ion conductance through the channels424 led researchers todevelop and apply continuum electrostatics theories of ionchannels103minus109 The availability of high-resolution crystalstructures stimulated development of new atomistic simulationtechniques for studying selectivity conductance and gatingbehaviors of K+ channels using either implicit110minus117 orexplicit2988111minus113116minus197 solvent models Ligand dockingcoupled with free energy calculations was recently used tostudy methods to enhance the specificity of naturally occurringneurotoxins for Kv13 which can suppress chronically activated

Figure 5 Pore region of the KcsA K+ ion channel embedded in a lipidbilayer membrane The image shows the first crystallographicallydetermined structure of a K+ channel1 which did not include the longcytoplasmic helices depicted in Figure 4 e One of the four subunits ofthe KcsA tetramer is not shown to provide a clear view of theselectivity filter The lipid bilayer is depicted as gray van der Waalsspheres

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memory T cells implicated in autoimmune disorders includingmultiple sclerosis422425 To overcome the time and length scalelimitations of the all-atom approaches several multiscalemethods have been developed107198minus202 using K+ channelsas target application systems

33 Mechanosensitive Channels

All living creatures have mechanosensors426427 For examplewe can hear sound because our auditory sensory cells candetect ciliary vibrations caused by acoustic waves We can feelthe pressure on our skin and blood vessels and feel full whenwe eat food because of tension sensors in cell membranesPlants which are immobile and less responsive also havemechanosensors a representative example is the gravity sensorwhich allow roots and shoots to grow in opposite directionsInterested readers are referred to a recent review by Kung andco-workers426427 for more detailed informationA breakthrough in the biophysical study of mechanosensa-

tion was the cloning428429 and structural characterizationof simple prokaryotic mechanosensit ive channels(MSCs)407408430431 When the concentration of osmolytes ina bacterial cell is significantly higher than the concentration ofosmolytes in the environment the gradient of osmolyteconcentration across the cell membrane can cause huge turgorpressure inside the bacterial cell If left to develop fully suchosmotic stress can easily rupture the cell wall killing thebacterium To prevent this from happening bacteria haveevolved ldquosafety valvesrdquothe MSCsthat open when thesurface tension in the membrane exceeds a threshold valuemaking the membrane permeable to most small solutes andwater molecules432 Most importantly the channels return to aclosed state when tension drops Thus MSCs are essential forthe survival of bacteriaIn 1998 Chang et al reported the first high-resolution

structure of MSC of large conductance (MscL) fromMycobacterium tuberculosis in a closed conformation407 MscLis a homopentamer with each subunit having two trans-membrane (TM) helices TM1 and TM2 see Figure 4b In theclosed conformation five TM1 helices form a pore and TM2helices surround the inner TM1 helices Recently Liu et alreported a crystal structure of tetrameric MscL from Staph-ylococcus aureus in an expanded intermediate state431 So fartwo crystal structures of the Escherichia coli MSC of smallconductance (MscS) have been reported one in a non-conductive conformation408 and the other in an openconformation430 Those high-resolution structures show thatthe MscS is a homoheptamer with three TM helices persubunit see Figure 4c Seven TM3 helices form a channel withdiameters of 5 and 13 Aring in closed and open conformationsrespectively see Figure 6430

Despite the fact that mechanosensation is universal andessential for all living creatures427 its mechanism is significantlyless understood if compared to the mechanisms of other sensessuch as vision smell and taste427 Since the first MSC wasdiscovered in 1987432 and the first crystal structures of MscLand MscS were revealed in 1998 and 2002407408 both MscLand MscS have served as model systems for the computationalstudies of mechanical gating Because of its very nature thisproblem has attracted the attention of investigators fromvarious disciplines including traditional MD simulationshomology modeling continuum mechanics and coarse-grainedMD simulations see sections 522 and 541 for more detailsThe computational methods developed for studies of MscL and

MscS will surely be of great value in future studies of morecomplex mechanisms of mechanosensation34 Porins

Outer-membrane porins (OMPs) of Gram-negative bacteria aretransmembrane proteins that allow the bacterial cells to interactwith their environment through passive diffusion of water ionsand small hydrophilic molecules (lt600 Da) across their outermembranes Wide channels such as OMPs and toxins facilitatethe permeation of metabolites rather than merely small ionsHowever often they exhibit interesting behavior such asselectivity toward certain ions and serve as model systems totest computational models of ion transport they are thereforeof interest in this reviewOMPs are β-barrel structures usually forming homotrimeric

water-filled pores The porin channel is partially blocked by aloop (L3) that is folded inside the β-barrel forming aconstriction region that determines the size of the solutesthat can traverse the channel Several crystal structures ofporins have been determined at high resolution415433minus437

Some porins exhibit moderate ion selectivity eg Escherichiacoli OmpF (shown in Figure 4i) and OmpC are two cation-selective porins whereas the Pseudomonas aeruginosa OprP438 isa phosphate-selective porin The cation selectivity is known todepend on the salt concentration and the valence of the ionsGram-negative bacteria that lack porins have other substrate-specific channels that allow the passage of small molecules Forinstance the OccK1 an archetype of the outer-membranecarboxylate channel family from Pseudomonas aeruginosa(previously named OpdK) is a monomeric β-barrel with akidney-shaped central pore as revealed by the X-raystructure439 The members of the OccK subfamily of channelsare believed to facilitate the uptake of basic amino acids440 Adetailed examination of the conductance characteristics ofseveral members of the OccK subfamily of channels by Liu andco-workers441 revealed diverse single-channel electrical signa-tures nonohmic voltage dependent conductance and transientgating behavior Single-molecule electrophysiology analysisalong with rational protein design have revealed discrete gatingdynamics involving both enthalpy- and entropy-driven currenttransitions442443

Studies of porins are relevant to the development ofantibiotics To affect bacteria antibiotics must first pass

Figure 6 Comparison of the pores formed by seven TM3 helices ofMscS in nonconducting408 (a) and open430 (b) conformations viewedfrom the periplasm (top) and from within the membrane (bottom)

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through their outer wall which is a process facilitated by porinsPorin alteration has been implicated in antibiotic resistance444

In addition engineered porins such as the OmpG havepotential for use as stochastic sensors77

Functionally related to porins α-hemolysina toxinproduced by Staphylococcus aureusis secreted as a monomerbut assembles on target cell membranes to form ahomoheptameric channel which leads to an uncontrolledpermeation of ions and small molecules and causes cell lysisThe X-ray structure of α-hemolysin445 revealed a mushroom-like shape with a β-barrel stem protruding from its cap domainsee Figure 4k Its ability to self-assemble in biological orsynthetic membranes and its structural stability over a widerange of ion concentrations temperatures and pHs make α-hemolysin an excellent platform for stochastic sensingapplications446 including detection of DNA sequence bymeasuring the ionic current447 An interesting feature is therectification behavior of the channel which has been exploredby both implicit solvent88 as well as all-atom MDsimulations9093

Another large water-filled biological nanopore is MspAthemajor outer-membrane porin of Mycobacterium smegmatis thatallows the uptake of hydrophilic nutrients from the environ-ment The crystal structure of MspA448 revealed a homo-octameric goblet-like structure with a central channel Theporin has a constriction that is lined by two belts of aspartateresidues (Asp90 and Asp91) that diminish the permeability ofnonpolar solutes Genetically modified variants of the MspAchannel may enable practical nanopore DNA sequencing449450

as they provide superior ionic current signals for nucleic aciddetection if compared with α-hemolysin451

35 Other Channels

The voltage-dependent anion channel (VDAC) residing in themitochondrial outer membrane serves as a conduit formetabolites and electrolytes VDACs mediate the passage ofions such as K+ Clminus and Ca2+ and small hydrophilic moleculessuch as ATP between the cytosol and the mitochondria andregulate the release of apoptotic proteins The pore has avoltage-dependent conductance with an anion-selective high-conductance state at low transmembrane potential and aslightly cation-selective low-conductance state at high poten-tial452 Several NMR and X-ray structures of human as well asmouse VDACs453minus455 have become available Initially thesignificance of these structures was questioned on account of anapparent conflict with biochemical and functional data456

However additional NMR457458 and theoretical stud-ies259262268 have shed light on the structureminusfunction relationreaffirming the biological relevance of the structuresThe ClC chloride channels found in both prokaryotic and

eukaryotic cells control the selective flow of Clminus ions and arebelieved to play an important role in regulation of bloodpressure pH and membrane excitability These channelsconduct not just Clminus but also other anions such as HCO3

minusSCNminus and NOminus Unlike cation channels they do notdiscriminate strongly between different species of anionsDefects in these channels are implicated in several diseasessuch as myotonia congenita Bartterrsquos syndrome andepilepsy459 In the past decade structures of ClC orthologuesfrom two bacterial species Salmonella serovar typhimurium andEscherichia coli have become available460 The X-ray structuresreveal the ClC channels to be homodimers with two identicalbut independent pores see Figure 4j Some prokaryotic

members of the ClC family of channels are now believed tobe ion transporters although the line between ion channels andtransporters is getting blurred461 There have been a fewsimulation studies of the permeation pathways260261 of the ClCchannelsThe nicotinic acetylcholine receptor (nAChR) belongs to a

superfamily of Cys-loop ligand-gated ion channels It couples acationic transmembrane ion channel with binding sites for theneurotransmitter acetylcholine (ACh) so that the gating of thechannel is linked to the binding of ACh The nAChR owes itsname to the ability of nicotine to mimic the effects of ACh inopening up the pore The nAChR is composed of a ring of fiveprotein subunits with three domains a large N-terminalextracellular ligand binding domain (LBD) a transmembranedomain (TM) and a small intracellular domain see Figure 4hThere are two ACh binding sites in the ligand-binding domainthe pore opens when both are occupied414 Although thecomplete high-resolution structure of the nAChR is absent atpresent X-ray and electron microscopy structures of some of itscomponents are available413414 The nAChR plays a critical rolein neuronal communication converting neurotransmitter bind-ing into membrane electric depolarization The channel isfound in high concentrations at the nerveminusmuscle synapsenAChR is implicated in a variety of diseases of the centralnervous system including Alzheimerrsquos disease Parkinsonrsquosdisease schizophrenia and epilepsy462 It is also believed toplay a critical role in mediating nicotine reward andaddiction463 Although detailed study of the gating mechanismis precluded by the lack of a complete structure of the nAChRas well as the time scales involved there have been severalstudies on the TM domain215212 and the LBD218

AmtB is a representative bacterial ammonium transporterwhich belongs to AmtMEP family464 Some bacteria andplants use ammonium as a nitrogen source and have variousforms of transporters for the uptake of ammonium464465 At thesame time ammonium is also a toxic metabolic waste whichshould be removed quickly by transporters usually formammals466 There exist several high-resolution crystalstructures of bacterial AmtB409467minus470 The Escherichia colicrystal structure (Figure 4d) has become the paradigm for thestudy of the transport mechanism of ammonium409 UsuallyAmtB proteins are crystallized as a homotrimer Each monomerconsists of 11 transmembrane helices that form a channel forammonium The channel is highly hydrophobic raising thepossibility that ammonium passes the channel in a deproto-nated form (ammonia)

4 MOST COMMON SIMULATION METHODSAmong a large number of computational approaches proposedand employed for studies of ion channels most fall within thefollowing three categories all-atom molecular dynamics (MD)which is a fully microscopic description with all atoms treatedexplicitly Brownian dynamics (BD) in which only the ions aretreated explicitly while the solvent and the protein and lipidsare represented implicitly and approaches based on PoissonminusNernstminusPlanck (PNP) theory in which the ionic concentrationis treated as a continuum Each of the three approaches haslimitations and advantages The MD method is considered themost computationally expensive but also the most accurateThe PNP and BD approaches are in general less computa-tionally expensive but also provide less detail At the same timethe MD method has the smallest temporal and spatial rangefollowed by BD methods followed by PNP approaches Figure

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7 schematically illustrates typical setups for the three modelingapproaches applied to the same systemThe above classification however is rather approximate and

can be misleading Thus the level of computational complexityoften depends on the desired level of detail whereas theaccuracy depends on the assumptions made in deriving theparameters of the model Even the most sophisticated MDsimulations rely on the MD force field which is a classicalmodel that may or may not be adequate for describing a certainphenomenon In this respect full quantum or combinedquantum mechanicsclassical mechanics approaches (QMMM) can in principle provide the highest degree of accuracyHowever the time scale accessible to these methods is severelylimiting Interested readers are directed to reviews of QMMMapproaches for simulations of biomolecules471472 and to arecent review of computational approaches to ion transport innanopores473 On the other hand it is possible to incorporateatomic-level details in BD and even PNP approaches see forexample recent work by Comer Carr and co-workers371373

Other considerations often neglected when evaluating theldquocomputational costrdquo of a certain approach are the qualificationsand ambitions of the researcher performing the modeling tasksand the availability of well-documented and ready-to-use codesFor example it is always possible to increase the computationalcomplexity of the problem by including an exorbitant amountof water in an all-atom simulation or using very fine mesh sizein continuum calculations One could also easily spend severalmonths writing debugging or porting a computationallyefficient code while the same time could have been used torun a more computationally intensive but ready-to-use andtested code Thus there are no simple rules in choosing anoptimal simulation method and researchers new to the field areurged to seek expert advice for their particular problem

41 Continuum Models

Ion channels are complex systems with many degrees offreedom and hence are challenging to model in atomisticdetail Continuum theories based on PoissonminusBoltzmann (PB)and PoissonminusNernstminusPlanck (PNP) equations are powerfultools that make simulation of such systems tractable The mainidea is to employ a continuum description for all componentsof the system ie the solvent the ions and the ion channelThe water the membrane and the channel are represented asfixed structureless dielectrics while the ions are described byspecifying the local density throughout the system Figure 7aschematically illustrates a PNP model of α-hemolysin

411 Electrostatics of Ion Channels The PB equation isthe most popular theoretical model for describing theelectrostatics around a charged biomolecule in ionic solutionIn a system of interacting mobile charged particles theelectrostatic potential arises due to the combined effect of thecharged biomolecules ions and dielectric properties of theenvironment The PB model assumes that the distribution ofcharges in the system is related to the electrostatic potentialaccording to Boltzmann statistics For the purpose of describingelectrostatics of a single biomolecule the PB equation whichwas first introduced independently by Gouy (1910) andChapman (1913) and later generalized by Debye and Huckel(1923) is most frequently written as

sumε ψ πρ π

ψλ

nablamiddot nabla = minus minus

minus

infin

⎛⎝⎜

⎞⎠⎟

c z q

z qk T

r r r

rr

( ( ) ( )) 4 ( ) 4

exp( )

( )

ii i

i

f

B (8)

where ε(r) is the position-dependent dielectric constant ψ(r) isthe electrostatic potential ρf(r) is the fixed charge density ofthe biomolecule ci

infin represents the concentration of ion speciesi at infinite distance from the biomolecule zi is the valency ofion species i q is the proton charge kB is the Boltzmannconstant T is the temperature and λ(r) describes theaccessibility of position r to ions (for example it is oftenassumed to be zero inside the biomolecule) A solution to thePB equation gives the electrostatic potential and equilibriumdensity of ions throughout the space The PB equation invokesa mean-field approximation that neglects nonelectrostatic ionminusion interactions (eg van der Waals or water-mediated) thedielectric response of the system to each ion and effects due tocorrelations in the instantaneous distribution of ions Becauseof these the PB equation fails to describe the electrostatics ofhighly charged objects such as DNA in high-concentration ionsolutions with quantitative accuracy474 In the context of ionchannels which rarely carry such a high charge density the PBtheory has been widely used to calculate the free energy cost oftransferring a charge from bulk solution to the interior of thechannel105287 (see Table 1) to characterize ion-channelinteractions88294 and to compute the distribution of thetransmembrane electrostatic potential103104294299 Such con-tinuum electrostatic calculations have also been used toestimate the relative stability of protonated and unprotonatedstates of ionizable residues in an ion channel (discussed in refs

Figure 7 Schematic illustrations of the PNP (a) BD (b) and all-atom MD (c) modeling methods applied to the same systeman α-hemolysinchannel embedded in a lipid bilayer membrane and surrounded by an electrolyte solution In panel (a) the ions are described as continuous densitywhereas the water protein and membrane are treated as continuum dielectric media In the BD model (panel b) only ions are represented explicitlywhereas all other components are either implicitly modeled or approximated by continuum media All atoms are treated explicitly in the all-atom MDmethod (panel c)

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61 and 475) DelPhi476 and APBS477 are two popular computercodes for numerically solving the PB equation412 Ion Transport Although the PB model provides

insights into the equilibrium energetics of an ion channelmodeling of the ion flux requires a nonequilibrium approach Inmost ion channels the time scale of ion permeation rangesfrom tens of nanoseconds (porins) to microseconds and evenmilliseconds (in active transport) Thus observing a statisticallysignificant number of ion-permeation events requires longtrajectories that are still rather expensive to obtain using an all-atom approach The PoissonminusNernstminusPlanck model givesaccess to long time scales albeit at lower temporal and spatialresolutions As in the PB model the lipid protein and watermolecules are approximated as dielectric continua while ionsare described as continuous density distributions The currentdensity is obtained from the NernstminusPlanck (NP) theorywhich is widely used in studies of electrolyte transport In theNP theory ion fluxes arise from two sources the gradient ofion concentration and the gradient of the electrostatic potentialTraditional NernstminusPlanck equations do not describe ion-channel interactions However the classical NernstminusPlanckequations may be modified to include the ion-channelinteractions via an effective potential Thus the flux of ionspecies i Ji is written as

= minus nabla + nabla⎛⎝⎜

⎞⎠⎟t D c t

c tk T

J r r rr

r( ) ( ) ( )( )

( )i i ii

iB

eff

(9)

where Di and ci are the diffusion constant and the numberdensity of ion species i respectively and r( )i

eff is theeffective potential that usually combines the electrostaticpotential ϕ(r) and a core-repulsive potential UCore(r) withthe latter describing interactions between ions and the proteinchannel and not between the ions themselvesThe concentration and the flux of each ionic species obey the

continuity equation

partpart

+ nablamiddot =c t

tt

rJ r

( )( ) 0i

i (10)

Under steady-state conditions the concentration and the fluxdo not vary with time and nablamiddotJi(r) = 0 The electrostaticpotential is calculated from the Poisson equation

sumε ϕ π ρnablamiddot nabla = minus +r q cr r r( ( ) (( ))) 4 ( ( ) ( ))i

i if

(11)

where ε(r) is the dielectric constant qi is the ion charge andρf(r) is again the (fixed) charge density due to the proteinThe above coupled partial differential equations constitute

the PNP equations and may be solved by a variety of methodsin one or three dimensions Typically the NP and the Poissonequations are solved self-consistently to simultaneously obtainthe electrostatic potential ϕ(r) and the ionic concentration ci(r)under appropriate boundary conditionsModeling ion channels within the PNP framework is

computationally inexpensive compared to MD and BDsimulations because the problem of many-body interactions isavoided through a mean-field approximation An undesirableside-effect is that some important physics is neglected by thisapproximation Below we discuss some of the shortcomings ofthe PNP equations in the context of ion channels as well asextensions to the equations that address these shortcomings

Interested readers are directed to comprehensive reviews onthis subject12299307310478

Prior to the surge of popularity of the all-atom MD methodcontinuum electrodiffusion theories played a major role indevelopment of our understanding of ion fluxes in nano-channels81255 Early attempts to use the electrodiffusion theoryto describe ion flux through nanochannels279minus281286 led to thedevelopment of simplified models based on a self-consistentcombination of the Poisson equation and the NernstminusPlanckequations that were subsequently applied to various channelsystems282minus284 Most of the early studies dealt with either one-dimensional models or simplified geometries that lacked adetailed description of the protein structure and static chargedistribution These studies connected qualitative features of thecurrentminusvoltageminusconcentration relationship to structural andphysical features of the models For example the PNP theorywas used to demonstrate how charges at the channel openingscan produce current rectification285479 as well as how achannel with ion-specific binding sites can exhibit lowerconductance in a mixture of two ion types than in a puresolution of either type480 A lattice-relaxation algorithm able tosolve the PNP equations for a 3D model was developed byKurnikova and co-workers8 in later years This procedure allowsthe protein and the membrane to be mapped onto a 3D cubiclattice with defined dielectric boundaries fixed chargedistribution and a flow region for the ionsLike the PB equation the system of PNP equations

constitutes a mean-field theory that neglects the finite size ofthe ions the dielectric response of the system to an ion andionminusion correlations In fact the PNP equations reduce to thePB equation for systems with zero flux everywhere The validityof a continuum dielectric description and mean-fieldapproaches in the context of narrow pores has been thesubject of much debate For example Chung and co-workersobserved considerable differences between the conductancethrough idealized pores using the BD and PNP ap-proaches287294 The authors argued that the mean-fieldapproximation breaks down in narrow ion channels due to anoverestimation of the screening effect by counterions within thepore Larger channels like porins at physiological or lower ionconcentrations are described quite accurately by the PNPequations However the currents computed based on the PNPmodels can be considerably higher (by 50 for OmpF) than inequivalent BD simulations55

When a charge in a high dielectric medium is brought near alow dielectric medium a repulsive surface charge is induced atthe dielectric boundary In continuum descriptions such as PBand PNP the induced charge density includes (usually)canceling components from both positive and negative averagecharge densities The interaction energy between a charge andits induced charge density is often called the dielectric self-energy The dielectric self-energy due to the average chargedensity and the average induced charge density at the dielectricboundary is in general smaller than the interaction energybetween point charges and corresponding induced chargeaveraged over all configurations Put another way a pointcharge approaching a low dielectric medium is strongly repelledby its induced image charge and this repulsion is largely lost bythe implicit averaging in mean-field descriptionsThe PB and PNP equations have been modified to include

the interaction of an ion with the charge density itinduces11294296 Although the corrections account for theinteraction of an ion with its induced dielectric charge they do

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXJ

not account for the interaction of the induced charge with asecond nearby ion Similarly the mean-field approximationinherently ignores effects involving correlations in theinstantaneous ion distribution For example the narrowestportion of the potassium channels almost always contains twoions that move in a concerted fashion (see section 511) whichcannot be properly treated by continuum theories Never-theless it was concluded that the dielectric self-energy accountsfor most of the discrepancy between PNP and BD results in thecase of narrow channels294

Although early electrodiffusion studies of Levitt consideredhard-sphere repulsion between ions by iteratively correcting theion concentration279 many studies have since ignored suchfinite-size effects Recently the PNP equations have beenadapted to incorporate finite-size effects using classical densityfunctional theory to describe many-body hard sphereinteractions between ions and solvent290291300481 Unfortu-nately these approaches often yield cumbersome integro-differential equations Finite-size effects can be included in thePNP equations by introducing an entropic term thatdiscourages solvent crowding by ions309 The latter approachyields a tractable set of corrected PNP equations Both the PNPand BD methods usually ignore thermal fluctuations of theprotein and lipid bilayer However these can be effectivelycaptured by combining results from MD or Monte Carlosimulations with 3-D PNP calculations92

The PNP approach continues to play a major role inimproving our understanding of the physics of ion channelsThe computational efficiency of the PNP model is unparallelledfor studies of ion conductance in a low ion concentrationregime where the PNP method is expected to be the mostaccurate The method is highly efficient at predicting the effectof a channelrsquos geometry on the currentminusvoltage dependence atphysiological voltages and can be used to screen for mutationsthat affect conductance of a channel The calculation of currentscan be quite accurate in the case of larger channels such asporins PNP is perhaps the only method that can presentlysimulate the interplay of ion conductances in an ensemble ofion channels (such as in a realistic biological membrane)explicitly taking the structural features of the channels intoaccount Finally the PNP approach is rather flexible to includedescriptions of additional physical effects for examplehydrodynamic interactions354364369370 or the effect of asemiconductor membrane on the ionic current361382383

42 Brownian Dynamics

The BD method allows for simulations of explicit ionpermeations on the microsecond-to-millisecond time scale bytreating solvent molecules implicitly In a way the BD methodoffers a good compromise between all-atom MD andcontinuum electrodiffusion approaches Computational effi-ciency is achieved by reducing the number of degrees offreedom Typically a moderate number of atoms of interest(usually the ions) are simulated explicitly while the solvent isaccounted for via friction and stochastic random forces that actin addition to the electrostatic and steric forces arising fromother ions the protein and the lipid bilayer For the calculationof electrostatic forces the water the membrane and the proteinchannel are usually treated as continuous dielectric media Thechannel is treated as a rigid structure and thermal fluctuationsare typically ignored Figure 7b schematically illustrates a BDmodel of α-hemolysin

421 General Formulation of the BD Method In theBrownian dynamics method a stochastic equation is integratedforward in time to create trajectories of atoms Theldquouninterestingrdquo degrees of motion usually corresponding tofast-moving solvent molecules are projected out in order todevelop a dynamic equation for the evolution of the ldquorelevantrdquodegrees of freedom The motion of the particles is described bya generalized Langevin equation

int = minus prime minus prime prime +m t dt M t t t tr r f( ) ( ) ( ) ( )i i i

t

i i i0 (12)

The force on the ith particle i is obtained from an effectivepotential = minusnabla r( )i i iThe potential function is a many-body potential of mean

force (PMF) that corresponds to the reversible thermodynamicwork function to assemble the relevant particles in a particularconformation while averaging out the remaining degrees offreedom ie the effect of all other atoms is implicitly present in

r( )i The second term on the right-hand side is thedamping force representing the frictional effect of theenvironment and finally fi(t) is a Gaussian fluctuating forcearising from random collisions The frictional force depends onprevious velocities through the memory kernel Mi(tminustprime) Thefirst and second moments of the random force are given by⟨fi(t)⟩ = 0 and ⟨fi(t)middotfj(0)⟩ = 3kBTMi(t)δij where kB is theBoltzmann constant and T is the temperature Both the dragforce and the stochastic force incorporate the effect of thesolvent In the Markovian limit the memory kernel is a Diracdelta function that leads to the traditional Langevin equation

γ = minus +m t t tr r f( ) ( ) ( )i i i i i i (13)

The friction coefficient γi is related to underlying molecularprocesses via the fluctuationminusdissipation theoremIn the overdamped regime (which applies to the motion of

an ion in water) the inertial term can be ignored so that theLangevin equation is reduced to

ζ = +tD

k Ttr( ) ( )i

ii i

B (14)

where Di = kBTγi is the diffusion coefficient of the ith particleand ζi(t) is a Gaussian random noise with a second momentgiven as ⟨ζi(t)middotζi(0)⟩ = 6Diδ(t)

422 BD Simulations of Ion Channels A Browniandynamics simulation requires two basic ingredients adescription of the forces applied to each ion and the diffusioncoefficient for each ion The diffusion coefficient for the ionsshould be in general position-dependent and can be obtainedfrom all-atom MD simulations373482483 or estimated usinganalytical techniques88484 However in most cases a singleposition-independent diffusion constant is used for all ions ofthe same speciesEach ion experiences a force that depends on its position as

well as the positions of all the other ions in the system Thepotential corresponding to the forces on the ions is the multi-ion PMF which is the multidimensional free energy surfacethat is usually broken into an ionminusion PMF and a PMF due tothe pore the solution and other biomolecules373 The PMFscan be calculated from all-atom MD or even quantumchemistry simulations but such calculations are computation-ally expensive

Chemical Reviews Review

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A more typical approach was presented by Roux and co-workers which we summarize here556263299 The multi-ionPMF can be written as

sum sum sum

sum ϕ ϕ

= | minus | +

+ +

αα γ α

α γ α γα

α

αα α α

neu U

q

r r r r

r r

( ) ( ) ( )

[ ( ) ( )]

core

sf rf(15)

where uαγ(r) is the ionminusion interaction Ucore is a repulsivepotential preventing the ions from entering the ion-inaccessibleregions ϕsf is the electrostatic potential arising from thepermanent protein charge distribution and ϕrf is the reactionfield potential arising from the electrostatic polarization of thevarious dielectric boundaries The static field may be computedfrom an atomic model of the pore using the PBequations556263485 Any externally imposed transmembranebias may be included in the calculation of the electrostaticpotential Usually the ionminusion interaction includes van derWaals and Coulomb terms

εσ σ

ε= minus +α γ α γ

α γ α γ α γ⎜ ⎟ ⎜ ⎟⎡⎣⎢⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎤⎦⎥u r

r r

q q

r( ) 4

12

6

bulk

where εαγ and σαγ are the parameters for the 6minus12 Lennard-Jones potential qα and qγ are the charges of the ions and εbulk isthe dielectric constant of bulk water The local dielectricconstant of the water in the interior of the pore may beextracted from atomistic simulations but it is usually assumedto have the bulk value of 80 Solvation effects can beapproximately described by including a short-range solvationpotential55287486 but that is rarely done in practice Web-basedinterface for GCMCBD simulations of ion channels hasrecently become available268

Early BD studies were performed using one-dimensionalrepresentations of channels487 Later these were extended tomore realistic three-dimensional geometries although theseoften lacked atomic detail63486 However the X-ray structure ofan ion channel can be used to create a more realistic model ofthe channel by computing electrostatic and core repulsionpotential maps from the all-atom structure Brownian dynamicssimulations have been applied to several biological channelsincluding OmpF5562minus64 K+ channels110minus115117 α-hemoly-sin8895 VDAC268 and gramicidin1617 Roux and co-workershave developed a grand canonical Monte CarloBrowniandynamics method (GCMCBD)6263103 to allow for fluctua-tions in the total number of ions in the system and asymmetricion concentration conditions For detailed treatment of thesubject interested readers are directed to a review of thecomputational methods299473

Recently Comer and Aksimentiev373 used all-atom MD todetermine full three-dimensional PMF maps at atomicresolution for ionminusion and ionminusbiomolecule interactionsthereby fully accounting for short-range effects associationwith solvation of ions and biomolecules Using such full 3-DPMFs in BD simulations of ion flow through a model nanoporecontaining DNA basepair triplets yielded ionic currents in closeagreement with the results of all-atom MD but at a fraction ofthe computational cost The authors indicate that such anatomic-resolution BD method can be developed further toincorporate the conformational flexibility of the pore and DNAby altering the PMF maps on-the-fly

43 All-Atom Molecular Dynamics

The all-atom MD method can provide unparalleled insight intothe physical mechanisms underlying the biological function ofbiomacromolecules By explicitly describing all the atoms of thesystem of interest and the majority of interatomic interactionsthis method has the potential to compete with the experimentin completeness and accuracy of the description of microscopicphenomena In the case of an ion channel one can in principledirectly observe ion conductance and gating at the spatialresolution of a hydrogen atom and the temporal resolution ofsingle femtoseconds Critical to the above statement is theassumption that the all-atom MD method is equipped with acorrect description of interatomic interactions and enoughcomputational power is available Despite ever-increasingavailability of massive parallel computing platforms makingquantitative predictions using MD remains challenging in partdue to imperfections of the interatom interaction modelsBelow we briefly review the formulations of the all-atom MDmethod and describe recent advances in the field

431 General Formulation of the All-Atom MDMethod In the MD simulations of biomacromoleculesatoms are represented as point particles and the connectivity(or covalent bonds) among those atom are given a prioriCovalently bonded atoms interact with each other throughbonded potentials while the other atom pairs interact throughnonbonded potentials

= +U U Ur r r( ) ( ) ( )N N Nbonded nonbonded (16)

where rN denotes the coordinates of N atoms in a systemBonded interactions model quantum mechanical behavior ofcovalently connected atoms by means of harmonic bond angleand improper dihedral angle restraints and periodic dihedralangle potentials

sum sum

sum

sum

θ θ

χ δ

ϕ ϕ

= minus + minus

+ + minus

+ minus

θ

χ

ϕ

U K b b K

K n

K

( ) ( )

1 cos( )

( )

bbondedbonds

02

angles0

2

torsions

impropers0

2

(17)

where Kb and b0 are the bond force constant and theequilibrium distance respectively Kθ and θ0 are the angleforce constant and the equilibrium angle respectively Kχ nand δ are the dihedral force constant the multiplicity and thephase angle respectively and Kϕ and ϕ0 are the improper forceconstant and the equilibrium improper angle488 The non-bonded potential usually consists of the Lennard-Jones (LJ)potential for van der Waals interactions and the Coulombpotential for electrostatic interactions

sum εσ σ

ε= minus +

⎧⎨⎪⎩⎪

⎡

⎣⎢⎢⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤

⎦⎥⎥

⎫⎬⎪⎭⎪

Ur r

q q

r4 ij

ij

ij

ij

ij

i j

ijnonbonded

nonbond

12 6

(18)

where εij is the well depth σij is the finite distance at which theLJ potential is zero rij is the interatomic distance and qij areatomic charges The bonded parameters are empiricallycalibrated based on the quantum mechanical calculations ofsmall molecules whereas the nonbonded parameters are mainlyderived from quantum chemistry calculations (eg partial

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXL

charges) and empirical matching of thermodynamic data (eghydration free energy)A biomolecular force field is a set of bonded and nonbonded

parameters defined in eqs 17 and 18 Presently severalbiomolecular force fields exist The force fields can becategorized into types based on whether all the atoms areexplicitly treated or not All-atom force fields which includeCHARMM489 AMBER490491 and OPLS-AA492493 treat allatoms explicitly In the united-atom force fields (egGROMOS494495) some nonpolar hydrogen atoms areneglectedFor the simulations of channel proteins a lipid force field is

as important as a protein force field because the channels areembedded in lipid bilayers Among the all-atom force fields theCHARMM force field includes parameters for lipids the latestupdate at the time of writing this review is CHARMM36496

Together with the AMBER force field for the protein thegeneral all-atom AMBER force field (GAFF) can be used todescribe the lipid bilayer497498 Officially OPLS does notinclude lipid parameters Among the united-atom force fieldsGROMOS comes with lipid parameters499 Berger et alreported improved GROMOS-based lipid parameters basedon the condensed-phase properties of pentadecane500 Thislipid force field has been widely used in combination with otherprotein force fields such as AMBER OPLS and GROMOS501

For an in-depth review of various force fields we referinterested readers to a comprehensive review by Mackerell488

432 Ion Channels in Native Environment Unlikesoluble proteins that are surrounded only by water ion-channelproteins are embedded in a lipid bilayer and therefore are incontact with both water and lipids Because of the drasticallydifferent chemical and electrostatic properties of lipid andwater proper descriptions of proteinminuslipid and proteinminuswaterinteractions are key for the successful simulation of amembrane channel To model ion conduction through arelatively rigid channel (eg gA or KcsA channel) it is possibleto use an implicit solvent model of the channelrsquos environmentin which the volume occupied by lipid and water is treated ascontinuum media of dielectric constants 2 and 78 respec-tively299 However when interactions between a channel and alipid membrane are significant (eg in mechanosensitivechannels) explicit modeling of lipid molecules is essentialThe tails of lipids are long and equilibrate slowly making it

significantly more difficult to assemble a model of a channelembedded in an explicit lipid bilayer than a model of a fullysoluble protein Usually the system setup involves thefollowing steps Starting from a pre-equilibrated and solvatedlipid bilayer membrane one makes a pore in the bilayer bydeleting a minimal number of lipid molecules so that theprotein can fit Next an all-atom model of the protein is placedin the pore which is followed by energy minimization andequilibration of the system using the MD method having thechannelrsquos coordinates restrained to their crystallographic valuesFinally when the proteinminuslipid interface is well equilibratedone can perform a production run without applying restraintson the channel For detailed step-by-step instructions forbuilding atomic-scale models of ion channels in lipid bilayerenvironment interested readers are directed to a tutorial onMD simulations of membrane proteins502 Even though a fullyautomated procedure is not yet available several programs canassist a beginner in building a new system VMD503 containsthe Membrane Builder plugin Jo et al have a web-based

service CHARMM GUI Membrane Builder (httpwwwcharmm-guiorgmembrane)504505

An alternative method for creating an all-atom model of anion channel in its native environment is to first carry out self-assembly simulations using a coarse-grained (CG) MDmethod74165379 The main difference between the CG andall-atom MD methods is the level of detail used to describe thecomponents of the system Typically one CG bead representsabout 5minus10 atoms Being much more computationally efficient(and lower resolution) the CG model allows millisecond-time-scale simulations to be performed on commodity computersInterested readers are directed toward recent reviews on thissubject506minus508

In the CG simulations of self-assembly CG models of lipidssolvent and a membrane protein are placed with randompositions in desired proportions During the course of CGMDsimulations the lipid molecules spontaneously form a lipidbilayer around a protein After obtaining a stable model the CGmodel can be reverse-coarse-grained into a fully atomisticmodel (see for example a study by Maffeo and Aksimen-tiev330) A great advantage of this approach is that it requiresno a priori knowledge of the position of the membranechannels relative to the membrane An obvious disadvantage isthat one has to have a reasonable CG model to carry out theself-assembly simulations and a reliable procedure to recoverthe all-atom details from the final CG model Currently it isnot possible to use a CG approach to model ion conductancethrough large membrane channels due to inaccurate treatmentsof the membrane and water electrostatics in most CG modelsHowever work to improve CG methods is ongoing509510 andsuch simulations should become possible in the near future

433 Homology Modeling Usually an all-atom MDsimulation of a channel protein can be performed only when anatomic-resolution structure of the channel is available Thisrequirement severely limits application of the MD methodFortunately membrane channels of different organisms oftenhave similar amino-acid sequences The sequence similarity canbe used to build an all-atom model of the channel that does nothave an experimentally determined structure through aprocedure called homology modeling511 Briefly homologymodeling proceeds as follows First a sequence alignmentbetween a target sequence and a homologous sequenceforwhich a structure is knownis performed Second thesecondary structures (eg α-helices and β-sheets) of the targetsequence from the homologous sequence are built Finallyloops connecting the secondary structures are modeled and theoverall structure is refined There exist many tools for thehomology modeling (eg Modeler by Sali and Blundell511)The homology modeling method has been successfully used

for building initial structures of several ion channels forsubsequent all-atom MD simulations Capener et al512 built aninward rectifier potassium channel (Kir) based on a high-resolution structure of KcsA1 Sukharev et al used the crystalstructure of Mycobacterium tuberculosis MscL407 to modelclosed intermediate and open structures of Escherichia coliMscL231232 Law et al combined the crystal structure of theLymnea stagnalis acetylcholine binding protein and the electronmicroscopy (EM) structure of the transmembrane domain ofthe torpedo electric ray nicotinic channel to build an entirehuman nicotinic acetylcholine receptor213

434 Free-Energy Methods Perhaps the greatestdisadvantage of the MD method is that simulations are costlyand are currently limited to the microsecond time scalea

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXM

where εNa is the emf of the sodium channel Analogously to nfor the potassium channel the behavior of h and m aredescribed by steady-state values hinfin and minfin and time constantsτh and τm obeying the differential equations

τ=

minusinfinht

h hdd h (4)

τ=

minusinfinmt

m mdd m (5)

The behavior of hinfin τh minfin and τm under a change of voltage isshown in Figure 3d The time constant τh is much higher thanτm meaning that the deactivating particle reacts much moreslowly to a change of external potential than the activatingparticles Thus we see how the conductance traces shown inFigure 2a are explained upon switching from the normalpolarized potential value (low V in Figure 3c d) to highervalues the activating particles quickly switch on due to theirlow time constant τm because of the relatively high value of τhthe inactivating particle is slow to react and continues to allowconduction eventually the inactivating particle does indeedswitch the channel back off and the conductance dropsFinally we would be remiss if we did not mention a related

theory the GoldmanminusHodgkinminusKatz (GHK) theory The GHK

theory relates voltage current and ionic permeabilities395 Oneform of the theory is the GHK voltage equation

=+ ++ +

VRTF

P P PP P P

ln[K] [Na] [Cl][K] [Na] [Cl]0

K o Na o Cl i

K i Na i Cl o (6)

Here V0 is the zero-current voltage R is the gas constant F isthe Faraday constant PX is the permeability of ion species Xand [X]o and [X]i are the concentrations of ion species X onthe outside and inside of the axon respectively Thepermeability PX describes how easily ions cross the membrane

equiv minus ΔP M cX X X (7)

where MX is the flux of X across the membrane and cX is theconcentration difference Among other things the GHK voltageequation may be used to find the action potential givenconcentrations and permeability ratios of potassium sodiumand chloride ions Interested readers are directed to Hille395 fora more thorough treatmentThe HH model was a great leap forward in our under-

standing of nerve cells and excitable membranes in general andcontinues to influence research work in the field Recent studieson expanding the HH model include incorporation of the HHmodel into finite element frameworks399400 adding noise tothe HH model401minus403 and the modeling of coupled neurons404

Wong et al400 proposed a model of cardiomyocytes thatdescribed concerted action of various types of ion channelsRowat401 examined the mechanisms behind the interspikefrequency of a stochastic HH model with applications toirregular neural spiking Tuckwell and Jost402 performed adetailed analysis of the first- and second-order moments ofvoltage and n m and h in a stochastic HH model Linaro etal403 developed a technique for mapping HH-derived Markovmodels of explicit channel activationminusdeactivation events to acomputationally more tractable form for more efficientsimulation Finally Che et al404 described behavior of neuronsexposed to a low-frequency electric field The power andsimplicity of the HH model will no doubt continue to influenceresearch for another 50 years

3 MOST COMMON TARGETS OF COMPUTERMODELING

Sustained unidirectional transport of ions across a biologicalmembrane requires energy input According to the type ofenergy sources ion transport can be assigned to one of thefollowing broad categories Passive transport is driven by theion-motive force or emf which combines the gradient of theelectrostatic potential with the concentration difference across amembrane In a typical biological setting the differencebetween cis and trans ion concentrations creates the trans-membrane gradient of the electrostatic potential In alaboratory setting the electrostatic gradient is most commonlyimposed by applying an external voltage source Theconcentration gradient across the membrane can act along oragainst the electrostatic gradient Despite being passive thetransport can still be selective and gated by voltage tensionand chemical stimuli The focus of this review is primarily onmembrane channels that facilitate passive transport of ionsOver the course of evolution nature has developed

numerous ways to transport ions against the ion-motiveforce The most prominent examples are ion pumps thatutilize the energy of ATP hydrolysis to transport ions across themembrane against the concentration gradient Some of these

Figure 3 (a and b) Schematics of potassium (a) and sodium (b)channels considered in the HodgkinminusHuxley model In the HHmodel the conductance of a potassium channel is controlled by fouractivating particles (black circles) whereas the conductance of asodium channel is controlled by three activating particles and oneinactivating particle (gray circle) (c and d) Behavior of the HH modelvariables describing potassium (c) and sodium (d) conductance as afunction of applied potential

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pumps can work in reverse synthesizing ATP by transportingions along the concentration gradient In so-called antiportersand cotransporters transport of one ion species is coupled totransport of the other Some membrane channels can coupletransport of ions to transport of larger uncharged solutes andor protons In turn proton transport can be coupled to electrontransport for example in respiratory chain proteins Thus theinner and outer membranes of a living cell are full of variousion-transporting entities whose concerted action and synchron-ized response to external stimuli keep the cell alive Interestedreaders are directed to the book by Alberts et al398 for a

complete overview of the field to a paper by Khalili-Araghi etal333 for a recent review of modeling efforts in the field ofactive transport and to a study by Beard405 for an example ofmodeling a system of ion channels in an organelleAt present modeling and simulations of ion channels are

generally limited by the experimental knowledge about themAlthough the HH theory is a beautiful example to the contrarymore often than not a theoretical study of an ion channelrequires some knowledge of the channelrsquos structure ideally atatomic resolution Whereas the ldquono structureno studyrdquo rule isadopted by the majority of researchers working in the field of

Figure 4 Molecular graphics images of membrane channels listed in Table 1 The channels shown are (a) gramicidin A (gA) 1JNO406 (b)mechanosensitive channel of large conductance (MscL) 2OAR407 (c) mechanosensitive channel of small conductance (MscS) 2OAU408 (d)ammonium transporter (AmtB) 2NUU409 (e) K+ channel (KcsA) 3EFF410 (f) voltage-gated K+ channel (Kv) 2R9R411 (g) aquaporin 0 (AQP0)2B6O412 (h) nicotinic acetylcholine receptors (nAchR) 2BG9413414 (i) bacterial outer-membrane porin (OmpF) 2OMF415 (j) bacterial chloridechannel (ClC) 1OTS416 (k) bacterial toxin (α-hemolysin) 7AHL417

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXE

computer modeling of ions channels there are notableexceptions418419 that deduce the structural architecture of thechannel from its ion-conductance propertiesPredicting the structure of a membrane channel from its

sequence is a formidable task Hence development ofcomputational models of ion channels was in a way led bycrystallographers and their ability to solve atomic structures ofion channels Membrane channels are notoriously difficult tocrystallize and are often too large for the NMR method towork Therefore atomic-resolution structures have beenobtained for only a very limited number of ion channels andhence many studies have focused on the same systems Belowwe briefly review the ion channels of known structures that arethe most common targets of computational studies

31 Gramicidin A

Gramicidins are small bacteria-produced antibiotics that whendimerized in a head-to-head fashion (Figure 4a) are able totransport a monovalent cation across a membrane once aboutevery 100 ns39 Gramicidin works by eliminating the iongradient across the membrane of Gram-positive bacteriaGramicidin was the first clinical antibiotic in use and is stillused today in conjunction with other antibioticsAll-atom molecular dynamics simulations (MD) have been

instrumental in the interpretation and refinement of NMRresults28 Gramicidin A was the subject of the first MDsimulation of an ion channel almost 30 years ago420 Advancesin the availability of computational resources have permitted farmore realistic models including lipid bilayers and full solvent tobe simulated for significant durations Gramicidin A now servesas a model system and test bed for new techniques21

32 Potassium Channels

Potassium ion channels are key constituents of electricalsignaling networks in the nervous system When openpotassium channels conduct K+ ions at rates remarkably closeto the diffusion limit (about 108 ions per second)421 and displayincredible sensitivity to the size and valency of ions Thus K+

channels can quickly release ions from within the cell inresponse to appropriate stimulus affecting the action potentialBecause some K+ channels are voltage-sensitive this can resultin a cascade of channel activations that propagates through anaxon K+ channels have been the target of prospectivetreatments for an array of disorders including multiplesclerosis422423

Taken from Gram-positive bacterium Streptomyces lividansthe K+ channel KcsA is similar in sequence to vertebratevoltage-dependent K+ channels but is easily expressed inEscherichia coli making it the prototypical K+ channel forlaboratory studies Like all K+ channels the sequence of KcsAcontains a completely conserved motif that is crucial for its K+

specificity Depicted in Figure 5 the first atomic-resolutionstructure of a K+ channel revealed a tetrameric transmembranepore with an intracellular passage leading to a large (10 Aringdiameter) cavity with a hydrophobic lining followed by anatomically narrow sim4 Aring long selectivity filter that leads to theextracellular side of the membrane1 A more complete structureof this channel was recently resolved410 featuring longcytoplasmic helices that appear to stabilize the closedconformation of KcsA at high pH In contrast to the poreregion the arrangement of cytoplasmic helices in KcsA is not auniversal structural element of K+ channelsIn the selectivity filter four rings each featuring four

negatively charged carbonyl-oxygen atoms hold two K+ ions

that are separated by a single water molecule The ions presentin the selectivity filter are mostly desolvated which carries anenormous free energy penalty that is offset by interactions withthe negatively charged surface of the filter Thus the largeforces experienced by translocating ions balance delicately toallow a smooth free energy landscape that permits rapidpermeation through the pore The balance of these forces mustbe carefully tuned to select K+ over other monovalent ions suchas Na+ Although the latter carries the same charge as K+ and isonly 04 Aring smaller experiments suggest that K+ channels bindK+ with as much as 1 000 times greater affinity than Na+1

The selectivity filter can become occupied by divalent ionswhich generally block the current through the channel The Kiror inward rectifying family of potassium channels uses thismechanism to impede K+ ions moving out of the cell Moregenerally potassium channels are regulated through a variety ofother means that include modification through ligand bindingand voltage- and pH-dependent gating Many biologicallyproduced toxins target K+ channels to interfere with a victimrsquosnervous systemBecause of the biological importance of K+ channels and the

fact that the pore domain of bacterial KcsA is homologous tothat of eukaryotic K+ channels the seminal structure of KcsA1

motivated many computational and theoretical studies148 Theformal analogy between electric current in man-made circuitsand ion conductance through the channels424 led researchers todevelop and apply continuum electrostatics theories of ionchannels103minus109 The availability of high-resolution crystalstructures stimulated development of new atomistic simulationtechniques for studying selectivity conductance and gatingbehaviors of K+ channels using either implicit110minus117 orexplicit2988111minus113116minus197 solvent models Ligand dockingcoupled with free energy calculations was recently used tostudy methods to enhance the specificity of naturally occurringneurotoxins for Kv13 which can suppress chronically activated

Figure 5 Pore region of the KcsA K+ ion channel embedded in a lipidbilayer membrane The image shows the first crystallographicallydetermined structure of a K+ channel1 which did not include the longcytoplasmic helices depicted in Figure 4 e One of the four subunits ofthe KcsA tetramer is not shown to provide a clear view of theselectivity filter The lipid bilayer is depicted as gray van der Waalsspheres

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXF

memory T cells implicated in autoimmune disorders includingmultiple sclerosis422425 To overcome the time and length scalelimitations of the all-atom approaches several multiscalemethods have been developed107198minus202 using K+ channelsas target application systems

33 Mechanosensitive Channels

All living creatures have mechanosensors426427 For examplewe can hear sound because our auditory sensory cells candetect ciliary vibrations caused by acoustic waves We can feelthe pressure on our skin and blood vessels and feel full whenwe eat food because of tension sensors in cell membranesPlants which are immobile and less responsive also havemechanosensors a representative example is the gravity sensorwhich allow roots and shoots to grow in opposite directionsInterested readers are referred to a recent review by Kung andco-workers426427 for more detailed informationA breakthrough in the biophysical study of mechanosensa-

tion was the cloning428429 and structural characterizationof simple prokaryotic mechanosensit ive channels(MSCs)407408430431 When the concentration of osmolytes ina bacterial cell is significantly higher than the concentration ofosmolytes in the environment the gradient of osmolyteconcentration across the cell membrane can cause huge turgorpressure inside the bacterial cell If left to develop fully suchosmotic stress can easily rupture the cell wall killing thebacterium To prevent this from happening bacteria haveevolved ldquosafety valvesrdquothe MSCsthat open when thesurface tension in the membrane exceeds a threshold valuemaking the membrane permeable to most small solutes andwater molecules432 Most importantly the channels return to aclosed state when tension drops Thus MSCs are essential forthe survival of bacteriaIn 1998 Chang et al reported the first high-resolution

structure of MSC of large conductance (MscL) fromMycobacterium tuberculosis in a closed conformation407 MscLis a homopentamer with each subunit having two trans-membrane (TM) helices TM1 and TM2 see Figure 4b In theclosed conformation five TM1 helices form a pore and TM2helices surround the inner TM1 helices Recently Liu et alreported a crystal structure of tetrameric MscL from Staph-ylococcus aureus in an expanded intermediate state431 So fartwo crystal structures of the Escherichia coli MSC of smallconductance (MscS) have been reported one in a non-conductive conformation408 and the other in an openconformation430 Those high-resolution structures show thatthe MscS is a homoheptamer with three TM helices persubunit see Figure 4c Seven TM3 helices form a channel withdiameters of 5 and 13 Aring in closed and open conformationsrespectively see Figure 6430

Despite the fact that mechanosensation is universal andessential for all living creatures427 its mechanism is significantlyless understood if compared to the mechanisms of other sensessuch as vision smell and taste427 Since the first MSC wasdiscovered in 1987432 and the first crystal structures of MscLand MscS were revealed in 1998 and 2002407408 both MscLand MscS have served as model systems for the computationalstudies of mechanical gating Because of its very nature thisproblem has attracted the attention of investigators fromvarious disciplines including traditional MD simulationshomology modeling continuum mechanics and coarse-grainedMD simulations see sections 522 and 541 for more detailsThe computational methods developed for studies of MscL and

MscS will surely be of great value in future studies of morecomplex mechanisms of mechanosensation34 Porins

Outer-membrane porins (OMPs) of Gram-negative bacteria aretransmembrane proteins that allow the bacterial cells to interactwith their environment through passive diffusion of water ionsand small hydrophilic molecules (lt600 Da) across their outermembranes Wide channels such as OMPs and toxins facilitatethe permeation of metabolites rather than merely small ionsHowever often they exhibit interesting behavior such asselectivity toward certain ions and serve as model systems totest computational models of ion transport they are thereforeof interest in this reviewOMPs are β-barrel structures usually forming homotrimeric

water-filled pores The porin channel is partially blocked by aloop (L3) that is folded inside the β-barrel forming aconstriction region that determines the size of the solutesthat can traverse the channel Several crystal structures ofporins have been determined at high resolution415433minus437

Some porins exhibit moderate ion selectivity eg Escherichiacoli OmpF (shown in Figure 4i) and OmpC are two cation-selective porins whereas the Pseudomonas aeruginosa OprP438 isa phosphate-selective porin The cation selectivity is known todepend on the salt concentration and the valence of the ionsGram-negative bacteria that lack porins have other substrate-specific channels that allow the passage of small molecules Forinstance the OccK1 an archetype of the outer-membranecarboxylate channel family from Pseudomonas aeruginosa(previously named OpdK) is a monomeric β-barrel with akidney-shaped central pore as revealed by the X-raystructure439 The members of the OccK subfamily of channelsare believed to facilitate the uptake of basic amino acids440 Adetailed examination of the conductance characteristics ofseveral members of the OccK subfamily of channels by Liu andco-workers441 revealed diverse single-channel electrical signa-tures nonohmic voltage dependent conductance and transientgating behavior Single-molecule electrophysiology analysisalong with rational protein design have revealed discrete gatingdynamics involving both enthalpy- and entropy-driven currenttransitions442443

Studies of porins are relevant to the development ofantibiotics To affect bacteria antibiotics must first pass

Figure 6 Comparison of the pores formed by seven TM3 helices ofMscS in nonconducting408 (a) and open430 (b) conformations viewedfrom the periplasm (top) and from within the membrane (bottom)

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through their outer wall which is a process facilitated by porinsPorin alteration has been implicated in antibiotic resistance444

In addition engineered porins such as the OmpG havepotential for use as stochastic sensors77

Functionally related to porins α-hemolysina toxinproduced by Staphylococcus aureusis secreted as a monomerbut assembles on target cell membranes to form ahomoheptameric channel which leads to an uncontrolledpermeation of ions and small molecules and causes cell lysisThe X-ray structure of α-hemolysin445 revealed a mushroom-like shape with a β-barrel stem protruding from its cap domainsee Figure 4k Its ability to self-assemble in biological orsynthetic membranes and its structural stability over a widerange of ion concentrations temperatures and pHs make α-hemolysin an excellent platform for stochastic sensingapplications446 including detection of DNA sequence bymeasuring the ionic current447 An interesting feature is therectification behavior of the channel which has been exploredby both implicit solvent88 as well as all-atom MDsimulations9093

Another large water-filled biological nanopore is MspAthemajor outer-membrane porin of Mycobacterium smegmatis thatallows the uptake of hydrophilic nutrients from the environ-ment The crystal structure of MspA448 revealed a homo-octameric goblet-like structure with a central channel Theporin has a constriction that is lined by two belts of aspartateresidues (Asp90 and Asp91) that diminish the permeability ofnonpolar solutes Genetically modified variants of the MspAchannel may enable practical nanopore DNA sequencing449450

as they provide superior ionic current signals for nucleic aciddetection if compared with α-hemolysin451

35 Other Channels

The voltage-dependent anion channel (VDAC) residing in themitochondrial outer membrane serves as a conduit formetabolites and electrolytes VDACs mediate the passage ofions such as K+ Clminus and Ca2+ and small hydrophilic moleculessuch as ATP between the cytosol and the mitochondria andregulate the release of apoptotic proteins The pore has avoltage-dependent conductance with an anion-selective high-conductance state at low transmembrane potential and aslightly cation-selective low-conductance state at high poten-tial452 Several NMR and X-ray structures of human as well asmouse VDACs453minus455 have become available Initially thesignificance of these structures was questioned on account of anapparent conflict with biochemical and functional data456

However additional NMR457458 and theoretical stud-ies259262268 have shed light on the structureminusfunction relationreaffirming the biological relevance of the structuresThe ClC chloride channels found in both prokaryotic and

eukaryotic cells control the selective flow of Clminus ions and arebelieved to play an important role in regulation of bloodpressure pH and membrane excitability These channelsconduct not just Clminus but also other anions such as HCO3

minusSCNminus and NOminus Unlike cation channels they do notdiscriminate strongly between different species of anionsDefects in these channels are implicated in several diseasessuch as myotonia congenita Bartterrsquos syndrome andepilepsy459 In the past decade structures of ClC orthologuesfrom two bacterial species Salmonella serovar typhimurium andEscherichia coli have become available460 The X-ray structuresreveal the ClC channels to be homodimers with two identicalbut independent pores see Figure 4j Some prokaryotic

members of the ClC family of channels are now believed tobe ion transporters although the line between ion channels andtransporters is getting blurred461 There have been a fewsimulation studies of the permeation pathways260261 of the ClCchannelsThe nicotinic acetylcholine receptor (nAChR) belongs to a

superfamily of Cys-loop ligand-gated ion channels It couples acationic transmembrane ion channel with binding sites for theneurotransmitter acetylcholine (ACh) so that the gating of thechannel is linked to the binding of ACh The nAChR owes itsname to the ability of nicotine to mimic the effects of ACh inopening up the pore The nAChR is composed of a ring of fiveprotein subunits with three domains a large N-terminalextracellular ligand binding domain (LBD) a transmembranedomain (TM) and a small intracellular domain see Figure 4hThere are two ACh binding sites in the ligand-binding domainthe pore opens when both are occupied414 Although thecomplete high-resolution structure of the nAChR is absent atpresent X-ray and electron microscopy structures of some of itscomponents are available413414 The nAChR plays a critical rolein neuronal communication converting neurotransmitter bind-ing into membrane electric depolarization The channel isfound in high concentrations at the nerveminusmuscle synapsenAChR is implicated in a variety of diseases of the centralnervous system including Alzheimerrsquos disease Parkinsonrsquosdisease schizophrenia and epilepsy462 It is also believed toplay a critical role in mediating nicotine reward andaddiction463 Although detailed study of the gating mechanismis precluded by the lack of a complete structure of the nAChRas well as the time scales involved there have been severalstudies on the TM domain215212 and the LBD218

AmtB is a representative bacterial ammonium transporterwhich belongs to AmtMEP family464 Some bacteria andplants use ammonium as a nitrogen source and have variousforms of transporters for the uptake of ammonium464465 At thesame time ammonium is also a toxic metabolic waste whichshould be removed quickly by transporters usually formammals466 There exist several high-resolution crystalstructures of bacterial AmtB409467minus470 The Escherichia colicrystal structure (Figure 4d) has become the paradigm for thestudy of the transport mechanism of ammonium409 UsuallyAmtB proteins are crystallized as a homotrimer Each monomerconsists of 11 transmembrane helices that form a channel forammonium The channel is highly hydrophobic raising thepossibility that ammonium passes the channel in a deproto-nated form (ammonia)

4 MOST COMMON SIMULATION METHODSAmong a large number of computational approaches proposedand employed for studies of ion channels most fall within thefollowing three categories all-atom molecular dynamics (MD)which is a fully microscopic description with all atoms treatedexplicitly Brownian dynamics (BD) in which only the ions aretreated explicitly while the solvent and the protein and lipidsare represented implicitly and approaches based on PoissonminusNernstminusPlanck (PNP) theory in which the ionic concentrationis treated as a continuum Each of the three approaches haslimitations and advantages The MD method is considered themost computationally expensive but also the most accurateThe PNP and BD approaches are in general less computa-tionally expensive but also provide less detail At the same timethe MD method has the smallest temporal and spatial rangefollowed by BD methods followed by PNP approaches Figure

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7 schematically illustrates typical setups for the three modelingapproaches applied to the same systemThe above classification however is rather approximate and

can be misleading Thus the level of computational complexityoften depends on the desired level of detail whereas theaccuracy depends on the assumptions made in deriving theparameters of the model Even the most sophisticated MDsimulations rely on the MD force field which is a classicalmodel that may or may not be adequate for describing a certainphenomenon In this respect full quantum or combinedquantum mechanicsclassical mechanics approaches (QMMM) can in principle provide the highest degree of accuracyHowever the time scale accessible to these methods is severelylimiting Interested readers are directed to reviews of QMMMapproaches for simulations of biomolecules471472 and to arecent review of computational approaches to ion transport innanopores473 On the other hand it is possible to incorporateatomic-level details in BD and even PNP approaches see forexample recent work by Comer Carr and co-workers371373

Other considerations often neglected when evaluating theldquocomputational costrdquo of a certain approach are the qualificationsand ambitions of the researcher performing the modeling tasksand the availability of well-documented and ready-to-use codesFor example it is always possible to increase the computationalcomplexity of the problem by including an exorbitant amountof water in an all-atom simulation or using very fine mesh sizein continuum calculations One could also easily spend severalmonths writing debugging or porting a computationallyefficient code while the same time could have been used torun a more computationally intensive but ready-to-use andtested code Thus there are no simple rules in choosing anoptimal simulation method and researchers new to the field areurged to seek expert advice for their particular problem

41 Continuum Models

Ion channels are complex systems with many degrees offreedom and hence are challenging to model in atomisticdetail Continuum theories based on PoissonminusBoltzmann (PB)and PoissonminusNernstminusPlanck (PNP) equations are powerfultools that make simulation of such systems tractable The mainidea is to employ a continuum description for all componentsof the system ie the solvent the ions and the ion channelThe water the membrane and the channel are represented asfixed structureless dielectrics while the ions are described byspecifying the local density throughout the system Figure 7aschematically illustrates a PNP model of α-hemolysin

411 Electrostatics of Ion Channels The PB equation isthe most popular theoretical model for describing theelectrostatics around a charged biomolecule in ionic solutionIn a system of interacting mobile charged particles theelectrostatic potential arises due to the combined effect of thecharged biomolecules ions and dielectric properties of theenvironment The PB model assumes that the distribution ofcharges in the system is related to the electrostatic potentialaccording to Boltzmann statistics For the purpose of describingelectrostatics of a single biomolecule the PB equation whichwas first introduced independently by Gouy (1910) andChapman (1913) and later generalized by Debye and Huckel(1923) is most frequently written as

sumε ψ πρ π

ψλ

nablamiddot nabla = minus minus

minus

infin

⎛⎝⎜

⎞⎠⎟

c z q

z qk T

r r r

rr

( ( ) ( )) 4 ( ) 4

exp( )

( )

ii i

i

f

B (8)

where ε(r) is the position-dependent dielectric constant ψ(r) isthe electrostatic potential ρf(r) is the fixed charge density ofthe biomolecule ci

infin represents the concentration of ion speciesi at infinite distance from the biomolecule zi is the valency ofion species i q is the proton charge kB is the Boltzmannconstant T is the temperature and λ(r) describes theaccessibility of position r to ions (for example it is oftenassumed to be zero inside the biomolecule) A solution to thePB equation gives the electrostatic potential and equilibriumdensity of ions throughout the space The PB equation invokesa mean-field approximation that neglects nonelectrostatic ionminusion interactions (eg van der Waals or water-mediated) thedielectric response of the system to each ion and effects due tocorrelations in the instantaneous distribution of ions Becauseof these the PB equation fails to describe the electrostatics ofhighly charged objects such as DNA in high-concentration ionsolutions with quantitative accuracy474 In the context of ionchannels which rarely carry such a high charge density the PBtheory has been widely used to calculate the free energy cost oftransferring a charge from bulk solution to the interior of thechannel105287 (see Table 1) to characterize ion-channelinteractions88294 and to compute the distribution of thetransmembrane electrostatic potential103104294299 Such con-tinuum electrostatic calculations have also been used toestimate the relative stability of protonated and unprotonatedstates of ionizable residues in an ion channel (discussed in refs

Figure 7 Schematic illustrations of the PNP (a) BD (b) and all-atom MD (c) modeling methods applied to the same systeman α-hemolysinchannel embedded in a lipid bilayer membrane and surrounded by an electrolyte solution In panel (a) the ions are described as continuous densitywhereas the water protein and membrane are treated as continuum dielectric media In the BD model (panel b) only ions are represented explicitlywhereas all other components are either implicitly modeled or approximated by continuum media All atoms are treated explicitly in the all-atom MDmethod (panel c)

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61 and 475) DelPhi476 and APBS477 are two popular computercodes for numerically solving the PB equation412 Ion Transport Although the PB model provides

insights into the equilibrium energetics of an ion channelmodeling of the ion flux requires a nonequilibrium approach Inmost ion channels the time scale of ion permeation rangesfrom tens of nanoseconds (porins) to microseconds and evenmilliseconds (in active transport) Thus observing a statisticallysignificant number of ion-permeation events requires longtrajectories that are still rather expensive to obtain using an all-atom approach The PoissonminusNernstminusPlanck model givesaccess to long time scales albeit at lower temporal and spatialresolutions As in the PB model the lipid protein and watermolecules are approximated as dielectric continua while ionsare described as continuous density distributions The currentdensity is obtained from the NernstminusPlanck (NP) theorywhich is widely used in studies of electrolyte transport In theNP theory ion fluxes arise from two sources the gradient ofion concentration and the gradient of the electrostatic potentialTraditional NernstminusPlanck equations do not describe ion-channel interactions However the classical NernstminusPlanckequations may be modified to include the ion-channelinteractions via an effective potential Thus the flux of ionspecies i Ji is written as

= minus nabla + nabla⎛⎝⎜

⎞⎠⎟t D c t

c tk T

J r r rr

r( ) ( ) ( )( )

( )i i ii

iB

eff

(9)

where Di and ci are the diffusion constant and the numberdensity of ion species i respectively and r( )i

eff is theeffective potential that usually combines the electrostaticpotential ϕ(r) and a core-repulsive potential UCore(r) withthe latter describing interactions between ions and the proteinchannel and not between the ions themselvesThe concentration and the flux of each ionic species obey the

continuity equation

partpart

+ nablamiddot =c t

tt

rJ r

( )( ) 0i

i (10)

Under steady-state conditions the concentration and the fluxdo not vary with time and nablamiddotJi(r) = 0 The electrostaticpotential is calculated from the Poisson equation

sumε ϕ π ρnablamiddot nabla = minus +r q cr r r( ( ) (( ))) 4 ( ( ) ( ))i

i if

(11)

where ε(r) is the dielectric constant qi is the ion charge andρf(r) is again the (fixed) charge density due to the proteinThe above coupled partial differential equations constitute

the PNP equations and may be solved by a variety of methodsin one or three dimensions Typically the NP and the Poissonequations are solved self-consistently to simultaneously obtainthe electrostatic potential ϕ(r) and the ionic concentration ci(r)under appropriate boundary conditionsModeling ion channels within the PNP framework is

computationally inexpensive compared to MD and BDsimulations because the problem of many-body interactions isavoided through a mean-field approximation An undesirableside-effect is that some important physics is neglected by thisapproximation Below we discuss some of the shortcomings ofthe PNP equations in the context of ion channels as well asextensions to the equations that address these shortcomings

Interested readers are directed to comprehensive reviews onthis subject12299307310478

Prior to the surge of popularity of the all-atom MD methodcontinuum electrodiffusion theories played a major role indevelopment of our understanding of ion fluxes in nano-channels81255 Early attempts to use the electrodiffusion theoryto describe ion flux through nanochannels279minus281286 led to thedevelopment of simplified models based on a self-consistentcombination of the Poisson equation and the NernstminusPlanckequations that were subsequently applied to various channelsystems282minus284 Most of the early studies dealt with either one-dimensional models or simplified geometries that lacked adetailed description of the protein structure and static chargedistribution These studies connected qualitative features of thecurrentminusvoltageminusconcentration relationship to structural andphysical features of the models For example the PNP theorywas used to demonstrate how charges at the channel openingscan produce current rectification285479 as well as how achannel with ion-specific binding sites can exhibit lowerconductance in a mixture of two ion types than in a puresolution of either type480 A lattice-relaxation algorithm able tosolve the PNP equations for a 3D model was developed byKurnikova and co-workers8 in later years This procedure allowsthe protein and the membrane to be mapped onto a 3D cubiclattice with defined dielectric boundaries fixed chargedistribution and a flow region for the ionsLike the PB equation the system of PNP equations

constitutes a mean-field theory that neglects the finite size ofthe ions the dielectric response of the system to an ion andionminusion correlations In fact the PNP equations reduce to thePB equation for systems with zero flux everywhere The validityof a continuum dielectric description and mean-fieldapproaches in the context of narrow pores has been thesubject of much debate For example Chung and co-workersobserved considerable differences between the conductancethrough idealized pores using the BD and PNP ap-proaches287294 The authors argued that the mean-fieldapproximation breaks down in narrow ion channels due to anoverestimation of the screening effect by counterions within thepore Larger channels like porins at physiological or lower ionconcentrations are described quite accurately by the PNPequations However the currents computed based on the PNPmodels can be considerably higher (by 50 for OmpF) than inequivalent BD simulations55

When a charge in a high dielectric medium is brought near alow dielectric medium a repulsive surface charge is induced atthe dielectric boundary In continuum descriptions such as PBand PNP the induced charge density includes (usually)canceling components from both positive and negative averagecharge densities The interaction energy between a charge andits induced charge density is often called the dielectric self-energy The dielectric self-energy due to the average chargedensity and the average induced charge density at the dielectricboundary is in general smaller than the interaction energybetween point charges and corresponding induced chargeaveraged over all configurations Put another way a pointcharge approaching a low dielectric medium is strongly repelledby its induced image charge and this repulsion is largely lost bythe implicit averaging in mean-field descriptionsThe PB and PNP equations have been modified to include

the interaction of an ion with the charge density itinduces11294296 Although the corrections account for theinteraction of an ion with its induced dielectric charge they do

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not account for the interaction of the induced charge with asecond nearby ion Similarly the mean-field approximationinherently ignores effects involving correlations in theinstantaneous ion distribution For example the narrowestportion of the potassium channels almost always contains twoions that move in a concerted fashion (see section 511) whichcannot be properly treated by continuum theories Never-theless it was concluded that the dielectric self-energy accountsfor most of the discrepancy between PNP and BD results in thecase of narrow channels294

Although early electrodiffusion studies of Levitt consideredhard-sphere repulsion between ions by iteratively correcting theion concentration279 many studies have since ignored suchfinite-size effects Recently the PNP equations have beenadapted to incorporate finite-size effects using classical densityfunctional theory to describe many-body hard sphereinteractions between ions and solvent290291300481 Unfortu-nately these approaches often yield cumbersome integro-differential equations Finite-size effects can be included in thePNP equations by introducing an entropic term thatdiscourages solvent crowding by ions309 The latter approachyields a tractable set of corrected PNP equations Both the PNPand BD methods usually ignore thermal fluctuations of theprotein and lipid bilayer However these can be effectivelycaptured by combining results from MD or Monte Carlosimulations with 3-D PNP calculations92

The PNP approach continues to play a major role inimproving our understanding of the physics of ion channelsThe computational efficiency of the PNP model is unparallelledfor studies of ion conductance in a low ion concentrationregime where the PNP method is expected to be the mostaccurate The method is highly efficient at predicting the effectof a channelrsquos geometry on the currentminusvoltage dependence atphysiological voltages and can be used to screen for mutationsthat affect conductance of a channel The calculation of currentscan be quite accurate in the case of larger channels such asporins PNP is perhaps the only method that can presentlysimulate the interplay of ion conductances in an ensemble ofion channels (such as in a realistic biological membrane)explicitly taking the structural features of the channels intoaccount Finally the PNP approach is rather flexible to includedescriptions of additional physical effects for examplehydrodynamic interactions354364369370 or the effect of asemiconductor membrane on the ionic current361382383

42 Brownian Dynamics

The BD method allows for simulations of explicit ionpermeations on the microsecond-to-millisecond time scale bytreating solvent molecules implicitly In a way the BD methodoffers a good compromise between all-atom MD andcontinuum electrodiffusion approaches Computational effi-ciency is achieved by reducing the number of degrees offreedom Typically a moderate number of atoms of interest(usually the ions) are simulated explicitly while the solvent isaccounted for via friction and stochastic random forces that actin addition to the electrostatic and steric forces arising fromother ions the protein and the lipid bilayer For the calculationof electrostatic forces the water the membrane and the proteinchannel are usually treated as continuous dielectric media Thechannel is treated as a rigid structure and thermal fluctuationsare typically ignored Figure 7b schematically illustrates a BDmodel of α-hemolysin

421 General Formulation of the BD Method In theBrownian dynamics method a stochastic equation is integratedforward in time to create trajectories of atoms Theldquouninterestingrdquo degrees of motion usually corresponding tofast-moving solvent molecules are projected out in order todevelop a dynamic equation for the evolution of the ldquorelevantrdquodegrees of freedom The motion of the particles is described bya generalized Langevin equation

int = minus prime minus prime prime +m t dt M t t t tr r f( ) ( ) ( ) ( )i i i

t

i i i0 (12)

The force on the ith particle i is obtained from an effectivepotential = minusnabla r( )i i iThe potential function is a many-body potential of mean

force (PMF) that corresponds to the reversible thermodynamicwork function to assemble the relevant particles in a particularconformation while averaging out the remaining degrees offreedom ie the effect of all other atoms is implicitly present in

r( )i The second term on the right-hand side is thedamping force representing the frictional effect of theenvironment and finally fi(t) is a Gaussian fluctuating forcearising from random collisions The frictional force depends onprevious velocities through the memory kernel Mi(tminustprime) Thefirst and second moments of the random force are given by⟨fi(t)⟩ = 0 and ⟨fi(t)middotfj(0)⟩ = 3kBTMi(t)δij where kB is theBoltzmann constant and T is the temperature Both the dragforce and the stochastic force incorporate the effect of thesolvent In the Markovian limit the memory kernel is a Diracdelta function that leads to the traditional Langevin equation

γ = minus +m t t tr r f( ) ( ) ( )i i i i i i (13)

The friction coefficient γi is related to underlying molecularprocesses via the fluctuationminusdissipation theoremIn the overdamped regime (which applies to the motion of

an ion in water) the inertial term can be ignored so that theLangevin equation is reduced to

ζ = +tD

k Ttr( ) ( )i

ii i

B (14)

where Di = kBTγi is the diffusion coefficient of the ith particleand ζi(t) is a Gaussian random noise with a second momentgiven as ⟨ζi(t)middotζi(0)⟩ = 6Diδ(t)

422 BD Simulations of Ion Channels A Browniandynamics simulation requires two basic ingredients adescription of the forces applied to each ion and the diffusioncoefficient for each ion The diffusion coefficient for the ionsshould be in general position-dependent and can be obtainedfrom all-atom MD simulations373482483 or estimated usinganalytical techniques88484 However in most cases a singleposition-independent diffusion constant is used for all ions ofthe same speciesEach ion experiences a force that depends on its position as

well as the positions of all the other ions in the system Thepotential corresponding to the forces on the ions is the multi-ion PMF which is the multidimensional free energy surfacethat is usually broken into an ionminusion PMF and a PMF due tothe pore the solution and other biomolecules373 The PMFscan be calculated from all-atom MD or even quantumchemistry simulations but such calculations are computation-ally expensive

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXK

A more typical approach was presented by Roux and co-workers which we summarize here556263299 The multi-ionPMF can be written as

sum sum sum

sum ϕ ϕ

= | minus | +

+ +

αα γ α

α γ α γα

α

αα α α

neu U

q

r r r r

r r

( ) ( ) ( )

[ ( ) ( )]

core

sf rf(15)

where uαγ(r) is the ionminusion interaction Ucore is a repulsivepotential preventing the ions from entering the ion-inaccessibleregions ϕsf is the electrostatic potential arising from thepermanent protein charge distribution and ϕrf is the reactionfield potential arising from the electrostatic polarization of thevarious dielectric boundaries The static field may be computedfrom an atomic model of the pore using the PBequations556263485 Any externally imposed transmembranebias may be included in the calculation of the electrostaticpotential Usually the ionminusion interaction includes van derWaals and Coulomb terms

εσ σ

ε= minus +α γ α γ

α γ α γ α γ⎜ ⎟ ⎜ ⎟⎡⎣⎢⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎤⎦⎥u r

r r

q q

r( ) 4

12

6

bulk

where εαγ and σαγ are the parameters for the 6minus12 Lennard-Jones potential qα and qγ are the charges of the ions and εbulk isthe dielectric constant of bulk water The local dielectricconstant of the water in the interior of the pore may beextracted from atomistic simulations but it is usually assumedto have the bulk value of 80 Solvation effects can beapproximately described by including a short-range solvationpotential55287486 but that is rarely done in practice Web-basedinterface for GCMCBD simulations of ion channels hasrecently become available268

Early BD studies were performed using one-dimensionalrepresentations of channels487 Later these were extended tomore realistic three-dimensional geometries although theseoften lacked atomic detail63486 However the X-ray structure ofan ion channel can be used to create a more realistic model ofthe channel by computing electrostatic and core repulsionpotential maps from the all-atom structure Brownian dynamicssimulations have been applied to several biological channelsincluding OmpF5562minus64 K+ channels110minus115117 α-hemoly-sin8895 VDAC268 and gramicidin1617 Roux and co-workershave developed a grand canonical Monte CarloBrowniandynamics method (GCMCBD)6263103 to allow for fluctua-tions in the total number of ions in the system and asymmetricion concentration conditions For detailed treatment of thesubject interested readers are directed to a review of thecomputational methods299473

Recently Comer and Aksimentiev373 used all-atom MD todetermine full three-dimensional PMF maps at atomicresolution for ionminusion and ionminusbiomolecule interactionsthereby fully accounting for short-range effects associationwith solvation of ions and biomolecules Using such full 3-DPMFs in BD simulations of ion flow through a model nanoporecontaining DNA basepair triplets yielded ionic currents in closeagreement with the results of all-atom MD but at a fraction ofthe computational cost The authors indicate that such anatomic-resolution BD method can be developed further toincorporate the conformational flexibility of the pore and DNAby altering the PMF maps on-the-fly

43 All-Atom Molecular Dynamics

The all-atom MD method can provide unparalleled insight intothe physical mechanisms underlying the biological function ofbiomacromolecules By explicitly describing all the atoms of thesystem of interest and the majority of interatomic interactionsthis method has the potential to compete with the experimentin completeness and accuracy of the description of microscopicphenomena In the case of an ion channel one can in principledirectly observe ion conductance and gating at the spatialresolution of a hydrogen atom and the temporal resolution ofsingle femtoseconds Critical to the above statement is theassumption that the all-atom MD method is equipped with acorrect description of interatomic interactions and enoughcomputational power is available Despite ever-increasingavailability of massive parallel computing platforms makingquantitative predictions using MD remains challenging in partdue to imperfections of the interatom interaction modelsBelow we briefly review the formulations of the all-atom MDmethod and describe recent advances in the field

431 General Formulation of the All-Atom MDMethod In the MD simulations of biomacromoleculesatoms are represented as point particles and the connectivity(or covalent bonds) among those atom are given a prioriCovalently bonded atoms interact with each other throughbonded potentials while the other atom pairs interact throughnonbonded potentials

= +U U Ur r r( ) ( ) ( )N N Nbonded nonbonded (16)

where rN denotes the coordinates of N atoms in a systemBonded interactions model quantum mechanical behavior ofcovalently connected atoms by means of harmonic bond angleand improper dihedral angle restraints and periodic dihedralangle potentials

sum sum

sum

sum

θ θ

χ δ

ϕ ϕ

= minus + minus

+ + minus

+ minus

θ

χ

ϕ

U K b b K

K n

K

( ) ( )

1 cos( )

( )

bbondedbonds

02

angles0

2

torsions

impropers0

2

(17)

where Kb and b0 are the bond force constant and theequilibrium distance respectively Kθ and θ0 are the angleforce constant and the equilibrium angle respectively Kχ nand δ are the dihedral force constant the multiplicity and thephase angle respectively and Kϕ and ϕ0 are the improper forceconstant and the equilibrium improper angle488 The non-bonded potential usually consists of the Lennard-Jones (LJ)potential for van der Waals interactions and the Coulombpotential for electrostatic interactions

sum εσ σ

ε= minus +

⎧⎨⎪⎩⎪

⎡

⎣⎢⎢⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤

⎦⎥⎥

⎫⎬⎪⎭⎪

Ur r

q q

r4 ij

ij

ij

ij

ij

i j

ijnonbonded

nonbond

12 6

(18)

where εij is the well depth σij is the finite distance at which theLJ potential is zero rij is the interatomic distance and qij areatomic charges The bonded parameters are empiricallycalibrated based on the quantum mechanical calculations ofsmall molecules whereas the nonbonded parameters are mainlyderived from quantum chemistry calculations (eg partial

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dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXL

charges) and empirical matching of thermodynamic data (eghydration free energy)A biomolecular force field is a set of bonded and nonbonded

parameters defined in eqs 17 and 18 Presently severalbiomolecular force fields exist The force fields can becategorized into types based on whether all the atoms areexplicitly treated or not All-atom force fields which includeCHARMM489 AMBER490491 and OPLS-AA492493 treat allatoms explicitly In the united-atom force fields (egGROMOS494495) some nonpolar hydrogen atoms areneglectedFor the simulations of channel proteins a lipid force field is

as important as a protein force field because the channels areembedded in lipid bilayers Among the all-atom force fields theCHARMM force field includes parameters for lipids the latestupdate at the time of writing this review is CHARMM36496

Together with the AMBER force field for the protein thegeneral all-atom AMBER force field (GAFF) can be used todescribe the lipid bilayer497498 Officially OPLS does notinclude lipid parameters Among the united-atom force fieldsGROMOS comes with lipid parameters499 Berger et alreported improved GROMOS-based lipid parameters basedon the condensed-phase properties of pentadecane500 Thislipid force field has been widely used in combination with otherprotein force fields such as AMBER OPLS and GROMOS501

For an in-depth review of various force fields we referinterested readers to a comprehensive review by Mackerell488

432 Ion Channels in Native Environment Unlikesoluble proteins that are surrounded only by water ion-channelproteins are embedded in a lipid bilayer and therefore are incontact with both water and lipids Because of the drasticallydifferent chemical and electrostatic properties of lipid andwater proper descriptions of proteinminuslipid and proteinminuswaterinteractions are key for the successful simulation of amembrane channel To model ion conduction through arelatively rigid channel (eg gA or KcsA channel) it is possibleto use an implicit solvent model of the channelrsquos environmentin which the volume occupied by lipid and water is treated ascontinuum media of dielectric constants 2 and 78 respec-tively299 However when interactions between a channel and alipid membrane are significant (eg in mechanosensitivechannels) explicit modeling of lipid molecules is essentialThe tails of lipids are long and equilibrate slowly making it

significantly more difficult to assemble a model of a channelembedded in an explicit lipid bilayer than a model of a fullysoluble protein Usually the system setup involves thefollowing steps Starting from a pre-equilibrated and solvatedlipid bilayer membrane one makes a pore in the bilayer bydeleting a minimal number of lipid molecules so that theprotein can fit Next an all-atom model of the protein is placedin the pore which is followed by energy minimization andequilibration of the system using the MD method having thechannelrsquos coordinates restrained to their crystallographic valuesFinally when the proteinminuslipid interface is well equilibratedone can perform a production run without applying restraintson the channel For detailed step-by-step instructions forbuilding atomic-scale models of ion channels in lipid bilayerenvironment interested readers are directed to a tutorial onMD simulations of membrane proteins502 Even though a fullyautomated procedure is not yet available several programs canassist a beginner in building a new system VMD503 containsthe Membrane Builder plugin Jo et al have a web-based

service CHARMM GUI Membrane Builder (httpwwwcharmm-guiorgmembrane)504505

An alternative method for creating an all-atom model of anion channel in its native environment is to first carry out self-assembly simulations using a coarse-grained (CG) MDmethod74165379 The main difference between the CG andall-atom MD methods is the level of detail used to describe thecomponents of the system Typically one CG bead representsabout 5minus10 atoms Being much more computationally efficient(and lower resolution) the CG model allows millisecond-time-scale simulations to be performed on commodity computersInterested readers are directed toward recent reviews on thissubject506minus508

In the CG simulations of self-assembly CG models of lipidssolvent and a membrane protein are placed with randompositions in desired proportions During the course of CGMDsimulations the lipid molecules spontaneously form a lipidbilayer around a protein After obtaining a stable model the CGmodel can be reverse-coarse-grained into a fully atomisticmodel (see for example a study by Maffeo and Aksimen-tiev330) A great advantage of this approach is that it requiresno a priori knowledge of the position of the membranechannels relative to the membrane An obvious disadvantage isthat one has to have a reasonable CG model to carry out theself-assembly simulations and a reliable procedure to recoverthe all-atom details from the final CG model Currently it isnot possible to use a CG approach to model ion conductancethrough large membrane channels due to inaccurate treatmentsof the membrane and water electrostatics in most CG modelsHowever work to improve CG methods is ongoing509510 andsuch simulations should become possible in the near future

433 Homology Modeling Usually an all-atom MDsimulation of a channel protein can be performed only when anatomic-resolution structure of the channel is available Thisrequirement severely limits application of the MD methodFortunately membrane channels of different organisms oftenhave similar amino-acid sequences The sequence similarity canbe used to build an all-atom model of the channel that does nothave an experimentally determined structure through aprocedure called homology modeling511 Briefly homologymodeling proceeds as follows First a sequence alignmentbetween a target sequence and a homologous sequenceforwhich a structure is knownis performed Second thesecondary structures (eg α-helices and β-sheets) of the targetsequence from the homologous sequence are built Finallyloops connecting the secondary structures are modeled and theoverall structure is refined There exist many tools for thehomology modeling (eg Modeler by Sali and Blundell511)The homology modeling method has been successfully used

for building initial structures of several ion channels forsubsequent all-atom MD simulations Capener et al512 built aninward rectifier potassium channel (Kir) based on a high-resolution structure of KcsA1 Sukharev et al used the crystalstructure of Mycobacterium tuberculosis MscL407 to modelclosed intermediate and open structures of Escherichia coliMscL231232 Law et al combined the crystal structure of theLymnea stagnalis acetylcholine binding protein and the electronmicroscopy (EM) structure of the transmembrane domain ofthe torpedo electric ray nicotinic channel to build an entirehuman nicotinic acetylcholine receptor213

434 Free-Energy Methods Perhaps the greatestdisadvantage of the MD method is that simulations are costlyand are currently limited to the microsecond time scalea

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pumps can work in reverse synthesizing ATP by transportingions along the concentration gradient In so-called antiportersand cotransporters transport of one ion species is coupled totransport of the other Some membrane channels can coupletransport of ions to transport of larger uncharged solutes andor protons In turn proton transport can be coupled to electrontransport for example in respiratory chain proteins Thus theinner and outer membranes of a living cell are full of variousion-transporting entities whose concerted action and synchron-ized response to external stimuli keep the cell alive Interestedreaders are directed to the book by Alberts et al398 for a

complete overview of the field to a paper by Khalili-Araghi etal333 for a recent review of modeling efforts in the field ofactive transport and to a study by Beard405 for an example ofmodeling a system of ion channels in an organelleAt present modeling and simulations of ion channels are

generally limited by the experimental knowledge about themAlthough the HH theory is a beautiful example to the contrarymore often than not a theoretical study of an ion channelrequires some knowledge of the channelrsquos structure ideally atatomic resolution Whereas the ldquono structureno studyrdquo rule isadopted by the majority of researchers working in the field of

Figure 4 Molecular graphics images of membrane channels listed in Table 1 The channels shown are (a) gramicidin A (gA) 1JNO406 (b)mechanosensitive channel of large conductance (MscL) 2OAR407 (c) mechanosensitive channel of small conductance (MscS) 2OAU408 (d)ammonium transporter (AmtB) 2NUU409 (e) K+ channel (KcsA) 3EFF410 (f) voltage-gated K+ channel (Kv) 2R9R411 (g) aquaporin 0 (AQP0)2B6O412 (h) nicotinic acetylcholine receptors (nAchR) 2BG9413414 (i) bacterial outer-membrane porin (OmpF) 2OMF415 (j) bacterial chloridechannel (ClC) 1OTS416 (k) bacterial toxin (α-hemolysin) 7AHL417

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computer modeling of ions channels there are notableexceptions418419 that deduce the structural architecture of thechannel from its ion-conductance propertiesPredicting the structure of a membrane channel from its

sequence is a formidable task Hence development ofcomputational models of ion channels was in a way led bycrystallographers and their ability to solve atomic structures ofion channels Membrane channels are notoriously difficult tocrystallize and are often too large for the NMR method towork Therefore atomic-resolution structures have beenobtained for only a very limited number of ion channels andhence many studies have focused on the same systems Belowwe briefly review the ion channels of known structures that arethe most common targets of computational studies

31 Gramicidin A

Gramicidins are small bacteria-produced antibiotics that whendimerized in a head-to-head fashion (Figure 4a) are able totransport a monovalent cation across a membrane once aboutevery 100 ns39 Gramicidin works by eliminating the iongradient across the membrane of Gram-positive bacteriaGramicidin was the first clinical antibiotic in use and is stillused today in conjunction with other antibioticsAll-atom molecular dynamics simulations (MD) have been

instrumental in the interpretation and refinement of NMRresults28 Gramicidin A was the subject of the first MDsimulation of an ion channel almost 30 years ago420 Advancesin the availability of computational resources have permitted farmore realistic models including lipid bilayers and full solvent tobe simulated for significant durations Gramicidin A now servesas a model system and test bed for new techniques21

32 Potassium Channels

Potassium ion channels are key constituents of electricalsignaling networks in the nervous system When openpotassium channels conduct K+ ions at rates remarkably closeto the diffusion limit (about 108 ions per second)421 and displayincredible sensitivity to the size and valency of ions Thus K+

channels can quickly release ions from within the cell inresponse to appropriate stimulus affecting the action potentialBecause some K+ channels are voltage-sensitive this can resultin a cascade of channel activations that propagates through anaxon K+ channels have been the target of prospectivetreatments for an array of disorders including multiplesclerosis422423

Taken from Gram-positive bacterium Streptomyces lividansthe K+ channel KcsA is similar in sequence to vertebratevoltage-dependent K+ channels but is easily expressed inEscherichia coli making it the prototypical K+ channel forlaboratory studies Like all K+ channels the sequence of KcsAcontains a completely conserved motif that is crucial for its K+

specificity Depicted in Figure 5 the first atomic-resolutionstructure of a K+ channel revealed a tetrameric transmembranepore with an intracellular passage leading to a large (10 Aringdiameter) cavity with a hydrophobic lining followed by anatomically narrow sim4 Aring long selectivity filter that leads to theextracellular side of the membrane1 A more complete structureof this channel was recently resolved410 featuring longcytoplasmic helices that appear to stabilize the closedconformation of KcsA at high pH In contrast to the poreregion the arrangement of cytoplasmic helices in KcsA is not auniversal structural element of K+ channelsIn the selectivity filter four rings each featuring four

negatively charged carbonyl-oxygen atoms hold two K+ ions

that are separated by a single water molecule The ions presentin the selectivity filter are mostly desolvated which carries anenormous free energy penalty that is offset by interactions withthe negatively charged surface of the filter Thus the largeforces experienced by translocating ions balance delicately toallow a smooth free energy landscape that permits rapidpermeation through the pore The balance of these forces mustbe carefully tuned to select K+ over other monovalent ions suchas Na+ Although the latter carries the same charge as K+ and isonly 04 Aring smaller experiments suggest that K+ channels bindK+ with as much as 1 000 times greater affinity than Na+1

The selectivity filter can become occupied by divalent ionswhich generally block the current through the channel The Kiror inward rectifying family of potassium channels uses thismechanism to impede K+ ions moving out of the cell Moregenerally potassium channels are regulated through a variety ofother means that include modification through ligand bindingand voltage- and pH-dependent gating Many biologicallyproduced toxins target K+ channels to interfere with a victimrsquosnervous systemBecause of the biological importance of K+ channels and the

fact that the pore domain of bacterial KcsA is homologous tothat of eukaryotic K+ channels the seminal structure of KcsA1

motivated many computational and theoretical studies148 Theformal analogy between electric current in man-made circuitsand ion conductance through the channels424 led researchers todevelop and apply continuum electrostatics theories of ionchannels103minus109 The availability of high-resolution crystalstructures stimulated development of new atomistic simulationtechniques for studying selectivity conductance and gatingbehaviors of K+ channels using either implicit110minus117 orexplicit2988111minus113116minus197 solvent models Ligand dockingcoupled with free energy calculations was recently used tostudy methods to enhance the specificity of naturally occurringneurotoxins for Kv13 which can suppress chronically activated

Figure 5 Pore region of the KcsA K+ ion channel embedded in a lipidbilayer membrane The image shows the first crystallographicallydetermined structure of a K+ channel1 which did not include the longcytoplasmic helices depicted in Figure 4 e One of the four subunits ofthe KcsA tetramer is not shown to provide a clear view of theselectivity filter The lipid bilayer is depicted as gray van der Waalsspheres

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memory T cells implicated in autoimmune disorders includingmultiple sclerosis422425 To overcome the time and length scalelimitations of the all-atom approaches several multiscalemethods have been developed107198minus202 using K+ channelsas target application systems

33 Mechanosensitive Channels

All living creatures have mechanosensors426427 For examplewe can hear sound because our auditory sensory cells candetect ciliary vibrations caused by acoustic waves We can feelthe pressure on our skin and blood vessels and feel full whenwe eat food because of tension sensors in cell membranesPlants which are immobile and less responsive also havemechanosensors a representative example is the gravity sensorwhich allow roots and shoots to grow in opposite directionsInterested readers are referred to a recent review by Kung andco-workers426427 for more detailed informationA breakthrough in the biophysical study of mechanosensa-

tion was the cloning428429 and structural characterizationof simple prokaryotic mechanosensit ive channels(MSCs)407408430431 When the concentration of osmolytes ina bacterial cell is significantly higher than the concentration ofosmolytes in the environment the gradient of osmolyteconcentration across the cell membrane can cause huge turgorpressure inside the bacterial cell If left to develop fully suchosmotic stress can easily rupture the cell wall killing thebacterium To prevent this from happening bacteria haveevolved ldquosafety valvesrdquothe MSCsthat open when thesurface tension in the membrane exceeds a threshold valuemaking the membrane permeable to most small solutes andwater molecules432 Most importantly the channels return to aclosed state when tension drops Thus MSCs are essential forthe survival of bacteriaIn 1998 Chang et al reported the first high-resolution

structure of MSC of large conductance (MscL) fromMycobacterium tuberculosis in a closed conformation407 MscLis a homopentamer with each subunit having two trans-membrane (TM) helices TM1 and TM2 see Figure 4b In theclosed conformation five TM1 helices form a pore and TM2helices surround the inner TM1 helices Recently Liu et alreported a crystal structure of tetrameric MscL from Staph-ylococcus aureus in an expanded intermediate state431 So fartwo crystal structures of the Escherichia coli MSC of smallconductance (MscS) have been reported one in a non-conductive conformation408 and the other in an openconformation430 Those high-resolution structures show thatthe MscS is a homoheptamer with three TM helices persubunit see Figure 4c Seven TM3 helices form a channel withdiameters of 5 and 13 Aring in closed and open conformationsrespectively see Figure 6430

Despite the fact that mechanosensation is universal andessential for all living creatures427 its mechanism is significantlyless understood if compared to the mechanisms of other sensessuch as vision smell and taste427 Since the first MSC wasdiscovered in 1987432 and the first crystal structures of MscLand MscS were revealed in 1998 and 2002407408 both MscLand MscS have served as model systems for the computationalstudies of mechanical gating Because of its very nature thisproblem has attracted the attention of investigators fromvarious disciplines including traditional MD simulationshomology modeling continuum mechanics and coarse-grainedMD simulations see sections 522 and 541 for more detailsThe computational methods developed for studies of MscL and

MscS will surely be of great value in future studies of morecomplex mechanisms of mechanosensation34 Porins

Outer-membrane porins (OMPs) of Gram-negative bacteria aretransmembrane proteins that allow the bacterial cells to interactwith their environment through passive diffusion of water ionsand small hydrophilic molecules (lt600 Da) across their outermembranes Wide channels such as OMPs and toxins facilitatethe permeation of metabolites rather than merely small ionsHowever often they exhibit interesting behavior such asselectivity toward certain ions and serve as model systems totest computational models of ion transport they are thereforeof interest in this reviewOMPs are β-barrel structures usually forming homotrimeric

water-filled pores The porin channel is partially blocked by aloop (L3) that is folded inside the β-barrel forming aconstriction region that determines the size of the solutesthat can traverse the channel Several crystal structures ofporins have been determined at high resolution415433minus437

Some porins exhibit moderate ion selectivity eg Escherichiacoli OmpF (shown in Figure 4i) and OmpC are two cation-selective porins whereas the Pseudomonas aeruginosa OprP438 isa phosphate-selective porin The cation selectivity is known todepend on the salt concentration and the valence of the ionsGram-negative bacteria that lack porins have other substrate-specific channels that allow the passage of small molecules Forinstance the OccK1 an archetype of the outer-membranecarboxylate channel family from Pseudomonas aeruginosa(previously named OpdK) is a monomeric β-barrel with akidney-shaped central pore as revealed by the X-raystructure439 The members of the OccK subfamily of channelsare believed to facilitate the uptake of basic amino acids440 Adetailed examination of the conductance characteristics ofseveral members of the OccK subfamily of channels by Liu andco-workers441 revealed diverse single-channel electrical signa-tures nonohmic voltage dependent conductance and transientgating behavior Single-molecule electrophysiology analysisalong with rational protein design have revealed discrete gatingdynamics involving both enthalpy- and entropy-driven currenttransitions442443

Studies of porins are relevant to the development ofantibiotics To affect bacteria antibiotics must first pass

Figure 6 Comparison of the pores formed by seven TM3 helices ofMscS in nonconducting408 (a) and open430 (b) conformations viewedfrom the periplasm (top) and from within the membrane (bottom)

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through their outer wall which is a process facilitated by porinsPorin alteration has been implicated in antibiotic resistance444

In addition engineered porins such as the OmpG havepotential for use as stochastic sensors77

Functionally related to porins α-hemolysina toxinproduced by Staphylococcus aureusis secreted as a monomerbut assembles on target cell membranes to form ahomoheptameric channel which leads to an uncontrolledpermeation of ions and small molecules and causes cell lysisThe X-ray structure of α-hemolysin445 revealed a mushroom-like shape with a β-barrel stem protruding from its cap domainsee Figure 4k Its ability to self-assemble in biological orsynthetic membranes and its structural stability over a widerange of ion concentrations temperatures and pHs make α-hemolysin an excellent platform for stochastic sensingapplications446 including detection of DNA sequence bymeasuring the ionic current447 An interesting feature is therectification behavior of the channel which has been exploredby both implicit solvent88 as well as all-atom MDsimulations9093

Another large water-filled biological nanopore is MspAthemajor outer-membrane porin of Mycobacterium smegmatis thatallows the uptake of hydrophilic nutrients from the environ-ment The crystal structure of MspA448 revealed a homo-octameric goblet-like structure with a central channel Theporin has a constriction that is lined by two belts of aspartateresidues (Asp90 and Asp91) that diminish the permeability ofnonpolar solutes Genetically modified variants of the MspAchannel may enable practical nanopore DNA sequencing449450

as they provide superior ionic current signals for nucleic aciddetection if compared with α-hemolysin451

35 Other Channels

The voltage-dependent anion channel (VDAC) residing in themitochondrial outer membrane serves as a conduit formetabolites and electrolytes VDACs mediate the passage ofions such as K+ Clminus and Ca2+ and small hydrophilic moleculessuch as ATP between the cytosol and the mitochondria andregulate the release of apoptotic proteins The pore has avoltage-dependent conductance with an anion-selective high-conductance state at low transmembrane potential and aslightly cation-selective low-conductance state at high poten-tial452 Several NMR and X-ray structures of human as well asmouse VDACs453minus455 have become available Initially thesignificance of these structures was questioned on account of anapparent conflict with biochemical and functional data456

However additional NMR457458 and theoretical stud-ies259262268 have shed light on the structureminusfunction relationreaffirming the biological relevance of the structuresThe ClC chloride channels found in both prokaryotic and

eukaryotic cells control the selective flow of Clminus ions and arebelieved to play an important role in regulation of bloodpressure pH and membrane excitability These channelsconduct not just Clminus but also other anions such as HCO3

minusSCNminus and NOminus Unlike cation channels they do notdiscriminate strongly between different species of anionsDefects in these channels are implicated in several diseasessuch as myotonia congenita Bartterrsquos syndrome andepilepsy459 In the past decade structures of ClC orthologuesfrom two bacterial species Salmonella serovar typhimurium andEscherichia coli have become available460 The X-ray structuresreveal the ClC channels to be homodimers with two identicalbut independent pores see Figure 4j Some prokaryotic

members of the ClC family of channels are now believed tobe ion transporters although the line between ion channels andtransporters is getting blurred461 There have been a fewsimulation studies of the permeation pathways260261 of the ClCchannelsThe nicotinic acetylcholine receptor (nAChR) belongs to a

superfamily of Cys-loop ligand-gated ion channels It couples acationic transmembrane ion channel with binding sites for theneurotransmitter acetylcholine (ACh) so that the gating of thechannel is linked to the binding of ACh The nAChR owes itsname to the ability of nicotine to mimic the effects of ACh inopening up the pore The nAChR is composed of a ring of fiveprotein subunits with three domains a large N-terminalextracellular ligand binding domain (LBD) a transmembranedomain (TM) and a small intracellular domain see Figure 4hThere are two ACh binding sites in the ligand-binding domainthe pore opens when both are occupied414 Although thecomplete high-resolution structure of the nAChR is absent atpresent X-ray and electron microscopy structures of some of itscomponents are available413414 The nAChR plays a critical rolein neuronal communication converting neurotransmitter bind-ing into membrane electric depolarization The channel isfound in high concentrations at the nerveminusmuscle synapsenAChR is implicated in a variety of diseases of the centralnervous system including Alzheimerrsquos disease Parkinsonrsquosdisease schizophrenia and epilepsy462 It is also believed toplay a critical role in mediating nicotine reward andaddiction463 Although detailed study of the gating mechanismis precluded by the lack of a complete structure of the nAChRas well as the time scales involved there have been severalstudies on the TM domain215212 and the LBD218

AmtB is a representative bacterial ammonium transporterwhich belongs to AmtMEP family464 Some bacteria andplants use ammonium as a nitrogen source and have variousforms of transporters for the uptake of ammonium464465 At thesame time ammonium is also a toxic metabolic waste whichshould be removed quickly by transporters usually formammals466 There exist several high-resolution crystalstructures of bacterial AmtB409467minus470 The Escherichia colicrystal structure (Figure 4d) has become the paradigm for thestudy of the transport mechanism of ammonium409 UsuallyAmtB proteins are crystallized as a homotrimer Each monomerconsists of 11 transmembrane helices that form a channel forammonium The channel is highly hydrophobic raising thepossibility that ammonium passes the channel in a deproto-nated form (ammonia)

4 MOST COMMON SIMULATION METHODSAmong a large number of computational approaches proposedand employed for studies of ion channels most fall within thefollowing three categories all-atom molecular dynamics (MD)which is a fully microscopic description with all atoms treatedexplicitly Brownian dynamics (BD) in which only the ions aretreated explicitly while the solvent and the protein and lipidsare represented implicitly and approaches based on PoissonminusNernstminusPlanck (PNP) theory in which the ionic concentrationis treated as a continuum Each of the three approaches haslimitations and advantages The MD method is considered themost computationally expensive but also the most accurateThe PNP and BD approaches are in general less computa-tionally expensive but also provide less detail At the same timethe MD method has the smallest temporal and spatial rangefollowed by BD methods followed by PNP approaches Figure

Chemical Reviews Review

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7 schematically illustrates typical setups for the three modelingapproaches applied to the same systemThe above classification however is rather approximate and

can be misleading Thus the level of computational complexityoften depends on the desired level of detail whereas theaccuracy depends on the assumptions made in deriving theparameters of the model Even the most sophisticated MDsimulations rely on the MD force field which is a classicalmodel that may or may not be adequate for describing a certainphenomenon In this respect full quantum or combinedquantum mechanicsclassical mechanics approaches (QMMM) can in principle provide the highest degree of accuracyHowever the time scale accessible to these methods is severelylimiting Interested readers are directed to reviews of QMMMapproaches for simulations of biomolecules471472 and to arecent review of computational approaches to ion transport innanopores473 On the other hand it is possible to incorporateatomic-level details in BD and even PNP approaches see forexample recent work by Comer Carr and co-workers371373

Other considerations often neglected when evaluating theldquocomputational costrdquo of a certain approach are the qualificationsand ambitions of the researcher performing the modeling tasksand the availability of well-documented and ready-to-use codesFor example it is always possible to increase the computationalcomplexity of the problem by including an exorbitant amountof water in an all-atom simulation or using very fine mesh sizein continuum calculations One could also easily spend severalmonths writing debugging or porting a computationallyefficient code while the same time could have been used torun a more computationally intensive but ready-to-use andtested code Thus there are no simple rules in choosing anoptimal simulation method and researchers new to the field areurged to seek expert advice for their particular problem

41 Continuum Models

Ion channels are complex systems with many degrees offreedom and hence are challenging to model in atomisticdetail Continuum theories based on PoissonminusBoltzmann (PB)and PoissonminusNernstminusPlanck (PNP) equations are powerfultools that make simulation of such systems tractable The mainidea is to employ a continuum description for all componentsof the system ie the solvent the ions and the ion channelThe water the membrane and the channel are represented asfixed structureless dielectrics while the ions are described byspecifying the local density throughout the system Figure 7aschematically illustrates a PNP model of α-hemolysin

411 Electrostatics of Ion Channels The PB equation isthe most popular theoretical model for describing theelectrostatics around a charged biomolecule in ionic solutionIn a system of interacting mobile charged particles theelectrostatic potential arises due to the combined effect of thecharged biomolecules ions and dielectric properties of theenvironment The PB model assumes that the distribution ofcharges in the system is related to the electrostatic potentialaccording to Boltzmann statistics For the purpose of describingelectrostatics of a single biomolecule the PB equation whichwas first introduced independently by Gouy (1910) andChapman (1913) and later generalized by Debye and Huckel(1923) is most frequently written as

sumε ψ πρ π

ψλ

nablamiddot nabla = minus minus

minus

infin

⎛⎝⎜

⎞⎠⎟

c z q

z qk T

r r r

rr

( ( ) ( )) 4 ( ) 4

exp( )

( )

ii i

i

f

B (8)

where ε(r) is the position-dependent dielectric constant ψ(r) isthe electrostatic potential ρf(r) is the fixed charge density ofthe biomolecule ci

infin represents the concentration of ion speciesi at infinite distance from the biomolecule zi is the valency ofion species i q is the proton charge kB is the Boltzmannconstant T is the temperature and λ(r) describes theaccessibility of position r to ions (for example it is oftenassumed to be zero inside the biomolecule) A solution to thePB equation gives the electrostatic potential and equilibriumdensity of ions throughout the space The PB equation invokesa mean-field approximation that neglects nonelectrostatic ionminusion interactions (eg van der Waals or water-mediated) thedielectric response of the system to each ion and effects due tocorrelations in the instantaneous distribution of ions Becauseof these the PB equation fails to describe the electrostatics ofhighly charged objects such as DNA in high-concentration ionsolutions with quantitative accuracy474 In the context of ionchannels which rarely carry such a high charge density the PBtheory has been widely used to calculate the free energy cost oftransferring a charge from bulk solution to the interior of thechannel105287 (see Table 1) to characterize ion-channelinteractions88294 and to compute the distribution of thetransmembrane electrostatic potential103104294299 Such con-tinuum electrostatic calculations have also been used toestimate the relative stability of protonated and unprotonatedstates of ionizable residues in an ion channel (discussed in refs

Figure 7 Schematic illustrations of the PNP (a) BD (b) and all-atom MD (c) modeling methods applied to the same systeman α-hemolysinchannel embedded in a lipid bilayer membrane and surrounded by an electrolyte solution In panel (a) the ions are described as continuous densitywhereas the water protein and membrane are treated as continuum dielectric media In the BD model (panel b) only ions are represented explicitlywhereas all other components are either implicitly modeled or approximated by continuum media All atoms are treated explicitly in the all-atom MDmethod (panel c)

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61 and 475) DelPhi476 and APBS477 are two popular computercodes for numerically solving the PB equation412 Ion Transport Although the PB model provides

insights into the equilibrium energetics of an ion channelmodeling of the ion flux requires a nonequilibrium approach Inmost ion channels the time scale of ion permeation rangesfrom tens of nanoseconds (porins) to microseconds and evenmilliseconds (in active transport) Thus observing a statisticallysignificant number of ion-permeation events requires longtrajectories that are still rather expensive to obtain using an all-atom approach The PoissonminusNernstminusPlanck model givesaccess to long time scales albeit at lower temporal and spatialresolutions As in the PB model the lipid protein and watermolecules are approximated as dielectric continua while ionsare described as continuous density distributions The currentdensity is obtained from the NernstminusPlanck (NP) theorywhich is widely used in studies of electrolyte transport In theNP theory ion fluxes arise from two sources the gradient ofion concentration and the gradient of the electrostatic potentialTraditional NernstminusPlanck equations do not describe ion-channel interactions However the classical NernstminusPlanckequations may be modified to include the ion-channelinteractions via an effective potential Thus the flux of ionspecies i Ji is written as

= minus nabla + nabla⎛⎝⎜

⎞⎠⎟t D c t

c tk T

J r r rr

r( ) ( ) ( )( )

( )i i ii

iB

eff

(9)

where Di and ci are the diffusion constant and the numberdensity of ion species i respectively and r( )i

eff is theeffective potential that usually combines the electrostaticpotential ϕ(r) and a core-repulsive potential UCore(r) withthe latter describing interactions between ions and the proteinchannel and not between the ions themselvesThe concentration and the flux of each ionic species obey the

continuity equation

partpart

+ nablamiddot =c t

tt

rJ r

( )( ) 0i

i (10)

Under steady-state conditions the concentration and the fluxdo not vary with time and nablamiddotJi(r) = 0 The electrostaticpotential is calculated from the Poisson equation

sumε ϕ π ρnablamiddot nabla = minus +r q cr r r( ( ) (( ))) 4 ( ( ) ( ))i

i if

(11)

where ε(r) is the dielectric constant qi is the ion charge andρf(r) is again the (fixed) charge density due to the proteinThe above coupled partial differential equations constitute

the PNP equations and may be solved by a variety of methodsin one or three dimensions Typically the NP and the Poissonequations are solved self-consistently to simultaneously obtainthe electrostatic potential ϕ(r) and the ionic concentration ci(r)under appropriate boundary conditionsModeling ion channels within the PNP framework is

computationally inexpensive compared to MD and BDsimulations because the problem of many-body interactions isavoided through a mean-field approximation An undesirableside-effect is that some important physics is neglected by thisapproximation Below we discuss some of the shortcomings ofthe PNP equations in the context of ion channels as well asextensions to the equations that address these shortcomings

Interested readers are directed to comprehensive reviews onthis subject12299307310478

Prior to the surge of popularity of the all-atom MD methodcontinuum electrodiffusion theories played a major role indevelopment of our understanding of ion fluxes in nano-channels81255 Early attempts to use the electrodiffusion theoryto describe ion flux through nanochannels279minus281286 led to thedevelopment of simplified models based on a self-consistentcombination of the Poisson equation and the NernstminusPlanckequations that were subsequently applied to various channelsystems282minus284 Most of the early studies dealt with either one-dimensional models or simplified geometries that lacked adetailed description of the protein structure and static chargedistribution These studies connected qualitative features of thecurrentminusvoltageminusconcentration relationship to structural andphysical features of the models For example the PNP theorywas used to demonstrate how charges at the channel openingscan produce current rectification285479 as well as how achannel with ion-specific binding sites can exhibit lowerconductance in a mixture of two ion types than in a puresolution of either type480 A lattice-relaxation algorithm able tosolve the PNP equations for a 3D model was developed byKurnikova and co-workers8 in later years This procedure allowsthe protein and the membrane to be mapped onto a 3D cubiclattice with defined dielectric boundaries fixed chargedistribution and a flow region for the ionsLike the PB equation the system of PNP equations

constitutes a mean-field theory that neglects the finite size ofthe ions the dielectric response of the system to an ion andionminusion correlations In fact the PNP equations reduce to thePB equation for systems with zero flux everywhere The validityof a continuum dielectric description and mean-fieldapproaches in the context of narrow pores has been thesubject of much debate For example Chung and co-workersobserved considerable differences between the conductancethrough idealized pores using the BD and PNP ap-proaches287294 The authors argued that the mean-fieldapproximation breaks down in narrow ion channels due to anoverestimation of the screening effect by counterions within thepore Larger channels like porins at physiological or lower ionconcentrations are described quite accurately by the PNPequations However the currents computed based on the PNPmodels can be considerably higher (by 50 for OmpF) than inequivalent BD simulations55

When a charge in a high dielectric medium is brought near alow dielectric medium a repulsive surface charge is induced atthe dielectric boundary In continuum descriptions such as PBand PNP the induced charge density includes (usually)canceling components from both positive and negative averagecharge densities The interaction energy between a charge andits induced charge density is often called the dielectric self-energy The dielectric self-energy due to the average chargedensity and the average induced charge density at the dielectricboundary is in general smaller than the interaction energybetween point charges and corresponding induced chargeaveraged over all configurations Put another way a pointcharge approaching a low dielectric medium is strongly repelledby its induced image charge and this repulsion is largely lost bythe implicit averaging in mean-field descriptionsThe PB and PNP equations have been modified to include

the interaction of an ion with the charge density itinduces11294296 Although the corrections account for theinteraction of an ion with its induced dielectric charge they do

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not account for the interaction of the induced charge with asecond nearby ion Similarly the mean-field approximationinherently ignores effects involving correlations in theinstantaneous ion distribution For example the narrowestportion of the potassium channels almost always contains twoions that move in a concerted fashion (see section 511) whichcannot be properly treated by continuum theories Never-theless it was concluded that the dielectric self-energy accountsfor most of the discrepancy between PNP and BD results in thecase of narrow channels294

Although early electrodiffusion studies of Levitt consideredhard-sphere repulsion between ions by iteratively correcting theion concentration279 many studies have since ignored suchfinite-size effects Recently the PNP equations have beenadapted to incorporate finite-size effects using classical densityfunctional theory to describe many-body hard sphereinteractions between ions and solvent290291300481 Unfortu-nately these approaches often yield cumbersome integro-differential equations Finite-size effects can be included in thePNP equations by introducing an entropic term thatdiscourages solvent crowding by ions309 The latter approachyields a tractable set of corrected PNP equations Both the PNPand BD methods usually ignore thermal fluctuations of theprotein and lipid bilayer However these can be effectivelycaptured by combining results from MD or Monte Carlosimulations with 3-D PNP calculations92

The PNP approach continues to play a major role inimproving our understanding of the physics of ion channelsThe computational efficiency of the PNP model is unparallelledfor studies of ion conductance in a low ion concentrationregime where the PNP method is expected to be the mostaccurate The method is highly efficient at predicting the effectof a channelrsquos geometry on the currentminusvoltage dependence atphysiological voltages and can be used to screen for mutationsthat affect conductance of a channel The calculation of currentscan be quite accurate in the case of larger channels such asporins PNP is perhaps the only method that can presentlysimulate the interplay of ion conductances in an ensemble ofion channels (such as in a realistic biological membrane)explicitly taking the structural features of the channels intoaccount Finally the PNP approach is rather flexible to includedescriptions of additional physical effects for examplehydrodynamic interactions354364369370 or the effect of asemiconductor membrane on the ionic current361382383

42 Brownian Dynamics

The BD method allows for simulations of explicit ionpermeations on the microsecond-to-millisecond time scale bytreating solvent molecules implicitly In a way the BD methodoffers a good compromise between all-atom MD andcontinuum electrodiffusion approaches Computational effi-ciency is achieved by reducing the number of degrees offreedom Typically a moderate number of atoms of interest(usually the ions) are simulated explicitly while the solvent isaccounted for via friction and stochastic random forces that actin addition to the electrostatic and steric forces arising fromother ions the protein and the lipid bilayer For the calculationof electrostatic forces the water the membrane and the proteinchannel are usually treated as continuous dielectric media Thechannel is treated as a rigid structure and thermal fluctuationsare typically ignored Figure 7b schematically illustrates a BDmodel of α-hemolysin

421 General Formulation of the BD Method In theBrownian dynamics method a stochastic equation is integratedforward in time to create trajectories of atoms Theldquouninterestingrdquo degrees of motion usually corresponding tofast-moving solvent molecules are projected out in order todevelop a dynamic equation for the evolution of the ldquorelevantrdquodegrees of freedom The motion of the particles is described bya generalized Langevin equation

int = minus prime minus prime prime +m t dt M t t t tr r f( ) ( ) ( ) ( )i i i

t

i i i0 (12)

The force on the ith particle i is obtained from an effectivepotential = minusnabla r( )i i iThe potential function is a many-body potential of mean

force (PMF) that corresponds to the reversible thermodynamicwork function to assemble the relevant particles in a particularconformation while averaging out the remaining degrees offreedom ie the effect of all other atoms is implicitly present in

r( )i The second term on the right-hand side is thedamping force representing the frictional effect of theenvironment and finally fi(t) is a Gaussian fluctuating forcearising from random collisions The frictional force depends onprevious velocities through the memory kernel Mi(tminustprime) Thefirst and second moments of the random force are given by⟨fi(t)⟩ = 0 and ⟨fi(t)middotfj(0)⟩ = 3kBTMi(t)δij where kB is theBoltzmann constant and T is the temperature Both the dragforce and the stochastic force incorporate the effect of thesolvent In the Markovian limit the memory kernel is a Diracdelta function that leads to the traditional Langevin equation

γ = minus +m t t tr r f( ) ( ) ( )i i i i i i (13)

The friction coefficient γi is related to underlying molecularprocesses via the fluctuationminusdissipation theoremIn the overdamped regime (which applies to the motion of

an ion in water) the inertial term can be ignored so that theLangevin equation is reduced to

ζ = +tD

k Ttr( ) ( )i

ii i

B (14)

where Di = kBTγi is the diffusion coefficient of the ith particleand ζi(t) is a Gaussian random noise with a second momentgiven as ⟨ζi(t)middotζi(0)⟩ = 6Diδ(t)

422 BD Simulations of Ion Channels A Browniandynamics simulation requires two basic ingredients adescription of the forces applied to each ion and the diffusioncoefficient for each ion The diffusion coefficient for the ionsshould be in general position-dependent and can be obtainedfrom all-atom MD simulations373482483 or estimated usinganalytical techniques88484 However in most cases a singleposition-independent diffusion constant is used for all ions ofthe same speciesEach ion experiences a force that depends on its position as

well as the positions of all the other ions in the system Thepotential corresponding to the forces on the ions is the multi-ion PMF which is the multidimensional free energy surfacethat is usually broken into an ionminusion PMF and a PMF due tothe pore the solution and other biomolecules373 The PMFscan be calculated from all-atom MD or even quantumchemistry simulations but such calculations are computation-ally expensive

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A more typical approach was presented by Roux and co-workers which we summarize here556263299 The multi-ionPMF can be written as

sum sum sum

sum ϕ ϕ

= | minus | +

+ +

αα γ α

α γ α γα

α

αα α α

neu U

q

r r r r

r r

( ) ( ) ( )

[ ( ) ( )]

core

sf rf(15)

where uαγ(r) is the ionminusion interaction Ucore is a repulsivepotential preventing the ions from entering the ion-inaccessibleregions ϕsf is the electrostatic potential arising from thepermanent protein charge distribution and ϕrf is the reactionfield potential arising from the electrostatic polarization of thevarious dielectric boundaries The static field may be computedfrom an atomic model of the pore using the PBequations556263485 Any externally imposed transmembranebias may be included in the calculation of the electrostaticpotential Usually the ionminusion interaction includes van derWaals and Coulomb terms

εσ σ

ε= minus +α γ α γ

α γ α γ α γ⎜ ⎟ ⎜ ⎟⎡⎣⎢⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎤⎦⎥u r

r r

q q

r( ) 4

12

6

bulk

where εαγ and σαγ are the parameters for the 6minus12 Lennard-Jones potential qα and qγ are the charges of the ions and εbulk isthe dielectric constant of bulk water The local dielectricconstant of the water in the interior of the pore may beextracted from atomistic simulations but it is usually assumedto have the bulk value of 80 Solvation effects can beapproximately described by including a short-range solvationpotential55287486 but that is rarely done in practice Web-basedinterface for GCMCBD simulations of ion channels hasrecently become available268

Early BD studies were performed using one-dimensionalrepresentations of channels487 Later these were extended tomore realistic three-dimensional geometries although theseoften lacked atomic detail63486 However the X-ray structure ofan ion channel can be used to create a more realistic model ofthe channel by computing electrostatic and core repulsionpotential maps from the all-atom structure Brownian dynamicssimulations have been applied to several biological channelsincluding OmpF5562minus64 K+ channels110minus115117 α-hemoly-sin8895 VDAC268 and gramicidin1617 Roux and co-workershave developed a grand canonical Monte CarloBrowniandynamics method (GCMCBD)6263103 to allow for fluctua-tions in the total number of ions in the system and asymmetricion concentration conditions For detailed treatment of thesubject interested readers are directed to a review of thecomputational methods299473

Recently Comer and Aksimentiev373 used all-atom MD todetermine full three-dimensional PMF maps at atomicresolution for ionminusion and ionminusbiomolecule interactionsthereby fully accounting for short-range effects associationwith solvation of ions and biomolecules Using such full 3-DPMFs in BD simulations of ion flow through a model nanoporecontaining DNA basepair triplets yielded ionic currents in closeagreement with the results of all-atom MD but at a fraction ofthe computational cost The authors indicate that such anatomic-resolution BD method can be developed further toincorporate the conformational flexibility of the pore and DNAby altering the PMF maps on-the-fly

43 All-Atom Molecular Dynamics

The all-atom MD method can provide unparalleled insight intothe physical mechanisms underlying the biological function ofbiomacromolecules By explicitly describing all the atoms of thesystem of interest and the majority of interatomic interactionsthis method has the potential to compete with the experimentin completeness and accuracy of the description of microscopicphenomena In the case of an ion channel one can in principledirectly observe ion conductance and gating at the spatialresolution of a hydrogen atom and the temporal resolution ofsingle femtoseconds Critical to the above statement is theassumption that the all-atom MD method is equipped with acorrect description of interatomic interactions and enoughcomputational power is available Despite ever-increasingavailability of massive parallel computing platforms makingquantitative predictions using MD remains challenging in partdue to imperfections of the interatom interaction modelsBelow we briefly review the formulations of the all-atom MDmethod and describe recent advances in the field

431 General Formulation of the All-Atom MDMethod In the MD simulations of biomacromoleculesatoms are represented as point particles and the connectivity(or covalent bonds) among those atom are given a prioriCovalently bonded atoms interact with each other throughbonded potentials while the other atom pairs interact throughnonbonded potentials

= +U U Ur r r( ) ( ) ( )N N Nbonded nonbonded (16)

where rN denotes the coordinates of N atoms in a systemBonded interactions model quantum mechanical behavior ofcovalently connected atoms by means of harmonic bond angleand improper dihedral angle restraints and periodic dihedralangle potentials

sum sum

sum

sum

θ θ

χ δ

ϕ ϕ

= minus + minus

+ + minus

+ minus

θ

χ

ϕ

U K b b K

K n

K

( ) ( )

1 cos( )

( )

bbondedbonds

02

angles0

2

torsions

impropers0

2

(17)

where Kb and b0 are the bond force constant and theequilibrium distance respectively Kθ and θ0 are the angleforce constant and the equilibrium angle respectively Kχ nand δ are the dihedral force constant the multiplicity and thephase angle respectively and Kϕ and ϕ0 are the improper forceconstant and the equilibrium improper angle488 The non-bonded potential usually consists of the Lennard-Jones (LJ)potential for van der Waals interactions and the Coulombpotential for electrostatic interactions

sum εσ σ

ε= minus +

⎧⎨⎪⎩⎪

⎡

⎣⎢⎢⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤

⎦⎥⎥

⎫⎬⎪⎭⎪

Ur r

q q

r4 ij

ij

ij

ij

ij

i j

ijnonbonded

nonbond

12 6

(18)

where εij is the well depth σij is the finite distance at which theLJ potential is zero rij is the interatomic distance and qij areatomic charges The bonded parameters are empiricallycalibrated based on the quantum mechanical calculations ofsmall molecules whereas the nonbonded parameters are mainlyderived from quantum chemistry calculations (eg partial

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charges) and empirical matching of thermodynamic data (eghydration free energy)A biomolecular force field is a set of bonded and nonbonded

parameters defined in eqs 17 and 18 Presently severalbiomolecular force fields exist The force fields can becategorized into types based on whether all the atoms areexplicitly treated or not All-atom force fields which includeCHARMM489 AMBER490491 and OPLS-AA492493 treat allatoms explicitly In the united-atom force fields (egGROMOS494495) some nonpolar hydrogen atoms areneglectedFor the simulations of channel proteins a lipid force field is

as important as a protein force field because the channels areembedded in lipid bilayers Among the all-atom force fields theCHARMM force field includes parameters for lipids the latestupdate at the time of writing this review is CHARMM36496

Together with the AMBER force field for the protein thegeneral all-atom AMBER force field (GAFF) can be used todescribe the lipid bilayer497498 Officially OPLS does notinclude lipid parameters Among the united-atom force fieldsGROMOS comes with lipid parameters499 Berger et alreported improved GROMOS-based lipid parameters basedon the condensed-phase properties of pentadecane500 Thislipid force field has been widely used in combination with otherprotein force fields such as AMBER OPLS and GROMOS501

For an in-depth review of various force fields we referinterested readers to a comprehensive review by Mackerell488

432 Ion Channels in Native Environment Unlikesoluble proteins that are surrounded only by water ion-channelproteins are embedded in a lipid bilayer and therefore are incontact with both water and lipids Because of the drasticallydifferent chemical and electrostatic properties of lipid andwater proper descriptions of proteinminuslipid and proteinminuswaterinteractions are key for the successful simulation of amembrane channel To model ion conduction through arelatively rigid channel (eg gA or KcsA channel) it is possibleto use an implicit solvent model of the channelrsquos environmentin which the volume occupied by lipid and water is treated ascontinuum media of dielectric constants 2 and 78 respec-tively299 However when interactions between a channel and alipid membrane are significant (eg in mechanosensitivechannels) explicit modeling of lipid molecules is essentialThe tails of lipids are long and equilibrate slowly making it

significantly more difficult to assemble a model of a channelembedded in an explicit lipid bilayer than a model of a fullysoluble protein Usually the system setup involves thefollowing steps Starting from a pre-equilibrated and solvatedlipid bilayer membrane one makes a pore in the bilayer bydeleting a minimal number of lipid molecules so that theprotein can fit Next an all-atom model of the protein is placedin the pore which is followed by energy minimization andequilibration of the system using the MD method having thechannelrsquos coordinates restrained to their crystallographic valuesFinally when the proteinminuslipid interface is well equilibratedone can perform a production run without applying restraintson the channel For detailed step-by-step instructions forbuilding atomic-scale models of ion channels in lipid bilayerenvironment interested readers are directed to a tutorial onMD simulations of membrane proteins502 Even though a fullyautomated procedure is not yet available several programs canassist a beginner in building a new system VMD503 containsthe Membrane Builder plugin Jo et al have a web-based

service CHARMM GUI Membrane Builder (httpwwwcharmm-guiorgmembrane)504505

An alternative method for creating an all-atom model of anion channel in its native environment is to first carry out self-assembly simulations using a coarse-grained (CG) MDmethod74165379 The main difference between the CG andall-atom MD methods is the level of detail used to describe thecomponents of the system Typically one CG bead representsabout 5minus10 atoms Being much more computationally efficient(and lower resolution) the CG model allows millisecond-time-scale simulations to be performed on commodity computersInterested readers are directed toward recent reviews on thissubject506minus508

In the CG simulations of self-assembly CG models of lipidssolvent and a membrane protein are placed with randompositions in desired proportions During the course of CGMDsimulations the lipid molecules spontaneously form a lipidbilayer around a protein After obtaining a stable model the CGmodel can be reverse-coarse-grained into a fully atomisticmodel (see for example a study by Maffeo and Aksimen-tiev330) A great advantage of this approach is that it requiresno a priori knowledge of the position of the membranechannels relative to the membrane An obvious disadvantage isthat one has to have a reasonable CG model to carry out theself-assembly simulations and a reliable procedure to recoverthe all-atom details from the final CG model Currently it isnot possible to use a CG approach to model ion conductancethrough large membrane channels due to inaccurate treatmentsof the membrane and water electrostatics in most CG modelsHowever work to improve CG methods is ongoing509510 andsuch simulations should become possible in the near future

433 Homology Modeling Usually an all-atom MDsimulation of a channel protein can be performed only when anatomic-resolution structure of the channel is available Thisrequirement severely limits application of the MD methodFortunately membrane channels of different organisms oftenhave similar amino-acid sequences The sequence similarity canbe used to build an all-atom model of the channel that does nothave an experimentally determined structure through aprocedure called homology modeling511 Briefly homologymodeling proceeds as follows First a sequence alignmentbetween a target sequence and a homologous sequenceforwhich a structure is knownis performed Second thesecondary structures (eg α-helices and β-sheets) of the targetsequence from the homologous sequence are built Finallyloops connecting the secondary structures are modeled and theoverall structure is refined There exist many tools for thehomology modeling (eg Modeler by Sali and Blundell511)The homology modeling method has been successfully used

for building initial structures of several ion channels forsubsequent all-atom MD simulations Capener et al512 built aninward rectifier potassium channel (Kir) based on a high-resolution structure of KcsA1 Sukharev et al used the crystalstructure of Mycobacterium tuberculosis MscL407 to modelclosed intermediate and open structures of Escherichia coliMscL231232 Law et al combined the crystal structure of theLymnea stagnalis acetylcholine binding protein and the electronmicroscopy (EM) structure of the transmembrane domain ofthe torpedo electric ray nicotinic channel to build an entirehuman nicotinic acetylcholine receptor213

434 Free-Energy Methods Perhaps the greatestdisadvantage of the MD method is that simulations are costlyand are currently limited to the microsecond time scalea

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computer modeling of ions channels there are notableexceptions418419 that deduce the structural architecture of thechannel from its ion-conductance propertiesPredicting the structure of a membrane channel from its

sequence is a formidable task Hence development ofcomputational models of ion channels was in a way led bycrystallographers and their ability to solve atomic structures ofion channels Membrane channels are notoriously difficult tocrystallize and are often too large for the NMR method towork Therefore atomic-resolution structures have beenobtained for only a very limited number of ion channels andhence many studies have focused on the same systems Belowwe briefly review the ion channels of known structures that arethe most common targets of computational studies

31 Gramicidin A

Gramicidins are small bacteria-produced antibiotics that whendimerized in a head-to-head fashion (Figure 4a) are able totransport a monovalent cation across a membrane once aboutevery 100 ns39 Gramicidin works by eliminating the iongradient across the membrane of Gram-positive bacteriaGramicidin was the first clinical antibiotic in use and is stillused today in conjunction with other antibioticsAll-atom molecular dynamics simulations (MD) have been

instrumental in the interpretation and refinement of NMRresults28 Gramicidin A was the subject of the first MDsimulation of an ion channel almost 30 years ago420 Advancesin the availability of computational resources have permitted farmore realistic models including lipid bilayers and full solvent tobe simulated for significant durations Gramicidin A now servesas a model system and test bed for new techniques21

32 Potassium Channels

Potassium ion channels are key constituents of electricalsignaling networks in the nervous system When openpotassium channels conduct K+ ions at rates remarkably closeto the diffusion limit (about 108 ions per second)421 and displayincredible sensitivity to the size and valency of ions Thus K+

channels can quickly release ions from within the cell inresponse to appropriate stimulus affecting the action potentialBecause some K+ channels are voltage-sensitive this can resultin a cascade of channel activations that propagates through anaxon K+ channels have been the target of prospectivetreatments for an array of disorders including multiplesclerosis422423

Taken from Gram-positive bacterium Streptomyces lividansthe K+ channel KcsA is similar in sequence to vertebratevoltage-dependent K+ channels but is easily expressed inEscherichia coli making it the prototypical K+ channel forlaboratory studies Like all K+ channels the sequence of KcsAcontains a completely conserved motif that is crucial for its K+

specificity Depicted in Figure 5 the first atomic-resolutionstructure of a K+ channel revealed a tetrameric transmembranepore with an intracellular passage leading to a large (10 Aringdiameter) cavity with a hydrophobic lining followed by anatomically narrow sim4 Aring long selectivity filter that leads to theextracellular side of the membrane1 A more complete structureof this channel was recently resolved410 featuring longcytoplasmic helices that appear to stabilize the closedconformation of KcsA at high pH In contrast to the poreregion the arrangement of cytoplasmic helices in KcsA is not auniversal structural element of K+ channelsIn the selectivity filter four rings each featuring four

negatively charged carbonyl-oxygen atoms hold two K+ ions

that are separated by a single water molecule The ions presentin the selectivity filter are mostly desolvated which carries anenormous free energy penalty that is offset by interactions withthe negatively charged surface of the filter Thus the largeforces experienced by translocating ions balance delicately toallow a smooth free energy landscape that permits rapidpermeation through the pore The balance of these forces mustbe carefully tuned to select K+ over other monovalent ions suchas Na+ Although the latter carries the same charge as K+ and isonly 04 Aring smaller experiments suggest that K+ channels bindK+ with as much as 1 000 times greater affinity than Na+1

The selectivity filter can become occupied by divalent ionswhich generally block the current through the channel The Kiror inward rectifying family of potassium channels uses thismechanism to impede K+ ions moving out of the cell Moregenerally potassium channels are regulated through a variety ofother means that include modification through ligand bindingand voltage- and pH-dependent gating Many biologicallyproduced toxins target K+ channels to interfere with a victimrsquosnervous systemBecause of the biological importance of K+ channels and the

fact that the pore domain of bacterial KcsA is homologous tothat of eukaryotic K+ channels the seminal structure of KcsA1

motivated many computational and theoretical studies148 Theformal analogy between electric current in man-made circuitsand ion conductance through the channels424 led researchers todevelop and apply continuum electrostatics theories of ionchannels103minus109 The availability of high-resolution crystalstructures stimulated development of new atomistic simulationtechniques for studying selectivity conductance and gatingbehaviors of K+ channels using either implicit110minus117 orexplicit2988111minus113116minus197 solvent models Ligand dockingcoupled with free energy calculations was recently used tostudy methods to enhance the specificity of naturally occurringneurotoxins for Kv13 which can suppress chronically activated

Figure 5 Pore region of the KcsA K+ ion channel embedded in a lipidbilayer membrane The image shows the first crystallographicallydetermined structure of a K+ channel1 which did not include the longcytoplasmic helices depicted in Figure 4 e One of the four subunits ofthe KcsA tetramer is not shown to provide a clear view of theselectivity filter The lipid bilayer is depicted as gray van der Waalsspheres

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memory T cells implicated in autoimmune disorders includingmultiple sclerosis422425 To overcome the time and length scalelimitations of the all-atom approaches several multiscalemethods have been developed107198minus202 using K+ channelsas target application systems

33 Mechanosensitive Channels

All living creatures have mechanosensors426427 For examplewe can hear sound because our auditory sensory cells candetect ciliary vibrations caused by acoustic waves We can feelthe pressure on our skin and blood vessels and feel full whenwe eat food because of tension sensors in cell membranesPlants which are immobile and less responsive also havemechanosensors a representative example is the gravity sensorwhich allow roots and shoots to grow in opposite directionsInterested readers are referred to a recent review by Kung andco-workers426427 for more detailed informationA breakthrough in the biophysical study of mechanosensa-

tion was the cloning428429 and structural characterizationof simple prokaryotic mechanosensit ive channels(MSCs)407408430431 When the concentration of osmolytes ina bacterial cell is significantly higher than the concentration ofosmolytes in the environment the gradient of osmolyteconcentration across the cell membrane can cause huge turgorpressure inside the bacterial cell If left to develop fully suchosmotic stress can easily rupture the cell wall killing thebacterium To prevent this from happening bacteria haveevolved ldquosafety valvesrdquothe MSCsthat open when thesurface tension in the membrane exceeds a threshold valuemaking the membrane permeable to most small solutes andwater molecules432 Most importantly the channels return to aclosed state when tension drops Thus MSCs are essential forthe survival of bacteriaIn 1998 Chang et al reported the first high-resolution

structure of MSC of large conductance (MscL) fromMycobacterium tuberculosis in a closed conformation407 MscLis a homopentamer with each subunit having two trans-membrane (TM) helices TM1 and TM2 see Figure 4b In theclosed conformation five TM1 helices form a pore and TM2helices surround the inner TM1 helices Recently Liu et alreported a crystal structure of tetrameric MscL from Staph-ylococcus aureus in an expanded intermediate state431 So fartwo crystal structures of the Escherichia coli MSC of smallconductance (MscS) have been reported one in a non-conductive conformation408 and the other in an openconformation430 Those high-resolution structures show thatthe MscS is a homoheptamer with three TM helices persubunit see Figure 4c Seven TM3 helices form a channel withdiameters of 5 and 13 Aring in closed and open conformationsrespectively see Figure 6430

Despite the fact that mechanosensation is universal andessential for all living creatures427 its mechanism is significantlyless understood if compared to the mechanisms of other sensessuch as vision smell and taste427 Since the first MSC wasdiscovered in 1987432 and the first crystal structures of MscLand MscS were revealed in 1998 and 2002407408 both MscLand MscS have served as model systems for the computationalstudies of mechanical gating Because of its very nature thisproblem has attracted the attention of investigators fromvarious disciplines including traditional MD simulationshomology modeling continuum mechanics and coarse-grainedMD simulations see sections 522 and 541 for more detailsThe computational methods developed for studies of MscL and

MscS will surely be of great value in future studies of morecomplex mechanisms of mechanosensation34 Porins

Outer-membrane porins (OMPs) of Gram-negative bacteria aretransmembrane proteins that allow the bacterial cells to interactwith their environment through passive diffusion of water ionsand small hydrophilic molecules (lt600 Da) across their outermembranes Wide channels such as OMPs and toxins facilitatethe permeation of metabolites rather than merely small ionsHowever often they exhibit interesting behavior such asselectivity toward certain ions and serve as model systems totest computational models of ion transport they are thereforeof interest in this reviewOMPs are β-barrel structures usually forming homotrimeric

water-filled pores The porin channel is partially blocked by aloop (L3) that is folded inside the β-barrel forming aconstriction region that determines the size of the solutesthat can traverse the channel Several crystal structures ofporins have been determined at high resolution415433minus437

Some porins exhibit moderate ion selectivity eg Escherichiacoli OmpF (shown in Figure 4i) and OmpC are two cation-selective porins whereas the Pseudomonas aeruginosa OprP438 isa phosphate-selective porin The cation selectivity is known todepend on the salt concentration and the valence of the ionsGram-negative bacteria that lack porins have other substrate-specific channels that allow the passage of small molecules Forinstance the OccK1 an archetype of the outer-membranecarboxylate channel family from Pseudomonas aeruginosa(previously named OpdK) is a monomeric β-barrel with akidney-shaped central pore as revealed by the X-raystructure439 The members of the OccK subfamily of channelsare believed to facilitate the uptake of basic amino acids440 Adetailed examination of the conductance characteristics ofseveral members of the OccK subfamily of channels by Liu andco-workers441 revealed diverse single-channel electrical signa-tures nonohmic voltage dependent conductance and transientgating behavior Single-molecule electrophysiology analysisalong with rational protein design have revealed discrete gatingdynamics involving both enthalpy- and entropy-driven currenttransitions442443

Studies of porins are relevant to the development ofantibiotics To affect bacteria antibiotics must first pass

Figure 6 Comparison of the pores formed by seven TM3 helices ofMscS in nonconducting408 (a) and open430 (b) conformations viewedfrom the periplasm (top) and from within the membrane (bottom)

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXG

through their outer wall which is a process facilitated by porinsPorin alteration has been implicated in antibiotic resistance444

In addition engineered porins such as the OmpG havepotential for use as stochastic sensors77

Functionally related to porins α-hemolysina toxinproduced by Staphylococcus aureusis secreted as a monomerbut assembles on target cell membranes to form ahomoheptameric channel which leads to an uncontrolledpermeation of ions and small molecules and causes cell lysisThe X-ray structure of α-hemolysin445 revealed a mushroom-like shape with a β-barrel stem protruding from its cap domainsee Figure 4k Its ability to self-assemble in biological orsynthetic membranes and its structural stability over a widerange of ion concentrations temperatures and pHs make α-hemolysin an excellent platform for stochastic sensingapplications446 including detection of DNA sequence bymeasuring the ionic current447 An interesting feature is therectification behavior of the channel which has been exploredby both implicit solvent88 as well as all-atom MDsimulations9093

Another large water-filled biological nanopore is MspAthemajor outer-membrane porin of Mycobacterium smegmatis thatallows the uptake of hydrophilic nutrients from the environ-ment The crystal structure of MspA448 revealed a homo-octameric goblet-like structure with a central channel Theporin has a constriction that is lined by two belts of aspartateresidues (Asp90 and Asp91) that diminish the permeability ofnonpolar solutes Genetically modified variants of the MspAchannel may enable practical nanopore DNA sequencing449450

as they provide superior ionic current signals for nucleic aciddetection if compared with α-hemolysin451

35 Other Channels

The voltage-dependent anion channel (VDAC) residing in themitochondrial outer membrane serves as a conduit formetabolites and electrolytes VDACs mediate the passage ofions such as K+ Clminus and Ca2+ and small hydrophilic moleculessuch as ATP between the cytosol and the mitochondria andregulate the release of apoptotic proteins The pore has avoltage-dependent conductance with an anion-selective high-conductance state at low transmembrane potential and aslightly cation-selective low-conductance state at high poten-tial452 Several NMR and X-ray structures of human as well asmouse VDACs453minus455 have become available Initially thesignificance of these structures was questioned on account of anapparent conflict with biochemical and functional data456

However additional NMR457458 and theoretical stud-ies259262268 have shed light on the structureminusfunction relationreaffirming the biological relevance of the structuresThe ClC chloride channels found in both prokaryotic and

eukaryotic cells control the selective flow of Clminus ions and arebelieved to play an important role in regulation of bloodpressure pH and membrane excitability These channelsconduct not just Clminus but also other anions such as HCO3

minusSCNminus and NOminus Unlike cation channels they do notdiscriminate strongly between different species of anionsDefects in these channels are implicated in several diseasessuch as myotonia congenita Bartterrsquos syndrome andepilepsy459 In the past decade structures of ClC orthologuesfrom two bacterial species Salmonella serovar typhimurium andEscherichia coli have become available460 The X-ray structuresreveal the ClC channels to be homodimers with two identicalbut independent pores see Figure 4j Some prokaryotic

members of the ClC family of channels are now believed tobe ion transporters although the line between ion channels andtransporters is getting blurred461 There have been a fewsimulation studies of the permeation pathways260261 of the ClCchannelsThe nicotinic acetylcholine receptor (nAChR) belongs to a

superfamily of Cys-loop ligand-gated ion channels It couples acationic transmembrane ion channel with binding sites for theneurotransmitter acetylcholine (ACh) so that the gating of thechannel is linked to the binding of ACh The nAChR owes itsname to the ability of nicotine to mimic the effects of ACh inopening up the pore The nAChR is composed of a ring of fiveprotein subunits with three domains a large N-terminalextracellular ligand binding domain (LBD) a transmembranedomain (TM) and a small intracellular domain see Figure 4hThere are two ACh binding sites in the ligand-binding domainthe pore opens when both are occupied414 Although thecomplete high-resolution structure of the nAChR is absent atpresent X-ray and electron microscopy structures of some of itscomponents are available413414 The nAChR plays a critical rolein neuronal communication converting neurotransmitter bind-ing into membrane electric depolarization The channel isfound in high concentrations at the nerveminusmuscle synapsenAChR is implicated in a variety of diseases of the centralnervous system including Alzheimerrsquos disease Parkinsonrsquosdisease schizophrenia and epilepsy462 It is also believed toplay a critical role in mediating nicotine reward andaddiction463 Although detailed study of the gating mechanismis precluded by the lack of a complete structure of the nAChRas well as the time scales involved there have been severalstudies on the TM domain215212 and the LBD218

AmtB is a representative bacterial ammonium transporterwhich belongs to AmtMEP family464 Some bacteria andplants use ammonium as a nitrogen source and have variousforms of transporters for the uptake of ammonium464465 At thesame time ammonium is also a toxic metabolic waste whichshould be removed quickly by transporters usually formammals466 There exist several high-resolution crystalstructures of bacterial AmtB409467minus470 The Escherichia colicrystal structure (Figure 4d) has become the paradigm for thestudy of the transport mechanism of ammonium409 UsuallyAmtB proteins are crystallized as a homotrimer Each monomerconsists of 11 transmembrane helices that form a channel forammonium The channel is highly hydrophobic raising thepossibility that ammonium passes the channel in a deproto-nated form (ammonia)

4 MOST COMMON SIMULATION METHODSAmong a large number of computational approaches proposedand employed for studies of ion channels most fall within thefollowing three categories all-atom molecular dynamics (MD)which is a fully microscopic description with all atoms treatedexplicitly Brownian dynamics (BD) in which only the ions aretreated explicitly while the solvent and the protein and lipidsare represented implicitly and approaches based on PoissonminusNernstminusPlanck (PNP) theory in which the ionic concentrationis treated as a continuum Each of the three approaches haslimitations and advantages The MD method is considered themost computationally expensive but also the most accurateThe PNP and BD approaches are in general less computa-tionally expensive but also provide less detail At the same timethe MD method has the smallest temporal and spatial rangefollowed by BD methods followed by PNP approaches Figure

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7 schematically illustrates typical setups for the three modelingapproaches applied to the same systemThe above classification however is rather approximate and

can be misleading Thus the level of computational complexityoften depends on the desired level of detail whereas theaccuracy depends on the assumptions made in deriving theparameters of the model Even the most sophisticated MDsimulations rely on the MD force field which is a classicalmodel that may or may not be adequate for describing a certainphenomenon In this respect full quantum or combinedquantum mechanicsclassical mechanics approaches (QMMM) can in principle provide the highest degree of accuracyHowever the time scale accessible to these methods is severelylimiting Interested readers are directed to reviews of QMMMapproaches for simulations of biomolecules471472 and to arecent review of computational approaches to ion transport innanopores473 On the other hand it is possible to incorporateatomic-level details in BD and even PNP approaches see forexample recent work by Comer Carr and co-workers371373

Other considerations often neglected when evaluating theldquocomputational costrdquo of a certain approach are the qualificationsand ambitions of the researcher performing the modeling tasksand the availability of well-documented and ready-to-use codesFor example it is always possible to increase the computationalcomplexity of the problem by including an exorbitant amountof water in an all-atom simulation or using very fine mesh sizein continuum calculations One could also easily spend severalmonths writing debugging or porting a computationallyefficient code while the same time could have been used torun a more computationally intensive but ready-to-use andtested code Thus there are no simple rules in choosing anoptimal simulation method and researchers new to the field areurged to seek expert advice for their particular problem

41 Continuum Models

Ion channels are complex systems with many degrees offreedom and hence are challenging to model in atomisticdetail Continuum theories based on PoissonminusBoltzmann (PB)and PoissonminusNernstminusPlanck (PNP) equations are powerfultools that make simulation of such systems tractable The mainidea is to employ a continuum description for all componentsof the system ie the solvent the ions and the ion channelThe water the membrane and the channel are represented asfixed structureless dielectrics while the ions are described byspecifying the local density throughout the system Figure 7aschematically illustrates a PNP model of α-hemolysin

411 Electrostatics of Ion Channels The PB equation isthe most popular theoretical model for describing theelectrostatics around a charged biomolecule in ionic solutionIn a system of interacting mobile charged particles theelectrostatic potential arises due to the combined effect of thecharged biomolecules ions and dielectric properties of theenvironment The PB model assumes that the distribution ofcharges in the system is related to the electrostatic potentialaccording to Boltzmann statistics For the purpose of describingelectrostatics of a single biomolecule the PB equation whichwas first introduced independently by Gouy (1910) andChapman (1913) and later generalized by Debye and Huckel(1923) is most frequently written as

sumε ψ πρ π

ψλ

nablamiddot nabla = minus minus

minus

infin

⎛⎝⎜

⎞⎠⎟

c z q

z qk T

r r r

rr

( ( ) ( )) 4 ( ) 4

exp( )

( )

ii i

i

f

B (8)

where ε(r) is the position-dependent dielectric constant ψ(r) isthe electrostatic potential ρf(r) is the fixed charge density ofthe biomolecule ci

infin represents the concentration of ion speciesi at infinite distance from the biomolecule zi is the valency ofion species i q is the proton charge kB is the Boltzmannconstant T is the temperature and λ(r) describes theaccessibility of position r to ions (for example it is oftenassumed to be zero inside the biomolecule) A solution to thePB equation gives the electrostatic potential and equilibriumdensity of ions throughout the space The PB equation invokesa mean-field approximation that neglects nonelectrostatic ionminusion interactions (eg van der Waals or water-mediated) thedielectric response of the system to each ion and effects due tocorrelations in the instantaneous distribution of ions Becauseof these the PB equation fails to describe the electrostatics ofhighly charged objects such as DNA in high-concentration ionsolutions with quantitative accuracy474 In the context of ionchannels which rarely carry such a high charge density the PBtheory has been widely used to calculate the free energy cost oftransferring a charge from bulk solution to the interior of thechannel105287 (see Table 1) to characterize ion-channelinteractions88294 and to compute the distribution of thetransmembrane electrostatic potential103104294299 Such con-tinuum electrostatic calculations have also been used toestimate the relative stability of protonated and unprotonatedstates of ionizable residues in an ion channel (discussed in refs

Figure 7 Schematic illustrations of the PNP (a) BD (b) and all-atom MD (c) modeling methods applied to the same systeman α-hemolysinchannel embedded in a lipid bilayer membrane and surrounded by an electrolyte solution In panel (a) the ions are described as continuous densitywhereas the water protein and membrane are treated as continuum dielectric media In the BD model (panel b) only ions are represented explicitlywhereas all other components are either implicitly modeled or approximated by continuum media All atoms are treated explicitly in the all-atom MDmethod (panel c)

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61 and 475) DelPhi476 and APBS477 are two popular computercodes for numerically solving the PB equation412 Ion Transport Although the PB model provides

insights into the equilibrium energetics of an ion channelmodeling of the ion flux requires a nonequilibrium approach Inmost ion channels the time scale of ion permeation rangesfrom tens of nanoseconds (porins) to microseconds and evenmilliseconds (in active transport) Thus observing a statisticallysignificant number of ion-permeation events requires longtrajectories that are still rather expensive to obtain using an all-atom approach The PoissonminusNernstminusPlanck model givesaccess to long time scales albeit at lower temporal and spatialresolutions As in the PB model the lipid protein and watermolecules are approximated as dielectric continua while ionsare described as continuous density distributions The currentdensity is obtained from the NernstminusPlanck (NP) theorywhich is widely used in studies of electrolyte transport In theNP theory ion fluxes arise from two sources the gradient ofion concentration and the gradient of the electrostatic potentialTraditional NernstminusPlanck equations do not describe ion-channel interactions However the classical NernstminusPlanckequations may be modified to include the ion-channelinteractions via an effective potential Thus the flux of ionspecies i Ji is written as

= minus nabla + nabla⎛⎝⎜

⎞⎠⎟t D c t

c tk T

J r r rr

r( ) ( ) ( )( )

( )i i ii

iB

eff

(9)

where Di and ci are the diffusion constant and the numberdensity of ion species i respectively and r( )i

eff is theeffective potential that usually combines the electrostaticpotential ϕ(r) and a core-repulsive potential UCore(r) withthe latter describing interactions between ions and the proteinchannel and not between the ions themselvesThe concentration and the flux of each ionic species obey the

continuity equation

partpart

+ nablamiddot =c t

tt

rJ r

( )( ) 0i

i (10)

Under steady-state conditions the concentration and the fluxdo not vary with time and nablamiddotJi(r) = 0 The electrostaticpotential is calculated from the Poisson equation

sumε ϕ π ρnablamiddot nabla = minus +r q cr r r( ( ) (( ))) 4 ( ( ) ( ))i

i if

(11)

where ε(r) is the dielectric constant qi is the ion charge andρf(r) is again the (fixed) charge density due to the proteinThe above coupled partial differential equations constitute

the PNP equations and may be solved by a variety of methodsin one or three dimensions Typically the NP and the Poissonequations are solved self-consistently to simultaneously obtainthe electrostatic potential ϕ(r) and the ionic concentration ci(r)under appropriate boundary conditionsModeling ion channels within the PNP framework is

computationally inexpensive compared to MD and BDsimulations because the problem of many-body interactions isavoided through a mean-field approximation An undesirableside-effect is that some important physics is neglected by thisapproximation Below we discuss some of the shortcomings ofthe PNP equations in the context of ion channels as well asextensions to the equations that address these shortcomings

Interested readers are directed to comprehensive reviews onthis subject12299307310478

Prior to the surge of popularity of the all-atom MD methodcontinuum electrodiffusion theories played a major role indevelopment of our understanding of ion fluxes in nano-channels81255 Early attempts to use the electrodiffusion theoryto describe ion flux through nanochannels279minus281286 led to thedevelopment of simplified models based on a self-consistentcombination of the Poisson equation and the NernstminusPlanckequations that were subsequently applied to various channelsystems282minus284 Most of the early studies dealt with either one-dimensional models or simplified geometries that lacked adetailed description of the protein structure and static chargedistribution These studies connected qualitative features of thecurrentminusvoltageminusconcentration relationship to structural andphysical features of the models For example the PNP theorywas used to demonstrate how charges at the channel openingscan produce current rectification285479 as well as how achannel with ion-specific binding sites can exhibit lowerconductance in a mixture of two ion types than in a puresolution of either type480 A lattice-relaxation algorithm able tosolve the PNP equations for a 3D model was developed byKurnikova and co-workers8 in later years This procedure allowsthe protein and the membrane to be mapped onto a 3D cubiclattice with defined dielectric boundaries fixed chargedistribution and a flow region for the ionsLike the PB equation the system of PNP equations

constitutes a mean-field theory that neglects the finite size ofthe ions the dielectric response of the system to an ion andionminusion correlations In fact the PNP equations reduce to thePB equation for systems with zero flux everywhere The validityof a continuum dielectric description and mean-fieldapproaches in the context of narrow pores has been thesubject of much debate For example Chung and co-workersobserved considerable differences between the conductancethrough idealized pores using the BD and PNP ap-proaches287294 The authors argued that the mean-fieldapproximation breaks down in narrow ion channels due to anoverestimation of the screening effect by counterions within thepore Larger channels like porins at physiological or lower ionconcentrations are described quite accurately by the PNPequations However the currents computed based on the PNPmodels can be considerably higher (by 50 for OmpF) than inequivalent BD simulations55

When a charge in a high dielectric medium is brought near alow dielectric medium a repulsive surface charge is induced atthe dielectric boundary In continuum descriptions such as PBand PNP the induced charge density includes (usually)canceling components from both positive and negative averagecharge densities The interaction energy between a charge andits induced charge density is often called the dielectric self-energy The dielectric self-energy due to the average chargedensity and the average induced charge density at the dielectricboundary is in general smaller than the interaction energybetween point charges and corresponding induced chargeaveraged over all configurations Put another way a pointcharge approaching a low dielectric medium is strongly repelledby its induced image charge and this repulsion is largely lost bythe implicit averaging in mean-field descriptionsThe PB and PNP equations have been modified to include

the interaction of an ion with the charge density itinduces11294296 Although the corrections account for theinteraction of an ion with its induced dielectric charge they do

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not account for the interaction of the induced charge with asecond nearby ion Similarly the mean-field approximationinherently ignores effects involving correlations in theinstantaneous ion distribution For example the narrowestportion of the potassium channels almost always contains twoions that move in a concerted fashion (see section 511) whichcannot be properly treated by continuum theories Never-theless it was concluded that the dielectric self-energy accountsfor most of the discrepancy between PNP and BD results in thecase of narrow channels294

Although early electrodiffusion studies of Levitt consideredhard-sphere repulsion between ions by iteratively correcting theion concentration279 many studies have since ignored suchfinite-size effects Recently the PNP equations have beenadapted to incorporate finite-size effects using classical densityfunctional theory to describe many-body hard sphereinteractions between ions and solvent290291300481 Unfortu-nately these approaches often yield cumbersome integro-differential equations Finite-size effects can be included in thePNP equations by introducing an entropic term thatdiscourages solvent crowding by ions309 The latter approachyields a tractable set of corrected PNP equations Both the PNPand BD methods usually ignore thermal fluctuations of theprotein and lipid bilayer However these can be effectivelycaptured by combining results from MD or Monte Carlosimulations with 3-D PNP calculations92

The PNP approach continues to play a major role inimproving our understanding of the physics of ion channelsThe computational efficiency of the PNP model is unparallelledfor studies of ion conductance in a low ion concentrationregime where the PNP method is expected to be the mostaccurate The method is highly efficient at predicting the effectof a channelrsquos geometry on the currentminusvoltage dependence atphysiological voltages and can be used to screen for mutationsthat affect conductance of a channel The calculation of currentscan be quite accurate in the case of larger channels such asporins PNP is perhaps the only method that can presentlysimulate the interplay of ion conductances in an ensemble ofion channels (such as in a realistic biological membrane)explicitly taking the structural features of the channels intoaccount Finally the PNP approach is rather flexible to includedescriptions of additional physical effects for examplehydrodynamic interactions354364369370 or the effect of asemiconductor membrane on the ionic current361382383

42 Brownian Dynamics

The BD method allows for simulations of explicit ionpermeations on the microsecond-to-millisecond time scale bytreating solvent molecules implicitly In a way the BD methodoffers a good compromise between all-atom MD andcontinuum electrodiffusion approaches Computational effi-ciency is achieved by reducing the number of degrees offreedom Typically a moderate number of atoms of interest(usually the ions) are simulated explicitly while the solvent isaccounted for via friction and stochastic random forces that actin addition to the electrostatic and steric forces arising fromother ions the protein and the lipid bilayer For the calculationof electrostatic forces the water the membrane and the proteinchannel are usually treated as continuous dielectric media Thechannel is treated as a rigid structure and thermal fluctuationsare typically ignored Figure 7b schematically illustrates a BDmodel of α-hemolysin

421 General Formulation of the BD Method In theBrownian dynamics method a stochastic equation is integratedforward in time to create trajectories of atoms Theldquouninterestingrdquo degrees of motion usually corresponding tofast-moving solvent molecules are projected out in order todevelop a dynamic equation for the evolution of the ldquorelevantrdquodegrees of freedom The motion of the particles is described bya generalized Langevin equation

int = minus prime minus prime prime +m t dt M t t t tr r f( ) ( ) ( ) ( )i i i

t

i i i0 (12)

The force on the ith particle i is obtained from an effectivepotential = minusnabla r( )i i iThe potential function is a many-body potential of mean

force (PMF) that corresponds to the reversible thermodynamicwork function to assemble the relevant particles in a particularconformation while averaging out the remaining degrees offreedom ie the effect of all other atoms is implicitly present in

r( )i The second term on the right-hand side is thedamping force representing the frictional effect of theenvironment and finally fi(t) is a Gaussian fluctuating forcearising from random collisions The frictional force depends onprevious velocities through the memory kernel Mi(tminustprime) Thefirst and second moments of the random force are given by⟨fi(t)⟩ = 0 and ⟨fi(t)middotfj(0)⟩ = 3kBTMi(t)δij where kB is theBoltzmann constant and T is the temperature Both the dragforce and the stochastic force incorporate the effect of thesolvent In the Markovian limit the memory kernel is a Diracdelta function that leads to the traditional Langevin equation

γ = minus +m t t tr r f( ) ( ) ( )i i i i i i (13)

The friction coefficient γi is related to underlying molecularprocesses via the fluctuationminusdissipation theoremIn the overdamped regime (which applies to the motion of

an ion in water) the inertial term can be ignored so that theLangevin equation is reduced to

ζ = +tD

k Ttr( ) ( )i

ii i

B (14)

where Di = kBTγi is the diffusion coefficient of the ith particleand ζi(t) is a Gaussian random noise with a second momentgiven as ⟨ζi(t)middotζi(0)⟩ = 6Diδ(t)

422 BD Simulations of Ion Channels A Browniandynamics simulation requires two basic ingredients adescription of the forces applied to each ion and the diffusioncoefficient for each ion The diffusion coefficient for the ionsshould be in general position-dependent and can be obtainedfrom all-atom MD simulations373482483 or estimated usinganalytical techniques88484 However in most cases a singleposition-independent diffusion constant is used for all ions ofthe same speciesEach ion experiences a force that depends on its position as

well as the positions of all the other ions in the system Thepotential corresponding to the forces on the ions is the multi-ion PMF which is the multidimensional free energy surfacethat is usually broken into an ionminusion PMF and a PMF due tothe pore the solution and other biomolecules373 The PMFscan be calculated from all-atom MD or even quantumchemistry simulations but such calculations are computation-ally expensive

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A more typical approach was presented by Roux and co-workers which we summarize here556263299 The multi-ionPMF can be written as

sum sum sum

sum ϕ ϕ

= | minus | +

+ +

αα γ α

α γ α γα

α

αα α α

neu U

q

r r r r

r r

( ) ( ) ( )

[ ( ) ( )]

core

sf rf(15)

where uαγ(r) is the ionminusion interaction Ucore is a repulsivepotential preventing the ions from entering the ion-inaccessibleregions ϕsf is the electrostatic potential arising from thepermanent protein charge distribution and ϕrf is the reactionfield potential arising from the electrostatic polarization of thevarious dielectric boundaries The static field may be computedfrom an atomic model of the pore using the PBequations556263485 Any externally imposed transmembranebias may be included in the calculation of the electrostaticpotential Usually the ionminusion interaction includes van derWaals and Coulomb terms

εσ σ

ε= minus +α γ α γ

α γ α γ α γ⎜ ⎟ ⎜ ⎟⎡⎣⎢⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎤⎦⎥u r

r r

q q

r( ) 4

12

6

bulk

where εαγ and σαγ are the parameters for the 6minus12 Lennard-Jones potential qα and qγ are the charges of the ions and εbulk isthe dielectric constant of bulk water The local dielectricconstant of the water in the interior of the pore may beextracted from atomistic simulations but it is usually assumedto have the bulk value of 80 Solvation effects can beapproximately described by including a short-range solvationpotential55287486 but that is rarely done in practice Web-basedinterface for GCMCBD simulations of ion channels hasrecently become available268

Early BD studies were performed using one-dimensionalrepresentations of channels487 Later these were extended tomore realistic three-dimensional geometries although theseoften lacked atomic detail63486 However the X-ray structure ofan ion channel can be used to create a more realistic model ofthe channel by computing electrostatic and core repulsionpotential maps from the all-atom structure Brownian dynamicssimulations have been applied to several biological channelsincluding OmpF5562minus64 K+ channels110minus115117 α-hemoly-sin8895 VDAC268 and gramicidin1617 Roux and co-workershave developed a grand canonical Monte CarloBrowniandynamics method (GCMCBD)6263103 to allow for fluctua-tions in the total number of ions in the system and asymmetricion concentration conditions For detailed treatment of thesubject interested readers are directed to a review of thecomputational methods299473

Recently Comer and Aksimentiev373 used all-atom MD todetermine full three-dimensional PMF maps at atomicresolution for ionminusion and ionminusbiomolecule interactionsthereby fully accounting for short-range effects associationwith solvation of ions and biomolecules Using such full 3-DPMFs in BD simulations of ion flow through a model nanoporecontaining DNA basepair triplets yielded ionic currents in closeagreement with the results of all-atom MD but at a fraction ofthe computational cost The authors indicate that such anatomic-resolution BD method can be developed further toincorporate the conformational flexibility of the pore and DNAby altering the PMF maps on-the-fly

43 All-Atom Molecular Dynamics

The all-atom MD method can provide unparalleled insight intothe physical mechanisms underlying the biological function ofbiomacromolecules By explicitly describing all the atoms of thesystem of interest and the majority of interatomic interactionsthis method has the potential to compete with the experimentin completeness and accuracy of the description of microscopicphenomena In the case of an ion channel one can in principledirectly observe ion conductance and gating at the spatialresolution of a hydrogen atom and the temporal resolution ofsingle femtoseconds Critical to the above statement is theassumption that the all-atom MD method is equipped with acorrect description of interatomic interactions and enoughcomputational power is available Despite ever-increasingavailability of massive parallel computing platforms makingquantitative predictions using MD remains challenging in partdue to imperfections of the interatom interaction modelsBelow we briefly review the formulations of the all-atom MDmethod and describe recent advances in the field

431 General Formulation of the All-Atom MDMethod In the MD simulations of biomacromoleculesatoms are represented as point particles and the connectivity(or covalent bonds) among those atom are given a prioriCovalently bonded atoms interact with each other throughbonded potentials while the other atom pairs interact throughnonbonded potentials

= +U U Ur r r( ) ( ) ( )N N Nbonded nonbonded (16)

where rN denotes the coordinates of N atoms in a systemBonded interactions model quantum mechanical behavior ofcovalently connected atoms by means of harmonic bond angleand improper dihedral angle restraints and periodic dihedralangle potentials

sum sum

sum

sum

θ θ

χ δ

ϕ ϕ

= minus + minus

+ + minus

+ minus

θ

χ

ϕ

U K b b K

K n

K

( ) ( )

1 cos( )

( )

bbondedbonds

02

angles0

2

torsions

impropers0

2

(17)

where Kb and b0 are the bond force constant and theequilibrium distance respectively Kθ and θ0 are the angleforce constant and the equilibrium angle respectively Kχ nand δ are the dihedral force constant the multiplicity and thephase angle respectively and Kϕ and ϕ0 are the improper forceconstant and the equilibrium improper angle488 The non-bonded potential usually consists of the Lennard-Jones (LJ)potential for van der Waals interactions and the Coulombpotential for electrostatic interactions

sum εσ σ

ε= minus +

⎧⎨⎪⎩⎪

⎡

⎣⎢⎢⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤

⎦⎥⎥

⎫⎬⎪⎭⎪

Ur r

q q

r4 ij

ij

ij

ij

ij

i j

ijnonbonded

nonbond

12 6

(18)

where εij is the well depth σij is the finite distance at which theLJ potential is zero rij is the interatomic distance and qij areatomic charges The bonded parameters are empiricallycalibrated based on the quantum mechanical calculations ofsmall molecules whereas the nonbonded parameters are mainlyderived from quantum chemistry calculations (eg partial

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXL

charges) and empirical matching of thermodynamic data (eghydration free energy)A biomolecular force field is a set of bonded and nonbonded

parameters defined in eqs 17 and 18 Presently severalbiomolecular force fields exist The force fields can becategorized into types based on whether all the atoms areexplicitly treated or not All-atom force fields which includeCHARMM489 AMBER490491 and OPLS-AA492493 treat allatoms explicitly In the united-atom force fields (egGROMOS494495) some nonpolar hydrogen atoms areneglectedFor the simulations of channel proteins a lipid force field is

as important as a protein force field because the channels areembedded in lipid bilayers Among the all-atom force fields theCHARMM force field includes parameters for lipids the latestupdate at the time of writing this review is CHARMM36496

Together with the AMBER force field for the protein thegeneral all-atom AMBER force field (GAFF) can be used todescribe the lipid bilayer497498 Officially OPLS does notinclude lipid parameters Among the united-atom force fieldsGROMOS comes with lipid parameters499 Berger et alreported improved GROMOS-based lipid parameters basedon the condensed-phase properties of pentadecane500 Thislipid force field has been widely used in combination with otherprotein force fields such as AMBER OPLS and GROMOS501

For an in-depth review of various force fields we referinterested readers to a comprehensive review by Mackerell488

432 Ion Channels in Native Environment Unlikesoluble proteins that are surrounded only by water ion-channelproteins are embedded in a lipid bilayer and therefore are incontact with both water and lipids Because of the drasticallydifferent chemical and electrostatic properties of lipid andwater proper descriptions of proteinminuslipid and proteinminuswaterinteractions are key for the successful simulation of amembrane channel To model ion conduction through arelatively rigid channel (eg gA or KcsA channel) it is possibleto use an implicit solvent model of the channelrsquos environmentin which the volume occupied by lipid and water is treated ascontinuum media of dielectric constants 2 and 78 respec-tively299 However when interactions between a channel and alipid membrane are significant (eg in mechanosensitivechannels) explicit modeling of lipid molecules is essentialThe tails of lipids are long and equilibrate slowly making it

significantly more difficult to assemble a model of a channelembedded in an explicit lipid bilayer than a model of a fullysoluble protein Usually the system setup involves thefollowing steps Starting from a pre-equilibrated and solvatedlipid bilayer membrane one makes a pore in the bilayer bydeleting a minimal number of lipid molecules so that theprotein can fit Next an all-atom model of the protein is placedin the pore which is followed by energy minimization andequilibration of the system using the MD method having thechannelrsquos coordinates restrained to their crystallographic valuesFinally when the proteinminuslipid interface is well equilibratedone can perform a production run without applying restraintson the channel For detailed step-by-step instructions forbuilding atomic-scale models of ion channels in lipid bilayerenvironment interested readers are directed to a tutorial onMD simulations of membrane proteins502 Even though a fullyautomated procedure is not yet available several programs canassist a beginner in building a new system VMD503 containsthe Membrane Builder plugin Jo et al have a web-based

service CHARMM GUI Membrane Builder (httpwwwcharmm-guiorgmembrane)504505

An alternative method for creating an all-atom model of anion channel in its native environment is to first carry out self-assembly simulations using a coarse-grained (CG) MDmethod74165379 The main difference between the CG andall-atom MD methods is the level of detail used to describe thecomponents of the system Typically one CG bead representsabout 5minus10 atoms Being much more computationally efficient(and lower resolution) the CG model allows millisecond-time-scale simulations to be performed on commodity computersInterested readers are directed toward recent reviews on thissubject506minus508

In the CG simulations of self-assembly CG models of lipidssolvent and a membrane protein are placed with randompositions in desired proportions During the course of CGMDsimulations the lipid molecules spontaneously form a lipidbilayer around a protein After obtaining a stable model the CGmodel can be reverse-coarse-grained into a fully atomisticmodel (see for example a study by Maffeo and Aksimen-tiev330) A great advantage of this approach is that it requiresno a priori knowledge of the position of the membranechannels relative to the membrane An obvious disadvantage isthat one has to have a reasonable CG model to carry out theself-assembly simulations and a reliable procedure to recoverthe all-atom details from the final CG model Currently it isnot possible to use a CG approach to model ion conductancethrough large membrane channels due to inaccurate treatmentsof the membrane and water electrostatics in most CG modelsHowever work to improve CG methods is ongoing509510 andsuch simulations should become possible in the near future

433 Homology Modeling Usually an all-atom MDsimulation of a channel protein can be performed only when anatomic-resolution structure of the channel is available Thisrequirement severely limits application of the MD methodFortunately membrane channels of different organisms oftenhave similar amino-acid sequences The sequence similarity canbe used to build an all-atom model of the channel that does nothave an experimentally determined structure through aprocedure called homology modeling511 Briefly homologymodeling proceeds as follows First a sequence alignmentbetween a target sequence and a homologous sequenceforwhich a structure is knownis performed Second thesecondary structures (eg α-helices and β-sheets) of the targetsequence from the homologous sequence are built Finallyloops connecting the secondary structures are modeled and theoverall structure is refined There exist many tools for thehomology modeling (eg Modeler by Sali and Blundell511)The homology modeling method has been successfully used

for building initial structures of several ion channels forsubsequent all-atom MD simulations Capener et al512 built aninward rectifier potassium channel (Kir) based on a high-resolution structure of KcsA1 Sukharev et al used the crystalstructure of Mycobacterium tuberculosis MscL407 to modelclosed intermediate and open structures of Escherichia coliMscL231232 Law et al combined the crystal structure of theLymnea stagnalis acetylcholine binding protein and the electronmicroscopy (EM) structure of the transmembrane domain ofthe torpedo electric ray nicotinic channel to build an entirehuman nicotinic acetylcholine receptor213

434 Free-Energy Methods Perhaps the greatestdisadvantage of the MD method is that simulations are costlyand are currently limited to the microsecond time scalea

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memory T cells implicated in autoimmune disorders includingmultiple sclerosis422425 To overcome the time and length scalelimitations of the all-atom approaches several multiscalemethods have been developed107198minus202 using K+ channelsas target application systems

33 Mechanosensitive Channels

All living creatures have mechanosensors426427 For examplewe can hear sound because our auditory sensory cells candetect ciliary vibrations caused by acoustic waves We can feelthe pressure on our skin and blood vessels and feel full whenwe eat food because of tension sensors in cell membranesPlants which are immobile and less responsive also havemechanosensors a representative example is the gravity sensorwhich allow roots and shoots to grow in opposite directionsInterested readers are referred to a recent review by Kung andco-workers426427 for more detailed informationA breakthrough in the biophysical study of mechanosensa-

tion was the cloning428429 and structural characterizationof simple prokaryotic mechanosensit ive channels(MSCs)407408430431 When the concentration of osmolytes ina bacterial cell is significantly higher than the concentration ofosmolytes in the environment the gradient of osmolyteconcentration across the cell membrane can cause huge turgorpressure inside the bacterial cell If left to develop fully suchosmotic stress can easily rupture the cell wall killing thebacterium To prevent this from happening bacteria haveevolved ldquosafety valvesrdquothe MSCsthat open when thesurface tension in the membrane exceeds a threshold valuemaking the membrane permeable to most small solutes andwater molecules432 Most importantly the channels return to aclosed state when tension drops Thus MSCs are essential forthe survival of bacteriaIn 1998 Chang et al reported the first high-resolution

structure of MSC of large conductance (MscL) fromMycobacterium tuberculosis in a closed conformation407 MscLis a homopentamer with each subunit having two trans-membrane (TM) helices TM1 and TM2 see Figure 4b In theclosed conformation five TM1 helices form a pore and TM2helices surround the inner TM1 helices Recently Liu et alreported a crystal structure of tetrameric MscL from Staph-ylococcus aureus in an expanded intermediate state431 So fartwo crystal structures of the Escherichia coli MSC of smallconductance (MscS) have been reported one in a non-conductive conformation408 and the other in an openconformation430 Those high-resolution structures show thatthe MscS is a homoheptamer with three TM helices persubunit see Figure 4c Seven TM3 helices form a channel withdiameters of 5 and 13 Aring in closed and open conformationsrespectively see Figure 6430

Despite the fact that mechanosensation is universal andessential for all living creatures427 its mechanism is significantlyless understood if compared to the mechanisms of other sensessuch as vision smell and taste427 Since the first MSC wasdiscovered in 1987432 and the first crystal structures of MscLand MscS were revealed in 1998 and 2002407408 both MscLand MscS have served as model systems for the computationalstudies of mechanical gating Because of its very nature thisproblem has attracted the attention of investigators fromvarious disciplines including traditional MD simulationshomology modeling continuum mechanics and coarse-grainedMD simulations see sections 522 and 541 for more detailsThe computational methods developed for studies of MscL and

MscS will surely be of great value in future studies of morecomplex mechanisms of mechanosensation34 Porins

Outer-membrane porins (OMPs) of Gram-negative bacteria aretransmembrane proteins that allow the bacterial cells to interactwith their environment through passive diffusion of water ionsand small hydrophilic molecules (lt600 Da) across their outermembranes Wide channels such as OMPs and toxins facilitatethe permeation of metabolites rather than merely small ionsHowever often they exhibit interesting behavior such asselectivity toward certain ions and serve as model systems totest computational models of ion transport they are thereforeof interest in this reviewOMPs are β-barrel structures usually forming homotrimeric

water-filled pores The porin channel is partially blocked by aloop (L3) that is folded inside the β-barrel forming aconstriction region that determines the size of the solutesthat can traverse the channel Several crystal structures ofporins have been determined at high resolution415433minus437

Some porins exhibit moderate ion selectivity eg Escherichiacoli OmpF (shown in Figure 4i) and OmpC are two cation-selective porins whereas the Pseudomonas aeruginosa OprP438 isa phosphate-selective porin The cation selectivity is known todepend on the salt concentration and the valence of the ionsGram-negative bacteria that lack porins have other substrate-specific channels that allow the passage of small molecules Forinstance the OccK1 an archetype of the outer-membranecarboxylate channel family from Pseudomonas aeruginosa(previously named OpdK) is a monomeric β-barrel with akidney-shaped central pore as revealed by the X-raystructure439 The members of the OccK subfamily of channelsare believed to facilitate the uptake of basic amino acids440 Adetailed examination of the conductance characteristics ofseveral members of the OccK subfamily of channels by Liu andco-workers441 revealed diverse single-channel electrical signa-tures nonohmic voltage dependent conductance and transientgating behavior Single-molecule electrophysiology analysisalong with rational protein design have revealed discrete gatingdynamics involving both enthalpy- and entropy-driven currenttransitions442443

Studies of porins are relevant to the development ofantibiotics To affect bacteria antibiotics must first pass

Figure 6 Comparison of the pores formed by seven TM3 helices ofMscS in nonconducting408 (a) and open430 (b) conformations viewedfrom the periplasm (top) and from within the membrane (bottom)

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through their outer wall which is a process facilitated by porinsPorin alteration has been implicated in antibiotic resistance444

In addition engineered porins such as the OmpG havepotential for use as stochastic sensors77

Functionally related to porins α-hemolysina toxinproduced by Staphylococcus aureusis secreted as a monomerbut assembles on target cell membranes to form ahomoheptameric channel which leads to an uncontrolledpermeation of ions and small molecules and causes cell lysisThe X-ray structure of α-hemolysin445 revealed a mushroom-like shape with a β-barrel stem protruding from its cap domainsee Figure 4k Its ability to self-assemble in biological orsynthetic membranes and its structural stability over a widerange of ion concentrations temperatures and pHs make α-hemolysin an excellent platform for stochastic sensingapplications446 including detection of DNA sequence bymeasuring the ionic current447 An interesting feature is therectification behavior of the channel which has been exploredby both implicit solvent88 as well as all-atom MDsimulations9093

Another large water-filled biological nanopore is MspAthemajor outer-membrane porin of Mycobacterium smegmatis thatallows the uptake of hydrophilic nutrients from the environ-ment The crystal structure of MspA448 revealed a homo-octameric goblet-like structure with a central channel Theporin has a constriction that is lined by two belts of aspartateresidues (Asp90 and Asp91) that diminish the permeability ofnonpolar solutes Genetically modified variants of the MspAchannel may enable practical nanopore DNA sequencing449450

as they provide superior ionic current signals for nucleic aciddetection if compared with α-hemolysin451

35 Other Channels

The voltage-dependent anion channel (VDAC) residing in themitochondrial outer membrane serves as a conduit formetabolites and electrolytes VDACs mediate the passage ofions such as K+ Clminus and Ca2+ and small hydrophilic moleculessuch as ATP between the cytosol and the mitochondria andregulate the release of apoptotic proteins The pore has avoltage-dependent conductance with an anion-selective high-conductance state at low transmembrane potential and aslightly cation-selective low-conductance state at high poten-tial452 Several NMR and X-ray structures of human as well asmouse VDACs453minus455 have become available Initially thesignificance of these structures was questioned on account of anapparent conflict with biochemical and functional data456

However additional NMR457458 and theoretical stud-ies259262268 have shed light on the structureminusfunction relationreaffirming the biological relevance of the structuresThe ClC chloride channels found in both prokaryotic and

eukaryotic cells control the selective flow of Clminus ions and arebelieved to play an important role in regulation of bloodpressure pH and membrane excitability These channelsconduct not just Clminus but also other anions such as HCO3

minusSCNminus and NOminus Unlike cation channels they do notdiscriminate strongly between different species of anionsDefects in these channels are implicated in several diseasessuch as myotonia congenita Bartterrsquos syndrome andepilepsy459 In the past decade structures of ClC orthologuesfrom two bacterial species Salmonella serovar typhimurium andEscherichia coli have become available460 The X-ray structuresreveal the ClC channels to be homodimers with two identicalbut independent pores see Figure 4j Some prokaryotic

members of the ClC family of channels are now believed tobe ion transporters although the line between ion channels andtransporters is getting blurred461 There have been a fewsimulation studies of the permeation pathways260261 of the ClCchannelsThe nicotinic acetylcholine receptor (nAChR) belongs to a

superfamily of Cys-loop ligand-gated ion channels It couples acationic transmembrane ion channel with binding sites for theneurotransmitter acetylcholine (ACh) so that the gating of thechannel is linked to the binding of ACh The nAChR owes itsname to the ability of nicotine to mimic the effects of ACh inopening up the pore The nAChR is composed of a ring of fiveprotein subunits with three domains a large N-terminalextracellular ligand binding domain (LBD) a transmembranedomain (TM) and a small intracellular domain see Figure 4hThere are two ACh binding sites in the ligand-binding domainthe pore opens when both are occupied414 Although thecomplete high-resolution structure of the nAChR is absent atpresent X-ray and electron microscopy structures of some of itscomponents are available413414 The nAChR plays a critical rolein neuronal communication converting neurotransmitter bind-ing into membrane electric depolarization The channel isfound in high concentrations at the nerveminusmuscle synapsenAChR is implicated in a variety of diseases of the centralnervous system including Alzheimerrsquos disease Parkinsonrsquosdisease schizophrenia and epilepsy462 It is also believed toplay a critical role in mediating nicotine reward andaddiction463 Although detailed study of the gating mechanismis precluded by the lack of a complete structure of the nAChRas well as the time scales involved there have been severalstudies on the TM domain215212 and the LBD218

AmtB is a representative bacterial ammonium transporterwhich belongs to AmtMEP family464 Some bacteria andplants use ammonium as a nitrogen source and have variousforms of transporters for the uptake of ammonium464465 At thesame time ammonium is also a toxic metabolic waste whichshould be removed quickly by transporters usually formammals466 There exist several high-resolution crystalstructures of bacterial AmtB409467minus470 The Escherichia colicrystal structure (Figure 4d) has become the paradigm for thestudy of the transport mechanism of ammonium409 UsuallyAmtB proteins are crystallized as a homotrimer Each monomerconsists of 11 transmembrane helices that form a channel forammonium The channel is highly hydrophobic raising thepossibility that ammonium passes the channel in a deproto-nated form (ammonia)

4 MOST COMMON SIMULATION METHODSAmong a large number of computational approaches proposedand employed for studies of ion channels most fall within thefollowing three categories all-atom molecular dynamics (MD)which is a fully microscopic description with all atoms treatedexplicitly Brownian dynamics (BD) in which only the ions aretreated explicitly while the solvent and the protein and lipidsare represented implicitly and approaches based on PoissonminusNernstminusPlanck (PNP) theory in which the ionic concentrationis treated as a continuum Each of the three approaches haslimitations and advantages The MD method is considered themost computationally expensive but also the most accurateThe PNP and BD approaches are in general less computa-tionally expensive but also provide less detail At the same timethe MD method has the smallest temporal and spatial rangefollowed by BD methods followed by PNP approaches Figure

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7 schematically illustrates typical setups for the three modelingapproaches applied to the same systemThe above classification however is rather approximate and

can be misleading Thus the level of computational complexityoften depends on the desired level of detail whereas theaccuracy depends on the assumptions made in deriving theparameters of the model Even the most sophisticated MDsimulations rely on the MD force field which is a classicalmodel that may or may not be adequate for describing a certainphenomenon In this respect full quantum or combinedquantum mechanicsclassical mechanics approaches (QMMM) can in principle provide the highest degree of accuracyHowever the time scale accessible to these methods is severelylimiting Interested readers are directed to reviews of QMMMapproaches for simulations of biomolecules471472 and to arecent review of computational approaches to ion transport innanopores473 On the other hand it is possible to incorporateatomic-level details in BD and even PNP approaches see forexample recent work by Comer Carr and co-workers371373

Other considerations often neglected when evaluating theldquocomputational costrdquo of a certain approach are the qualificationsand ambitions of the researcher performing the modeling tasksand the availability of well-documented and ready-to-use codesFor example it is always possible to increase the computationalcomplexity of the problem by including an exorbitant amountof water in an all-atom simulation or using very fine mesh sizein continuum calculations One could also easily spend severalmonths writing debugging or porting a computationallyefficient code while the same time could have been used torun a more computationally intensive but ready-to-use andtested code Thus there are no simple rules in choosing anoptimal simulation method and researchers new to the field areurged to seek expert advice for their particular problem

41 Continuum Models

Ion channels are complex systems with many degrees offreedom and hence are challenging to model in atomisticdetail Continuum theories based on PoissonminusBoltzmann (PB)and PoissonminusNernstminusPlanck (PNP) equations are powerfultools that make simulation of such systems tractable The mainidea is to employ a continuum description for all componentsof the system ie the solvent the ions and the ion channelThe water the membrane and the channel are represented asfixed structureless dielectrics while the ions are described byspecifying the local density throughout the system Figure 7aschematically illustrates a PNP model of α-hemolysin

411 Electrostatics of Ion Channels The PB equation isthe most popular theoretical model for describing theelectrostatics around a charged biomolecule in ionic solutionIn a system of interacting mobile charged particles theelectrostatic potential arises due to the combined effect of thecharged biomolecules ions and dielectric properties of theenvironment The PB model assumes that the distribution ofcharges in the system is related to the electrostatic potentialaccording to Boltzmann statistics For the purpose of describingelectrostatics of a single biomolecule the PB equation whichwas first introduced independently by Gouy (1910) andChapman (1913) and later generalized by Debye and Huckel(1923) is most frequently written as

sumε ψ πρ π

ψλ

nablamiddot nabla = minus minus

minus

infin

⎛⎝⎜

⎞⎠⎟

c z q

z qk T

r r r

rr

( ( ) ( )) 4 ( ) 4

exp( )

( )

ii i

i

f

B (8)

where ε(r) is the position-dependent dielectric constant ψ(r) isthe electrostatic potential ρf(r) is the fixed charge density ofthe biomolecule ci

infin represents the concentration of ion speciesi at infinite distance from the biomolecule zi is the valency ofion species i q is the proton charge kB is the Boltzmannconstant T is the temperature and λ(r) describes theaccessibility of position r to ions (for example it is oftenassumed to be zero inside the biomolecule) A solution to thePB equation gives the electrostatic potential and equilibriumdensity of ions throughout the space The PB equation invokesa mean-field approximation that neglects nonelectrostatic ionminusion interactions (eg van der Waals or water-mediated) thedielectric response of the system to each ion and effects due tocorrelations in the instantaneous distribution of ions Becauseof these the PB equation fails to describe the electrostatics ofhighly charged objects such as DNA in high-concentration ionsolutions with quantitative accuracy474 In the context of ionchannels which rarely carry such a high charge density the PBtheory has been widely used to calculate the free energy cost oftransferring a charge from bulk solution to the interior of thechannel105287 (see Table 1) to characterize ion-channelinteractions88294 and to compute the distribution of thetransmembrane electrostatic potential103104294299 Such con-tinuum electrostatic calculations have also been used toestimate the relative stability of protonated and unprotonatedstates of ionizable residues in an ion channel (discussed in refs

Figure 7 Schematic illustrations of the PNP (a) BD (b) and all-atom MD (c) modeling methods applied to the same systeman α-hemolysinchannel embedded in a lipid bilayer membrane and surrounded by an electrolyte solution In panel (a) the ions are described as continuous densitywhereas the water protein and membrane are treated as continuum dielectric media In the BD model (panel b) only ions are represented explicitlywhereas all other components are either implicitly modeled or approximated by continuum media All atoms are treated explicitly in the all-atom MDmethod (panel c)

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61 and 475) DelPhi476 and APBS477 are two popular computercodes for numerically solving the PB equation412 Ion Transport Although the PB model provides

insights into the equilibrium energetics of an ion channelmodeling of the ion flux requires a nonequilibrium approach Inmost ion channels the time scale of ion permeation rangesfrom tens of nanoseconds (porins) to microseconds and evenmilliseconds (in active transport) Thus observing a statisticallysignificant number of ion-permeation events requires longtrajectories that are still rather expensive to obtain using an all-atom approach The PoissonminusNernstminusPlanck model givesaccess to long time scales albeit at lower temporal and spatialresolutions As in the PB model the lipid protein and watermolecules are approximated as dielectric continua while ionsare described as continuous density distributions The currentdensity is obtained from the NernstminusPlanck (NP) theorywhich is widely used in studies of electrolyte transport In theNP theory ion fluxes arise from two sources the gradient ofion concentration and the gradient of the electrostatic potentialTraditional NernstminusPlanck equations do not describe ion-channel interactions However the classical NernstminusPlanckequations may be modified to include the ion-channelinteractions via an effective potential Thus the flux of ionspecies i Ji is written as

= minus nabla + nabla⎛⎝⎜

⎞⎠⎟t D c t

c tk T

J r r rr

r( ) ( ) ( )( )

( )i i ii

iB

eff

(9)

where Di and ci are the diffusion constant and the numberdensity of ion species i respectively and r( )i

eff is theeffective potential that usually combines the electrostaticpotential ϕ(r) and a core-repulsive potential UCore(r) withthe latter describing interactions between ions and the proteinchannel and not between the ions themselvesThe concentration and the flux of each ionic species obey the

continuity equation

partpart

+ nablamiddot =c t

tt

rJ r

( )( ) 0i

i (10)

Under steady-state conditions the concentration and the fluxdo not vary with time and nablamiddotJi(r) = 0 The electrostaticpotential is calculated from the Poisson equation

sumε ϕ π ρnablamiddot nabla = minus +r q cr r r( ( ) (( ))) 4 ( ( ) ( ))i

i if

(11)

where ε(r) is the dielectric constant qi is the ion charge andρf(r) is again the (fixed) charge density due to the proteinThe above coupled partial differential equations constitute

the PNP equations and may be solved by a variety of methodsin one or three dimensions Typically the NP and the Poissonequations are solved self-consistently to simultaneously obtainthe electrostatic potential ϕ(r) and the ionic concentration ci(r)under appropriate boundary conditionsModeling ion channels within the PNP framework is

computationally inexpensive compared to MD and BDsimulations because the problem of many-body interactions isavoided through a mean-field approximation An undesirableside-effect is that some important physics is neglected by thisapproximation Below we discuss some of the shortcomings ofthe PNP equations in the context of ion channels as well asextensions to the equations that address these shortcomings

Interested readers are directed to comprehensive reviews onthis subject12299307310478

Prior to the surge of popularity of the all-atom MD methodcontinuum electrodiffusion theories played a major role indevelopment of our understanding of ion fluxes in nano-channels81255 Early attempts to use the electrodiffusion theoryto describe ion flux through nanochannels279minus281286 led to thedevelopment of simplified models based on a self-consistentcombination of the Poisson equation and the NernstminusPlanckequations that were subsequently applied to various channelsystems282minus284 Most of the early studies dealt with either one-dimensional models or simplified geometries that lacked adetailed description of the protein structure and static chargedistribution These studies connected qualitative features of thecurrentminusvoltageminusconcentration relationship to structural andphysical features of the models For example the PNP theorywas used to demonstrate how charges at the channel openingscan produce current rectification285479 as well as how achannel with ion-specific binding sites can exhibit lowerconductance in a mixture of two ion types than in a puresolution of either type480 A lattice-relaxation algorithm able tosolve the PNP equations for a 3D model was developed byKurnikova and co-workers8 in later years This procedure allowsthe protein and the membrane to be mapped onto a 3D cubiclattice with defined dielectric boundaries fixed chargedistribution and a flow region for the ionsLike the PB equation the system of PNP equations

constitutes a mean-field theory that neglects the finite size ofthe ions the dielectric response of the system to an ion andionminusion correlations In fact the PNP equations reduce to thePB equation for systems with zero flux everywhere The validityof a continuum dielectric description and mean-fieldapproaches in the context of narrow pores has been thesubject of much debate For example Chung and co-workersobserved considerable differences between the conductancethrough idealized pores using the BD and PNP ap-proaches287294 The authors argued that the mean-fieldapproximation breaks down in narrow ion channels due to anoverestimation of the screening effect by counterions within thepore Larger channels like porins at physiological or lower ionconcentrations are described quite accurately by the PNPequations However the currents computed based on the PNPmodels can be considerably higher (by 50 for OmpF) than inequivalent BD simulations55

When a charge in a high dielectric medium is brought near alow dielectric medium a repulsive surface charge is induced atthe dielectric boundary In continuum descriptions such as PBand PNP the induced charge density includes (usually)canceling components from both positive and negative averagecharge densities The interaction energy between a charge andits induced charge density is often called the dielectric self-energy The dielectric self-energy due to the average chargedensity and the average induced charge density at the dielectricboundary is in general smaller than the interaction energybetween point charges and corresponding induced chargeaveraged over all configurations Put another way a pointcharge approaching a low dielectric medium is strongly repelledby its induced image charge and this repulsion is largely lost bythe implicit averaging in mean-field descriptionsThe PB and PNP equations have been modified to include

the interaction of an ion with the charge density itinduces11294296 Although the corrections account for theinteraction of an ion with its induced dielectric charge they do

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not account for the interaction of the induced charge with asecond nearby ion Similarly the mean-field approximationinherently ignores effects involving correlations in theinstantaneous ion distribution For example the narrowestportion of the potassium channels almost always contains twoions that move in a concerted fashion (see section 511) whichcannot be properly treated by continuum theories Never-theless it was concluded that the dielectric self-energy accountsfor most of the discrepancy between PNP and BD results in thecase of narrow channels294

Although early electrodiffusion studies of Levitt consideredhard-sphere repulsion between ions by iteratively correcting theion concentration279 many studies have since ignored suchfinite-size effects Recently the PNP equations have beenadapted to incorporate finite-size effects using classical densityfunctional theory to describe many-body hard sphereinteractions between ions and solvent290291300481 Unfortu-nately these approaches often yield cumbersome integro-differential equations Finite-size effects can be included in thePNP equations by introducing an entropic term thatdiscourages solvent crowding by ions309 The latter approachyields a tractable set of corrected PNP equations Both the PNPand BD methods usually ignore thermal fluctuations of theprotein and lipid bilayer However these can be effectivelycaptured by combining results from MD or Monte Carlosimulations with 3-D PNP calculations92

The PNP approach continues to play a major role inimproving our understanding of the physics of ion channelsThe computational efficiency of the PNP model is unparallelledfor studies of ion conductance in a low ion concentrationregime where the PNP method is expected to be the mostaccurate The method is highly efficient at predicting the effectof a channelrsquos geometry on the currentminusvoltage dependence atphysiological voltages and can be used to screen for mutationsthat affect conductance of a channel The calculation of currentscan be quite accurate in the case of larger channels such asporins PNP is perhaps the only method that can presentlysimulate the interplay of ion conductances in an ensemble ofion channels (such as in a realistic biological membrane)explicitly taking the structural features of the channels intoaccount Finally the PNP approach is rather flexible to includedescriptions of additional physical effects for examplehydrodynamic interactions354364369370 or the effect of asemiconductor membrane on the ionic current361382383

42 Brownian Dynamics

The BD method allows for simulations of explicit ionpermeations on the microsecond-to-millisecond time scale bytreating solvent molecules implicitly In a way the BD methodoffers a good compromise between all-atom MD andcontinuum electrodiffusion approaches Computational effi-ciency is achieved by reducing the number of degrees offreedom Typically a moderate number of atoms of interest(usually the ions) are simulated explicitly while the solvent isaccounted for via friction and stochastic random forces that actin addition to the electrostatic and steric forces arising fromother ions the protein and the lipid bilayer For the calculationof electrostatic forces the water the membrane and the proteinchannel are usually treated as continuous dielectric media Thechannel is treated as a rigid structure and thermal fluctuationsare typically ignored Figure 7b schematically illustrates a BDmodel of α-hemolysin

421 General Formulation of the BD Method In theBrownian dynamics method a stochastic equation is integratedforward in time to create trajectories of atoms Theldquouninterestingrdquo degrees of motion usually corresponding tofast-moving solvent molecules are projected out in order todevelop a dynamic equation for the evolution of the ldquorelevantrdquodegrees of freedom The motion of the particles is described bya generalized Langevin equation

int = minus prime minus prime prime +m t dt M t t t tr r f( ) ( ) ( ) ( )i i i

t

i i i0 (12)

The force on the ith particle i is obtained from an effectivepotential = minusnabla r( )i i iThe potential function is a many-body potential of mean

force (PMF) that corresponds to the reversible thermodynamicwork function to assemble the relevant particles in a particularconformation while averaging out the remaining degrees offreedom ie the effect of all other atoms is implicitly present in

r( )i The second term on the right-hand side is thedamping force representing the frictional effect of theenvironment and finally fi(t) is a Gaussian fluctuating forcearising from random collisions The frictional force depends onprevious velocities through the memory kernel Mi(tminustprime) Thefirst and second moments of the random force are given by⟨fi(t)⟩ = 0 and ⟨fi(t)middotfj(0)⟩ = 3kBTMi(t)δij where kB is theBoltzmann constant and T is the temperature Both the dragforce and the stochastic force incorporate the effect of thesolvent In the Markovian limit the memory kernel is a Diracdelta function that leads to the traditional Langevin equation

γ = minus +m t t tr r f( ) ( ) ( )i i i i i i (13)

The friction coefficient γi is related to underlying molecularprocesses via the fluctuationminusdissipation theoremIn the overdamped regime (which applies to the motion of

an ion in water) the inertial term can be ignored so that theLangevin equation is reduced to

ζ = +tD

k Ttr( ) ( )i

ii i

B (14)

where Di = kBTγi is the diffusion coefficient of the ith particleand ζi(t) is a Gaussian random noise with a second momentgiven as ⟨ζi(t)middotζi(0)⟩ = 6Diδ(t)

422 BD Simulations of Ion Channels A Browniandynamics simulation requires two basic ingredients adescription of the forces applied to each ion and the diffusioncoefficient for each ion The diffusion coefficient for the ionsshould be in general position-dependent and can be obtainedfrom all-atom MD simulations373482483 or estimated usinganalytical techniques88484 However in most cases a singleposition-independent diffusion constant is used for all ions ofthe same speciesEach ion experiences a force that depends on its position as

well as the positions of all the other ions in the system Thepotential corresponding to the forces on the ions is the multi-ion PMF which is the multidimensional free energy surfacethat is usually broken into an ionminusion PMF and a PMF due tothe pore the solution and other biomolecules373 The PMFscan be calculated from all-atom MD or even quantumchemistry simulations but such calculations are computation-ally expensive

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A more typical approach was presented by Roux and co-workers which we summarize here556263299 The multi-ionPMF can be written as

sum sum sum

sum ϕ ϕ

= | minus | +

+ +

αα γ α

α γ α γα

α

αα α α

neu U

q

r r r r

r r

( ) ( ) ( )

[ ( ) ( )]

core

sf rf(15)

where uαγ(r) is the ionminusion interaction Ucore is a repulsivepotential preventing the ions from entering the ion-inaccessibleregions ϕsf is the electrostatic potential arising from thepermanent protein charge distribution and ϕrf is the reactionfield potential arising from the electrostatic polarization of thevarious dielectric boundaries The static field may be computedfrom an atomic model of the pore using the PBequations556263485 Any externally imposed transmembranebias may be included in the calculation of the electrostaticpotential Usually the ionminusion interaction includes van derWaals and Coulomb terms

εσ σ

ε= minus +α γ α γ

α γ α γ α γ⎜ ⎟ ⎜ ⎟⎡⎣⎢⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎤⎦⎥u r

r r

q q

r( ) 4

12

6

bulk

where εαγ and σαγ are the parameters for the 6minus12 Lennard-Jones potential qα and qγ are the charges of the ions and εbulk isthe dielectric constant of bulk water The local dielectricconstant of the water in the interior of the pore may beextracted from atomistic simulations but it is usually assumedto have the bulk value of 80 Solvation effects can beapproximately described by including a short-range solvationpotential55287486 but that is rarely done in practice Web-basedinterface for GCMCBD simulations of ion channels hasrecently become available268

Early BD studies were performed using one-dimensionalrepresentations of channels487 Later these were extended tomore realistic three-dimensional geometries although theseoften lacked atomic detail63486 However the X-ray structure ofan ion channel can be used to create a more realistic model ofthe channel by computing electrostatic and core repulsionpotential maps from the all-atom structure Brownian dynamicssimulations have been applied to several biological channelsincluding OmpF5562minus64 K+ channels110minus115117 α-hemoly-sin8895 VDAC268 and gramicidin1617 Roux and co-workershave developed a grand canonical Monte CarloBrowniandynamics method (GCMCBD)6263103 to allow for fluctua-tions in the total number of ions in the system and asymmetricion concentration conditions For detailed treatment of thesubject interested readers are directed to a review of thecomputational methods299473

Recently Comer and Aksimentiev373 used all-atom MD todetermine full three-dimensional PMF maps at atomicresolution for ionminusion and ionminusbiomolecule interactionsthereby fully accounting for short-range effects associationwith solvation of ions and biomolecules Using such full 3-DPMFs in BD simulations of ion flow through a model nanoporecontaining DNA basepair triplets yielded ionic currents in closeagreement with the results of all-atom MD but at a fraction ofthe computational cost The authors indicate that such anatomic-resolution BD method can be developed further toincorporate the conformational flexibility of the pore and DNAby altering the PMF maps on-the-fly

43 All-Atom Molecular Dynamics

The all-atom MD method can provide unparalleled insight intothe physical mechanisms underlying the biological function ofbiomacromolecules By explicitly describing all the atoms of thesystem of interest and the majority of interatomic interactionsthis method has the potential to compete with the experimentin completeness and accuracy of the description of microscopicphenomena In the case of an ion channel one can in principledirectly observe ion conductance and gating at the spatialresolution of a hydrogen atom and the temporal resolution ofsingle femtoseconds Critical to the above statement is theassumption that the all-atom MD method is equipped with acorrect description of interatomic interactions and enoughcomputational power is available Despite ever-increasingavailability of massive parallel computing platforms makingquantitative predictions using MD remains challenging in partdue to imperfections of the interatom interaction modelsBelow we briefly review the formulations of the all-atom MDmethod and describe recent advances in the field

431 General Formulation of the All-Atom MDMethod In the MD simulations of biomacromoleculesatoms are represented as point particles and the connectivity(or covalent bonds) among those atom are given a prioriCovalently bonded atoms interact with each other throughbonded potentials while the other atom pairs interact throughnonbonded potentials

= +U U Ur r r( ) ( ) ( )N N Nbonded nonbonded (16)

where rN denotes the coordinates of N atoms in a systemBonded interactions model quantum mechanical behavior ofcovalently connected atoms by means of harmonic bond angleand improper dihedral angle restraints and periodic dihedralangle potentials

sum sum

sum

sum

θ θ

χ δ

ϕ ϕ

= minus + minus

+ + minus

+ minus

θ

χ

ϕ

U K b b K

K n

K

( ) ( )

1 cos( )

( )

bbondedbonds

02

angles0

2

torsions

impropers0

2

(17)

where Kb and b0 are the bond force constant and theequilibrium distance respectively Kθ and θ0 are the angleforce constant and the equilibrium angle respectively Kχ nand δ are the dihedral force constant the multiplicity and thephase angle respectively and Kϕ and ϕ0 are the improper forceconstant and the equilibrium improper angle488 The non-bonded potential usually consists of the Lennard-Jones (LJ)potential for van der Waals interactions and the Coulombpotential for electrostatic interactions

sum εσ σ

ε= minus +

⎧⎨⎪⎩⎪

⎡

⎣⎢⎢⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤

⎦⎥⎥

⎫⎬⎪⎭⎪

Ur r

q q

r4 ij

ij

ij

ij

ij

i j

ijnonbonded

nonbond

12 6

(18)

where εij is the well depth σij is the finite distance at which theLJ potential is zero rij is the interatomic distance and qij areatomic charges The bonded parameters are empiricallycalibrated based on the quantum mechanical calculations ofsmall molecules whereas the nonbonded parameters are mainlyderived from quantum chemistry calculations (eg partial

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charges) and empirical matching of thermodynamic data (eghydration free energy)A biomolecular force field is a set of bonded and nonbonded

parameters defined in eqs 17 and 18 Presently severalbiomolecular force fields exist The force fields can becategorized into types based on whether all the atoms areexplicitly treated or not All-atom force fields which includeCHARMM489 AMBER490491 and OPLS-AA492493 treat allatoms explicitly In the united-atom force fields (egGROMOS494495) some nonpolar hydrogen atoms areneglectedFor the simulations of channel proteins a lipid force field is

as important as a protein force field because the channels areembedded in lipid bilayers Among the all-atom force fields theCHARMM force field includes parameters for lipids the latestupdate at the time of writing this review is CHARMM36496

Together with the AMBER force field for the protein thegeneral all-atom AMBER force field (GAFF) can be used todescribe the lipid bilayer497498 Officially OPLS does notinclude lipid parameters Among the united-atom force fieldsGROMOS comes with lipid parameters499 Berger et alreported improved GROMOS-based lipid parameters basedon the condensed-phase properties of pentadecane500 Thislipid force field has been widely used in combination with otherprotein force fields such as AMBER OPLS and GROMOS501

For an in-depth review of various force fields we referinterested readers to a comprehensive review by Mackerell488

432 Ion Channels in Native Environment Unlikesoluble proteins that are surrounded only by water ion-channelproteins are embedded in a lipid bilayer and therefore are incontact with both water and lipids Because of the drasticallydifferent chemical and electrostatic properties of lipid andwater proper descriptions of proteinminuslipid and proteinminuswaterinteractions are key for the successful simulation of amembrane channel To model ion conduction through arelatively rigid channel (eg gA or KcsA channel) it is possibleto use an implicit solvent model of the channelrsquos environmentin which the volume occupied by lipid and water is treated ascontinuum media of dielectric constants 2 and 78 respec-tively299 However when interactions between a channel and alipid membrane are significant (eg in mechanosensitivechannels) explicit modeling of lipid molecules is essentialThe tails of lipids are long and equilibrate slowly making it

significantly more difficult to assemble a model of a channelembedded in an explicit lipid bilayer than a model of a fullysoluble protein Usually the system setup involves thefollowing steps Starting from a pre-equilibrated and solvatedlipid bilayer membrane one makes a pore in the bilayer bydeleting a minimal number of lipid molecules so that theprotein can fit Next an all-atom model of the protein is placedin the pore which is followed by energy minimization andequilibration of the system using the MD method having thechannelrsquos coordinates restrained to their crystallographic valuesFinally when the proteinminuslipid interface is well equilibratedone can perform a production run without applying restraintson the channel For detailed step-by-step instructions forbuilding atomic-scale models of ion channels in lipid bilayerenvironment interested readers are directed to a tutorial onMD simulations of membrane proteins502 Even though a fullyautomated procedure is not yet available several programs canassist a beginner in building a new system VMD503 containsthe Membrane Builder plugin Jo et al have a web-based

service CHARMM GUI Membrane Builder (httpwwwcharmm-guiorgmembrane)504505

An alternative method for creating an all-atom model of anion channel in its native environment is to first carry out self-assembly simulations using a coarse-grained (CG) MDmethod74165379 The main difference between the CG andall-atom MD methods is the level of detail used to describe thecomponents of the system Typically one CG bead representsabout 5minus10 atoms Being much more computationally efficient(and lower resolution) the CG model allows millisecond-time-scale simulations to be performed on commodity computersInterested readers are directed toward recent reviews on thissubject506minus508

In the CG simulations of self-assembly CG models of lipidssolvent and a membrane protein are placed with randompositions in desired proportions During the course of CGMDsimulations the lipid molecules spontaneously form a lipidbilayer around a protein After obtaining a stable model the CGmodel can be reverse-coarse-grained into a fully atomisticmodel (see for example a study by Maffeo and Aksimen-tiev330) A great advantage of this approach is that it requiresno a priori knowledge of the position of the membranechannels relative to the membrane An obvious disadvantage isthat one has to have a reasonable CG model to carry out theself-assembly simulations and a reliable procedure to recoverthe all-atom details from the final CG model Currently it isnot possible to use a CG approach to model ion conductancethrough large membrane channels due to inaccurate treatmentsof the membrane and water electrostatics in most CG modelsHowever work to improve CG methods is ongoing509510 andsuch simulations should become possible in the near future

433 Homology Modeling Usually an all-atom MDsimulation of a channel protein can be performed only when anatomic-resolution structure of the channel is available Thisrequirement severely limits application of the MD methodFortunately membrane channels of different organisms oftenhave similar amino-acid sequences The sequence similarity canbe used to build an all-atom model of the channel that does nothave an experimentally determined structure through aprocedure called homology modeling511 Briefly homologymodeling proceeds as follows First a sequence alignmentbetween a target sequence and a homologous sequenceforwhich a structure is knownis performed Second thesecondary structures (eg α-helices and β-sheets) of the targetsequence from the homologous sequence are built Finallyloops connecting the secondary structures are modeled and theoverall structure is refined There exist many tools for thehomology modeling (eg Modeler by Sali and Blundell511)The homology modeling method has been successfully used

for building initial structures of several ion channels forsubsequent all-atom MD simulations Capener et al512 built aninward rectifier potassium channel (Kir) based on a high-resolution structure of KcsA1 Sukharev et al used the crystalstructure of Mycobacterium tuberculosis MscL407 to modelclosed intermediate and open structures of Escherichia coliMscL231232 Law et al combined the crystal structure of theLymnea stagnalis acetylcholine binding protein and the electronmicroscopy (EM) structure of the transmembrane domain ofthe torpedo electric ray nicotinic channel to build an entirehuman nicotinic acetylcholine receptor213

434 Free-Energy Methods Perhaps the greatestdisadvantage of the MD method is that simulations are costlyand are currently limited to the microsecond time scalea

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through their outer wall which is a process facilitated by porinsPorin alteration has been implicated in antibiotic resistance444

In addition engineered porins such as the OmpG havepotential for use as stochastic sensors77

Functionally related to porins α-hemolysina toxinproduced by Staphylococcus aureusis secreted as a monomerbut assembles on target cell membranes to form ahomoheptameric channel which leads to an uncontrolledpermeation of ions and small molecules and causes cell lysisThe X-ray structure of α-hemolysin445 revealed a mushroom-like shape with a β-barrel stem protruding from its cap domainsee Figure 4k Its ability to self-assemble in biological orsynthetic membranes and its structural stability over a widerange of ion concentrations temperatures and pHs make α-hemolysin an excellent platform for stochastic sensingapplications446 including detection of DNA sequence bymeasuring the ionic current447 An interesting feature is therectification behavior of the channel which has been exploredby both implicit solvent88 as well as all-atom MDsimulations9093

Another large water-filled biological nanopore is MspAthemajor outer-membrane porin of Mycobacterium smegmatis thatallows the uptake of hydrophilic nutrients from the environ-ment The crystal structure of MspA448 revealed a homo-octameric goblet-like structure with a central channel Theporin has a constriction that is lined by two belts of aspartateresidues (Asp90 and Asp91) that diminish the permeability ofnonpolar solutes Genetically modified variants of the MspAchannel may enable practical nanopore DNA sequencing449450

as they provide superior ionic current signals for nucleic aciddetection if compared with α-hemolysin451

35 Other Channels

The voltage-dependent anion channel (VDAC) residing in themitochondrial outer membrane serves as a conduit formetabolites and electrolytes VDACs mediate the passage ofions such as K+ Clminus and Ca2+ and small hydrophilic moleculessuch as ATP between the cytosol and the mitochondria andregulate the release of apoptotic proteins The pore has avoltage-dependent conductance with an anion-selective high-conductance state at low transmembrane potential and aslightly cation-selective low-conductance state at high poten-tial452 Several NMR and X-ray structures of human as well asmouse VDACs453minus455 have become available Initially thesignificance of these structures was questioned on account of anapparent conflict with biochemical and functional data456

However additional NMR457458 and theoretical stud-ies259262268 have shed light on the structureminusfunction relationreaffirming the biological relevance of the structuresThe ClC chloride channels found in both prokaryotic and

eukaryotic cells control the selective flow of Clminus ions and arebelieved to play an important role in regulation of bloodpressure pH and membrane excitability These channelsconduct not just Clminus but also other anions such as HCO3

minusSCNminus and NOminus Unlike cation channels they do notdiscriminate strongly between different species of anionsDefects in these channels are implicated in several diseasessuch as myotonia congenita Bartterrsquos syndrome andepilepsy459 In the past decade structures of ClC orthologuesfrom two bacterial species Salmonella serovar typhimurium andEscherichia coli have become available460 The X-ray structuresreveal the ClC channels to be homodimers with two identicalbut independent pores see Figure 4j Some prokaryotic

members of the ClC family of channels are now believed tobe ion transporters although the line between ion channels andtransporters is getting blurred461 There have been a fewsimulation studies of the permeation pathways260261 of the ClCchannelsThe nicotinic acetylcholine receptor (nAChR) belongs to a

superfamily of Cys-loop ligand-gated ion channels It couples acationic transmembrane ion channel with binding sites for theneurotransmitter acetylcholine (ACh) so that the gating of thechannel is linked to the binding of ACh The nAChR owes itsname to the ability of nicotine to mimic the effects of ACh inopening up the pore The nAChR is composed of a ring of fiveprotein subunits with three domains a large N-terminalextracellular ligand binding domain (LBD) a transmembranedomain (TM) and a small intracellular domain see Figure 4hThere are two ACh binding sites in the ligand-binding domainthe pore opens when both are occupied414 Although thecomplete high-resolution structure of the nAChR is absent atpresent X-ray and electron microscopy structures of some of itscomponents are available413414 The nAChR plays a critical rolein neuronal communication converting neurotransmitter bind-ing into membrane electric depolarization The channel isfound in high concentrations at the nerveminusmuscle synapsenAChR is implicated in a variety of diseases of the centralnervous system including Alzheimerrsquos disease Parkinsonrsquosdisease schizophrenia and epilepsy462 It is also believed toplay a critical role in mediating nicotine reward andaddiction463 Although detailed study of the gating mechanismis precluded by the lack of a complete structure of the nAChRas well as the time scales involved there have been severalstudies on the TM domain215212 and the LBD218

AmtB is a representative bacterial ammonium transporterwhich belongs to AmtMEP family464 Some bacteria andplants use ammonium as a nitrogen source and have variousforms of transporters for the uptake of ammonium464465 At thesame time ammonium is also a toxic metabolic waste whichshould be removed quickly by transporters usually formammals466 There exist several high-resolution crystalstructures of bacterial AmtB409467minus470 The Escherichia colicrystal structure (Figure 4d) has become the paradigm for thestudy of the transport mechanism of ammonium409 UsuallyAmtB proteins are crystallized as a homotrimer Each monomerconsists of 11 transmembrane helices that form a channel forammonium The channel is highly hydrophobic raising thepossibility that ammonium passes the channel in a deproto-nated form (ammonia)

4 MOST COMMON SIMULATION METHODSAmong a large number of computational approaches proposedand employed for studies of ion channels most fall within thefollowing three categories all-atom molecular dynamics (MD)which is a fully microscopic description with all atoms treatedexplicitly Brownian dynamics (BD) in which only the ions aretreated explicitly while the solvent and the protein and lipidsare represented implicitly and approaches based on PoissonminusNernstminusPlanck (PNP) theory in which the ionic concentrationis treated as a continuum Each of the three approaches haslimitations and advantages The MD method is considered themost computationally expensive but also the most accurateThe PNP and BD approaches are in general less computa-tionally expensive but also provide less detail At the same timethe MD method has the smallest temporal and spatial rangefollowed by BD methods followed by PNP approaches Figure

Chemical Reviews Review

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7 schematically illustrates typical setups for the three modelingapproaches applied to the same systemThe above classification however is rather approximate and

can be misleading Thus the level of computational complexityoften depends on the desired level of detail whereas theaccuracy depends on the assumptions made in deriving theparameters of the model Even the most sophisticated MDsimulations rely on the MD force field which is a classicalmodel that may or may not be adequate for describing a certainphenomenon In this respect full quantum or combinedquantum mechanicsclassical mechanics approaches (QMMM) can in principle provide the highest degree of accuracyHowever the time scale accessible to these methods is severelylimiting Interested readers are directed to reviews of QMMMapproaches for simulations of biomolecules471472 and to arecent review of computational approaches to ion transport innanopores473 On the other hand it is possible to incorporateatomic-level details in BD and even PNP approaches see forexample recent work by Comer Carr and co-workers371373

Other considerations often neglected when evaluating theldquocomputational costrdquo of a certain approach are the qualificationsand ambitions of the researcher performing the modeling tasksand the availability of well-documented and ready-to-use codesFor example it is always possible to increase the computationalcomplexity of the problem by including an exorbitant amountof water in an all-atom simulation or using very fine mesh sizein continuum calculations One could also easily spend severalmonths writing debugging or porting a computationallyefficient code while the same time could have been used torun a more computationally intensive but ready-to-use andtested code Thus there are no simple rules in choosing anoptimal simulation method and researchers new to the field areurged to seek expert advice for their particular problem

41 Continuum Models

Ion channels are complex systems with many degrees offreedom and hence are challenging to model in atomisticdetail Continuum theories based on PoissonminusBoltzmann (PB)and PoissonminusNernstminusPlanck (PNP) equations are powerfultools that make simulation of such systems tractable The mainidea is to employ a continuum description for all componentsof the system ie the solvent the ions and the ion channelThe water the membrane and the channel are represented asfixed structureless dielectrics while the ions are described byspecifying the local density throughout the system Figure 7aschematically illustrates a PNP model of α-hemolysin

411 Electrostatics of Ion Channels The PB equation isthe most popular theoretical model for describing theelectrostatics around a charged biomolecule in ionic solutionIn a system of interacting mobile charged particles theelectrostatic potential arises due to the combined effect of thecharged biomolecules ions and dielectric properties of theenvironment The PB model assumes that the distribution ofcharges in the system is related to the electrostatic potentialaccording to Boltzmann statistics For the purpose of describingelectrostatics of a single biomolecule the PB equation whichwas first introduced independently by Gouy (1910) andChapman (1913) and later generalized by Debye and Huckel(1923) is most frequently written as

sumε ψ πρ π

ψλ

nablamiddot nabla = minus minus

minus

infin

⎛⎝⎜

⎞⎠⎟

c z q

z qk T

r r r

rr

( ( ) ( )) 4 ( ) 4

exp( )

( )

ii i

i

f

B (8)

where ε(r) is the position-dependent dielectric constant ψ(r) isthe electrostatic potential ρf(r) is the fixed charge density ofthe biomolecule ci

infin represents the concentration of ion speciesi at infinite distance from the biomolecule zi is the valency ofion species i q is the proton charge kB is the Boltzmannconstant T is the temperature and λ(r) describes theaccessibility of position r to ions (for example it is oftenassumed to be zero inside the biomolecule) A solution to thePB equation gives the electrostatic potential and equilibriumdensity of ions throughout the space The PB equation invokesa mean-field approximation that neglects nonelectrostatic ionminusion interactions (eg van der Waals or water-mediated) thedielectric response of the system to each ion and effects due tocorrelations in the instantaneous distribution of ions Becauseof these the PB equation fails to describe the electrostatics ofhighly charged objects such as DNA in high-concentration ionsolutions with quantitative accuracy474 In the context of ionchannels which rarely carry such a high charge density the PBtheory has been widely used to calculate the free energy cost oftransferring a charge from bulk solution to the interior of thechannel105287 (see Table 1) to characterize ion-channelinteractions88294 and to compute the distribution of thetransmembrane electrostatic potential103104294299 Such con-tinuum electrostatic calculations have also been used toestimate the relative stability of protonated and unprotonatedstates of ionizable residues in an ion channel (discussed in refs

Figure 7 Schematic illustrations of the PNP (a) BD (b) and all-atom MD (c) modeling methods applied to the same systeman α-hemolysinchannel embedded in a lipid bilayer membrane and surrounded by an electrolyte solution In panel (a) the ions are described as continuous densitywhereas the water protein and membrane are treated as continuum dielectric media In the BD model (panel b) only ions are represented explicitlywhereas all other components are either implicitly modeled or approximated by continuum media All atoms are treated explicitly in the all-atom MDmethod (panel c)

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61 and 475) DelPhi476 and APBS477 are two popular computercodes for numerically solving the PB equation412 Ion Transport Although the PB model provides

insights into the equilibrium energetics of an ion channelmodeling of the ion flux requires a nonequilibrium approach Inmost ion channels the time scale of ion permeation rangesfrom tens of nanoseconds (porins) to microseconds and evenmilliseconds (in active transport) Thus observing a statisticallysignificant number of ion-permeation events requires longtrajectories that are still rather expensive to obtain using an all-atom approach The PoissonminusNernstminusPlanck model givesaccess to long time scales albeit at lower temporal and spatialresolutions As in the PB model the lipid protein and watermolecules are approximated as dielectric continua while ionsare described as continuous density distributions The currentdensity is obtained from the NernstminusPlanck (NP) theorywhich is widely used in studies of electrolyte transport In theNP theory ion fluxes arise from two sources the gradient ofion concentration and the gradient of the electrostatic potentialTraditional NernstminusPlanck equations do not describe ion-channel interactions However the classical NernstminusPlanckequations may be modified to include the ion-channelinteractions via an effective potential Thus the flux of ionspecies i Ji is written as

= minus nabla + nabla⎛⎝⎜

⎞⎠⎟t D c t

c tk T

J r r rr

r( ) ( ) ( )( )

( )i i ii

iB

eff

(9)

where Di and ci are the diffusion constant and the numberdensity of ion species i respectively and r( )i

eff is theeffective potential that usually combines the electrostaticpotential ϕ(r) and a core-repulsive potential UCore(r) withthe latter describing interactions between ions and the proteinchannel and not between the ions themselvesThe concentration and the flux of each ionic species obey the

continuity equation

partpart

+ nablamiddot =c t

tt

rJ r

( )( ) 0i

i (10)

Under steady-state conditions the concentration and the fluxdo not vary with time and nablamiddotJi(r) = 0 The electrostaticpotential is calculated from the Poisson equation

sumε ϕ π ρnablamiddot nabla = minus +r q cr r r( ( ) (( ))) 4 ( ( ) ( ))i

i if

(11)

where ε(r) is the dielectric constant qi is the ion charge andρf(r) is again the (fixed) charge density due to the proteinThe above coupled partial differential equations constitute

the PNP equations and may be solved by a variety of methodsin one or three dimensions Typically the NP and the Poissonequations are solved self-consistently to simultaneously obtainthe electrostatic potential ϕ(r) and the ionic concentration ci(r)under appropriate boundary conditionsModeling ion channels within the PNP framework is

computationally inexpensive compared to MD and BDsimulations because the problem of many-body interactions isavoided through a mean-field approximation An undesirableside-effect is that some important physics is neglected by thisapproximation Below we discuss some of the shortcomings ofthe PNP equations in the context of ion channels as well asextensions to the equations that address these shortcomings

Interested readers are directed to comprehensive reviews onthis subject12299307310478

Prior to the surge of popularity of the all-atom MD methodcontinuum electrodiffusion theories played a major role indevelopment of our understanding of ion fluxes in nano-channels81255 Early attempts to use the electrodiffusion theoryto describe ion flux through nanochannels279minus281286 led to thedevelopment of simplified models based on a self-consistentcombination of the Poisson equation and the NernstminusPlanckequations that were subsequently applied to various channelsystems282minus284 Most of the early studies dealt with either one-dimensional models or simplified geometries that lacked adetailed description of the protein structure and static chargedistribution These studies connected qualitative features of thecurrentminusvoltageminusconcentration relationship to structural andphysical features of the models For example the PNP theorywas used to demonstrate how charges at the channel openingscan produce current rectification285479 as well as how achannel with ion-specific binding sites can exhibit lowerconductance in a mixture of two ion types than in a puresolution of either type480 A lattice-relaxation algorithm able tosolve the PNP equations for a 3D model was developed byKurnikova and co-workers8 in later years This procedure allowsthe protein and the membrane to be mapped onto a 3D cubiclattice with defined dielectric boundaries fixed chargedistribution and a flow region for the ionsLike the PB equation the system of PNP equations

constitutes a mean-field theory that neglects the finite size ofthe ions the dielectric response of the system to an ion andionminusion correlations In fact the PNP equations reduce to thePB equation for systems with zero flux everywhere The validityof a continuum dielectric description and mean-fieldapproaches in the context of narrow pores has been thesubject of much debate For example Chung and co-workersobserved considerable differences between the conductancethrough idealized pores using the BD and PNP ap-proaches287294 The authors argued that the mean-fieldapproximation breaks down in narrow ion channels due to anoverestimation of the screening effect by counterions within thepore Larger channels like porins at physiological or lower ionconcentrations are described quite accurately by the PNPequations However the currents computed based on the PNPmodels can be considerably higher (by 50 for OmpF) than inequivalent BD simulations55

When a charge in a high dielectric medium is brought near alow dielectric medium a repulsive surface charge is induced atthe dielectric boundary In continuum descriptions such as PBand PNP the induced charge density includes (usually)canceling components from both positive and negative averagecharge densities The interaction energy between a charge andits induced charge density is often called the dielectric self-energy The dielectric self-energy due to the average chargedensity and the average induced charge density at the dielectricboundary is in general smaller than the interaction energybetween point charges and corresponding induced chargeaveraged over all configurations Put another way a pointcharge approaching a low dielectric medium is strongly repelledby its induced image charge and this repulsion is largely lost bythe implicit averaging in mean-field descriptionsThe PB and PNP equations have been modified to include

the interaction of an ion with the charge density itinduces11294296 Although the corrections account for theinteraction of an ion with its induced dielectric charge they do

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXJ

not account for the interaction of the induced charge with asecond nearby ion Similarly the mean-field approximationinherently ignores effects involving correlations in theinstantaneous ion distribution For example the narrowestportion of the potassium channels almost always contains twoions that move in a concerted fashion (see section 511) whichcannot be properly treated by continuum theories Never-theless it was concluded that the dielectric self-energy accountsfor most of the discrepancy between PNP and BD results in thecase of narrow channels294

Although early electrodiffusion studies of Levitt consideredhard-sphere repulsion between ions by iteratively correcting theion concentration279 many studies have since ignored suchfinite-size effects Recently the PNP equations have beenadapted to incorporate finite-size effects using classical densityfunctional theory to describe many-body hard sphereinteractions between ions and solvent290291300481 Unfortu-nately these approaches often yield cumbersome integro-differential equations Finite-size effects can be included in thePNP equations by introducing an entropic term thatdiscourages solvent crowding by ions309 The latter approachyields a tractable set of corrected PNP equations Both the PNPand BD methods usually ignore thermal fluctuations of theprotein and lipid bilayer However these can be effectivelycaptured by combining results from MD or Monte Carlosimulations with 3-D PNP calculations92

The PNP approach continues to play a major role inimproving our understanding of the physics of ion channelsThe computational efficiency of the PNP model is unparallelledfor studies of ion conductance in a low ion concentrationregime where the PNP method is expected to be the mostaccurate The method is highly efficient at predicting the effectof a channelrsquos geometry on the currentminusvoltage dependence atphysiological voltages and can be used to screen for mutationsthat affect conductance of a channel The calculation of currentscan be quite accurate in the case of larger channels such asporins PNP is perhaps the only method that can presentlysimulate the interplay of ion conductances in an ensemble ofion channels (such as in a realistic biological membrane)explicitly taking the structural features of the channels intoaccount Finally the PNP approach is rather flexible to includedescriptions of additional physical effects for examplehydrodynamic interactions354364369370 or the effect of asemiconductor membrane on the ionic current361382383

42 Brownian Dynamics

The BD method allows for simulations of explicit ionpermeations on the microsecond-to-millisecond time scale bytreating solvent molecules implicitly In a way the BD methodoffers a good compromise between all-atom MD andcontinuum electrodiffusion approaches Computational effi-ciency is achieved by reducing the number of degrees offreedom Typically a moderate number of atoms of interest(usually the ions) are simulated explicitly while the solvent isaccounted for via friction and stochastic random forces that actin addition to the electrostatic and steric forces arising fromother ions the protein and the lipid bilayer For the calculationof electrostatic forces the water the membrane and the proteinchannel are usually treated as continuous dielectric media Thechannel is treated as a rigid structure and thermal fluctuationsare typically ignored Figure 7b schematically illustrates a BDmodel of α-hemolysin

421 General Formulation of the BD Method In theBrownian dynamics method a stochastic equation is integratedforward in time to create trajectories of atoms Theldquouninterestingrdquo degrees of motion usually corresponding tofast-moving solvent molecules are projected out in order todevelop a dynamic equation for the evolution of the ldquorelevantrdquodegrees of freedom The motion of the particles is described bya generalized Langevin equation

int = minus prime minus prime prime +m t dt M t t t tr r f( ) ( ) ( ) ( )i i i

t

i i i0 (12)

The force on the ith particle i is obtained from an effectivepotential = minusnabla r( )i i iThe potential function is a many-body potential of mean

force (PMF) that corresponds to the reversible thermodynamicwork function to assemble the relevant particles in a particularconformation while averaging out the remaining degrees offreedom ie the effect of all other atoms is implicitly present in

r( )i The second term on the right-hand side is thedamping force representing the frictional effect of theenvironment and finally fi(t) is a Gaussian fluctuating forcearising from random collisions The frictional force depends onprevious velocities through the memory kernel Mi(tminustprime) Thefirst and second moments of the random force are given by⟨fi(t)⟩ = 0 and ⟨fi(t)middotfj(0)⟩ = 3kBTMi(t)δij where kB is theBoltzmann constant and T is the temperature Both the dragforce and the stochastic force incorporate the effect of thesolvent In the Markovian limit the memory kernel is a Diracdelta function that leads to the traditional Langevin equation

γ = minus +m t t tr r f( ) ( ) ( )i i i i i i (13)

The friction coefficient γi is related to underlying molecularprocesses via the fluctuationminusdissipation theoremIn the overdamped regime (which applies to the motion of

an ion in water) the inertial term can be ignored so that theLangevin equation is reduced to

ζ = +tD

k Ttr( ) ( )i

ii i

B (14)

where Di = kBTγi is the diffusion coefficient of the ith particleand ζi(t) is a Gaussian random noise with a second momentgiven as ⟨ζi(t)middotζi(0)⟩ = 6Diδ(t)

422 BD Simulations of Ion Channels A Browniandynamics simulation requires two basic ingredients adescription of the forces applied to each ion and the diffusioncoefficient for each ion The diffusion coefficient for the ionsshould be in general position-dependent and can be obtainedfrom all-atom MD simulations373482483 or estimated usinganalytical techniques88484 However in most cases a singleposition-independent diffusion constant is used for all ions ofthe same speciesEach ion experiences a force that depends on its position as

well as the positions of all the other ions in the system Thepotential corresponding to the forces on the ions is the multi-ion PMF which is the multidimensional free energy surfacethat is usually broken into an ionminusion PMF and a PMF due tothe pore the solution and other biomolecules373 The PMFscan be calculated from all-atom MD or even quantumchemistry simulations but such calculations are computation-ally expensive

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dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXK

A more typical approach was presented by Roux and co-workers which we summarize here556263299 The multi-ionPMF can be written as

sum sum sum

sum ϕ ϕ

= | minus | +

+ +

αα γ α

α γ α γα

α

αα α α

neu U

q

r r r r

r r

( ) ( ) ( )

[ ( ) ( )]

core

sf rf(15)

where uαγ(r) is the ionminusion interaction Ucore is a repulsivepotential preventing the ions from entering the ion-inaccessibleregions ϕsf is the electrostatic potential arising from thepermanent protein charge distribution and ϕrf is the reactionfield potential arising from the electrostatic polarization of thevarious dielectric boundaries The static field may be computedfrom an atomic model of the pore using the PBequations556263485 Any externally imposed transmembranebias may be included in the calculation of the electrostaticpotential Usually the ionminusion interaction includes van derWaals and Coulomb terms

εσ σ

ε= minus +α γ α γ

α γ α γ α γ⎜ ⎟ ⎜ ⎟⎡⎣⎢⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎤⎦⎥u r

r r

q q

r( ) 4

12

6

bulk

where εαγ and σαγ are the parameters for the 6minus12 Lennard-Jones potential qα and qγ are the charges of the ions and εbulk isthe dielectric constant of bulk water The local dielectricconstant of the water in the interior of the pore may beextracted from atomistic simulations but it is usually assumedto have the bulk value of 80 Solvation effects can beapproximately described by including a short-range solvationpotential55287486 but that is rarely done in practice Web-basedinterface for GCMCBD simulations of ion channels hasrecently become available268

Early BD studies were performed using one-dimensionalrepresentations of channels487 Later these were extended tomore realistic three-dimensional geometries although theseoften lacked atomic detail63486 However the X-ray structure ofan ion channel can be used to create a more realistic model ofthe channel by computing electrostatic and core repulsionpotential maps from the all-atom structure Brownian dynamicssimulations have been applied to several biological channelsincluding OmpF5562minus64 K+ channels110minus115117 α-hemoly-sin8895 VDAC268 and gramicidin1617 Roux and co-workershave developed a grand canonical Monte CarloBrowniandynamics method (GCMCBD)6263103 to allow for fluctua-tions in the total number of ions in the system and asymmetricion concentration conditions For detailed treatment of thesubject interested readers are directed to a review of thecomputational methods299473

Recently Comer and Aksimentiev373 used all-atom MD todetermine full three-dimensional PMF maps at atomicresolution for ionminusion and ionminusbiomolecule interactionsthereby fully accounting for short-range effects associationwith solvation of ions and biomolecules Using such full 3-DPMFs in BD simulations of ion flow through a model nanoporecontaining DNA basepair triplets yielded ionic currents in closeagreement with the results of all-atom MD but at a fraction ofthe computational cost The authors indicate that such anatomic-resolution BD method can be developed further toincorporate the conformational flexibility of the pore and DNAby altering the PMF maps on-the-fly

43 All-Atom Molecular Dynamics

The all-atom MD method can provide unparalleled insight intothe physical mechanisms underlying the biological function ofbiomacromolecules By explicitly describing all the atoms of thesystem of interest and the majority of interatomic interactionsthis method has the potential to compete with the experimentin completeness and accuracy of the description of microscopicphenomena In the case of an ion channel one can in principledirectly observe ion conductance and gating at the spatialresolution of a hydrogen atom and the temporal resolution ofsingle femtoseconds Critical to the above statement is theassumption that the all-atom MD method is equipped with acorrect description of interatomic interactions and enoughcomputational power is available Despite ever-increasingavailability of massive parallel computing platforms makingquantitative predictions using MD remains challenging in partdue to imperfections of the interatom interaction modelsBelow we briefly review the formulations of the all-atom MDmethod and describe recent advances in the field

431 General Formulation of the All-Atom MDMethod In the MD simulations of biomacromoleculesatoms are represented as point particles and the connectivity(or covalent bonds) among those atom are given a prioriCovalently bonded atoms interact with each other throughbonded potentials while the other atom pairs interact throughnonbonded potentials

= +U U Ur r r( ) ( ) ( )N N Nbonded nonbonded (16)

where rN denotes the coordinates of N atoms in a systemBonded interactions model quantum mechanical behavior ofcovalently connected atoms by means of harmonic bond angleand improper dihedral angle restraints and periodic dihedralangle potentials

sum sum

sum

sum

θ θ

χ δ

ϕ ϕ

= minus + minus

+ + minus

+ minus

θ

χ

ϕ

U K b b K

K n

K

( ) ( )

1 cos( )

( )

bbondedbonds

02

angles0

2

torsions

impropers0

2

(17)

where Kb and b0 are the bond force constant and theequilibrium distance respectively Kθ and θ0 are the angleforce constant and the equilibrium angle respectively Kχ nand δ are the dihedral force constant the multiplicity and thephase angle respectively and Kϕ and ϕ0 are the improper forceconstant and the equilibrium improper angle488 The non-bonded potential usually consists of the Lennard-Jones (LJ)potential for van der Waals interactions and the Coulombpotential for electrostatic interactions

sum εσ σ

ε= minus +

⎧⎨⎪⎩⎪

⎡

⎣⎢⎢⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤

⎦⎥⎥

⎫⎬⎪⎭⎪

Ur r

q q

r4 ij

ij

ij

ij

ij

i j

ijnonbonded

nonbond

12 6

(18)

where εij is the well depth σij is the finite distance at which theLJ potential is zero rij is the interatomic distance and qij areatomic charges The bonded parameters are empiricallycalibrated based on the quantum mechanical calculations ofsmall molecules whereas the nonbonded parameters are mainlyderived from quantum chemistry calculations (eg partial

Chemical Reviews Review

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charges) and empirical matching of thermodynamic data (eghydration free energy)A biomolecular force field is a set of bonded and nonbonded

parameters defined in eqs 17 and 18 Presently severalbiomolecular force fields exist The force fields can becategorized into types based on whether all the atoms areexplicitly treated or not All-atom force fields which includeCHARMM489 AMBER490491 and OPLS-AA492493 treat allatoms explicitly In the united-atom force fields (egGROMOS494495) some nonpolar hydrogen atoms areneglectedFor the simulations of channel proteins a lipid force field is

as important as a protein force field because the channels areembedded in lipid bilayers Among the all-atom force fields theCHARMM force field includes parameters for lipids the latestupdate at the time of writing this review is CHARMM36496

Together with the AMBER force field for the protein thegeneral all-atom AMBER force field (GAFF) can be used todescribe the lipid bilayer497498 Officially OPLS does notinclude lipid parameters Among the united-atom force fieldsGROMOS comes with lipid parameters499 Berger et alreported improved GROMOS-based lipid parameters basedon the condensed-phase properties of pentadecane500 Thislipid force field has been widely used in combination with otherprotein force fields such as AMBER OPLS and GROMOS501

For an in-depth review of various force fields we referinterested readers to a comprehensive review by Mackerell488

432 Ion Channels in Native Environment Unlikesoluble proteins that are surrounded only by water ion-channelproteins are embedded in a lipid bilayer and therefore are incontact with both water and lipids Because of the drasticallydifferent chemical and electrostatic properties of lipid andwater proper descriptions of proteinminuslipid and proteinminuswaterinteractions are key for the successful simulation of amembrane channel To model ion conduction through arelatively rigid channel (eg gA or KcsA channel) it is possibleto use an implicit solvent model of the channelrsquos environmentin which the volume occupied by lipid and water is treated ascontinuum media of dielectric constants 2 and 78 respec-tively299 However when interactions between a channel and alipid membrane are significant (eg in mechanosensitivechannels) explicit modeling of lipid molecules is essentialThe tails of lipids are long and equilibrate slowly making it

significantly more difficult to assemble a model of a channelembedded in an explicit lipid bilayer than a model of a fullysoluble protein Usually the system setup involves thefollowing steps Starting from a pre-equilibrated and solvatedlipid bilayer membrane one makes a pore in the bilayer bydeleting a minimal number of lipid molecules so that theprotein can fit Next an all-atom model of the protein is placedin the pore which is followed by energy minimization andequilibration of the system using the MD method having thechannelrsquos coordinates restrained to their crystallographic valuesFinally when the proteinminuslipid interface is well equilibratedone can perform a production run without applying restraintson the channel For detailed step-by-step instructions forbuilding atomic-scale models of ion channels in lipid bilayerenvironment interested readers are directed to a tutorial onMD simulations of membrane proteins502 Even though a fullyautomated procedure is not yet available several programs canassist a beginner in building a new system VMD503 containsthe Membrane Builder plugin Jo et al have a web-based

service CHARMM GUI Membrane Builder (httpwwwcharmm-guiorgmembrane)504505

An alternative method for creating an all-atom model of anion channel in its native environment is to first carry out self-assembly simulations using a coarse-grained (CG) MDmethod74165379 The main difference between the CG andall-atom MD methods is the level of detail used to describe thecomponents of the system Typically one CG bead representsabout 5minus10 atoms Being much more computationally efficient(and lower resolution) the CG model allows millisecond-time-scale simulations to be performed on commodity computersInterested readers are directed toward recent reviews on thissubject506minus508

In the CG simulations of self-assembly CG models of lipidssolvent and a membrane protein are placed with randompositions in desired proportions During the course of CGMDsimulations the lipid molecules spontaneously form a lipidbilayer around a protein After obtaining a stable model the CGmodel can be reverse-coarse-grained into a fully atomisticmodel (see for example a study by Maffeo and Aksimen-tiev330) A great advantage of this approach is that it requiresno a priori knowledge of the position of the membranechannels relative to the membrane An obvious disadvantage isthat one has to have a reasonable CG model to carry out theself-assembly simulations and a reliable procedure to recoverthe all-atom details from the final CG model Currently it isnot possible to use a CG approach to model ion conductancethrough large membrane channels due to inaccurate treatmentsof the membrane and water electrostatics in most CG modelsHowever work to improve CG methods is ongoing509510 andsuch simulations should become possible in the near future

433 Homology Modeling Usually an all-atom MDsimulation of a channel protein can be performed only when anatomic-resolution structure of the channel is available Thisrequirement severely limits application of the MD methodFortunately membrane channels of different organisms oftenhave similar amino-acid sequences The sequence similarity canbe used to build an all-atom model of the channel that does nothave an experimentally determined structure through aprocedure called homology modeling511 Briefly homologymodeling proceeds as follows First a sequence alignmentbetween a target sequence and a homologous sequenceforwhich a structure is knownis performed Second thesecondary structures (eg α-helices and β-sheets) of the targetsequence from the homologous sequence are built Finallyloops connecting the secondary structures are modeled and theoverall structure is refined There exist many tools for thehomology modeling (eg Modeler by Sali and Blundell511)The homology modeling method has been successfully used

for building initial structures of several ion channels forsubsequent all-atom MD simulations Capener et al512 built aninward rectifier potassium channel (Kir) based on a high-resolution structure of KcsA1 Sukharev et al used the crystalstructure of Mycobacterium tuberculosis MscL407 to modelclosed intermediate and open structures of Escherichia coliMscL231232 Law et al combined the crystal structure of theLymnea stagnalis acetylcholine binding protein and the electronmicroscopy (EM) structure of the transmembrane domain ofthe torpedo electric ray nicotinic channel to build an entirehuman nicotinic acetylcholine receptor213

434 Free-Energy Methods Perhaps the greatestdisadvantage of the MD method is that simulations are costlyand are currently limited to the microsecond time scalea

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7 schematically illustrates typical setups for the three modelingapproaches applied to the same systemThe above classification however is rather approximate and

can be misleading Thus the level of computational complexityoften depends on the desired level of detail whereas theaccuracy depends on the assumptions made in deriving theparameters of the model Even the most sophisticated MDsimulations rely on the MD force field which is a classicalmodel that may or may not be adequate for describing a certainphenomenon In this respect full quantum or combinedquantum mechanicsclassical mechanics approaches (QMMM) can in principle provide the highest degree of accuracyHowever the time scale accessible to these methods is severelylimiting Interested readers are directed to reviews of QMMMapproaches for simulations of biomolecules471472 and to arecent review of computational approaches to ion transport innanopores473 On the other hand it is possible to incorporateatomic-level details in BD and even PNP approaches see forexample recent work by Comer Carr and co-workers371373

Other considerations often neglected when evaluating theldquocomputational costrdquo of a certain approach are the qualificationsand ambitions of the researcher performing the modeling tasksand the availability of well-documented and ready-to-use codesFor example it is always possible to increase the computationalcomplexity of the problem by including an exorbitant amountof water in an all-atom simulation or using very fine mesh sizein continuum calculations One could also easily spend severalmonths writing debugging or porting a computationallyefficient code while the same time could have been used torun a more computationally intensive but ready-to-use andtested code Thus there are no simple rules in choosing anoptimal simulation method and researchers new to the field areurged to seek expert advice for their particular problem

41 Continuum Models

Ion channels are complex systems with many degrees offreedom and hence are challenging to model in atomisticdetail Continuum theories based on PoissonminusBoltzmann (PB)and PoissonminusNernstminusPlanck (PNP) equations are powerfultools that make simulation of such systems tractable The mainidea is to employ a continuum description for all componentsof the system ie the solvent the ions and the ion channelThe water the membrane and the channel are represented asfixed structureless dielectrics while the ions are described byspecifying the local density throughout the system Figure 7aschematically illustrates a PNP model of α-hemolysin

411 Electrostatics of Ion Channels The PB equation isthe most popular theoretical model for describing theelectrostatics around a charged biomolecule in ionic solutionIn a system of interacting mobile charged particles theelectrostatic potential arises due to the combined effect of thecharged biomolecules ions and dielectric properties of theenvironment The PB model assumes that the distribution ofcharges in the system is related to the electrostatic potentialaccording to Boltzmann statistics For the purpose of describingelectrostatics of a single biomolecule the PB equation whichwas first introduced independently by Gouy (1910) andChapman (1913) and later generalized by Debye and Huckel(1923) is most frequently written as

sumε ψ πρ π

ψλ

nablamiddot nabla = minus minus

minus

infin

⎛⎝⎜

⎞⎠⎟

c z q

z qk T

r r r

rr

( ( ) ( )) 4 ( ) 4

exp( )

( )

ii i

i

f

B (8)

where ε(r) is the position-dependent dielectric constant ψ(r) isthe electrostatic potential ρf(r) is the fixed charge density ofthe biomolecule ci

infin represents the concentration of ion speciesi at infinite distance from the biomolecule zi is the valency ofion species i q is the proton charge kB is the Boltzmannconstant T is the temperature and λ(r) describes theaccessibility of position r to ions (for example it is oftenassumed to be zero inside the biomolecule) A solution to thePB equation gives the electrostatic potential and equilibriumdensity of ions throughout the space The PB equation invokesa mean-field approximation that neglects nonelectrostatic ionminusion interactions (eg van der Waals or water-mediated) thedielectric response of the system to each ion and effects due tocorrelations in the instantaneous distribution of ions Becauseof these the PB equation fails to describe the electrostatics ofhighly charged objects such as DNA in high-concentration ionsolutions with quantitative accuracy474 In the context of ionchannels which rarely carry such a high charge density the PBtheory has been widely used to calculate the free energy cost oftransferring a charge from bulk solution to the interior of thechannel105287 (see Table 1) to characterize ion-channelinteractions88294 and to compute the distribution of thetransmembrane electrostatic potential103104294299 Such con-tinuum electrostatic calculations have also been used toestimate the relative stability of protonated and unprotonatedstates of ionizable residues in an ion channel (discussed in refs

Figure 7 Schematic illustrations of the PNP (a) BD (b) and all-atom MD (c) modeling methods applied to the same systeman α-hemolysinchannel embedded in a lipid bilayer membrane and surrounded by an electrolyte solution In panel (a) the ions are described as continuous densitywhereas the water protein and membrane are treated as continuum dielectric media In the BD model (panel b) only ions are represented explicitlywhereas all other components are either implicitly modeled or approximated by continuum media All atoms are treated explicitly in the all-atom MDmethod (panel c)

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61 and 475) DelPhi476 and APBS477 are two popular computercodes for numerically solving the PB equation412 Ion Transport Although the PB model provides

insights into the equilibrium energetics of an ion channelmodeling of the ion flux requires a nonequilibrium approach Inmost ion channels the time scale of ion permeation rangesfrom tens of nanoseconds (porins) to microseconds and evenmilliseconds (in active transport) Thus observing a statisticallysignificant number of ion-permeation events requires longtrajectories that are still rather expensive to obtain using an all-atom approach The PoissonminusNernstminusPlanck model givesaccess to long time scales albeit at lower temporal and spatialresolutions As in the PB model the lipid protein and watermolecules are approximated as dielectric continua while ionsare described as continuous density distributions The currentdensity is obtained from the NernstminusPlanck (NP) theorywhich is widely used in studies of electrolyte transport In theNP theory ion fluxes arise from two sources the gradient ofion concentration and the gradient of the electrostatic potentialTraditional NernstminusPlanck equations do not describe ion-channel interactions However the classical NernstminusPlanckequations may be modified to include the ion-channelinteractions via an effective potential Thus the flux of ionspecies i Ji is written as

= minus nabla + nabla⎛⎝⎜

⎞⎠⎟t D c t

c tk T

J r r rr

r( ) ( ) ( )( )

( )i i ii

iB

eff

(9)

where Di and ci are the diffusion constant and the numberdensity of ion species i respectively and r( )i

eff is theeffective potential that usually combines the electrostaticpotential ϕ(r) and a core-repulsive potential UCore(r) withthe latter describing interactions between ions and the proteinchannel and not between the ions themselvesThe concentration and the flux of each ionic species obey the

continuity equation

partpart

+ nablamiddot =c t

tt

rJ r

( )( ) 0i

i (10)

Under steady-state conditions the concentration and the fluxdo not vary with time and nablamiddotJi(r) = 0 The electrostaticpotential is calculated from the Poisson equation

sumε ϕ π ρnablamiddot nabla = minus +r q cr r r( ( ) (( ))) 4 ( ( ) ( ))i

i if

(11)

where ε(r) is the dielectric constant qi is the ion charge andρf(r) is again the (fixed) charge density due to the proteinThe above coupled partial differential equations constitute

the PNP equations and may be solved by a variety of methodsin one or three dimensions Typically the NP and the Poissonequations are solved self-consistently to simultaneously obtainthe electrostatic potential ϕ(r) and the ionic concentration ci(r)under appropriate boundary conditionsModeling ion channels within the PNP framework is

computationally inexpensive compared to MD and BDsimulations because the problem of many-body interactions isavoided through a mean-field approximation An undesirableside-effect is that some important physics is neglected by thisapproximation Below we discuss some of the shortcomings ofthe PNP equations in the context of ion channels as well asextensions to the equations that address these shortcomings

Interested readers are directed to comprehensive reviews onthis subject12299307310478

Prior to the surge of popularity of the all-atom MD methodcontinuum electrodiffusion theories played a major role indevelopment of our understanding of ion fluxes in nano-channels81255 Early attempts to use the electrodiffusion theoryto describe ion flux through nanochannels279minus281286 led to thedevelopment of simplified models based on a self-consistentcombination of the Poisson equation and the NernstminusPlanckequations that were subsequently applied to various channelsystems282minus284 Most of the early studies dealt with either one-dimensional models or simplified geometries that lacked adetailed description of the protein structure and static chargedistribution These studies connected qualitative features of thecurrentminusvoltageminusconcentration relationship to structural andphysical features of the models For example the PNP theorywas used to demonstrate how charges at the channel openingscan produce current rectification285479 as well as how achannel with ion-specific binding sites can exhibit lowerconductance in a mixture of two ion types than in a puresolution of either type480 A lattice-relaxation algorithm able tosolve the PNP equations for a 3D model was developed byKurnikova and co-workers8 in later years This procedure allowsthe protein and the membrane to be mapped onto a 3D cubiclattice with defined dielectric boundaries fixed chargedistribution and a flow region for the ionsLike the PB equation the system of PNP equations

constitutes a mean-field theory that neglects the finite size ofthe ions the dielectric response of the system to an ion andionminusion correlations In fact the PNP equations reduce to thePB equation for systems with zero flux everywhere The validityof a continuum dielectric description and mean-fieldapproaches in the context of narrow pores has been thesubject of much debate For example Chung and co-workersobserved considerable differences between the conductancethrough idealized pores using the BD and PNP ap-proaches287294 The authors argued that the mean-fieldapproximation breaks down in narrow ion channels due to anoverestimation of the screening effect by counterions within thepore Larger channels like porins at physiological or lower ionconcentrations are described quite accurately by the PNPequations However the currents computed based on the PNPmodels can be considerably higher (by 50 for OmpF) than inequivalent BD simulations55

When a charge in a high dielectric medium is brought near alow dielectric medium a repulsive surface charge is induced atthe dielectric boundary In continuum descriptions such as PBand PNP the induced charge density includes (usually)canceling components from both positive and negative averagecharge densities The interaction energy between a charge andits induced charge density is often called the dielectric self-energy The dielectric self-energy due to the average chargedensity and the average induced charge density at the dielectricboundary is in general smaller than the interaction energybetween point charges and corresponding induced chargeaveraged over all configurations Put another way a pointcharge approaching a low dielectric medium is strongly repelledby its induced image charge and this repulsion is largely lost bythe implicit averaging in mean-field descriptionsThe PB and PNP equations have been modified to include

the interaction of an ion with the charge density itinduces11294296 Although the corrections account for theinteraction of an ion with its induced dielectric charge they do

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dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXJ

not account for the interaction of the induced charge with asecond nearby ion Similarly the mean-field approximationinherently ignores effects involving correlations in theinstantaneous ion distribution For example the narrowestportion of the potassium channels almost always contains twoions that move in a concerted fashion (see section 511) whichcannot be properly treated by continuum theories Never-theless it was concluded that the dielectric self-energy accountsfor most of the discrepancy between PNP and BD results in thecase of narrow channels294

Although early electrodiffusion studies of Levitt consideredhard-sphere repulsion between ions by iteratively correcting theion concentration279 many studies have since ignored suchfinite-size effects Recently the PNP equations have beenadapted to incorporate finite-size effects using classical densityfunctional theory to describe many-body hard sphereinteractions between ions and solvent290291300481 Unfortu-nately these approaches often yield cumbersome integro-differential equations Finite-size effects can be included in thePNP equations by introducing an entropic term thatdiscourages solvent crowding by ions309 The latter approachyields a tractable set of corrected PNP equations Both the PNPand BD methods usually ignore thermal fluctuations of theprotein and lipid bilayer However these can be effectivelycaptured by combining results from MD or Monte Carlosimulations with 3-D PNP calculations92

The PNP approach continues to play a major role inimproving our understanding of the physics of ion channelsThe computational efficiency of the PNP model is unparallelledfor studies of ion conductance in a low ion concentrationregime where the PNP method is expected to be the mostaccurate The method is highly efficient at predicting the effectof a channelrsquos geometry on the currentminusvoltage dependence atphysiological voltages and can be used to screen for mutationsthat affect conductance of a channel The calculation of currentscan be quite accurate in the case of larger channels such asporins PNP is perhaps the only method that can presentlysimulate the interplay of ion conductances in an ensemble ofion channels (such as in a realistic biological membrane)explicitly taking the structural features of the channels intoaccount Finally the PNP approach is rather flexible to includedescriptions of additional physical effects for examplehydrodynamic interactions354364369370 or the effect of asemiconductor membrane on the ionic current361382383

42 Brownian Dynamics

The BD method allows for simulations of explicit ionpermeations on the microsecond-to-millisecond time scale bytreating solvent molecules implicitly In a way the BD methodoffers a good compromise between all-atom MD andcontinuum electrodiffusion approaches Computational effi-ciency is achieved by reducing the number of degrees offreedom Typically a moderate number of atoms of interest(usually the ions) are simulated explicitly while the solvent isaccounted for via friction and stochastic random forces that actin addition to the electrostatic and steric forces arising fromother ions the protein and the lipid bilayer For the calculationof electrostatic forces the water the membrane and the proteinchannel are usually treated as continuous dielectric media Thechannel is treated as a rigid structure and thermal fluctuationsare typically ignored Figure 7b schematically illustrates a BDmodel of α-hemolysin

421 General Formulation of the BD Method In theBrownian dynamics method a stochastic equation is integratedforward in time to create trajectories of atoms Theldquouninterestingrdquo degrees of motion usually corresponding tofast-moving solvent molecules are projected out in order todevelop a dynamic equation for the evolution of the ldquorelevantrdquodegrees of freedom The motion of the particles is described bya generalized Langevin equation

int = minus prime minus prime prime +m t dt M t t t tr r f( ) ( ) ( ) ( )i i i

t

i i i0 (12)

The force on the ith particle i is obtained from an effectivepotential = minusnabla r( )i i iThe potential function is a many-body potential of mean

force (PMF) that corresponds to the reversible thermodynamicwork function to assemble the relevant particles in a particularconformation while averaging out the remaining degrees offreedom ie the effect of all other atoms is implicitly present in

r( )i The second term on the right-hand side is thedamping force representing the frictional effect of theenvironment and finally fi(t) is a Gaussian fluctuating forcearising from random collisions The frictional force depends onprevious velocities through the memory kernel Mi(tminustprime) Thefirst and second moments of the random force are given by⟨fi(t)⟩ = 0 and ⟨fi(t)middotfj(0)⟩ = 3kBTMi(t)δij where kB is theBoltzmann constant and T is the temperature Both the dragforce and the stochastic force incorporate the effect of thesolvent In the Markovian limit the memory kernel is a Diracdelta function that leads to the traditional Langevin equation

γ = minus +m t t tr r f( ) ( ) ( )i i i i i i (13)

The friction coefficient γi is related to underlying molecularprocesses via the fluctuationminusdissipation theoremIn the overdamped regime (which applies to the motion of

an ion in water) the inertial term can be ignored so that theLangevin equation is reduced to

ζ = +tD

k Ttr( ) ( )i

ii i

B (14)

where Di = kBTγi is the diffusion coefficient of the ith particleand ζi(t) is a Gaussian random noise with a second momentgiven as ⟨ζi(t)middotζi(0)⟩ = 6Diδ(t)

422 BD Simulations of Ion Channels A Browniandynamics simulation requires two basic ingredients adescription of the forces applied to each ion and the diffusioncoefficient for each ion The diffusion coefficient for the ionsshould be in general position-dependent and can be obtainedfrom all-atom MD simulations373482483 or estimated usinganalytical techniques88484 However in most cases a singleposition-independent diffusion constant is used for all ions ofthe same speciesEach ion experiences a force that depends on its position as

well as the positions of all the other ions in the system Thepotential corresponding to the forces on the ions is the multi-ion PMF which is the multidimensional free energy surfacethat is usually broken into an ionminusion PMF and a PMF due tothe pore the solution and other biomolecules373 The PMFscan be calculated from all-atom MD or even quantumchemistry simulations but such calculations are computation-ally expensive

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXK

A more typical approach was presented by Roux and co-workers which we summarize here556263299 The multi-ionPMF can be written as

sum sum sum

sum ϕ ϕ

= | minus | +

+ +

αα γ α

α γ α γα

α

αα α α

neu U

q

r r r r

r r

( ) ( ) ( )

[ ( ) ( )]

core

sf rf(15)

where uαγ(r) is the ionminusion interaction Ucore is a repulsivepotential preventing the ions from entering the ion-inaccessibleregions ϕsf is the electrostatic potential arising from thepermanent protein charge distribution and ϕrf is the reactionfield potential arising from the electrostatic polarization of thevarious dielectric boundaries The static field may be computedfrom an atomic model of the pore using the PBequations556263485 Any externally imposed transmembranebias may be included in the calculation of the electrostaticpotential Usually the ionminusion interaction includes van derWaals and Coulomb terms

εσ σ

ε= minus +α γ α γ

α γ α γ α γ⎜ ⎟ ⎜ ⎟⎡⎣⎢⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎤⎦⎥u r

r r

q q

r( ) 4

12

6

bulk

where εαγ and σαγ are the parameters for the 6minus12 Lennard-Jones potential qα and qγ are the charges of the ions and εbulk isthe dielectric constant of bulk water The local dielectricconstant of the water in the interior of the pore may beextracted from atomistic simulations but it is usually assumedto have the bulk value of 80 Solvation effects can beapproximately described by including a short-range solvationpotential55287486 but that is rarely done in practice Web-basedinterface for GCMCBD simulations of ion channels hasrecently become available268

Early BD studies were performed using one-dimensionalrepresentations of channels487 Later these were extended tomore realistic three-dimensional geometries although theseoften lacked atomic detail63486 However the X-ray structure ofan ion channel can be used to create a more realistic model ofthe channel by computing electrostatic and core repulsionpotential maps from the all-atom structure Brownian dynamicssimulations have been applied to several biological channelsincluding OmpF5562minus64 K+ channels110minus115117 α-hemoly-sin8895 VDAC268 and gramicidin1617 Roux and co-workershave developed a grand canonical Monte CarloBrowniandynamics method (GCMCBD)6263103 to allow for fluctua-tions in the total number of ions in the system and asymmetricion concentration conditions For detailed treatment of thesubject interested readers are directed to a review of thecomputational methods299473

Recently Comer and Aksimentiev373 used all-atom MD todetermine full three-dimensional PMF maps at atomicresolution for ionminusion and ionminusbiomolecule interactionsthereby fully accounting for short-range effects associationwith solvation of ions and biomolecules Using such full 3-DPMFs in BD simulations of ion flow through a model nanoporecontaining DNA basepair triplets yielded ionic currents in closeagreement with the results of all-atom MD but at a fraction ofthe computational cost The authors indicate that such anatomic-resolution BD method can be developed further toincorporate the conformational flexibility of the pore and DNAby altering the PMF maps on-the-fly

43 All-Atom Molecular Dynamics

The all-atom MD method can provide unparalleled insight intothe physical mechanisms underlying the biological function ofbiomacromolecules By explicitly describing all the atoms of thesystem of interest and the majority of interatomic interactionsthis method has the potential to compete with the experimentin completeness and accuracy of the description of microscopicphenomena In the case of an ion channel one can in principledirectly observe ion conductance and gating at the spatialresolution of a hydrogen atom and the temporal resolution ofsingle femtoseconds Critical to the above statement is theassumption that the all-atom MD method is equipped with acorrect description of interatomic interactions and enoughcomputational power is available Despite ever-increasingavailability of massive parallel computing platforms makingquantitative predictions using MD remains challenging in partdue to imperfections of the interatom interaction modelsBelow we briefly review the formulations of the all-atom MDmethod and describe recent advances in the field

431 General Formulation of the All-Atom MDMethod In the MD simulations of biomacromoleculesatoms are represented as point particles and the connectivity(or covalent bonds) among those atom are given a prioriCovalently bonded atoms interact with each other throughbonded potentials while the other atom pairs interact throughnonbonded potentials

= +U U Ur r r( ) ( ) ( )N N Nbonded nonbonded (16)

where rN denotes the coordinates of N atoms in a systemBonded interactions model quantum mechanical behavior ofcovalently connected atoms by means of harmonic bond angleand improper dihedral angle restraints and periodic dihedralangle potentials

sum sum

sum

sum

θ θ

χ δ

ϕ ϕ

= minus + minus

+ + minus

+ minus

θ

χ

ϕ

U K b b K

K n

K

( ) ( )

1 cos( )

( )

bbondedbonds

02

angles0

2

torsions

impropers0

2

(17)

where Kb and b0 are the bond force constant and theequilibrium distance respectively Kθ and θ0 are the angleforce constant and the equilibrium angle respectively Kχ nand δ are the dihedral force constant the multiplicity and thephase angle respectively and Kϕ and ϕ0 are the improper forceconstant and the equilibrium improper angle488 The non-bonded potential usually consists of the Lennard-Jones (LJ)potential for van der Waals interactions and the Coulombpotential for electrostatic interactions

sum εσ σ

ε= minus +

⎧⎨⎪⎩⎪

⎡

⎣⎢⎢⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤

⎦⎥⎥

⎫⎬⎪⎭⎪

Ur r

q q

r4 ij

ij

ij

ij

ij

i j

ijnonbonded

nonbond

12 6

(18)

where εij is the well depth σij is the finite distance at which theLJ potential is zero rij is the interatomic distance and qij areatomic charges The bonded parameters are empiricallycalibrated based on the quantum mechanical calculations ofsmall molecules whereas the nonbonded parameters are mainlyderived from quantum chemistry calculations (eg partial

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXL

charges) and empirical matching of thermodynamic data (eghydration free energy)A biomolecular force field is a set of bonded and nonbonded

parameters defined in eqs 17 and 18 Presently severalbiomolecular force fields exist The force fields can becategorized into types based on whether all the atoms areexplicitly treated or not All-atom force fields which includeCHARMM489 AMBER490491 and OPLS-AA492493 treat allatoms explicitly In the united-atom force fields (egGROMOS494495) some nonpolar hydrogen atoms areneglectedFor the simulations of channel proteins a lipid force field is

as important as a protein force field because the channels areembedded in lipid bilayers Among the all-atom force fields theCHARMM force field includes parameters for lipids the latestupdate at the time of writing this review is CHARMM36496

Together with the AMBER force field for the protein thegeneral all-atom AMBER force field (GAFF) can be used todescribe the lipid bilayer497498 Officially OPLS does notinclude lipid parameters Among the united-atom force fieldsGROMOS comes with lipid parameters499 Berger et alreported improved GROMOS-based lipid parameters basedon the condensed-phase properties of pentadecane500 Thislipid force field has been widely used in combination with otherprotein force fields such as AMBER OPLS and GROMOS501

For an in-depth review of various force fields we referinterested readers to a comprehensive review by Mackerell488

432 Ion Channels in Native Environment Unlikesoluble proteins that are surrounded only by water ion-channelproteins are embedded in a lipid bilayer and therefore are incontact with both water and lipids Because of the drasticallydifferent chemical and electrostatic properties of lipid andwater proper descriptions of proteinminuslipid and proteinminuswaterinteractions are key for the successful simulation of amembrane channel To model ion conduction through arelatively rigid channel (eg gA or KcsA channel) it is possibleto use an implicit solvent model of the channelrsquos environmentin which the volume occupied by lipid and water is treated ascontinuum media of dielectric constants 2 and 78 respec-tively299 However when interactions between a channel and alipid membrane are significant (eg in mechanosensitivechannels) explicit modeling of lipid molecules is essentialThe tails of lipids are long and equilibrate slowly making it

significantly more difficult to assemble a model of a channelembedded in an explicit lipid bilayer than a model of a fullysoluble protein Usually the system setup involves thefollowing steps Starting from a pre-equilibrated and solvatedlipid bilayer membrane one makes a pore in the bilayer bydeleting a minimal number of lipid molecules so that theprotein can fit Next an all-atom model of the protein is placedin the pore which is followed by energy minimization andequilibration of the system using the MD method having thechannelrsquos coordinates restrained to their crystallographic valuesFinally when the proteinminuslipid interface is well equilibratedone can perform a production run without applying restraintson the channel For detailed step-by-step instructions forbuilding atomic-scale models of ion channels in lipid bilayerenvironment interested readers are directed to a tutorial onMD simulations of membrane proteins502 Even though a fullyautomated procedure is not yet available several programs canassist a beginner in building a new system VMD503 containsthe Membrane Builder plugin Jo et al have a web-based

service CHARMM GUI Membrane Builder (httpwwwcharmm-guiorgmembrane)504505

An alternative method for creating an all-atom model of anion channel in its native environment is to first carry out self-assembly simulations using a coarse-grained (CG) MDmethod74165379 The main difference between the CG andall-atom MD methods is the level of detail used to describe thecomponents of the system Typically one CG bead representsabout 5minus10 atoms Being much more computationally efficient(and lower resolution) the CG model allows millisecond-time-scale simulations to be performed on commodity computersInterested readers are directed toward recent reviews on thissubject506minus508

In the CG simulations of self-assembly CG models of lipidssolvent and a membrane protein are placed with randompositions in desired proportions During the course of CGMDsimulations the lipid molecules spontaneously form a lipidbilayer around a protein After obtaining a stable model the CGmodel can be reverse-coarse-grained into a fully atomisticmodel (see for example a study by Maffeo and Aksimen-tiev330) A great advantage of this approach is that it requiresno a priori knowledge of the position of the membranechannels relative to the membrane An obvious disadvantage isthat one has to have a reasonable CG model to carry out theself-assembly simulations and a reliable procedure to recoverthe all-atom details from the final CG model Currently it isnot possible to use a CG approach to model ion conductancethrough large membrane channels due to inaccurate treatmentsof the membrane and water electrostatics in most CG modelsHowever work to improve CG methods is ongoing509510 andsuch simulations should become possible in the near future

433 Homology Modeling Usually an all-atom MDsimulation of a channel protein can be performed only when anatomic-resolution structure of the channel is available Thisrequirement severely limits application of the MD methodFortunately membrane channels of different organisms oftenhave similar amino-acid sequences The sequence similarity canbe used to build an all-atom model of the channel that does nothave an experimentally determined structure through aprocedure called homology modeling511 Briefly homologymodeling proceeds as follows First a sequence alignmentbetween a target sequence and a homologous sequenceforwhich a structure is knownis performed Second thesecondary structures (eg α-helices and β-sheets) of the targetsequence from the homologous sequence are built Finallyloops connecting the secondary structures are modeled and theoverall structure is refined There exist many tools for thehomology modeling (eg Modeler by Sali and Blundell511)The homology modeling method has been successfully used

for building initial structures of several ion channels forsubsequent all-atom MD simulations Capener et al512 built aninward rectifier potassium channel (Kir) based on a high-resolution structure of KcsA1 Sukharev et al used the crystalstructure of Mycobacterium tuberculosis MscL407 to modelclosed intermediate and open structures of Escherichia coliMscL231232 Law et al combined the crystal structure of theLymnea stagnalis acetylcholine binding protein and the electronmicroscopy (EM) structure of the transmembrane domain ofthe torpedo electric ray nicotinic channel to build an entirehuman nicotinic acetylcholine receptor213

434 Free-Energy Methods Perhaps the greatestdisadvantage of the MD method is that simulations are costlyand are currently limited to the microsecond time scalea

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXM

61 and 475) DelPhi476 and APBS477 are two popular computercodes for numerically solving the PB equation412 Ion Transport Although the PB model provides

insights into the equilibrium energetics of an ion channelmodeling of the ion flux requires a nonequilibrium approach Inmost ion channels the time scale of ion permeation rangesfrom tens of nanoseconds (porins) to microseconds and evenmilliseconds (in active transport) Thus observing a statisticallysignificant number of ion-permeation events requires longtrajectories that are still rather expensive to obtain using an all-atom approach The PoissonminusNernstminusPlanck model givesaccess to long time scales albeit at lower temporal and spatialresolutions As in the PB model the lipid protein and watermolecules are approximated as dielectric continua while ionsare described as continuous density distributions The currentdensity is obtained from the NernstminusPlanck (NP) theorywhich is widely used in studies of electrolyte transport In theNP theory ion fluxes arise from two sources the gradient ofion concentration and the gradient of the electrostatic potentialTraditional NernstminusPlanck equations do not describe ion-channel interactions However the classical NernstminusPlanckequations may be modified to include the ion-channelinteractions via an effective potential Thus the flux of ionspecies i Ji is written as

= minus nabla + nabla⎛⎝⎜

⎞⎠⎟t D c t

c tk T

J r r rr

r( ) ( ) ( )( )

( )i i ii

iB

eff

(9)

where Di and ci are the diffusion constant and the numberdensity of ion species i respectively and r( )i

eff is theeffective potential that usually combines the electrostaticpotential ϕ(r) and a core-repulsive potential UCore(r) withthe latter describing interactions between ions and the proteinchannel and not between the ions themselvesThe concentration and the flux of each ionic species obey the

continuity equation

partpart

+ nablamiddot =c t

tt

rJ r

( )( ) 0i

i (10)

Under steady-state conditions the concentration and the fluxdo not vary with time and nablamiddotJi(r) = 0 The electrostaticpotential is calculated from the Poisson equation

sumε ϕ π ρnablamiddot nabla = minus +r q cr r r( ( ) (( ))) 4 ( ( ) ( ))i

i if

(11)

where ε(r) is the dielectric constant qi is the ion charge andρf(r) is again the (fixed) charge density due to the proteinThe above coupled partial differential equations constitute

the PNP equations and may be solved by a variety of methodsin one or three dimensions Typically the NP and the Poissonequations are solved self-consistently to simultaneously obtainthe electrostatic potential ϕ(r) and the ionic concentration ci(r)under appropriate boundary conditionsModeling ion channels within the PNP framework is

computationally inexpensive compared to MD and BDsimulations because the problem of many-body interactions isavoided through a mean-field approximation An undesirableside-effect is that some important physics is neglected by thisapproximation Below we discuss some of the shortcomings ofthe PNP equations in the context of ion channels as well asextensions to the equations that address these shortcomings

Interested readers are directed to comprehensive reviews onthis subject12299307310478

Prior to the surge of popularity of the all-atom MD methodcontinuum electrodiffusion theories played a major role indevelopment of our understanding of ion fluxes in nano-channels81255 Early attempts to use the electrodiffusion theoryto describe ion flux through nanochannels279minus281286 led to thedevelopment of simplified models based on a self-consistentcombination of the Poisson equation and the NernstminusPlanckequations that were subsequently applied to various channelsystems282minus284 Most of the early studies dealt with either one-dimensional models or simplified geometries that lacked adetailed description of the protein structure and static chargedistribution These studies connected qualitative features of thecurrentminusvoltageminusconcentration relationship to structural andphysical features of the models For example the PNP theorywas used to demonstrate how charges at the channel openingscan produce current rectification285479 as well as how achannel with ion-specific binding sites can exhibit lowerconductance in a mixture of two ion types than in a puresolution of either type480 A lattice-relaxation algorithm able tosolve the PNP equations for a 3D model was developed byKurnikova and co-workers8 in later years This procedure allowsthe protein and the membrane to be mapped onto a 3D cubiclattice with defined dielectric boundaries fixed chargedistribution and a flow region for the ionsLike the PB equation the system of PNP equations

constitutes a mean-field theory that neglects the finite size ofthe ions the dielectric response of the system to an ion andionminusion correlations In fact the PNP equations reduce to thePB equation for systems with zero flux everywhere The validityof a continuum dielectric description and mean-fieldapproaches in the context of narrow pores has been thesubject of much debate For example Chung and co-workersobserved considerable differences between the conductancethrough idealized pores using the BD and PNP ap-proaches287294 The authors argued that the mean-fieldapproximation breaks down in narrow ion channels due to anoverestimation of the screening effect by counterions within thepore Larger channels like porins at physiological or lower ionconcentrations are described quite accurately by the PNPequations However the currents computed based on the PNPmodels can be considerably higher (by 50 for OmpF) than inequivalent BD simulations55

When a charge in a high dielectric medium is brought near alow dielectric medium a repulsive surface charge is induced atthe dielectric boundary In continuum descriptions such as PBand PNP the induced charge density includes (usually)canceling components from both positive and negative averagecharge densities The interaction energy between a charge andits induced charge density is often called the dielectric self-energy The dielectric self-energy due to the average chargedensity and the average induced charge density at the dielectricboundary is in general smaller than the interaction energybetween point charges and corresponding induced chargeaveraged over all configurations Put another way a pointcharge approaching a low dielectric medium is strongly repelledby its induced image charge and this repulsion is largely lost bythe implicit averaging in mean-field descriptionsThe PB and PNP equations have been modified to include

the interaction of an ion with the charge density itinduces11294296 Although the corrections account for theinteraction of an ion with its induced dielectric charge they do

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXJ

not account for the interaction of the induced charge with asecond nearby ion Similarly the mean-field approximationinherently ignores effects involving correlations in theinstantaneous ion distribution For example the narrowestportion of the potassium channels almost always contains twoions that move in a concerted fashion (see section 511) whichcannot be properly treated by continuum theories Never-theless it was concluded that the dielectric self-energy accountsfor most of the discrepancy between PNP and BD results in thecase of narrow channels294

Although early electrodiffusion studies of Levitt consideredhard-sphere repulsion between ions by iteratively correcting theion concentration279 many studies have since ignored suchfinite-size effects Recently the PNP equations have beenadapted to incorporate finite-size effects using classical densityfunctional theory to describe many-body hard sphereinteractions between ions and solvent290291300481 Unfortu-nately these approaches often yield cumbersome integro-differential equations Finite-size effects can be included in thePNP equations by introducing an entropic term thatdiscourages solvent crowding by ions309 The latter approachyields a tractable set of corrected PNP equations Both the PNPand BD methods usually ignore thermal fluctuations of theprotein and lipid bilayer However these can be effectivelycaptured by combining results from MD or Monte Carlosimulations with 3-D PNP calculations92

The PNP approach continues to play a major role inimproving our understanding of the physics of ion channelsThe computational efficiency of the PNP model is unparallelledfor studies of ion conductance in a low ion concentrationregime where the PNP method is expected to be the mostaccurate The method is highly efficient at predicting the effectof a channelrsquos geometry on the currentminusvoltage dependence atphysiological voltages and can be used to screen for mutationsthat affect conductance of a channel The calculation of currentscan be quite accurate in the case of larger channels such asporins PNP is perhaps the only method that can presentlysimulate the interplay of ion conductances in an ensemble ofion channels (such as in a realistic biological membrane)explicitly taking the structural features of the channels intoaccount Finally the PNP approach is rather flexible to includedescriptions of additional physical effects for examplehydrodynamic interactions354364369370 or the effect of asemiconductor membrane on the ionic current361382383

42 Brownian Dynamics

The BD method allows for simulations of explicit ionpermeations on the microsecond-to-millisecond time scale bytreating solvent molecules implicitly In a way the BD methodoffers a good compromise between all-atom MD andcontinuum electrodiffusion approaches Computational effi-ciency is achieved by reducing the number of degrees offreedom Typically a moderate number of atoms of interest(usually the ions) are simulated explicitly while the solvent isaccounted for via friction and stochastic random forces that actin addition to the electrostatic and steric forces arising fromother ions the protein and the lipid bilayer For the calculationof electrostatic forces the water the membrane and the proteinchannel are usually treated as continuous dielectric media Thechannel is treated as a rigid structure and thermal fluctuationsare typically ignored Figure 7b schematically illustrates a BDmodel of α-hemolysin

421 General Formulation of the BD Method In theBrownian dynamics method a stochastic equation is integratedforward in time to create trajectories of atoms Theldquouninterestingrdquo degrees of motion usually corresponding tofast-moving solvent molecules are projected out in order todevelop a dynamic equation for the evolution of the ldquorelevantrdquodegrees of freedom The motion of the particles is described bya generalized Langevin equation

int = minus prime minus prime prime +m t dt M t t t tr r f( ) ( ) ( ) ( )i i i

t

i i i0 (12)

The force on the ith particle i is obtained from an effectivepotential = minusnabla r( )i i iThe potential function is a many-body potential of mean

force (PMF) that corresponds to the reversible thermodynamicwork function to assemble the relevant particles in a particularconformation while averaging out the remaining degrees offreedom ie the effect of all other atoms is implicitly present in

r( )i The second term on the right-hand side is thedamping force representing the frictional effect of theenvironment and finally fi(t) is a Gaussian fluctuating forcearising from random collisions The frictional force depends onprevious velocities through the memory kernel Mi(tminustprime) Thefirst and second moments of the random force are given by⟨fi(t)⟩ = 0 and ⟨fi(t)middotfj(0)⟩ = 3kBTMi(t)δij where kB is theBoltzmann constant and T is the temperature Both the dragforce and the stochastic force incorporate the effect of thesolvent In the Markovian limit the memory kernel is a Diracdelta function that leads to the traditional Langevin equation

γ = minus +m t t tr r f( ) ( ) ( )i i i i i i (13)

The friction coefficient γi is related to underlying molecularprocesses via the fluctuationminusdissipation theoremIn the overdamped regime (which applies to the motion of

an ion in water) the inertial term can be ignored so that theLangevin equation is reduced to

ζ = +tD

k Ttr( ) ( )i

ii i

B (14)

where Di = kBTγi is the diffusion coefficient of the ith particleand ζi(t) is a Gaussian random noise with a second momentgiven as ⟨ζi(t)middotζi(0)⟩ = 6Diδ(t)

422 BD Simulations of Ion Channels A Browniandynamics simulation requires two basic ingredients adescription of the forces applied to each ion and the diffusioncoefficient for each ion The diffusion coefficient for the ionsshould be in general position-dependent and can be obtainedfrom all-atom MD simulations373482483 or estimated usinganalytical techniques88484 However in most cases a singleposition-independent diffusion constant is used for all ions ofthe same speciesEach ion experiences a force that depends on its position as

well as the positions of all the other ions in the system Thepotential corresponding to the forces on the ions is the multi-ion PMF which is the multidimensional free energy surfacethat is usually broken into an ionminusion PMF and a PMF due tothe pore the solution and other biomolecules373 The PMFscan be calculated from all-atom MD or even quantumchemistry simulations but such calculations are computation-ally expensive

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXK

A more typical approach was presented by Roux and co-workers which we summarize here556263299 The multi-ionPMF can be written as

sum sum sum

sum ϕ ϕ

= | minus | +

+ +

αα γ α

α γ α γα

α

αα α α

neu U

q

r r r r

r r

( ) ( ) ( )

[ ( ) ( )]

core

sf rf(15)

where uαγ(r) is the ionminusion interaction Ucore is a repulsivepotential preventing the ions from entering the ion-inaccessibleregions ϕsf is the electrostatic potential arising from thepermanent protein charge distribution and ϕrf is the reactionfield potential arising from the electrostatic polarization of thevarious dielectric boundaries The static field may be computedfrom an atomic model of the pore using the PBequations556263485 Any externally imposed transmembranebias may be included in the calculation of the electrostaticpotential Usually the ionminusion interaction includes van derWaals and Coulomb terms

εσ σ

ε= minus +α γ α γ

α γ α γ α γ⎜ ⎟ ⎜ ⎟⎡⎣⎢⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎤⎦⎥u r

r r

q q

r( ) 4

12

6

bulk

where εαγ and σαγ are the parameters for the 6minus12 Lennard-Jones potential qα and qγ are the charges of the ions and εbulk isthe dielectric constant of bulk water The local dielectricconstant of the water in the interior of the pore may beextracted from atomistic simulations but it is usually assumedto have the bulk value of 80 Solvation effects can beapproximately described by including a short-range solvationpotential55287486 but that is rarely done in practice Web-basedinterface for GCMCBD simulations of ion channels hasrecently become available268

Early BD studies were performed using one-dimensionalrepresentations of channels487 Later these were extended tomore realistic three-dimensional geometries although theseoften lacked atomic detail63486 However the X-ray structure ofan ion channel can be used to create a more realistic model ofthe channel by computing electrostatic and core repulsionpotential maps from the all-atom structure Brownian dynamicssimulations have been applied to several biological channelsincluding OmpF5562minus64 K+ channels110minus115117 α-hemoly-sin8895 VDAC268 and gramicidin1617 Roux and co-workershave developed a grand canonical Monte CarloBrowniandynamics method (GCMCBD)6263103 to allow for fluctua-tions in the total number of ions in the system and asymmetricion concentration conditions For detailed treatment of thesubject interested readers are directed to a review of thecomputational methods299473

Recently Comer and Aksimentiev373 used all-atom MD todetermine full three-dimensional PMF maps at atomicresolution for ionminusion and ionminusbiomolecule interactionsthereby fully accounting for short-range effects associationwith solvation of ions and biomolecules Using such full 3-DPMFs in BD simulations of ion flow through a model nanoporecontaining DNA basepair triplets yielded ionic currents in closeagreement with the results of all-atom MD but at a fraction ofthe computational cost The authors indicate that such anatomic-resolution BD method can be developed further toincorporate the conformational flexibility of the pore and DNAby altering the PMF maps on-the-fly

43 All-Atom Molecular Dynamics

The all-atom MD method can provide unparalleled insight intothe physical mechanisms underlying the biological function ofbiomacromolecules By explicitly describing all the atoms of thesystem of interest and the majority of interatomic interactionsthis method has the potential to compete with the experimentin completeness and accuracy of the description of microscopicphenomena In the case of an ion channel one can in principledirectly observe ion conductance and gating at the spatialresolution of a hydrogen atom and the temporal resolution ofsingle femtoseconds Critical to the above statement is theassumption that the all-atom MD method is equipped with acorrect description of interatomic interactions and enoughcomputational power is available Despite ever-increasingavailability of massive parallel computing platforms makingquantitative predictions using MD remains challenging in partdue to imperfections of the interatom interaction modelsBelow we briefly review the formulations of the all-atom MDmethod and describe recent advances in the field

431 General Formulation of the All-Atom MDMethod In the MD simulations of biomacromoleculesatoms are represented as point particles and the connectivity(or covalent bonds) among those atom are given a prioriCovalently bonded atoms interact with each other throughbonded potentials while the other atom pairs interact throughnonbonded potentials

= +U U Ur r r( ) ( ) ( )N N Nbonded nonbonded (16)

where rN denotes the coordinates of N atoms in a systemBonded interactions model quantum mechanical behavior ofcovalently connected atoms by means of harmonic bond angleand improper dihedral angle restraints and periodic dihedralangle potentials

sum sum

sum

sum

θ θ

χ δ

ϕ ϕ

= minus + minus

+ + minus

+ minus

θ

χ

ϕ

U K b b K

K n

K

( ) ( )

1 cos( )

( )

bbondedbonds

02

angles0

2

torsions

impropers0

2

(17)

where Kb and b0 are the bond force constant and theequilibrium distance respectively Kθ and θ0 are the angleforce constant and the equilibrium angle respectively Kχ nand δ are the dihedral force constant the multiplicity and thephase angle respectively and Kϕ and ϕ0 are the improper forceconstant and the equilibrium improper angle488 The non-bonded potential usually consists of the Lennard-Jones (LJ)potential for van der Waals interactions and the Coulombpotential for electrostatic interactions

sum εσ σ

ε= minus +

⎧⎨⎪⎩⎪

⎡

⎣⎢⎢⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤

⎦⎥⎥

⎫⎬⎪⎭⎪

Ur r

q q

r4 ij

ij

ij

ij

ij

i j

ijnonbonded

nonbond

12 6

(18)

where εij is the well depth σij is the finite distance at which theLJ potential is zero rij is the interatomic distance and qij areatomic charges The bonded parameters are empiricallycalibrated based on the quantum mechanical calculations ofsmall molecules whereas the nonbonded parameters are mainlyderived from quantum chemistry calculations (eg partial

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXL

charges) and empirical matching of thermodynamic data (eghydration free energy)A biomolecular force field is a set of bonded and nonbonded

parameters defined in eqs 17 and 18 Presently severalbiomolecular force fields exist The force fields can becategorized into types based on whether all the atoms areexplicitly treated or not All-atom force fields which includeCHARMM489 AMBER490491 and OPLS-AA492493 treat allatoms explicitly In the united-atom force fields (egGROMOS494495) some nonpolar hydrogen atoms areneglectedFor the simulations of channel proteins a lipid force field is

as important as a protein force field because the channels areembedded in lipid bilayers Among the all-atom force fields theCHARMM force field includes parameters for lipids the latestupdate at the time of writing this review is CHARMM36496

Together with the AMBER force field for the protein thegeneral all-atom AMBER force field (GAFF) can be used todescribe the lipid bilayer497498 Officially OPLS does notinclude lipid parameters Among the united-atom force fieldsGROMOS comes with lipid parameters499 Berger et alreported improved GROMOS-based lipid parameters basedon the condensed-phase properties of pentadecane500 Thislipid force field has been widely used in combination with otherprotein force fields such as AMBER OPLS and GROMOS501

For an in-depth review of various force fields we referinterested readers to a comprehensive review by Mackerell488

432 Ion Channels in Native Environment Unlikesoluble proteins that are surrounded only by water ion-channelproteins are embedded in a lipid bilayer and therefore are incontact with both water and lipids Because of the drasticallydifferent chemical and electrostatic properties of lipid andwater proper descriptions of proteinminuslipid and proteinminuswaterinteractions are key for the successful simulation of amembrane channel To model ion conduction through arelatively rigid channel (eg gA or KcsA channel) it is possibleto use an implicit solvent model of the channelrsquos environmentin which the volume occupied by lipid and water is treated ascontinuum media of dielectric constants 2 and 78 respec-tively299 However when interactions between a channel and alipid membrane are significant (eg in mechanosensitivechannels) explicit modeling of lipid molecules is essentialThe tails of lipids are long and equilibrate slowly making it

significantly more difficult to assemble a model of a channelembedded in an explicit lipid bilayer than a model of a fullysoluble protein Usually the system setup involves thefollowing steps Starting from a pre-equilibrated and solvatedlipid bilayer membrane one makes a pore in the bilayer bydeleting a minimal number of lipid molecules so that theprotein can fit Next an all-atom model of the protein is placedin the pore which is followed by energy minimization andequilibration of the system using the MD method having thechannelrsquos coordinates restrained to their crystallographic valuesFinally when the proteinminuslipid interface is well equilibratedone can perform a production run without applying restraintson the channel For detailed step-by-step instructions forbuilding atomic-scale models of ion channels in lipid bilayerenvironment interested readers are directed to a tutorial onMD simulations of membrane proteins502 Even though a fullyautomated procedure is not yet available several programs canassist a beginner in building a new system VMD503 containsthe Membrane Builder plugin Jo et al have a web-based

service CHARMM GUI Membrane Builder (httpwwwcharmm-guiorgmembrane)504505

An alternative method for creating an all-atom model of anion channel in its native environment is to first carry out self-assembly simulations using a coarse-grained (CG) MDmethod74165379 The main difference between the CG andall-atom MD methods is the level of detail used to describe thecomponents of the system Typically one CG bead representsabout 5minus10 atoms Being much more computationally efficient(and lower resolution) the CG model allows millisecond-time-scale simulations to be performed on commodity computersInterested readers are directed toward recent reviews on thissubject506minus508

In the CG simulations of self-assembly CG models of lipidssolvent and a membrane protein are placed with randompositions in desired proportions During the course of CGMDsimulations the lipid molecules spontaneously form a lipidbilayer around a protein After obtaining a stable model the CGmodel can be reverse-coarse-grained into a fully atomisticmodel (see for example a study by Maffeo and Aksimen-tiev330) A great advantage of this approach is that it requiresno a priori knowledge of the position of the membranechannels relative to the membrane An obvious disadvantage isthat one has to have a reasonable CG model to carry out theself-assembly simulations and a reliable procedure to recoverthe all-atom details from the final CG model Currently it isnot possible to use a CG approach to model ion conductancethrough large membrane channels due to inaccurate treatmentsof the membrane and water electrostatics in most CG modelsHowever work to improve CG methods is ongoing509510 andsuch simulations should become possible in the near future

433 Homology Modeling Usually an all-atom MDsimulation of a channel protein can be performed only when anatomic-resolution structure of the channel is available Thisrequirement severely limits application of the MD methodFortunately membrane channels of different organisms oftenhave similar amino-acid sequences The sequence similarity canbe used to build an all-atom model of the channel that does nothave an experimentally determined structure through aprocedure called homology modeling511 Briefly homologymodeling proceeds as follows First a sequence alignmentbetween a target sequence and a homologous sequenceforwhich a structure is knownis performed Second thesecondary structures (eg α-helices and β-sheets) of the targetsequence from the homologous sequence are built Finallyloops connecting the secondary structures are modeled and theoverall structure is refined There exist many tools for thehomology modeling (eg Modeler by Sali and Blundell511)The homology modeling method has been successfully used

for building initial structures of several ion channels forsubsequent all-atom MD simulations Capener et al512 built aninward rectifier potassium channel (Kir) based on a high-resolution structure of KcsA1 Sukharev et al used the crystalstructure of Mycobacterium tuberculosis MscL407 to modelclosed intermediate and open structures of Escherichia coliMscL231232 Law et al combined the crystal structure of theLymnea stagnalis acetylcholine binding protein and the electronmicroscopy (EM) structure of the transmembrane domain ofthe torpedo electric ray nicotinic channel to build an entirehuman nicotinic acetylcholine receptor213

434 Free-Energy Methods Perhaps the greatestdisadvantage of the MD method is that simulations are costlyand are currently limited to the microsecond time scalea

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXM

not account for the interaction of the induced charge with asecond nearby ion Similarly the mean-field approximationinherently ignores effects involving correlations in theinstantaneous ion distribution For example the narrowestportion of the potassium channels almost always contains twoions that move in a concerted fashion (see section 511) whichcannot be properly treated by continuum theories Never-theless it was concluded that the dielectric self-energy accountsfor most of the discrepancy between PNP and BD results in thecase of narrow channels294

Although early electrodiffusion studies of Levitt consideredhard-sphere repulsion between ions by iteratively correcting theion concentration279 many studies have since ignored suchfinite-size effects Recently the PNP equations have beenadapted to incorporate finite-size effects using classical densityfunctional theory to describe many-body hard sphereinteractions between ions and solvent290291300481 Unfortu-nately these approaches often yield cumbersome integro-differential equations Finite-size effects can be included in thePNP equations by introducing an entropic term thatdiscourages solvent crowding by ions309 The latter approachyields a tractable set of corrected PNP equations Both the PNPand BD methods usually ignore thermal fluctuations of theprotein and lipid bilayer However these can be effectivelycaptured by combining results from MD or Monte Carlosimulations with 3-D PNP calculations92

The PNP approach continues to play a major role inimproving our understanding of the physics of ion channelsThe computational efficiency of the PNP model is unparallelledfor studies of ion conductance in a low ion concentrationregime where the PNP method is expected to be the mostaccurate The method is highly efficient at predicting the effectof a channelrsquos geometry on the currentminusvoltage dependence atphysiological voltages and can be used to screen for mutationsthat affect conductance of a channel The calculation of currentscan be quite accurate in the case of larger channels such asporins PNP is perhaps the only method that can presentlysimulate the interplay of ion conductances in an ensemble ofion channels (such as in a realistic biological membrane)explicitly taking the structural features of the channels intoaccount Finally the PNP approach is rather flexible to includedescriptions of additional physical effects for examplehydrodynamic interactions354364369370 or the effect of asemiconductor membrane on the ionic current361382383

42 Brownian Dynamics

The BD method allows for simulations of explicit ionpermeations on the microsecond-to-millisecond time scale bytreating solvent molecules implicitly In a way the BD methodoffers a good compromise between all-atom MD andcontinuum electrodiffusion approaches Computational effi-ciency is achieved by reducing the number of degrees offreedom Typically a moderate number of atoms of interest(usually the ions) are simulated explicitly while the solvent isaccounted for via friction and stochastic random forces that actin addition to the electrostatic and steric forces arising fromother ions the protein and the lipid bilayer For the calculationof electrostatic forces the water the membrane and the proteinchannel are usually treated as continuous dielectric media Thechannel is treated as a rigid structure and thermal fluctuationsare typically ignored Figure 7b schematically illustrates a BDmodel of α-hemolysin

421 General Formulation of the BD Method In theBrownian dynamics method a stochastic equation is integratedforward in time to create trajectories of atoms Theldquouninterestingrdquo degrees of motion usually corresponding tofast-moving solvent molecules are projected out in order todevelop a dynamic equation for the evolution of the ldquorelevantrdquodegrees of freedom The motion of the particles is described bya generalized Langevin equation

int = minus prime minus prime prime +m t dt M t t t tr r f( ) ( ) ( ) ( )i i i

t

i i i0 (12)

The force on the ith particle i is obtained from an effectivepotential = minusnabla r( )i i iThe potential function is a many-body potential of mean

force (PMF) that corresponds to the reversible thermodynamicwork function to assemble the relevant particles in a particularconformation while averaging out the remaining degrees offreedom ie the effect of all other atoms is implicitly present in

r( )i The second term on the right-hand side is thedamping force representing the frictional effect of theenvironment and finally fi(t) is a Gaussian fluctuating forcearising from random collisions The frictional force depends onprevious velocities through the memory kernel Mi(tminustprime) Thefirst and second moments of the random force are given by⟨fi(t)⟩ = 0 and ⟨fi(t)middotfj(0)⟩ = 3kBTMi(t)δij where kB is theBoltzmann constant and T is the temperature Both the dragforce and the stochastic force incorporate the effect of thesolvent In the Markovian limit the memory kernel is a Diracdelta function that leads to the traditional Langevin equation

γ = minus +m t t tr r f( ) ( ) ( )i i i i i i (13)

The friction coefficient γi is related to underlying molecularprocesses via the fluctuationminusdissipation theoremIn the overdamped regime (which applies to the motion of

an ion in water) the inertial term can be ignored so that theLangevin equation is reduced to

ζ = +tD

k Ttr( ) ( )i

ii i

B (14)

where Di = kBTγi is the diffusion coefficient of the ith particleand ζi(t) is a Gaussian random noise with a second momentgiven as ⟨ζi(t)middotζi(0)⟩ = 6Diδ(t)

422 BD Simulations of Ion Channels A Browniandynamics simulation requires two basic ingredients adescription of the forces applied to each ion and the diffusioncoefficient for each ion The diffusion coefficient for the ionsshould be in general position-dependent and can be obtainedfrom all-atom MD simulations373482483 or estimated usinganalytical techniques88484 However in most cases a singleposition-independent diffusion constant is used for all ions ofthe same speciesEach ion experiences a force that depends on its position as

well as the positions of all the other ions in the system Thepotential corresponding to the forces on the ions is the multi-ion PMF which is the multidimensional free energy surfacethat is usually broken into an ionminusion PMF and a PMF due tothe pore the solution and other biomolecules373 The PMFscan be calculated from all-atom MD or even quantumchemistry simulations but such calculations are computation-ally expensive

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXK

A more typical approach was presented by Roux and co-workers which we summarize here556263299 The multi-ionPMF can be written as

sum sum sum

sum ϕ ϕ

= | minus | +

+ +

αα γ α

α γ α γα

α

αα α α

neu U

q

r r r r

r r

( ) ( ) ( )

[ ( ) ( )]

core

sf rf(15)

where uαγ(r) is the ionminusion interaction Ucore is a repulsivepotential preventing the ions from entering the ion-inaccessibleregions ϕsf is the electrostatic potential arising from thepermanent protein charge distribution and ϕrf is the reactionfield potential arising from the electrostatic polarization of thevarious dielectric boundaries The static field may be computedfrom an atomic model of the pore using the PBequations556263485 Any externally imposed transmembranebias may be included in the calculation of the electrostaticpotential Usually the ionminusion interaction includes van derWaals and Coulomb terms

εσ σ

ε= minus +α γ α γ

α γ α γ α γ⎜ ⎟ ⎜ ⎟⎡⎣⎢⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎤⎦⎥u r

r r

q q

r( ) 4

12

6

bulk

where εαγ and σαγ are the parameters for the 6minus12 Lennard-Jones potential qα and qγ are the charges of the ions and εbulk isthe dielectric constant of bulk water The local dielectricconstant of the water in the interior of the pore may beextracted from atomistic simulations but it is usually assumedto have the bulk value of 80 Solvation effects can beapproximately described by including a short-range solvationpotential55287486 but that is rarely done in practice Web-basedinterface for GCMCBD simulations of ion channels hasrecently become available268

Early BD studies were performed using one-dimensionalrepresentations of channels487 Later these were extended tomore realistic three-dimensional geometries although theseoften lacked atomic detail63486 However the X-ray structure ofan ion channel can be used to create a more realistic model ofthe channel by computing electrostatic and core repulsionpotential maps from the all-atom structure Brownian dynamicssimulations have been applied to several biological channelsincluding OmpF5562minus64 K+ channels110minus115117 α-hemoly-sin8895 VDAC268 and gramicidin1617 Roux and co-workershave developed a grand canonical Monte CarloBrowniandynamics method (GCMCBD)6263103 to allow for fluctua-tions in the total number of ions in the system and asymmetricion concentration conditions For detailed treatment of thesubject interested readers are directed to a review of thecomputational methods299473

Recently Comer and Aksimentiev373 used all-atom MD todetermine full three-dimensional PMF maps at atomicresolution for ionminusion and ionminusbiomolecule interactionsthereby fully accounting for short-range effects associationwith solvation of ions and biomolecules Using such full 3-DPMFs in BD simulations of ion flow through a model nanoporecontaining DNA basepair triplets yielded ionic currents in closeagreement with the results of all-atom MD but at a fraction ofthe computational cost The authors indicate that such anatomic-resolution BD method can be developed further toincorporate the conformational flexibility of the pore and DNAby altering the PMF maps on-the-fly

43 All-Atom Molecular Dynamics

The all-atom MD method can provide unparalleled insight intothe physical mechanisms underlying the biological function ofbiomacromolecules By explicitly describing all the atoms of thesystem of interest and the majority of interatomic interactionsthis method has the potential to compete with the experimentin completeness and accuracy of the description of microscopicphenomena In the case of an ion channel one can in principledirectly observe ion conductance and gating at the spatialresolution of a hydrogen atom and the temporal resolution ofsingle femtoseconds Critical to the above statement is theassumption that the all-atom MD method is equipped with acorrect description of interatomic interactions and enoughcomputational power is available Despite ever-increasingavailability of massive parallel computing platforms makingquantitative predictions using MD remains challenging in partdue to imperfections of the interatom interaction modelsBelow we briefly review the formulations of the all-atom MDmethod and describe recent advances in the field

431 General Formulation of the All-Atom MDMethod In the MD simulations of biomacromoleculesatoms are represented as point particles and the connectivity(or covalent bonds) among those atom are given a prioriCovalently bonded atoms interact with each other throughbonded potentials while the other atom pairs interact throughnonbonded potentials

= +U U Ur r r( ) ( ) ( )N N Nbonded nonbonded (16)

where rN denotes the coordinates of N atoms in a systemBonded interactions model quantum mechanical behavior ofcovalently connected atoms by means of harmonic bond angleand improper dihedral angle restraints and periodic dihedralangle potentials

sum sum

sum

sum

θ θ

χ δ

ϕ ϕ

= minus + minus

+ + minus

+ minus

θ

χ

ϕ

U K b b K

K n

K

( ) ( )

1 cos( )

( )

bbondedbonds

02

angles0

2

torsions

impropers0

2

(17)

where Kb and b0 are the bond force constant and theequilibrium distance respectively Kθ and θ0 are the angleforce constant and the equilibrium angle respectively Kχ nand δ are the dihedral force constant the multiplicity and thephase angle respectively and Kϕ and ϕ0 are the improper forceconstant and the equilibrium improper angle488 The non-bonded potential usually consists of the Lennard-Jones (LJ)potential for van der Waals interactions and the Coulombpotential for electrostatic interactions

sum εσ σ

ε= minus +

⎧⎨⎪⎩⎪

⎡

⎣⎢⎢⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤

⎦⎥⎥

⎫⎬⎪⎭⎪

Ur r

q q

r4 ij

ij

ij

ij

ij

i j

ijnonbonded

nonbond

12 6

(18)

where εij is the well depth σij is the finite distance at which theLJ potential is zero rij is the interatomic distance and qij areatomic charges The bonded parameters are empiricallycalibrated based on the quantum mechanical calculations ofsmall molecules whereas the nonbonded parameters are mainlyderived from quantum chemistry calculations (eg partial

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXL

charges) and empirical matching of thermodynamic data (eghydration free energy)A biomolecular force field is a set of bonded and nonbonded

parameters defined in eqs 17 and 18 Presently severalbiomolecular force fields exist The force fields can becategorized into types based on whether all the atoms areexplicitly treated or not All-atom force fields which includeCHARMM489 AMBER490491 and OPLS-AA492493 treat allatoms explicitly In the united-atom force fields (egGROMOS494495) some nonpolar hydrogen atoms areneglectedFor the simulations of channel proteins a lipid force field is

as important as a protein force field because the channels areembedded in lipid bilayers Among the all-atom force fields theCHARMM force field includes parameters for lipids the latestupdate at the time of writing this review is CHARMM36496

Together with the AMBER force field for the protein thegeneral all-atom AMBER force field (GAFF) can be used todescribe the lipid bilayer497498 Officially OPLS does notinclude lipid parameters Among the united-atom force fieldsGROMOS comes with lipid parameters499 Berger et alreported improved GROMOS-based lipid parameters basedon the condensed-phase properties of pentadecane500 Thislipid force field has been widely used in combination with otherprotein force fields such as AMBER OPLS and GROMOS501

For an in-depth review of various force fields we referinterested readers to a comprehensive review by Mackerell488

432 Ion Channels in Native Environment Unlikesoluble proteins that are surrounded only by water ion-channelproteins are embedded in a lipid bilayer and therefore are incontact with both water and lipids Because of the drasticallydifferent chemical and electrostatic properties of lipid andwater proper descriptions of proteinminuslipid and proteinminuswaterinteractions are key for the successful simulation of amembrane channel To model ion conduction through arelatively rigid channel (eg gA or KcsA channel) it is possibleto use an implicit solvent model of the channelrsquos environmentin which the volume occupied by lipid and water is treated ascontinuum media of dielectric constants 2 and 78 respec-tively299 However when interactions between a channel and alipid membrane are significant (eg in mechanosensitivechannels) explicit modeling of lipid molecules is essentialThe tails of lipids are long and equilibrate slowly making it

significantly more difficult to assemble a model of a channelembedded in an explicit lipid bilayer than a model of a fullysoluble protein Usually the system setup involves thefollowing steps Starting from a pre-equilibrated and solvatedlipid bilayer membrane one makes a pore in the bilayer bydeleting a minimal number of lipid molecules so that theprotein can fit Next an all-atom model of the protein is placedin the pore which is followed by energy minimization andequilibration of the system using the MD method having thechannelrsquos coordinates restrained to their crystallographic valuesFinally when the proteinminuslipid interface is well equilibratedone can perform a production run without applying restraintson the channel For detailed step-by-step instructions forbuilding atomic-scale models of ion channels in lipid bilayerenvironment interested readers are directed to a tutorial onMD simulations of membrane proteins502 Even though a fullyautomated procedure is not yet available several programs canassist a beginner in building a new system VMD503 containsthe Membrane Builder plugin Jo et al have a web-based

service CHARMM GUI Membrane Builder (httpwwwcharmm-guiorgmembrane)504505

An alternative method for creating an all-atom model of anion channel in its native environment is to first carry out self-assembly simulations using a coarse-grained (CG) MDmethod74165379 The main difference between the CG andall-atom MD methods is the level of detail used to describe thecomponents of the system Typically one CG bead representsabout 5minus10 atoms Being much more computationally efficient(and lower resolution) the CG model allows millisecond-time-scale simulations to be performed on commodity computersInterested readers are directed toward recent reviews on thissubject506minus508

In the CG simulations of self-assembly CG models of lipidssolvent and a membrane protein are placed with randompositions in desired proportions During the course of CGMDsimulations the lipid molecules spontaneously form a lipidbilayer around a protein After obtaining a stable model the CGmodel can be reverse-coarse-grained into a fully atomisticmodel (see for example a study by Maffeo and Aksimen-tiev330) A great advantage of this approach is that it requiresno a priori knowledge of the position of the membranechannels relative to the membrane An obvious disadvantage isthat one has to have a reasonable CG model to carry out theself-assembly simulations and a reliable procedure to recoverthe all-atom details from the final CG model Currently it isnot possible to use a CG approach to model ion conductancethrough large membrane channels due to inaccurate treatmentsof the membrane and water electrostatics in most CG modelsHowever work to improve CG methods is ongoing509510 andsuch simulations should become possible in the near future

433 Homology Modeling Usually an all-atom MDsimulation of a channel protein can be performed only when anatomic-resolution structure of the channel is available Thisrequirement severely limits application of the MD methodFortunately membrane channels of different organisms oftenhave similar amino-acid sequences The sequence similarity canbe used to build an all-atom model of the channel that does nothave an experimentally determined structure through aprocedure called homology modeling511 Briefly homologymodeling proceeds as follows First a sequence alignmentbetween a target sequence and a homologous sequenceforwhich a structure is knownis performed Second thesecondary structures (eg α-helices and β-sheets) of the targetsequence from the homologous sequence are built Finallyloops connecting the secondary structures are modeled and theoverall structure is refined There exist many tools for thehomology modeling (eg Modeler by Sali and Blundell511)The homology modeling method has been successfully used

for building initial structures of several ion channels forsubsequent all-atom MD simulations Capener et al512 built aninward rectifier potassium channel (Kir) based on a high-resolution structure of KcsA1 Sukharev et al used the crystalstructure of Mycobacterium tuberculosis MscL407 to modelclosed intermediate and open structures of Escherichia coliMscL231232 Law et al combined the crystal structure of theLymnea stagnalis acetylcholine binding protein and the electronmicroscopy (EM) structure of the transmembrane domain ofthe torpedo electric ray nicotinic channel to build an entirehuman nicotinic acetylcholine receptor213

434 Free-Energy Methods Perhaps the greatestdisadvantage of the MD method is that simulations are costlyand are currently limited to the microsecond time scalea

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXM

A more typical approach was presented by Roux and co-workers which we summarize here556263299 The multi-ionPMF can be written as

sum sum sum

sum ϕ ϕ

= | minus | +

+ +

αα γ α

α γ α γα

α

αα α α

neu U

q

r r r r

r r

( ) ( ) ( )

[ ( ) ( )]

core

sf rf(15)

where uαγ(r) is the ionminusion interaction Ucore is a repulsivepotential preventing the ions from entering the ion-inaccessibleregions ϕsf is the electrostatic potential arising from thepermanent protein charge distribution and ϕrf is the reactionfield potential arising from the electrostatic polarization of thevarious dielectric boundaries The static field may be computedfrom an atomic model of the pore using the PBequations556263485 Any externally imposed transmembranebias may be included in the calculation of the electrostaticpotential Usually the ionminusion interaction includes van derWaals and Coulomb terms

εσ σ

ε= minus +α γ α γ

α γ α γ α γ⎜ ⎟ ⎜ ⎟⎡⎣⎢⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎤⎦⎥u r

r r

q q

r( ) 4

12

6

bulk

where εαγ and σαγ are the parameters for the 6minus12 Lennard-Jones potential qα and qγ are the charges of the ions and εbulk isthe dielectric constant of bulk water The local dielectricconstant of the water in the interior of the pore may beextracted from atomistic simulations but it is usually assumedto have the bulk value of 80 Solvation effects can beapproximately described by including a short-range solvationpotential55287486 but that is rarely done in practice Web-basedinterface for GCMCBD simulations of ion channels hasrecently become available268

Early BD studies were performed using one-dimensionalrepresentations of channels487 Later these were extended tomore realistic three-dimensional geometries although theseoften lacked atomic detail63486 However the X-ray structure ofan ion channel can be used to create a more realistic model ofthe channel by computing electrostatic and core repulsionpotential maps from the all-atom structure Brownian dynamicssimulations have been applied to several biological channelsincluding OmpF5562minus64 K+ channels110minus115117 α-hemoly-sin8895 VDAC268 and gramicidin1617 Roux and co-workershave developed a grand canonical Monte CarloBrowniandynamics method (GCMCBD)6263103 to allow for fluctua-tions in the total number of ions in the system and asymmetricion concentration conditions For detailed treatment of thesubject interested readers are directed to a review of thecomputational methods299473

Recently Comer and Aksimentiev373 used all-atom MD todetermine full three-dimensional PMF maps at atomicresolution for ionminusion and ionminusbiomolecule interactionsthereby fully accounting for short-range effects associationwith solvation of ions and biomolecules Using such full 3-DPMFs in BD simulations of ion flow through a model nanoporecontaining DNA basepair triplets yielded ionic currents in closeagreement with the results of all-atom MD but at a fraction ofthe computational cost The authors indicate that such anatomic-resolution BD method can be developed further toincorporate the conformational flexibility of the pore and DNAby altering the PMF maps on-the-fly

43 All-Atom Molecular Dynamics

The all-atom MD method can provide unparalleled insight intothe physical mechanisms underlying the biological function ofbiomacromolecules By explicitly describing all the atoms of thesystem of interest and the majority of interatomic interactionsthis method has the potential to compete with the experimentin completeness and accuracy of the description of microscopicphenomena In the case of an ion channel one can in principledirectly observe ion conductance and gating at the spatialresolution of a hydrogen atom and the temporal resolution ofsingle femtoseconds Critical to the above statement is theassumption that the all-atom MD method is equipped with acorrect description of interatomic interactions and enoughcomputational power is available Despite ever-increasingavailability of massive parallel computing platforms makingquantitative predictions using MD remains challenging in partdue to imperfections of the interatom interaction modelsBelow we briefly review the formulations of the all-atom MDmethod and describe recent advances in the field

431 General Formulation of the All-Atom MDMethod In the MD simulations of biomacromoleculesatoms are represented as point particles and the connectivity(or covalent bonds) among those atom are given a prioriCovalently bonded atoms interact with each other throughbonded potentials while the other atom pairs interact throughnonbonded potentials

= +U U Ur r r( ) ( ) ( )N N Nbonded nonbonded (16)

where rN denotes the coordinates of N atoms in a systemBonded interactions model quantum mechanical behavior ofcovalently connected atoms by means of harmonic bond angleand improper dihedral angle restraints and periodic dihedralangle potentials

sum sum

sum

sum

θ θ

χ δ

ϕ ϕ

= minus + minus

+ + minus

+ minus

θ

χ

ϕ

U K b b K

K n

K

( ) ( )

1 cos( )

( )

bbondedbonds

02

angles0

2

torsions

impropers0

2

(17)

where Kb and b0 are the bond force constant and theequilibrium distance respectively Kθ and θ0 are the angleforce constant and the equilibrium angle respectively Kχ nand δ are the dihedral force constant the multiplicity and thephase angle respectively and Kϕ and ϕ0 are the improper forceconstant and the equilibrium improper angle488 The non-bonded potential usually consists of the Lennard-Jones (LJ)potential for van der Waals interactions and the Coulombpotential for electrostatic interactions

sum εσ σ

ε= minus +

⎧⎨⎪⎩⎪

⎡

⎣⎢⎢⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤

⎦⎥⎥

⎫⎬⎪⎭⎪

Ur r

q q

r4 ij

ij

ij

ij

ij

i j

ijnonbonded

nonbond

12 6

(18)

where εij is the well depth σij is the finite distance at which theLJ potential is zero rij is the interatomic distance and qij areatomic charges The bonded parameters are empiricallycalibrated based on the quantum mechanical calculations ofsmall molecules whereas the nonbonded parameters are mainlyderived from quantum chemistry calculations (eg partial

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXL

charges) and empirical matching of thermodynamic data (eghydration free energy)A biomolecular force field is a set of bonded and nonbonded

parameters defined in eqs 17 and 18 Presently severalbiomolecular force fields exist The force fields can becategorized into types based on whether all the atoms areexplicitly treated or not All-atom force fields which includeCHARMM489 AMBER490491 and OPLS-AA492493 treat allatoms explicitly In the united-atom force fields (egGROMOS494495) some nonpolar hydrogen atoms areneglectedFor the simulations of channel proteins a lipid force field is

as important as a protein force field because the channels areembedded in lipid bilayers Among the all-atom force fields theCHARMM force field includes parameters for lipids the latestupdate at the time of writing this review is CHARMM36496

Together with the AMBER force field for the protein thegeneral all-atom AMBER force field (GAFF) can be used todescribe the lipid bilayer497498 Officially OPLS does notinclude lipid parameters Among the united-atom force fieldsGROMOS comes with lipid parameters499 Berger et alreported improved GROMOS-based lipid parameters basedon the condensed-phase properties of pentadecane500 Thislipid force field has been widely used in combination with otherprotein force fields such as AMBER OPLS and GROMOS501

For an in-depth review of various force fields we referinterested readers to a comprehensive review by Mackerell488

432 Ion Channels in Native Environment Unlikesoluble proteins that are surrounded only by water ion-channelproteins are embedded in a lipid bilayer and therefore are incontact with both water and lipids Because of the drasticallydifferent chemical and electrostatic properties of lipid andwater proper descriptions of proteinminuslipid and proteinminuswaterinteractions are key for the successful simulation of amembrane channel To model ion conduction through arelatively rigid channel (eg gA or KcsA channel) it is possibleto use an implicit solvent model of the channelrsquos environmentin which the volume occupied by lipid and water is treated ascontinuum media of dielectric constants 2 and 78 respec-tively299 However when interactions between a channel and alipid membrane are significant (eg in mechanosensitivechannels) explicit modeling of lipid molecules is essentialThe tails of lipids are long and equilibrate slowly making it

significantly more difficult to assemble a model of a channelembedded in an explicit lipid bilayer than a model of a fullysoluble protein Usually the system setup involves thefollowing steps Starting from a pre-equilibrated and solvatedlipid bilayer membrane one makes a pore in the bilayer bydeleting a minimal number of lipid molecules so that theprotein can fit Next an all-atom model of the protein is placedin the pore which is followed by energy minimization andequilibration of the system using the MD method having thechannelrsquos coordinates restrained to their crystallographic valuesFinally when the proteinminuslipid interface is well equilibratedone can perform a production run without applying restraintson the channel For detailed step-by-step instructions forbuilding atomic-scale models of ion channels in lipid bilayerenvironment interested readers are directed to a tutorial onMD simulations of membrane proteins502 Even though a fullyautomated procedure is not yet available several programs canassist a beginner in building a new system VMD503 containsthe Membrane Builder plugin Jo et al have a web-based

service CHARMM GUI Membrane Builder (httpwwwcharmm-guiorgmembrane)504505

An alternative method for creating an all-atom model of anion channel in its native environment is to first carry out self-assembly simulations using a coarse-grained (CG) MDmethod74165379 The main difference between the CG andall-atom MD methods is the level of detail used to describe thecomponents of the system Typically one CG bead representsabout 5minus10 atoms Being much more computationally efficient(and lower resolution) the CG model allows millisecond-time-scale simulations to be performed on commodity computersInterested readers are directed toward recent reviews on thissubject506minus508

In the CG simulations of self-assembly CG models of lipidssolvent and a membrane protein are placed with randompositions in desired proportions During the course of CGMDsimulations the lipid molecules spontaneously form a lipidbilayer around a protein After obtaining a stable model the CGmodel can be reverse-coarse-grained into a fully atomisticmodel (see for example a study by Maffeo and Aksimen-tiev330) A great advantage of this approach is that it requiresno a priori knowledge of the position of the membranechannels relative to the membrane An obvious disadvantage isthat one has to have a reasonable CG model to carry out theself-assembly simulations and a reliable procedure to recoverthe all-atom details from the final CG model Currently it isnot possible to use a CG approach to model ion conductancethrough large membrane channels due to inaccurate treatmentsof the membrane and water electrostatics in most CG modelsHowever work to improve CG methods is ongoing509510 andsuch simulations should become possible in the near future

433 Homology Modeling Usually an all-atom MDsimulation of a channel protein can be performed only when anatomic-resolution structure of the channel is available Thisrequirement severely limits application of the MD methodFortunately membrane channels of different organisms oftenhave similar amino-acid sequences The sequence similarity canbe used to build an all-atom model of the channel that does nothave an experimentally determined structure through aprocedure called homology modeling511 Briefly homologymodeling proceeds as follows First a sequence alignmentbetween a target sequence and a homologous sequenceforwhich a structure is knownis performed Second thesecondary structures (eg α-helices and β-sheets) of the targetsequence from the homologous sequence are built Finallyloops connecting the secondary structures are modeled and theoverall structure is refined There exist many tools for thehomology modeling (eg Modeler by Sali and Blundell511)The homology modeling method has been successfully used

for building initial structures of several ion channels forsubsequent all-atom MD simulations Capener et al512 built aninward rectifier potassium channel (Kir) based on a high-resolution structure of KcsA1 Sukharev et al used the crystalstructure of Mycobacterium tuberculosis MscL407 to modelclosed intermediate and open structures of Escherichia coliMscL231232 Law et al combined the crystal structure of theLymnea stagnalis acetylcholine binding protein and the electronmicroscopy (EM) structure of the transmembrane domain ofthe torpedo electric ray nicotinic channel to build an entirehuman nicotinic acetylcholine receptor213

434 Free-Energy Methods Perhaps the greatestdisadvantage of the MD method is that simulations are costlyand are currently limited to the microsecond time scalea

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charges) and empirical matching of thermodynamic data (eghydration free energy)A biomolecular force field is a set of bonded and nonbonded

parameters defined in eqs 17 and 18 Presently severalbiomolecular force fields exist The force fields can becategorized into types based on whether all the atoms areexplicitly treated or not All-atom force fields which includeCHARMM489 AMBER490491 and OPLS-AA492493 treat allatoms explicitly In the united-atom force fields (egGROMOS494495) some nonpolar hydrogen atoms areneglectedFor the simulations of channel proteins a lipid force field is

as important as a protein force field because the channels areembedded in lipid bilayers Among the all-atom force fields theCHARMM force field includes parameters for lipids the latestupdate at the time of writing this review is CHARMM36496

Together with the AMBER force field for the protein thegeneral all-atom AMBER force field (GAFF) can be used todescribe the lipid bilayer497498 Officially OPLS does notinclude lipid parameters Among the united-atom force fieldsGROMOS comes with lipid parameters499 Berger et alreported improved GROMOS-based lipid parameters basedon the condensed-phase properties of pentadecane500 Thislipid force field has been widely used in combination with otherprotein force fields such as AMBER OPLS and GROMOS501

For an in-depth review of various force fields we referinterested readers to a comprehensive review by Mackerell488

432 Ion Channels in Native Environment Unlikesoluble proteins that are surrounded only by water ion-channelproteins are embedded in a lipid bilayer and therefore are incontact with both water and lipids Because of the drasticallydifferent chemical and electrostatic properties of lipid andwater proper descriptions of proteinminuslipid and proteinminuswaterinteractions are key for the successful simulation of amembrane channel To model ion conduction through arelatively rigid channel (eg gA or KcsA channel) it is possibleto use an implicit solvent model of the channelrsquos environmentin which the volume occupied by lipid and water is treated ascontinuum media of dielectric constants 2 and 78 respec-tively299 However when interactions between a channel and alipid membrane are significant (eg in mechanosensitivechannels) explicit modeling of lipid molecules is essentialThe tails of lipids are long and equilibrate slowly making it

significantly more difficult to assemble a model of a channelembedded in an explicit lipid bilayer than a model of a fullysoluble protein Usually the system setup involves thefollowing steps Starting from a pre-equilibrated and solvatedlipid bilayer membrane one makes a pore in the bilayer bydeleting a minimal number of lipid molecules so that theprotein can fit Next an all-atom model of the protein is placedin the pore which is followed by energy minimization andequilibration of the system using the MD method having thechannelrsquos coordinates restrained to their crystallographic valuesFinally when the proteinminuslipid interface is well equilibratedone can perform a production run without applying restraintson the channel For detailed step-by-step instructions forbuilding atomic-scale models of ion channels in lipid bilayerenvironment interested readers are directed to a tutorial onMD simulations of membrane proteins502 Even though a fullyautomated procedure is not yet available several programs canassist a beginner in building a new system VMD503 containsthe Membrane Builder plugin Jo et al have a web-based

service CHARMM GUI Membrane Builder (httpwwwcharmm-guiorgmembrane)504505

An alternative method for creating an all-atom model of anion channel in its native environment is to first carry out self-assembly simulations using a coarse-grained (CG) MDmethod74165379 The main difference between the CG andall-atom MD methods is the level of detail used to describe thecomponents of the system Typically one CG bead representsabout 5minus10 atoms Being much more computationally efficient(and lower resolution) the CG model allows millisecond-time-scale simulations to be performed on commodity computersInterested readers are directed toward recent reviews on thissubject506minus508

In the CG simulations of self-assembly CG models of lipidssolvent and a membrane protein are placed with randompositions in desired proportions During the course of CGMDsimulations the lipid molecules spontaneously form a lipidbilayer around a protein After obtaining a stable model the CGmodel can be reverse-coarse-grained into a fully atomisticmodel (see for example a study by Maffeo and Aksimen-tiev330) A great advantage of this approach is that it requiresno a priori knowledge of the position of the membranechannels relative to the membrane An obvious disadvantage isthat one has to have a reasonable CG model to carry out theself-assembly simulations and a reliable procedure to recoverthe all-atom details from the final CG model Currently it isnot possible to use a CG approach to model ion conductancethrough large membrane channels due to inaccurate treatmentsof the membrane and water electrostatics in most CG modelsHowever work to improve CG methods is ongoing509510 andsuch simulations should become possible in the near future

433 Homology Modeling Usually an all-atom MDsimulation of a channel protein can be performed only when anatomic-resolution structure of the channel is available Thisrequirement severely limits application of the MD methodFortunately membrane channels of different organisms oftenhave similar amino-acid sequences The sequence similarity canbe used to build an all-atom model of the channel that does nothave an experimentally determined structure through aprocedure called homology modeling511 Briefly homologymodeling proceeds as follows First a sequence alignmentbetween a target sequence and a homologous sequenceforwhich a structure is knownis performed Second thesecondary structures (eg α-helices and β-sheets) of the targetsequence from the homologous sequence are built Finallyloops connecting the secondary structures are modeled and theoverall structure is refined There exist many tools for thehomology modeling (eg Modeler by Sali and Blundell511)The homology modeling method has been successfully used

for building initial structures of several ion channels forsubsequent all-atom MD simulations Capener et al512 built aninward rectifier potassium channel (Kir) based on a high-resolution structure of KcsA1 Sukharev et al used the crystalstructure of Mycobacterium tuberculosis MscL407 to modelclosed intermediate and open structures of Escherichia coliMscL231232 Law et al combined the crystal structure of theLymnea stagnalis acetylcholine binding protein and the electronmicroscopy (EM) structure of the transmembrane domain ofthe torpedo electric ray nicotinic channel to build an entirehuman nicotinic acetylcholine receptor213

434 Free-Energy Methods Perhaps the greatestdisadvantage of the MD method is that simulations are costlyand are currently limited to the microsecond time scalea

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duration insufficient to observe statistically significant numbersof most biologically relevant processes such as gating or ion-permeation events for most channels Very often a researcher isinterested in the free-energy difference between two conforma-tional states of the system as well as the free-energy landscapethat the system must traverse to transition between the statesFor this landscape to be well-defined an order parameter x thatdescribes when the system is in one of these states must beidentified Then the free energy along this order parameter isjust the potential of the mean force (PMF) W(x) experiencedby the system at any given value of x By definition

ρρ

= minus ⟨ ⟩⟨ ⟩

⎡⎣⎢

⎤⎦⎥W x W x k T

xx

( ) ( ) log( )

( )B

⟨ρ(x)⟩ is the average distribution function and x and W(x)are arbitrary constants usually representing the bulk withW(x) = 0513 The PMF can be calculated from brute-force all-atom simulations simply by observing the fraction of time xdwells at a particular value and building a histogram to estimate⟨ρ(x)⟩ In practice such simulations do not efficiently sample xand are therefore too computationally demanding to enjoyregular use Fortunately a host of techniques have beendeveloped for the purpose of calculating the PMF Interestedreaders are directed to recent comprehensive reviews on thissubject514515

One of the most important and widely used methods forobtaining the PMF is the umbrella sampling method which isemployed to enforce uniform sampling along one or moreorder parameters Typically external potentials are used torestrain the system about the specified values of the orderparameters in an ensemble of equilibrium simulations516 Theeffect of the restraining potentials can be removed and datafrom multiple simulations can be combined to construct thepotential of mean force (PMF) along the order parameter byusing the weighted histogram analysis method517 This methodis considered to be a gold standard against which other PMF-producing methods are compared although the simulations aregenerally recognized as being rather costly to performA similar method free-energy perturbation (FEP) allows

one to estimate the free-energy difference between two similarsystems In practice one creates a path from one system to theother that can be taken in small discrete steps that connect aseries of intermediate states The small differences in thesystemrsquos total energy between two adjacent states are averagedto obtain the free-energy change for the step connecting thestates These small free-energy changes are summed to find thetotal free-energy difference between the systems518519 TheFEP method is in principle very flexible and can be used tofind the free energy of enforcing a restraint upon the systemallowing one to estimate the PMF In practice the umbrellasampling method is easier for finding the PMF but FEP can beapplied to problems beyond the scope of umbrella samplingFor example by using FEP one can model the effect of ratherabstract changes to the system including the free energyrequired to create or destroy atoms or to mutate atoms fromone type to another Such procedures must carefully considerthe complete thermodynamic cycle for the results to remainphysically meaningfulOther equilibrium methods for finding the PMF exist but it

is also possible to estimate the PMF from nonequilibriumsimulations520minus526 For example during a steered MD (SMD)simulation one end of a spring is tethered to an atom and the

other end of the spring is pulled at a constant velocity Theforce applied on the atom is recorded allowing one to estimatethe PMF using the Jarzynski equality527 which averages thework over a large ensemble of simulations

435 Ionization States of Titratable Groups There arenumerous examples demonstrating that channel gating and ionconductance depend on the ionization states of several keyresidues (typically Asp Glu and His) of the chan-nel707184118124127528529 Therefore assigning correct ioniza-tion states to titratable amino acid groups is critical tosuccessful MD simulations of ion channelsFor the titration process shown in Figure 8 (Rminus + H+

RH) the equilibrium constant Ka and pKa are defined by

=minus +

K[R ][H ]

[RH]a(19)

and

= minus +minus

Kp log[R ]

[RH]pHa

(20)

where eq 20 is the HendersonminusHasselbalch equation Equation20 indicates that the relative populations of ionization statesdepend on both pKa of the group and pH of the environmentFor example a titrating group with pKa = 7 in water has a 50chance of being in a protonated state at pH = 7 Because thepKa of all amino acids in water is known determining ionizationstates of amino acids in water at a given pH is trivial Howeverdetermining the ionization states of amino acids buried in aprotein or a membrane is nontrivial because the pKasignificantly depends on the local environment475530

Figure 8 illustrates a thermodynamic cycle that is used for thecalculation of a pKa shift

475530 Here ΔG and ΔGref indicatethe free-energy difference between two ionization forms of atitratable group in water and in protein or membraneenvironment respectively whereas ΔG1 and ΔG2 indicate thetransfer free energy of RH and Rminus from water to the protein ormembrane environment respectively In a given environmentone can estimate the probability of observing two ionizationstates RH and Rminus if ΔG is known

=minus

minusΔ[R ][RH]

e G k T B

(21)

Figure 8 Thermodynamic cycle for calculations of a pKa shift RH andRminus denote protonated and deprotonated states respectively of atitratable group The gray box indicates a region near a protein or amembrane ΔGref and ΔG denote free energies of deprotonation inwater and in protein or membrane environment respectively ΔG1 andΔG2 are transfer free energies of RH and Rminus from water to protein ormembrane environment respectively

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However accurate calculation of ΔG is nontrivial even in purewater because the protonation process involves various free-energy components such as transfer of a hydrogen ion fromwater to the vicinity of a protein formation of a bond betweenthe hydrogen and a protein and charge redistribution after thebond is formed475530 Instead one calculates the differencebetween ΔG and ΔGref ΔΔG = ΔG minus ΔGref Then the pKa ofan ionizable residue buried in a protein or a membrane isobtained as

= + ΔΔK Kk T

Gp p1

2303a arefB (22)

where pKaref is the experimentally determined pKa in waterCalculating ΔΔG instead of ΔG is convenient because one canusually assume that nonelectrostatic components cancel outand ΔΔG can be approximated by a simple charging freeenergy using either an all-atom force field or continuumelectrostatic model475

Usually ΔΔG is computed by performing free energycalculations (eg FEP see section 434) in water (ΔGref) andin protein or membrane environment (ΔG) and taking thedifference between them An alternative method of computingΔΔG (and hence the pKa shift) is to perform PMF calculationsto obtain transfer free energies ΔG1 and ΔG2 (see Figure 8)utilizing the following equality ΔΔG = ΔG minus ΔGref = ΔG2 minusΔG1 Therefore one can calculate ΔΔG by performing twoPMF calculations for RH and Rminus and taking the differencebetween them A series of pKa shift calculations of model aminoacids in the membrane environment demonstrated how thosetwo different methods can be used consistently to determinethe ionization states of amino acids531minus536

Although free-energy calculations using atomistic MDsimulations are the most rigorous way to estimate the pKashift this approach is computationally expensive AlternativelypKa shifts can be more efficiently calculated using continuumelectrostatic models such as the PB theory91537minus547 see section411 for details In the continuum electrostatic frameworkmembrane and water can be represented as continuum mediawith dielectric constants of sim80 and lt10 respectively548549

and the pKa shifts can be computed using popular computercodes for numerically solving the PB equation such asDelPhi476 and APBS477 Several web applications automatesuch pKa shift calculations including H++

550 PROPKA551 andPBEQ-Solver552

436 Accelerated Molecular Dynamics Simulationson a Special-Purpose Machine Presently the practical timescale of a continuous all-atom MD simulation is at mostseveral microseconds much shorter than the duration of typicalbiologically important processes even when using state-of-the-art supercomputers and MD codes Recently D E Shaw andco-workers demonstrated that millisecond all-atom MDsimulations can be performed by using Anton a special-purpose hardware designed only for MD simulations553minus556

Such a groundbreaking advance in MD simulation techniqueequipped with an accurate model for biomolecules mightindeed lead to a ldquocomputational microscoperdquo with which onecan observe biochemical processes at spatial and temporalresolutions unreachable by any experimental method553556

Indeed Anton is named after Anton van Leeuwenhoek an earlymicroscopist who made great advances in the fieldEvery modern computer including Anton utilizes a parallel

architecturea simulation is performed using multiplecomputational nodes that communicate with one another

Thus overall performance depends on not only thecomputation speed of each node but also communicationspeed The Anton developers accelerated the computationspeed by designing an application-specific integrated circuit(ASIC) that is optimized to almost all common routines usedin MD simulations including computation of nonbonded andbonded forces computation of long-range electrostaticinteractions constraints of chemical bonds and integration ofthe Newton equation To enhance the communication speedthey optimized the network within an ASIC as well as betweenASICs to the common communication patterns of MDsimulations Detailed information on the design of Anton canbe found in a recent publication553

Since Anton went into production D E Shaw and co-workers have demonstrated the potential of the special-purposemachine to revolutionize computational studies of ion channelsAntonrsquos unique ability to probe biologically relevant time scaleshas led to a number of discoveries For example they haveshown explicitly how a voltage-gated potassium channel (KV)switches between activated and deactivated states183196

successfully simulated drug-binding and allostery of G-protein-coupled receptors (GPCRs) in collaboration withseveral experimental groups557minus559 identified Tyr residuesthat are responsible for the low permeability of Aquaporin 0(AQP0) compared with the other aquaporins560 and revealedthe transport mechanism of Na+H+ antiporters (NhaA)showing that the protonation states of three Asp residues in thecenter of the channel are essential529 Anton has shown thetremendous advantages of special-purpose hardware for MDsimulation and there is little doubt that more such machineswill be developed and lead to even more illuminatingdiscoveries

44 Polarizable Models

All currently popular force fields represent nonpolarizablemodels of biomolecules and use fixed atomic charges Howeverthere are several known issues that can possibly limit theapplication of such nonpolarizable force fields to simulations ofchannel proteins First the electrostatic environment in achannel can be drastically different from that in the solventenvironment For example the selectivity filter of KcsA consistsof carbonyl oxygens and the filter is occupied by only a fewions or water molecules1 Thus the parameters describing ion-carbonyl interactions that were empirically calibrated in thesolvent environment could cause artifacts when used in theselectivity filter which was pointed out by Noskov et al141

Second the dielectric constant of lipid hydrocarbons withnonpolarizable force fields is 1 a factor of 2 less than in theexperiment561 The 2-fold underestimation of the dielectricconstant doubles the energy barrier for an ion crossing amembrane424 In the PMF studies of ion conductance througha gramicidin channel2930 Allen et al proposed to correct forthis artifact a posteriori however a polarizable force field couldbe a much better solution Third multivalent cations such asMg2+ and Ca2+ are difficult to describe using a nonpolarizablemodel because their high charge density induces polarization ofwater in the first solvation shell562563 Therefore a polarizablemodel might be essential in MD simulations of channelspermeated by divalent cations Fourth spatial separation ofpositively and negatively charged groups in lipids creates adipole along the membrane normal that deviates considerablyfrom experimental estimations when computed from all-atomsimulations564 Harder et al pointed out that this artifact arises

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from the lack of polarizability by showing that the agreementwith the experiment is significantly better when employing apolarizable model565

Motivated by the apparent limitations of the currentnonpolarizable models many research groups proposed variouspolarizable models566 However their development is still at theinitial stage and the application of polarizable models to thechannel proteins is still limited The two most practicalpolarizable models of biomolecules are the Drude oscillator andAMOEBA force fields566 Ponder and co-workers developed theAMOEBA force field in which molecular polarization can beachieved by using permanent atomic multipoles567minus569

Equipped with an analytic solution that treats intramolecularpolarization the AMOEBA force field can deal with flexiblemolecules such as peptides and lipids567 Even though theAMOEBA force field is not ready for all biomolecules (eglipid) it shows promising results for example reproducingstructural and thermodynamic data such as solvation structureand solvation free energy of small drug-like molecules569 andion solvation568

In the classical Drude oscillator model (eg ref 570)polarization is achieved by a charge harmonically bound to anatomic center In the presence of an electric field the mobilecharge oscillates around a position slightly displaced from theatomic center inducing a dipole moment By using the Drudemodel several promising results have been reported Forexample the description of monovalent and divalent cations isimproved563 and hydration free energies of small molecules canbe calculated more accurately571 However as for theAMOEBA force field the application of the Drude oscillatormodel is currently limited to small molecules in an aqueoussolution Thus the polarizable models must be furtherdeveloped and tested before they can be applied to an ion-channel systemAlthough it will take some time for the polarizable models to

replace the currently popular nonpolarizable models especiallyfor the simulations of channels there already have beenmeaningful attempts to test the polarizable models in themembrane environment For example Vorobyov et al appliedthe Drude oscillator model to calculate the transfer free energyof an arginine analogue to the lipid bilayer572 More recentlyWang et al used the Drude oscillator model in combinationwith a nonpolarizable model to study the transfer ofammonium through an ammonium transporter277 In thisstudy ammonium water and side-chains were treated usingthe polarizable model to better describe the less aqueouscharacter of the channel while the other parts were treatedusing the nonpolarizable model The successful demonstrationof such a hybrid approach is a very promising development thatwill likely grow in popularity until full polarizable simulationsbecome feasible

5 TYPICAL QUESTIONS OF INTERESTIdeally a simulation study of an ion channel would provide acomprehensive description of all aspects of the channelrsquosfunction In reality computational studies are limited by theaccuracy of the methods chosen the availability of computerresources and experimental knowledge of the system Amongthe many topics that could be probed about the function andbiological role of an ion channel we focus on the followingfour ion-binding sites and permeation pathways ionicconductance selectivity and gating The fifth subsection ofthis section details the use of computational methods in

biosensing applications of ion channels Although all five can beintegral parts of the same ion-transport mechanism suchdivision is possible in part due to the separation of the timescales Thus for some channels the time scale of 100 ns issufficient to observe selective ionic transport whereas for theother channels this time scale is barely sufficient to determinethe most probable locations of ions In general theexperimental conductance of an ion channel gives a goodestimate of the time scale of ion-permeation events and can beused to choose an adequate simulation method

51 Ion-Binding Sites and Permeation Pathways

To understand the microscopic details of ion selectivity andconductance one must know where ions are likely to be in thechannel The density of ions in a channel can be obtainedthrough all-atom simulation and is directly related to thepotential of mean force (PMF) The PMF is enormouslyvaluable because it plainly exposes the pits and barriers an ionmust traverse during its journey across a membrane The PMFmay yield significant insights into the specificity of a channel forcertain ionic species and it can support conjectures regardingthe impact of the protein structure on ionic conductanceBinding of multivalent ions can alter the structural features of amembrane channel573 and influence the outcome of structuredetermination studies574575

511 Potassium-Selective Channels Potassium ionpermeation across cell membranes has a long history ofquantitative study Hodgkin and Keynes found a relationbetween the ratio of K+ ions flowing into and out of a cell andthe voltage difference across the cell membrane that describedthe data across a wide range of intra- and extracellular K+

concentrations with only one free parameter n576 Seeking atheoretical explanation for the excellent fit of their heuristicequation they proposed the ldquoknock-onrdquo model in which K+

ions move single file through a chain of (n minus 1) K+ occupiedsites colliding with one another so they all move in a concertedfashion Hodgkin and Keynes found that the channel isoccupied by 2minus3 K+ ions Their explanation is remarkably closeto the mechanism revealed through X-ray crystallography andscores of simulation studies which showed that the selectivityfilter includes four binding sites usually occupied by two ionswith a third ion sometimes present near one of the twoopenings (see Figure 9)Simulation studies of the KcsA K+ channel have employed a

broad spectrum of methods to study occupancy of theselectivity filter by a set of ions The most used is the umbrellasampling method described in section 434The three-ion PMF for the process of ion permeation

through the KcsA filter was obtained in 2001126 The PMFallowed the authors to identify concerted transition pathwaysfor the ions demonstrating that the shallowest pathways forpermeation involved concerted motions of pairs of ionsHowever pathways involving all three ions were also observedwith barriers that were sim1 kcalmol larger than pathwaysinvolving only two ions The simulations revealed which of thebinding sites were most attractive to K+ A subsequent SMDstudy confirmed the concerted motion of pairs of K+ ions in theselectivity filter164

In 2008 a study compared several methodologies for findingthe PMF namely SMD in conjunction with the Jarzynskiequality (JE) umbrella sampling and another free-energycalculation technique called metadynamics176 Metadynamicsbelongs to a class of newer enhanced sampling protocols in

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which the system is pushed away from regions of phase spacethat have already been sampled577minus579 All of these methodsseek to map the free energy along one or more coordinatesalthough SMD is inherently one-dimensional A typical choicefor studies of single-file ion permeation is the position of one ormore ions along the pore axisThe PMFs of ion permeation through KcsA obtained from

SMD and umbrella sampling simulations were qualitativelysimilar and revealed overlapping minima and maxima176 Theresults obtained using these two methods were found to besensitive to the conformation of the residues in the filter andthe position of the ion in the cavity just outside the filter whichcould change on the time scale of the simulations The PMFsobtained using the SMD method were created by combiningdata from multiple simulations demonstrating the advantage ofincreased parallelization However for such an approach to bevalid individual simulations should be sufficiently long toaverage over conformational fluctuations Unfortunately theauthors did not sample equivalent amounts using these twomethods and thus a direct comparison could not be obtainedIn general the SMD method results in a PMF that has barriersconsiderably larger than those determined from umbrellasampling simulations512 Gramicidin A For details of the history of gramicidin

A in all-atom simulation we refer interested readers to recentreviews2139 Here we highlight the methodologies used tostudy ion channels that have been validated using gramicidin AThe first applications of quantitative MD methods to the

study of ion channels were free-energy perturbation calculations(FEP see section 434) on gramicidin A which providedsignificant insight into the ion-translocation process The firstsuch study was performed over 20 years ago and compared thesolvation free energy of a Na+ ion in gramicidin A at differentpositions in the pore to the solvation free energy in bulksolution18 The results of this study can be considered as a low-resolution PMF that indicated a series of rather large (sim5 kcalmol) pits and barriers within the channel Another FEP studydetermined the relative solvation free energy for Na+ in a singlyand doubly occupied gramicidin A relative to bulk water19 TheNa+ ions were then mutated into the other four commonmonovalent cations These calculations demonstrated thatsmall ions are less likely to doubly occupy gramicidin A

compared to large ions agreeing with experiment andsupporting the validity of the underlying model The umbrellasampling method was recently used to determine a two-ionPMF demonstrating that double occupancy in gramicidin A isnot favorable46

Single-ion permeation through gramicidin A has since beenstudied numerous times using the umbrella sampling35415051

and SMD38424348 methodologies Studies employing theumbrella sampling50 and SMD48 approaches have cautionedthat extensive simulations are needed to obtain completeconvergence using either method Sampling on the order ofhundreds of nanoseconds may be required to achieve theconvergence irrespective of the chosen method althoughunidirectional SMD simulations were found to exhibit severehysteresis in relatively short simulation when compared toumbrella sampling41

513 Others Channels PLN The uptake of Ca2+ by Ca2+-ATPase is regulated by the membrane protein phospholamban(PLN) which acts as an inhibitor Although more than 75 ofPLN in a lipid bilayer membrane is pentameric the only knownfunction of PLN ie Ca2+-ATPase inhibition involves a PLNmonomer and not a pentamer although there were a fewexperimental reports of ion conductance involving PLN580581

Using SMD330 and the umbrella sampling345 methods it wasrecently shown that the channel-like NMR model of the PLNpentamer does not conduct ions in agreement with morerecent experimental studies582

VDAC The Im group carried out all-atom MD study of thehuman VDAC1 to characterize the ion permeation andselectivity of the pore262 The study revealed that negativelycharged Asp and Glu residues serve as traps for K+ ions as theypass through the channel The one-dimensional multi-ion PMFcomputed for K+ and Clminus revealed the reason for the anionselectivity of the channel a higher free-energy barrier for K+

ions to enter the channelOmpF Im and Roux explored the ion density profiles and

the conductance of the Escherichia coli porin OmpF in adetailed study employing MD BD and PNP approaches5567

All three approaches revealed distinct ion pathways for K+ andClminus ions through the pore determined by the distribution ofcharged residues in the porin The phosphate selective porinOprP was recently studied using equilibrium SMD andumbrella sampling simulations80 The study revealed twonegatively charged phosphate-binding sites in the interior ofthe pore in close proximity to one another each with a freeenergy minimum of sim8 kBT Findings relating to thepreference of OprP for phosphate over Clminus will be discussedbelow

AmtB Luzhkov et al performed FEP and pKa calculations(see sections 434 and 435) using all-atom MD simulations tostudy the interaction of ammonium with the external bindingsites and determine the protonation states of ammonium278

They concluded that ammonium (NH4+) is dominant over

ammonia (NH3) near the external binding sites and thatdeprotonation can occur only inside the channel Bostick andco-workers also performed free-energy calculations using all-atom MD simulations275276 By calculating the transfer freeenergy of both ammonium and ammonia they showed apossible transport mechanism of ammonium through thechannel Moreover they emphasized the importance ofdehydration in the channel for the deprotonation ofammonium Most recently Wang et al used hybrid polarizablemechanicsmolecular mechanics (PMMM) simulations and

Figure 9 Selectivity filter of KcsA The system is depicted as in Figure5 but additionally with K+ ions resolved in the X-ray structure (orangespheres) In the active state the selectivity filter will always contain atleast two K+ ions separated by a single water molecule

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hybrid quantum mechanicsmolecular mechanics (QMMM)simulations to elucidate the permeation mechanism of bothammonium and protons277

ClC Cohen and Schulten260 explored the mechanism ofanion conduction across the ClC chloride channel by PMFcalculations using atomistic simulations The resulting PMFrevealed that the energy barrier for conduction of a single Clminus

ion is prohibitively high Interestingly the energy barrier wasreduced to 4 kcalmol in the presence of two Clminus ions in thepore suggesting that the incoming Clminus pushes the central ClminusSuenaga et al performed all-atom MD simulations to test thehypothesis that ClC channels are H+minusClminus exchange trans-porters Their results suggested that cations such as H+ and Na+

facilitate the channel opening and Clminus conduction261 Chungand co-workers utilized BD and MD simulations to reveal thebinding site of Clminus in the channel the electrostatic barrier ofClminus and the gating by an external Glu residue in atomisticdetail265266 Recently the first eukaryotic ClC transporter wascrystallized583 and Cheng and Coalson compared the Clminus

transport through the eukaryotic channel with that throughthe prokaryotic channel264 Their PMFs of Clminus in the channelsuggested that proper protonation of the external Glu gate iscritical for conduction

52 Ion Conductance

The force driving the permeation of ions through an ionchannel is the transmembrane potential arising from an unequaldistribution of ions on the two sides of the membrane A smallcharge imbalance in the vicinity of the pore gives rise to thepotential difference173 Explicit modeling of such chargeimbalance is difficult in all-atom MD simulations of a singlebilayer system as such simulations usually employ periodicboundary conditions so that the solution found at the two sidesof the membrane is one continuous volume One possibility isto use a single bilayer and two electrolyte compartmentsterminated by a vacuumwater interface329 An alternativeapproach is to use a twin bilayer system that includes twosolution phases584 of unequal ionic makeup that can generate atransmembrane electric field solely based on ion dynamics Inearly studies employing the twin bilayer setup the twomembranes were used to define the compartments of differention concentration A transmembrane potential was establisheddue to a small charge imbalance between the two compart-ments which was sufficient to generate short unsustained ionflux through the membrane channels To produce a continuousion flux the charge imbalance between the two compartmentshas to be maintained Kutzner et al recently demonstrated amethod to exchange ionwater pairs between the compart-ments and thus sustain the charge imbalance339 This methodwas applied to bacterial porin PorB of Neisseria meningitis todetermine the ion conductance and selectivity of the porinThe double-membrane approach however requires larger

systems which significantly increases the computationaloverhead A simpler alternative is to apply an external electricfield normal to the membrane to generate ionic flux throughthe pore Despite the apparent artificiality of the methodRoux173 provided a rigorous theoretical framework for thisstrategy An early study by Crozier et al289 in which the flow ofsodium ions was simulated through a simplified channel-membrane system under an imposed electric field demon-strated the feasibility of modeling an ionic current through amembrane In 2005 Aksimentiev and Schulten90 showed thatthe currentminusvoltage relationship of α-hemolysin could be

directly computed from all-atom MD simulations by applyingan external electric field The multinanosecond trajectoriesobtained in this 2005 study firmly established all-atom MD asthe method of choice for exploring conductance properties ofnanopores and using MD simulations to guide the developmentof nanopore sensors585 A similar approach was later applied inthe studies of MscS by Sotomayor et al244 and of Escherichiacoli porins OmpF and OmpC by Pezeshki et al7981 A recentstudy provides a detailed description of the external electricfield approach346

521 Potassium Channels MD simulations of K+

translocation through the selectivity filter of Kv12 allowedfor direct observation of the ldquoknock-onrdquo mechanism during asmall number of permeation events151 Subsequent brute-forcesimulations permitted estimation of the channelrsquos conductanceat several transmembrane biases151183 The simulated con-ductance was found to be nearly three times larger than theexperimentally measured one The discrepancy could bepartially attributed to a domain that was missing in thesimulated structure and may obstruct ion access in experimentThe simulations determined a five-step map of the trans-location cycle which was in agreement with the cyclesproposed from multi-ion free-energy calculations126 Thebrute-force approach allowed for direct observation of thekinetics between these steps identifying dehydration of theincoming K+ ion as the rate-limiting step of ion transportthrough the selectivity filter

522 Mechanosensitive Channels Among the twobacterial mechanosensitive channels with known high-reso-lution structure (MscL and MscS) MscS has been the subjectof ion conductance studies for several reasons Theconductance of the open MscL channel was experimentallydetermined to be fairly large suggesting a pore diameter of upto 30 Aring231232 Through such a wide channel small solutes canpass almost freely making the study of ion conductance lessinteresting In contrast the first MscS conformation reportedby Bass et al408 had been initially thought to capture thechannel in an open ion-conducting form However subsequentcomputational studies determined that the transmembranechannel in that MscS structure was not wide enough to furnisha fully hydrated transmembrane pore241242

Anishkin et al and Sotomayor et al performed pioneeringMD simulations of MscS241242247 In their all-atom MDsimulations they characterized the structural stability of MscSbased on the structure determined by Bass et al408 Thesimulations revealed partial collapse of the pore suggesting thatthe MscS conformation was at best partially open Thesimulations examined the distribution of water and ions in thechannel revealing dehydration of the narrowest part of thetransmembrane pore Anishkin et al also performed SMDsimulations by pulling a chloride ion along the channelconcluding that the pore was not large enough for theconductance of chloride242 Vora et al studied ion conductancethrough MscS using the BD method also concluding that thepore in the crystal structure of MscS was not large enough forthat structure to represent a fully open conformation229

Unlike the previous studies in the all-atom MD simulationsof Spronk et al243 an external electric field was appliedmimicking the physiological transmembrane potential In thelatter study the authors observed an increase in hydration andion conduction through the channel suggesting that the crystalstructure captured a conformation close to an open stateSubsequently Sotomayer et al also reported an increase of the

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MscS pore radius upon the application of large transmembranepotential (12 V) in an all-atom MD simulation244

Recently Vasquez et al proposed fully closed and openconformations of MscS based on electron paramagneticresonance spectroscopy and all-atom MD simulations256257

In this open MscS conformation the pore diameter was sim10 Aringthroughout the channel which is large enough to yield aconductance consistent with the experimental measurementsMscS has a large balloon-like cytoplasmic domain which

might play an important role in ion conductance see Figure 4c Recently Gamini et al probed ion conductance through thepores in the cytoplasmic domain using Gluminus and K+ as modelions248 Their results suggested that the cytoplasmic domain isa molecular sieve that balances effluxes of Gluminus and K+ throughMscSThe conductance of MscS has also been modeled using

continuum electrostatics methods (see sections 41) Forexample Sotomayor et al used atomistic MD simulations togenerate multiple conformations of the channels and thecontinuum transport theory to compute the ionic current forthese conformations258586 Recently Song and Corry calculatedthe ionic currents through MscS using a simplified NernstminusPlanck (NP) theory and rather realistic BD simulations225 Thestudy has shown the ability of the NP theory to reproduce theresults of the corresponding BD simulations523 α-Hemolysin Noskov and co-workers88 explored the

currentminusvoltage relationship of the α-hemolysin channel usingGCMCBD and 3D-PNP approaches (described in sections422 and 412 respectively) One of the inputs for theGCMCBD study was the position-dependent diffusioncoefficient of each ion type To incorporate the effect of thechannel size a reduction factor for the diffusivities wascalculated as per Paine and Scherr587 The study showed theIminusV characteristic to be asymmetric with a higher current atpositive bias (with the trans-entrance at a higher potential thanthe cis) which was in qualitative agreement with experi-ments588589 The study also revealed that by switching off thecharges on the pore the asymmetry in the conductancepractically disappeared indicating that it is the chargedistribution of the pore that is responsible for the asymmetryrather than the shapeThe MD study by Aksimentiev and Schulten90 was the first

to demonstrate that atomistic simulations can be used to obtainchannel conductances with quantitative accuracy Specificallythe study found the transmembrane currents driven by anexternal electric field applied normal to the membrane to be inexcellent agreement with experiment The large pore diameterand the high salt concentration made direct comparisonbetween simulation and experiment possible A recent MDstudy by Bhattacharya et al93 probed the cation-dependentrectification of the α-hemolysin nanopore The rectification ofthe ionic current was found to be dependent on the type ofcations and increased from Li+ to Cs+ both in simulations andin experiments The MD simulations showed that the cationiccontribution to the ionic current was the dominant factorinfluencing current asymmetry The cation type-dependentasymmetry of the ionic current was explained by differentialaffinity of the cations to the charged residues at the trans-entrance of the pore which modulated the number of ionsentering the narrowest part of the pore Recent experimentalstudies using site-directed mutagenesis590 and cysteine-scanning mutagenesis347 of the α-hemolysin channel revealedthat the ion-selectivity gating and conductance properties are

significantly affected by the location and the type of charges onthe pore

524 Outer-Membrane Porins Over the past 10 yearsthere have been a number of studies addressing ion-conductance properties of various OMPs (see Table 1) Imand co-workers carried out pioneering studies of OmpF using acombination of GCMCBD6263 MD5567 and continuum55

methods These first studies of OmpF revealed asymmetriccharacter of ionic conductance and produced concentrationminusconductance relations that were in good agreement withexperiment55 OmpF was a test bed for development of theGCMCBD methodUsing the all-atom MD method Pezeshki and co-workers

explored ion conductance of two structurally similar E coliporins OmpC and OmpF over a range of temperatures pHvalues and KCl concentrations7981 The results of the MDsimulations were in good agreement with experiment at low saltconcentrations and room temperature The authors observedconsiderable differences between the simulated temperaturedependence of conductance and experiment which wasattributed to the MD force field because the latter wasoptimized for simulations at room temperature The temper-ature dependence of the channelrsquos conductance was found todiffer from that of a corresponding bulk solution indicating theimportance of ion-pore interactions Using all-atom MD Modiand co-workers investigated the temperature-dependent trans-port of the ionic liquid 1-butyl-3-methyl-imidazolium chloride(BMIM-Cl) through OmpF86 The study indicated thataqueous solution of BMIM-Cl can reduce the rate of antibioticstransport through OmpF which could lead to practicalapplications of BMIM-Cl in the field of nanopore sensorsThe transmembrane pore of OmpF contains several titratable

residues Hence its conductance can depend on the solutionpH Varma et al used all-atom MD simulations to determinepKa (see section 435) of several key residues of OmpF7071

The study has shown that the pore size and conductance ofOmpF become consistent with the X-ray structure andelectrophysiology data correspondingly only when appropriateprotonation states are assigned to the key Asp residues7071

The study of Vrouenraets and Miedema has investigated theeffect of point mutations in OmpF finding ionization states ofthe residues to be the key factor affecting the ionconductance84

53 Selective Permeability

Concentration gradients of different types of ions support avariety of intra- and intercellular signals It is therefore vital tohave membrane channels that can distinguish and selectivelyconduct ions of different types One can easily imagine anelectrostatic mechanism for regulating the flux of different ionspecies based on the ion charge but what about channels thatselect a particular ion from all ions of the same chargeExperimental studies suggesting existence of Na+ and K+

selective channels began as early as 1960591 By 1971 it hadbeen inferred that the K+ channel has a wide inner openingleading to a narrow passage which blocks the passage of largecations However the K+ channel also prefers the conductanceof K+ over Na+ and Li+ even though the latter are smaller Theldquosnug-fitrdquo explanation offered in 1972592 suggested that it isnot electrostatically favorable for a Na+ ion to enter an oxygen-lined cage unless that cage is of the same size as the Na+ ionotherwise the Na+ will not form favorable electrostatic contactscompared to its solvation shell However the ldquosnug-fitrdquo

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mechanism requires a rather rigid pore incompatible with mostprotein structures which can only be described as soft andflexible Given that sodium and potassium appear to differ onlyon a scale significantly smaller than the size of an atom it isincredible that f lexible atomic-scale structures can yieldpermeabilities for the ions that may differ by a factor of1000593 The importance of subangstrom-scale structures andthe requirement of distinguishing between various physicalfactors naturally lend the study of ion selectivity to the all-atomMD methodology531 Potassium Channels The structures of all K+

channels feature a completely conserved constriction calledthe selectivity filter which is lined with four rings of negativecarbonyl-oxygen groups The structure of KcsA revealed two K+

ions separated by a single water molecule occupying this regionIn K+ channels the selectivity filter presents a barrier to iontransport and in general the larger the barrier the slower is theexpected rate of transport Thus early MD studies have focusedon the free energy difference experienced by K+ and Na+ ions inthe selectivity filter Because of the great similarity of these ionsthe free-energy perturbation (FEP) method has been theprotocol of choice for such studiesThe FEP method introduced in section 434 can evaluate

the free energy cost of transforming one atom into anotherthrough an unphysical pathway Because the end points of thistransformation are physically meaningful the change in freeenergy is also physically meaningful when considered as a stepin a thermodynamic cycle For example the difference inbinding free energy between K+ and Na+ in an ion channelΔΔG can be found from the free energies of transforming K+

into Na+ inside the channel and of transforming Na+ to K+ in abulk solution123 Both of these terms can be obtained fromFEP however care must be taken that the FEP simulations arelong enough that the system relaxes completely and fluctuationsare fully averagedEarly FEP simulations demonstrated a preference for K+ over

Na+ in the selectivity filter of KcsA120123141594 Howeverlimited by the computational resources available at the timethese simulations also suffered from problems small systemsizes that treated the lipid bilayer protein or water inunrealistic ways subnanosecond durations of simulations ateach FEP step andor external restraints that enforced crystalstructure-like conformation on the selectivity filter Despitethese limitations the range of values for ΔΔG (5minus17 kcalmolfor a single ion) were in apparent agreement with experimentalmeasurements of relief of Ba2+ blockades by Na+ and K+Recently a combination of MD simulations and X-ray

crystallography suggested that the smaller monovalent cationsNa+ and Li+ have their own binding site in the plane of acarbonyl-oxygen ring of the selectivity filter of KcsA as depictedin Figure 10 rather than between two rings as for K+595

Subsequently one- two- three- and four-ion umbrellasampling simulations provided PMFs for a Na+ or K+ ionpermeating K+-filled selectivity filters of KcsA and Kir-Bac11191596 The authors of one study note that FEPsimulations utilizing short trajectories may not provide theion with enough opportunity to find its preferred binding siteand that such studies likely overestimate ΔΔG which theauthors estimated to be 2minus3 kcalmol596 Additional umbrellasampling simulations of a Ba2+-occupied filter demonstratedthat the results can be quantitatively reconciled with Ba2+

blockade measurements because the Na+ and K+ ions areinfluenced differently by the bound Ba2+ ion Although the

latter study596 has not yet garnered response it demonstratesthe utility of a thorough simulation for interpretation ofexperimental measurements Thus the story of potassiumchannel selectivity may still be incomplete

532 Outer-Membrane Porins Porins often exhibitselectivity toward specific molecules For instance the outer-membrane protein OprP of Pseudomonas aeruginosa ananalogue of the PhoE porin of Escherichia coli is aphosphate-selective pore What is particularly interesting isthat it is not just anion-selective but can discriminate betweenanions OprP is highly selective toward the permeation ofinorganic phosphate (Pi) over other anions from the externalenvironment to the interior of the cell597 Atomistic simulationsperformed by Pongprayoon et al80 employing constant velocitySMD and umbrella sampling demonstrated that a lysine clusternear the periplasmic end of the pore selected ions by binding Pi

with greater affinity than small anions such as Clminus Theperiplasmic mouth of the pore can accommodate a fullysolvated Clminus ion which is therefore dielectrically screened fromthe positively charged lysine cluster Pi on the other hand ispartially dehydrated when it enters the pore at the periplasmicside and therefore interacts strongly with the lysine residuesThe extracellular end of the porin however allows the passageof both Clminus and PiAnother interesting porin that has been widely studied using

computational methods is the moderately cation-selectiveOmpF trimer The IK+IClminus ratio obtained from atomisticsimulations by Pezeshki et al79 was found to be sim12 which issimilar to older estimations by Im and Roux obtained fromGCMCBD and PNP approaches55 The key to theconductance and selectivity of the porin lies in its structureOne of the loops on the extracellular side the L3 is of specialimportance as it folds back into the β-barrel constricting thechannel Positively charged arginine residues on the wall of theporin face the negatively charged residues on the loop creatinga transverse electric field in the constriction region of theOmpF This field can orient molecules and cause a separationof ion fluxes5565 Experimental as well as computationalstudies83 have shown that it is possible to alter and evenreverse the selectivity of the OmpF by mutating the chargedresidues in the constriction region (both on the L3 loop andthe pore wall)

Figure 10 Na+ (green sphere) and K+ (red spheres) ions occupydifferent binding sites in the selectivity filter of a potassium channelEarly FEP simulations indicated a large free-energy cost ΔΔG forexchanging K+ with Na+ at the K+ binding sites ΔΔG may actually besmaller if the ion is free to move to its preferred binding site Adaptedwith permission from ref 595 Copyright 2009 Macmillan PublishersLtd Nature Structural amp Molecular Biology

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54 Ion-Channel Gating and Blockages

Proper cellular function requires that ions be released at certaintimes but not at other times and this variable ion conductanceis called gating For example the mechanosensitive channels inbacteria open to prevent rupture of the cell when tension in thebilayer increases due to osmotic stress Mechanosensitivechannels also initiate the conversion of mechanical vibrationsin the inner ear into electrical signals Similarly voltage- pH-and ligand-induced gating allow signals to be initiated orpropagated depending on the cellular conditionsGating almost always involves changes in the conformation

of the channel Until very recently brute-force atomisticsimulations of such changes were not possible because of thetime-scale limitations Below we discuss exemplary studiesincluding mechanical gating of the bacterial mechanosensitivechannels of small and large conductance and voltage gating of aK+ channel Additionally we discuss blockades of ion channelscaused by neurotoxins which may have pharmacologicalsignificance541 Mechanical Gating Even though several crystal

structures of MSCs are available the gating mechanisms remainelusive Unlike ligand- or voltage-gated ion channels wheregating is triggered by a relatively local structural change gatingof mechanosensitive channels involves a global structuraltransition231232 Consequently the time scale of the gating issignificantly greater than in other channels as is the length scalethat needs to be considered222 Although the large length scaleand long time scale of the mechanosensitive gating posepractical problems in computational studies of the gatingmechanism the prokaryotic MscL and MscS channels are idealsystems to develop the computational methodology because ofthe relative simplicity of these channels that are believed to betension sensors onlyWhen only one MSC crystal structure was available (a closed

conformation of MscL from Mycobacterium tuberculosis Tb-MscL) Sukharev and co-workers proposed a gating model forEscherichia coli MscL (Ec-MscL) in which the channel opensvia an ldquoiris-likerdquo mechanism231minus233 Starting from the closedconformation they modeled the intermediate and final openconformations in atomistic detail by utilizing various exper-imental information and empirical energy functions of theCHARMM force field In the open conformation the pore sizewas predicted to be sim30 Aring while the pore size of the closedcrystal structure was only a few angstroms impermeable tosmall molecules Physiological studies provided estimates of theopen pore diameter that were close to the result of theSukharev model (eg refs 255 598 and 599)Using the gating model of Ec-MscL several groups

performed MD simulations to test the model and observe thegating transition in all-atom detail230234236minus239 Kong et alcarried out targeted MD simulations to observe the transitionfrom closed to open conformations of the Ec-MscL230

Gullingsrud et al used SMD to induce opening of the closedconformation of Ec-MscL234238 In the SMD simulations it wasassumed that the forces on the protein by membrane stretchingapply only to the residues at the waterminuslipid interface whichwas based on observations of the pressure profile in pure lipidbilayers239 The same study used the pressure-profilecalculations to estimate the magnitude of the SMD force(35minus70 pN)Other than gating by tension Elmore and Dougherty

considered the effects of point mutations and lipidcompositions on the Tb-MscL structures using MD simu-

lations235240 Later Meyer et al studied the effect of a single-tailed lipid (which has high spontaneous curvature) on thestructure of Ec-MscL249 The simulations began from amanually built dome-shaped structure containing an Ec-MscLchannel embedded at the top of the dome During a 95-nssimulation the researchers observed spontaneous restructuringof the periplasmic loops of MscL which was in agreement withexperimental observations Recently Debret et al simulated Ec-MscL embedded in a lipid bilayer whose hydrophobic thicknesswas significantly smaller than the height of Ec-MscL250 Theresearchers observed tilting of transmembrane helices suggest-ing that hydrophobic mismatch can lower the activation energyof Ec-MscL opening Another all-atom MD simulations of Tb-MscL emphasized the interplay between protein and lipidbilayer by showing that inclusion of the protein significantlyincreases the mechanical rigidity of a lipid annulus251

Despite a number of ingenious efforts gating by tension hasnot been observed in all-atom MD simulations withoutapplying artificial driving forces The main difficulty is thetime scale of the mechanical gating which is significantly longerthan the time scale of an all-atom MD simulation To overcomethe time-scale problem several researchers applied morecomputationally efficient methods at the expense of accuracyPhillips and co-workers used continuum elasticity theory toevaluate the energetics of membrane deformation by theinclusion of MscL neglecting the internal energy of MscL forsimplicity226minus228 Their analytic calculations showed that gatingof MscL proteins can be modulated by the mechanicalproperties of the membrane226227 Moreover they alsodemonstrated how the function of multiple MscL channelscan be coupled Later Chen and co-workers applied computa-tional continuum mechanics to study the gating ofMscL221minus223 In their novel approach they explicitly consideredthe conformational change of MscL by modeling the MscLstructure using a simple elastic rodlike representation of thetransmembrane helices By combining such a simple model ofMscL with a continuum model of the membrane in a finite-element framework and parametrizing the models using all-atom MD simulations they were able to observe mechanicalgating of MscL just by stretching the membraneParticle-based coarse-graining offers another route toward a

simpler model of mechanical gating In this framework groupsof atoms are represented by single interaction beads whichdramatically increases the computational efficiency of the MDsimulation The interactions between such coarse-grained beadsare calibrated to reproduce the thermodynamic properties ofmodel systems obtained from all-atom MD simulations orexperiments (eg transfer free energy of small molecules fromwater to hydrocarbon) Marrink and co-workers applied theirnovel coarse-grained model MARTINI252 to Tb-MscL253254

Specifically they were able to simulate gating of MscL just bystretching the membrane253 or pressurizing a vesicle thatcontained embedded MscL channels254

When the time scale accessible to an MD simulation issignificantly shorter than the time scale of gating one canaccelerate the simulation by applying biasing forces (egSMD) However the quality of such accelerated simulationsdepends critically on how realistic the biasing forces are In thissense combining single-molecule experiments with SMDsimulations can be very successful For example Corry et alrecently demonstrated that the distance measurements fromForster resonance energy transfer (FRET) confocal microscopycan be used as a guide for the SMD simulation255 Starting from

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a closed conformation the researchers induced a closed-to-open conformational transition by performing SMD simu-lations that utilized distance constraints derived from FRETmeasurements on an open MscL channel Because of thedistance constraints the simulations produced a reasonablestructural model of the MscL pore in an open state542 Potassium Channels Potassium channels which all

share a common sequence for the selectivity filter demonstratevoltage- pH- and Ca2+-dependent gating of an intracellulargate which limits K+ access to the selectivity filter andextracellular solution However the selectivity filter is itself afragile structure that can be inactivated Inactivation of theselectivity filter occurs more readily when the intracellular gateis open186

It may be insightful to consider purely solution-dependentinactivation and inhibition of the selectivity filter A potassiumion channel will nearly irreversibly inactivate if it is placed inelectrolyte solution of very low ion concentration All-atom MDsimulations suggested a mechanism of such inactivation bydemonstrating severe distortion of the selectivity filter when itis depleted of K+ ions that partially neutralize the negativecarbonyl-oxygens lining of this structure137143182 Similarlyconductance of K+ channels can be blocked by other ions suchas Na+ or Cs+ that bind to the selectivity channelThe Kv channels are all voltage-gated Crystallographic

studies have provided structures for several open-pore Kvchannels featuring a charged voltage-sensitive subunit sur-rounded by lipids for each monomer of the tetramer411600601

The voltage-sensitive subunits are expected to move andrearrange in response to a voltage change in such a way that asmall but measurable transient capacitative current is observedacross the membrane The associated charge is known as thegating chargeThe gating charge times the change in the potential provides

the free energy required to change conformations and gate thechannel Using all-atom simulations the gating charge can bedirectly computed by measuring the difference in the center ofcharge of the system between open and closed conforma-tions185 A more sophisticated approach allows the assessmentof each residuersquos contribution to the gating charge through thecalculation of the difference between the free-energy cost ofcharging each residue in the closed and open states185

There is currently no crystallographically obtained closed-pore structure of a voltage-gated K+ channel However in astudy that utilized 13 μs of all-atom MD simulation the open-pore structure was refined and a possible closed-pore structurefor Kv12 was obtained185 Using these structures the gatingcharge was found to be somewhat smaller than theexperimentally measured gating charge suggesting that thecomputational model represented an intermediate conforma-tion at the onset of activationVery recently special-purpose hardware enabled all-atom

simulations of a Kv12Kv21 chimera on the gating-time scaleas observed experimentally (gt300 μs)196 The simulationsdemonstrated that the crystal structure accurately representsthe functional open pore In a series of simulations differentonly by the transmembrane voltage and the initial conditionsthe channel was brought from the open state to a fully closedstate Simulations were also performed to simulate differentstages of channel activation Gating of the channel occurred bystructural rearrangements of the voltage-sensitive domains thataffected the hydrophobic cavity leading to the selectivity filterThese rearrangements caused dewetting and collapse of the

cavity The time scales of various steps during the processagreed well with available experimental measurements196

Although not based on such long simulations a study of apH-sensitive potassium channel suggested that gating for thisprotein may occur through a rather different mechanism Anarginine residue near the extracellular side of the membranewas identified through mutagenesis as providing pH-sensitiv-ity602 The PMF of K+ ions in the selectivity filter was obtainedthrough all-atom MD when the protonation state of thatarginine residue was varied The authors of this study suggestedthat the observed 3minus4 kcalmol increase in the barriers for K+

translocation accounted for gating and arose from additionalflexibility that protonation of the arginine sensors granted tothe selectivity filter602 However it should be noted thatbecause no X-ray structure is available a homology model ofthe K2P channel built from Kv12 was used for this studyThus potassium channels share a great deal of structural and

sequence similarity around the selectivity filter but can be gatedin a variety of ways All-atom simulation techniques haveprovided a great deal of insight into the structural mechanismsof the gating processes In one exemplary study196 brute-forceall-atom MD simulations described the complete gating processof a voltage-sensitive potassium channel on a time scale ofhundreds of microseconds At this time it remains to be seenwhether other potassium channels use similar mechanisms togate

543 Blockades Some toxins bind and inactivateparticular target channels The potential for specificity ofchannel-binding toxins makes them an attractive source forpharmaceutical innovation The all-atom MD methodology hasbeen used to find the standard binding free energies of manysmall ligands but only recently have researchers attempted tofind the binding free energies of large ligands In particularseveral studies demonstrated challenges and shortcuts whencomputing standard binding free energies of charbydotoxinbinding to various voltage sensitive potassium chan-nels116603604

Of greater pharmacological interest the Kv13 K+ channelhas been identified as a target treatment of multiple sclerosisand other autoimmune disorders422 In a recent study the toxinShK which blocks Kv13 but also Kv11 was docked to severalK+ channels and the binding free energy was calculated425

Surprisingly the simulations revealed different binding geo-metries to Kv13 and Kv11 but similar binding free energiesthat agree well with experimentally determined values Theauthors concluded with mutations to ShK that may enhance theselectivity of Kv13 over Kv11At present free-energy calculations require too much

computing power and are not automated enough to be usedas a predictive tool by the pharmaceutical industry Inparticular reliably docking potential drug candidates remainsa challenge Nevertheless the combination of special-purposehardware for performing MD simulations very quickly andimproved automation of tools for calculating binding freeenergies may give rise to the use of all-atom simulations inadvanced computation drug screening within the pharmaceut-ical industry

55 Biosensing with Channels

About 20 years ago Bezrukov et al605 and Kasianowicz447 andco-workers demonstrated the possibility of using ionic channelsas molecular Coulter counters to detect the presence andcharacterize the type of biomolecules The basic principle of the

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approach is the following A membrane containing a single-ionchannel separates electrolyte solution into two compartmentsconnected only through the transmembrane pore of thechannel A transmembrane bias is imposed using an externalvoltage source producing a steady ionic current through anopen pore The transmembrane bias facilitates unidirectionaltransport of charged biomolecules from one compartment tothe other Each passage is detected as transient reduction (ablockade) of the ionic current flowing through the pore Theduration and magnitude of the ionic current blockades canindicate the length and chemical composition of a nucleic acidpolymer447606minus608 suggesting the possibility of recording thenucleotide sequence of a DNA strand directly by measuring theionic current flowing through a nanoporeCritical to the success of the above approach is the lack of

spontaneous gating of the ion conductance which if presentcan easily be confused with the signal resulting from interactionof the channel with a biomolecule Because of its superiorstructural stability the α-hemolysin channel was the firstnanopore to be considered for biosensing applications447609

However other channels such as the bacterial porinMspA449minus451 and man-made silicon-based610minus612 and gra-phene613minus615 nanopores have been successfully used fordetection of biomolecules Apart from DNA sequencingnumerous other applications have been proposed for nano-pores including detection of small analytes589616617 drugdesign390618 pathogen detection619 and force spectrosco-py620minus622 Interested readers are directed to several reviews onthis subject446623minus627

Modeling and computer simulations have played a major rolein development of nanopore applications585 There have alsobeen numerous theoretical studies of various aspects ofpolymer capture and translocation through nanoporesTypically such studies involve the application of scalingconcepts of polymer physics or transport equations628minus630 toelucidate the dynamics of charged polymer capture andtranslocation All-atom simulations have been used as a kindof a computational force microscope to directly relate themicroscopic events taking place in a nanopore to the ioniccurrent blockades recorded in experiment377585

551 α-Hemolysin Among many β-barrel proteins α-hemolysin has been the channel of choice for mostexperimental studies because of its exceptional structuralstability under harsh experimental conditions The knowncrystallographic structure and relatively straightforward site-directed mutagenesis procedures permit rational engineering ofthis channel to enhance sensitivity of ionic current blockadesfor example by introducing a molecular adapter616 or othersite-specific mutations631632

The 2005 publication by Aksimentiev and Schulten90

pioneered the application of the all-atom MD method forprediction of the ionic conductance of membrane channelsThe simulations demonstrated for the first time quantitativeaccuracy of the MD method in predicting the absolute value ofthe ionic current reproducing the asymmetric currentminusvoltagedependence of α-hemolysin and characterizing the electro-osmotic effect The simulations also suggested a microscopicmechanism explaining the pH-dependence of the noise in theionic current recordings633 The study has also demonstrated amethod for computing the average distribution of theelectrostatic potential in a membrane channel directly froman all-atom MD simulation90 Following the successful study ofionic conductance through α-hemolysin the researchers were

challenged by an experimentalist (A Meller Boston University)to predict the influence of the global orientation of a DNAstrand in α-hemolysin on the velocity of DNA transport andthe ionic current blockades This was a blind test as no priorinformation about the outcome of experiments was given Tofind out the molecular origin of the observed differences MDsimulations were performed on α-hemolysin systems havingDNA threaded through in two different global orientationsfrom 3prime to 5prime and from 5prime to 3prime The outcome of the simulationsrevealed a propensity for DNA nucleotides to tilt toward their5prime-ends in confined environments which was linked toobservable differences in DNA translocation dynamics andionic current blockades97 The results of the MD simulationswere in qualitative agreement with experiment Because oflimited computational resources direct quantitative comparisonwas not possible at that timeThe α-hemolysin channel has been a test bed for developing

advanced simulation techniques The Roux group exploredpermeation of ions through the α-hemolysin channel using 3D-PNP as well as the grand canonical Monte Carlo Browniandynamics (GCMCBD) approaches88 in the absence of anyanalytes The study revealed that the asymmetric conductanceof the pore arises from the permanent charge distribution in thepore Another PNP study examined the influence of chargedresidues in α-hemolysin on the asymmetry of the currentminusvoltage dependence89100 Shilov and Kurnikova96 employedMD simulations to investigate the energetics and dynamics of aβ-cyclodextrin (βCD) molecule confined inside the α-hemolysin pore The Roux group investigated the effect ofβCD on the ion selectivity of the α-hemolysin through MDsimulations and PMF calculations94 The simulations haveshown that electrically neutral βCD enhances the concentrationof Clminus in the nanopore by causing a partial desolvation of theions which reduces the dielectric shielding by the solvent TheGCMCBD method was used to account for multi-ion effectsin a subsequent study94 Simakov and Kurnikova devised amodified PNP approach to incorporate a soft repulsion modelof short-range interactions between mobile ions and protein92

To overcome the time-scale limitation of the MD methodthe Aksimentiev group developed a method for acceleratingsimulations of DNA transport through nanopores thatpreserves all-atom features of the MD model98 The key ideaof the method dubbed grid-steered MD (G-SMD) was theselective amplification of the electrostatic potential that drivesDNA transport while maintaining all other interactionsunchanged Using G-SMD the Aksimentiev group performedmultiple simulations of DNA transport through α-hemolysinand determined the dependence of the translocation velocityon the sequence and orientation of the DNA strands98 a taskthat was considered formidable at that time634 De Biase andco-workers recently developed a theoretical framework tomodel DNA translocation across a nanopore by combining theGCMCBD algorithm with a coarse-grained polymer model forDNA102 which enabled multimicrosecond simulations at afraction of the cost of all-atom MD When applied to modeltranslocation of poly(dA) and poly(dC) strands through α-hemolysin the model yielded results in reasonable agreementwith experiments Reiner et al367 developed an elegantcontinuum theory to describe the results of nanopore massspectroscopy experiments with quantitative accuracy635 Bondet al employed all-atom MD simulations to explore thetranslocation of short strands of DNA through a simplifiedmodel of the α-hemolysin pore comprising the stem of the pore

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surrounded by a membrane mimetic slab99 The studyexamined the effect of cationic amino acids on the translocationdynamics of DNA Compared to wild type α-hemolysinarginine mutations were found to reduce the transport rate ofDNA through the pore as well as the ionic current552 MspA The long stem of α-hemolysin can

accommodate up to 12 DNA nucleotides which makes difficultthe detection of single nucleotides by measuring ionic currentThe MspA porin has recently emerged as a viable alternative toα-hemolysin on account of its superior architecture MspA has agoblet-like structure with a constriction region that is sim1 nmideal for holding just one or two nucleotides see Figure 11aButler and co-workers showed that by eliminating the negativecharge in the constriction a variant of MspA called M1MspAwas capable of detecting a single DNA strand electrophoreti-cally driven through the pore449 A series of subsequentexperimental work in the Niederweis and Gundlach groupshave since established that the current resolution of the MspAvariant is superior to that of α-hemolysin636 and that singlenucleotide substitutions can be detected on a randomheteropolymeric background using a tethered DNA451

However the primary challenge is that the translocation rateof DNA through MspA is several orders of magnitude higherthan the rate required to resolve the type of DNA nucleotidesby measuring ionic current The two main strategies to controlDNA translocation are to engineer intrinsic brakes in the MspAstructure or use an auxiliary enzyme such as DNA polymer-ase637

The first computational study of MspA was recently carriedout by Bhattacharya and co-workers348 The study reportsextensive all-atom MD simulations that explored the effect ofpositively charged arginine residues on the translocation rate ofDNA and the ionic current On account of the highcomputational overhead due to the large system size theauthors performed the majority of the simulations using a

truncated version of the pore (see Figure 11b c) Since theDNA was found to be quite mobile even when confined to thenanopore the authors adopted an ensemble approach tosample the configurational dynamics of the DNA Theensemble method was shown to be a viable alternative tofollowing a single long-time-scale trajectory which is currentlypossible only using special-purpose supercomputers such asAnton The ensemble approach allowed the use of traditionalsupercomputers to obtain combined trajectory lengths of tensof microseconds within reasonable physical time Thesimulations have shown that by introducing several arginineresidues near the constriction of MspA the DNA permeationrate can be reduced by a factor of 10minus30 due to the formationof multiple salt bridges between the DNA backbone and theguanidinium groups of the arginine substitutions as well as dueto base-stacking interactions Furthermore the simulationspredicted that such mutations would not eliminate thenucleotide sensitivity of the ionic-current blockades Thestudy explained why similar mutations introduced in α-hemolysin reduced the ionic current practically to zero638

making such mutants unsuitable for DNA sequencingapplications

553 Other Nanopore Systems Other β-barrel nano-pores have been explored for stochastic sensing applicationsFor instance an MD study of the bacterial porin OmpG wascarried out by Chen and co-workers to determine the origin ofits spontaneous gating activity77 On the basis of the simulationstudy a variant of the porin with stabilizing mutations wascreated and was used for detection of adenosine diphosphateafter inserting a cyclodextrin molecular adapter77

Using 3D-Poisson equations and linear transport theory360

Vidal and co-workers demonstrated that a nanopore in a heavilydoped silicon membrane connected to a voltage source can beused as an electrically tunable ion filter The PNP model wasused to study ion transport through synthetic nanopores in

Figure 11 (a) Cut-away view of the full-length MspA nanopore embedded in a lipid membrane with a DNA strand threaded through The MspA isrepresented by a teal molecular surface the lipid membrane is represented by purple lines and the DNA bases are shown in magenta-colored licoricerepresentation (b) Average electrostatic potentials along the symmetry axis of the full and truncated MspA nanopores at a transmembrane bias of180 mV The electrostatic potentials are computed from MD simulations of open-pore MspA nanopores (c) Cut-away view of the reduced MspAsystem The DNA is covalently joined to itself across the periodic boundary (d) The ionic current trace of a sample trajectory of a poly(dC) strandthreaded through the MspA nanopore (e) Ionic current histograms obtained from ensemble simulations of the M1MspA (yellow) and its argininevariant M1 L88RA96RS116R (blue) The overlap of the two histograms is shown in green The histograms were constructed using 100 nsaverages of the instantaneous ionic current Adapted with permission from ref 348 Copyright 2012 American Chemical Society

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several studies359363366 exploring rectification and ionselectivity A Langevin dynamics approach to study thetransport of flexible macromolecules in confined geometrieswas proposed by Peters372 Recently an atomic resolution BDmethod was developed by Comer and co-workers that was usedto study the sequence dependence of ionic current in syntheticnanopores373374 All-atom MD simulations have been usedwith considerable success to investigate nanopore transport ofDNA and ionic current blockades375376 nanopore unzipping ofDNA hairpins380 the microscopic origin of the electrophoreticforce on DNA in a nanopore378381 and the effect of electrolyteon the DNA translocation rates391 For detailed description ofthe simulation protocols interested readers are directed torecent reviews on this subject585639640

6 OUTLOOK

Advances in computational technologies and membraneprotein structure-determination methods are poised to makemodeling and simulations of ion channels an integral part offuture drug-development efforts The greatest obstacle so far isthe lack of atomic-resolution structures of the majority ofbiomedically relevant ion channels Several limitations pertainto the computational technology itself Whereas all-atommolecular dynamics simulation of an ion channel can providethe most detailed information about the microscopicmechanism of its function the method is currently limited bythe accuracy of the classical force field and the microsecondtime scale of the simulations on conventional computerclustersTremendous advances in addressing both limitations have

already been made The first computational studies of ionchannel systems using polarizable models have already beenreported277563 Thus it is very likely that a full polarizable forcefield will become available within the next 10 years Anothermajor advancement was the millisecond simulation of amembrane channel in its native environment that revealedthe microscopic details of its voltage-dependent gatingmechanism196 We hope that such a tremendous success ofspecial-purpose hardware will prompt the development ofcommodity special-purpose hardware which will make suchlong-time-scale simulations available to mainstream researchersFinally advances in computational methods will also aid thediscovery of atomic-resolution structures through either denovo structure prediction641 or refinement of low-resolution X-ray and cryo-EM structures443

It would be misleading however to think that all questionspertaining to ion channels would be answered through all-atomMD From a drug-development perspective high-throughputand accurate calculation of binding free energies of smallchemical compounds is more important than long-time-scalesimulations of a single channelrsquos action Enabling such high-throughput docking is dependent on the availability of accurategeneric force fields Furthermore as millisecond simulationsbecome more available describing possible chemical reactionsbetween components of the system will become increasinglyimportant Finally modeling a single channel in a membrane isonly a first step toward the realistic modeling of in vivoprocesses We anticipate continuum and implicit solventapproaches to play a pivotal role in the development ofdetailed quantitative models of realistic biological membranesand small organelles that incorporate an ensemble of ionchannels

AUTHOR INFORMATION

Corresponding Author

E-mail aksimentillinoisedu

Notes

The authors declare no competing financial interest

Biographies

Christopher Maffeo received his BSc in physics from the University of

California Santa Barbara in 2006 He joined the Aksimentiev group in

December 2006 After studying the structural and conductance

properties of the phospholamban pentamer he has focused his efforts

on understanding the kinetics energetics and electrostatics of various

DNAminusDNA and DNAminusprotein interactions

Swati Bhattacharya is a postdoctoral fellow in the group of Aleksei

Aksimentiev at the University of Illinois at UrbanaminusChampaign She

received her PhD in physics for work on the adsorption of polymers

at surfaces under the supervision of Thomas Vilgis in 2009 from the

Max Planck Institute for Polymer Research in Mainz Her current

research activities include computational modeling aimed at

developing applications of nanopores particularly for DNA sequencing

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However accurate calculation of ΔG is nontrivial even in purewater because the protonation process involves various free-energy components such as transfer of a hydrogen ion fromwater to the vicinity of a protein formation of a bond betweenthe hydrogen and a protein and charge redistribution after thebond is formed475530 Instead one calculates the differencebetween ΔG and ΔGref ΔΔG = ΔG minus ΔGref Then the pKa ofan ionizable residue buried in a protein or a membrane isobtained as

= + ΔΔK Kk T

Gp p1

2303a arefB (22)

where pKaref is the experimentally determined pKa in waterCalculating ΔΔG instead of ΔG is convenient because one canusually assume that nonelectrostatic components cancel outand ΔΔG can be approximated by a simple charging freeenergy using either an all-atom force field or continuumelectrostatic model475

Usually ΔΔG is computed by performing free energycalculations (eg FEP see section 434) in water (ΔGref) andin protein or membrane environment (ΔG) and taking thedifference between them An alternative method of computingΔΔG (and hence the pKa shift) is to perform PMF calculationsto obtain transfer free energies ΔG1 and ΔG2 (see Figure 8)utilizing the following equality ΔΔG = ΔG minus ΔGref = ΔG2 minusΔG1 Therefore one can calculate ΔΔG by performing twoPMF calculations for RH and Rminus and taking the differencebetween them A series of pKa shift calculations of model aminoacids in the membrane environment demonstrated how thosetwo different methods can be used consistently to determinethe ionization states of amino acids531minus536

Although free-energy calculations using atomistic MDsimulations are the most rigorous way to estimate the pKashift this approach is computationally expensive AlternativelypKa shifts can be more efficiently calculated using continuumelectrostatic models such as the PB theory91537minus547 see section411 for details In the continuum electrostatic frameworkmembrane and water can be represented as continuum mediawith dielectric constants of sim80 and lt10 respectively548549

and the pKa shifts can be computed using popular computercodes for numerically solving the PB equation such asDelPhi476 and APBS477 Several web applications automatesuch pKa shift calculations including H++

550 PROPKA551 andPBEQ-Solver552

436 Accelerated Molecular Dynamics Simulationson a Special-Purpose Machine Presently the practical timescale of a continuous all-atom MD simulation is at mostseveral microseconds much shorter than the duration of typicalbiologically important processes even when using state-of-the-art supercomputers and MD codes Recently D E Shaw andco-workers demonstrated that millisecond all-atom MDsimulations can be performed by using Anton a special-purpose hardware designed only for MD simulations553minus556

Such a groundbreaking advance in MD simulation techniqueequipped with an accurate model for biomolecules mightindeed lead to a ldquocomputational microscoperdquo with which onecan observe biochemical processes at spatial and temporalresolutions unreachable by any experimental method553556

Indeed Anton is named after Anton van Leeuwenhoek an earlymicroscopist who made great advances in the fieldEvery modern computer including Anton utilizes a parallel

architecturea simulation is performed using multiplecomputational nodes that communicate with one another

Thus overall performance depends on not only thecomputation speed of each node but also communicationspeed The Anton developers accelerated the computationspeed by designing an application-specific integrated circuit(ASIC) that is optimized to almost all common routines usedin MD simulations including computation of nonbonded andbonded forces computation of long-range electrostaticinteractions constraints of chemical bonds and integration ofthe Newton equation To enhance the communication speedthey optimized the network within an ASIC as well as betweenASICs to the common communication patterns of MDsimulations Detailed information on the design of Anton canbe found in a recent publication553

Since Anton went into production D E Shaw and co-workers have demonstrated the potential of the special-purposemachine to revolutionize computational studies of ion channelsAntonrsquos unique ability to probe biologically relevant time scaleshas led to a number of discoveries For example they haveshown explicitly how a voltage-gated potassium channel (KV)switches between activated and deactivated states183196

successfully simulated drug-binding and allostery of G-protein-coupled receptors (GPCRs) in collaboration withseveral experimental groups557minus559 identified Tyr residuesthat are responsible for the low permeability of Aquaporin 0(AQP0) compared with the other aquaporins560 and revealedthe transport mechanism of Na+H+ antiporters (NhaA)showing that the protonation states of three Asp residues in thecenter of the channel are essential529 Anton has shown thetremendous advantages of special-purpose hardware for MDsimulation and there is little doubt that more such machineswill be developed and lead to even more illuminatingdiscoveries

44 Polarizable Models

All currently popular force fields represent nonpolarizablemodels of biomolecules and use fixed atomic charges Howeverthere are several known issues that can possibly limit theapplication of such nonpolarizable force fields to simulations ofchannel proteins First the electrostatic environment in achannel can be drastically different from that in the solventenvironment For example the selectivity filter of KcsA consistsof carbonyl oxygens and the filter is occupied by only a fewions or water molecules1 Thus the parameters describing ion-carbonyl interactions that were empirically calibrated in thesolvent environment could cause artifacts when used in theselectivity filter which was pointed out by Noskov et al141

Second the dielectric constant of lipid hydrocarbons withnonpolarizable force fields is 1 a factor of 2 less than in theexperiment561 The 2-fold underestimation of the dielectricconstant doubles the energy barrier for an ion crossing amembrane424 In the PMF studies of ion conductance througha gramicidin channel2930 Allen et al proposed to correct forthis artifact a posteriori however a polarizable force field couldbe a much better solution Third multivalent cations such asMg2+ and Ca2+ are difficult to describe using a nonpolarizablemodel because their high charge density induces polarization ofwater in the first solvation shell562563 Therefore a polarizablemodel might be essential in MD simulations of channelspermeated by divalent cations Fourth spatial separation ofpositively and negatively charged groups in lipids creates adipole along the membrane normal that deviates considerablyfrom experimental estimations when computed from all-atomsimulations564 Harder et al pointed out that this artifact arises

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from the lack of polarizability by showing that the agreementwith the experiment is significantly better when employing apolarizable model565

Motivated by the apparent limitations of the currentnonpolarizable models many research groups proposed variouspolarizable models566 However their development is still at theinitial stage and the application of polarizable models to thechannel proteins is still limited The two most practicalpolarizable models of biomolecules are the Drude oscillator andAMOEBA force fields566 Ponder and co-workers developed theAMOEBA force field in which molecular polarization can beachieved by using permanent atomic multipoles567minus569

Equipped with an analytic solution that treats intramolecularpolarization the AMOEBA force field can deal with flexiblemolecules such as peptides and lipids567 Even though theAMOEBA force field is not ready for all biomolecules (eglipid) it shows promising results for example reproducingstructural and thermodynamic data such as solvation structureand solvation free energy of small drug-like molecules569 andion solvation568

In the classical Drude oscillator model (eg ref 570)polarization is achieved by a charge harmonically bound to anatomic center In the presence of an electric field the mobilecharge oscillates around a position slightly displaced from theatomic center inducing a dipole moment By using the Drudemodel several promising results have been reported Forexample the description of monovalent and divalent cations isimproved563 and hydration free energies of small molecules canbe calculated more accurately571 However as for theAMOEBA force field the application of the Drude oscillatormodel is currently limited to small molecules in an aqueoussolution Thus the polarizable models must be furtherdeveloped and tested before they can be applied to an ion-channel systemAlthough it will take some time for the polarizable models to

replace the currently popular nonpolarizable models especiallyfor the simulations of channels there already have beenmeaningful attempts to test the polarizable models in themembrane environment For example Vorobyov et al appliedthe Drude oscillator model to calculate the transfer free energyof an arginine analogue to the lipid bilayer572 More recentlyWang et al used the Drude oscillator model in combinationwith a nonpolarizable model to study the transfer ofammonium through an ammonium transporter277 In thisstudy ammonium water and side-chains were treated usingthe polarizable model to better describe the less aqueouscharacter of the channel while the other parts were treatedusing the nonpolarizable model The successful demonstrationof such a hybrid approach is a very promising development thatwill likely grow in popularity until full polarizable simulationsbecome feasible

5 TYPICAL QUESTIONS OF INTERESTIdeally a simulation study of an ion channel would provide acomprehensive description of all aspects of the channelrsquosfunction In reality computational studies are limited by theaccuracy of the methods chosen the availability of computerresources and experimental knowledge of the system Amongthe many topics that could be probed about the function andbiological role of an ion channel we focus on the followingfour ion-binding sites and permeation pathways ionicconductance selectivity and gating The fifth subsection ofthis section details the use of computational methods in

biosensing applications of ion channels Although all five can beintegral parts of the same ion-transport mechanism suchdivision is possible in part due to the separation of the timescales Thus for some channels the time scale of 100 ns issufficient to observe selective ionic transport whereas for theother channels this time scale is barely sufficient to determinethe most probable locations of ions In general theexperimental conductance of an ion channel gives a goodestimate of the time scale of ion-permeation events and can beused to choose an adequate simulation method

51 Ion-Binding Sites and Permeation Pathways

To understand the microscopic details of ion selectivity andconductance one must know where ions are likely to be in thechannel The density of ions in a channel can be obtainedthrough all-atom simulation and is directly related to thepotential of mean force (PMF) The PMF is enormouslyvaluable because it plainly exposes the pits and barriers an ionmust traverse during its journey across a membrane The PMFmay yield significant insights into the specificity of a channel forcertain ionic species and it can support conjectures regardingthe impact of the protein structure on ionic conductanceBinding of multivalent ions can alter the structural features of amembrane channel573 and influence the outcome of structuredetermination studies574575

511 Potassium-Selective Channels Potassium ionpermeation across cell membranes has a long history ofquantitative study Hodgkin and Keynes found a relationbetween the ratio of K+ ions flowing into and out of a cell andthe voltage difference across the cell membrane that describedthe data across a wide range of intra- and extracellular K+

concentrations with only one free parameter n576 Seeking atheoretical explanation for the excellent fit of their heuristicequation they proposed the ldquoknock-onrdquo model in which K+

ions move single file through a chain of (n minus 1) K+ occupiedsites colliding with one another so they all move in a concertedfashion Hodgkin and Keynes found that the channel isoccupied by 2minus3 K+ ions Their explanation is remarkably closeto the mechanism revealed through X-ray crystallography andscores of simulation studies which showed that the selectivityfilter includes four binding sites usually occupied by two ionswith a third ion sometimes present near one of the twoopenings (see Figure 9)Simulation studies of the KcsA K+ channel have employed a

broad spectrum of methods to study occupancy of theselectivity filter by a set of ions The most used is the umbrellasampling method described in section 434The three-ion PMF for the process of ion permeation

through the KcsA filter was obtained in 2001126 The PMFallowed the authors to identify concerted transition pathwaysfor the ions demonstrating that the shallowest pathways forpermeation involved concerted motions of pairs of ionsHowever pathways involving all three ions were also observedwith barriers that were sim1 kcalmol larger than pathwaysinvolving only two ions The simulations revealed which of thebinding sites were most attractive to K+ A subsequent SMDstudy confirmed the concerted motion of pairs of K+ ions in theselectivity filter164

In 2008 a study compared several methodologies for findingthe PMF namely SMD in conjunction with the Jarzynskiequality (JE) umbrella sampling and another free-energycalculation technique called metadynamics176 Metadynamicsbelongs to a class of newer enhanced sampling protocols in

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which the system is pushed away from regions of phase spacethat have already been sampled577minus579 All of these methodsseek to map the free energy along one or more coordinatesalthough SMD is inherently one-dimensional A typical choicefor studies of single-file ion permeation is the position of one ormore ions along the pore axisThe PMFs of ion permeation through KcsA obtained from

SMD and umbrella sampling simulations were qualitativelysimilar and revealed overlapping minima and maxima176 Theresults obtained using these two methods were found to besensitive to the conformation of the residues in the filter andthe position of the ion in the cavity just outside the filter whichcould change on the time scale of the simulations The PMFsobtained using the SMD method were created by combiningdata from multiple simulations demonstrating the advantage ofincreased parallelization However for such an approach to bevalid individual simulations should be sufficiently long toaverage over conformational fluctuations Unfortunately theauthors did not sample equivalent amounts using these twomethods and thus a direct comparison could not be obtainedIn general the SMD method results in a PMF that has barriersconsiderably larger than those determined from umbrellasampling simulations512 Gramicidin A For details of the history of gramicidin

A in all-atom simulation we refer interested readers to recentreviews2139 Here we highlight the methodologies used tostudy ion channels that have been validated using gramicidin AThe first applications of quantitative MD methods to the

study of ion channels were free-energy perturbation calculations(FEP see section 434) on gramicidin A which providedsignificant insight into the ion-translocation process The firstsuch study was performed over 20 years ago and compared thesolvation free energy of a Na+ ion in gramicidin A at differentpositions in the pore to the solvation free energy in bulksolution18 The results of this study can be considered as a low-resolution PMF that indicated a series of rather large (sim5 kcalmol) pits and barriers within the channel Another FEP studydetermined the relative solvation free energy for Na+ in a singlyand doubly occupied gramicidin A relative to bulk water19 TheNa+ ions were then mutated into the other four commonmonovalent cations These calculations demonstrated thatsmall ions are less likely to doubly occupy gramicidin A

compared to large ions agreeing with experiment andsupporting the validity of the underlying model The umbrellasampling method was recently used to determine a two-ionPMF demonstrating that double occupancy in gramicidin A isnot favorable46

Single-ion permeation through gramicidin A has since beenstudied numerous times using the umbrella sampling35415051

and SMD38424348 methodologies Studies employing theumbrella sampling50 and SMD48 approaches have cautionedthat extensive simulations are needed to obtain completeconvergence using either method Sampling on the order ofhundreds of nanoseconds may be required to achieve theconvergence irrespective of the chosen method althoughunidirectional SMD simulations were found to exhibit severehysteresis in relatively short simulation when compared toumbrella sampling41

513 Others Channels PLN The uptake of Ca2+ by Ca2+-ATPase is regulated by the membrane protein phospholamban(PLN) which acts as an inhibitor Although more than 75 ofPLN in a lipid bilayer membrane is pentameric the only knownfunction of PLN ie Ca2+-ATPase inhibition involves a PLNmonomer and not a pentamer although there were a fewexperimental reports of ion conductance involving PLN580581

Using SMD330 and the umbrella sampling345 methods it wasrecently shown that the channel-like NMR model of the PLNpentamer does not conduct ions in agreement with morerecent experimental studies582

VDAC The Im group carried out all-atom MD study of thehuman VDAC1 to characterize the ion permeation andselectivity of the pore262 The study revealed that negativelycharged Asp and Glu residues serve as traps for K+ ions as theypass through the channel The one-dimensional multi-ion PMFcomputed for K+ and Clminus revealed the reason for the anionselectivity of the channel a higher free-energy barrier for K+

ions to enter the channelOmpF Im and Roux explored the ion density profiles and

the conductance of the Escherichia coli porin OmpF in adetailed study employing MD BD and PNP approaches5567

All three approaches revealed distinct ion pathways for K+ andClminus ions through the pore determined by the distribution ofcharged residues in the porin The phosphate selective porinOprP was recently studied using equilibrium SMD andumbrella sampling simulations80 The study revealed twonegatively charged phosphate-binding sites in the interior ofthe pore in close proximity to one another each with a freeenergy minimum of sim8 kBT Findings relating to thepreference of OprP for phosphate over Clminus will be discussedbelow

AmtB Luzhkov et al performed FEP and pKa calculations(see sections 434 and 435) using all-atom MD simulations tostudy the interaction of ammonium with the external bindingsites and determine the protonation states of ammonium278

They concluded that ammonium (NH4+) is dominant over

ammonia (NH3) near the external binding sites and thatdeprotonation can occur only inside the channel Bostick andco-workers also performed free-energy calculations using all-atom MD simulations275276 By calculating the transfer freeenergy of both ammonium and ammonia they showed apossible transport mechanism of ammonium through thechannel Moreover they emphasized the importance ofdehydration in the channel for the deprotonation ofammonium Most recently Wang et al used hybrid polarizablemechanicsmolecular mechanics (PMMM) simulations and

Figure 9 Selectivity filter of KcsA The system is depicted as in Figure5 but additionally with K+ ions resolved in the X-ray structure (orangespheres) In the active state the selectivity filter will always contain atleast two K+ ions separated by a single water molecule

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hybrid quantum mechanicsmolecular mechanics (QMMM)simulations to elucidate the permeation mechanism of bothammonium and protons277

ClC Cohen and Schulten260 explored the mechanism ofanion conduction across the ClC chloride channel by PMFcalculations using atomistic simulations The resulting PMFrevealed that the energy barrier for conduction of a single Clminus

ion is prohibitively high Interestingly the energy barrier wasreduced to 4 kcalmol in the presence of two Clminus ions in thepore suggesting that the incoming Clminus pushes the central ClminusSuenaga et al performed all-atom MD simulations to test thehypothesis that ClC channels are H+minusClminus exchange trans-porters Their results suggested that cations such as H+ and Na+

facilitate the channel opening and Clminus conduction261 Chungand co-workers utilized BD and MD simulations to reveal thebinding site of Clminus in the channel the electrostatic barrier ofClminus and the gating by an external Glu residue in atomisticdetail265266 Recently the first eukaryotic ClC transporter wascrystallized583 and Cheng and Coalson compared the Clminus

transport through the eukaryotic channel with that throughthe prokaryotic channel264 Their PMFs of Clminus in the channelsuggested that proper protonation of the external Glu gate iscritical for conduction

52 Ion Conductance

The force driving the permeation of ions through an ionchannel is the transmembrane potential arising from an unequaldistribution of ions on the two sides of the membrane A smallcharge imbalance in the vicinity of the pore gives rise to thepotential difference173 Explicit modeling of such chargeimbalance is difficult in all-atom MD simulations of a singlebilayer system as such simulations usually employ periodicboundary conditions so that the solution found at the two sidesof the membrane is one continuous volume One possibility isto use a single bilayer and two electrolyte compartmentsterminated by a vacuumwater interface329 An alternativeapproach is to use a twin bilayer system that includes twosolution phases584 of unequal ionic makeup that can generate atransmembrane electric field solely based on ion dynamics Inearly studies employing the twin bilayer setup the twomembranes were used to define the compartments of differention concentration A transmembrane potential was establisheddue to a small charge imbalance between the two compart-ments which was sufficient to generate short unsustained ionflux through the membrane channels To produce a continuousion flux the charge imbalance between the two compartmentshas to be maintained Kutzner et al recently demonstrated amethod to exchange ionwater pairs between the compart-ments and thus sustain the charge imbalance339 This methodwas applied to bacterial porin PorB of Neisseria meningitis todetermine the ion conductance and selectivity of the porinThe double-membrane approach however requires larger

systems which significantly increases the computationaloverhead A simpler alternative is to apply an external electricfield normal to the membrane to generate ionic flux throughthe pore Despite the apparent artificiality of the methodRoux173 provided a rigorous theoretical framework for thisstrategy An early study by Crozier et al289 in which the flow ofsodium ions was simulated through a simplified channel-membrane system under an imposed electric field demon-strated the feasibility of modeling an ionic current through amembrane In 2005 Aksimentiev and Schulten90 showed thatthe currentminusvoltage relationship of α-hemolysin could be

directly computed from all-atom MD simulations by applyingan external electric field The multinanosecond trajectoriesobtained in this 2005 study firmly established all-atom MD asthe method of choice for exploring conductance properties ofnanopores and using MD simulations to guide the developmentof nanopore sensors585 A similar approach was later applied inthe studies of MscS by Sotomayor et al244 and of Escherichiacoli porins OmpF and OmpC by Pezeshki et al7981 A recentstudy provides a detailed description of the external electricfield approach346

521 Potassium Channels MD simulations of K+

translocation through the selectivity filter of Kv12 allowedfor direct observation of the ldquoknock-onrdquo mechanism during asmall number of permeation events151 Subsequent brute-forcesimulations permitted estimation of the channelrsquos conductanceat several transmembrane biases151183 The simulated con-ductance was found to be nearly three times larger than theexperimentally measured one The discrepancy could bepartially attributed to a domain that was missing in thesimulated structure and may obstruct ion access in experimentThe simulations determined a five-step map of the trans-location cycle which was in agreement with the cyclesproposed from multi-ion free-energy calculations126 Thebrute-force approach allowed for direct observation of thekinetics between these steps identifying dehydration of theincoming K+ ion as the rate-limiting step of ion transportthrough the selectivity filter

522 Mechanosensitive Channels Among the twobacterial mechanosensitive channels with known high-reso-lution structure (MscL and MscS) MscS has been the subjectof ion conductance studies for several reasons Theconductance of the open MscL channel was experimentallydetermined to be fairly large suggesting a pore diameter of upto 30 Aring231232 Through such a wide channel small solutes canpass almost freely making the study of ion conductance lessinteresting In contrast the first MscS conformation reportedby Bass et al408 had been initially thought to capture thechannel in an open ion-conducting form However subsequentcomputational studies determined that the transmembranechannel in that MscS structure was not wide enough to furnisha fully hydrated transmembrane pore241242

Anishkin et al and Sotomayor et al performed pioneeringMD simulations of MscS241242247 In their all-atom MDsimulations they characterized the structural stability of MscSbased on the structure determined by Bass et al408 Thesimulations revealed partial collapse of the pore suggesting thatthe MscS conformation was at best partially open Thesimulations examined the distribution of water and ions in thechannel revealing dehydration of the narrowest part of thetransmembrane pore Anishkin et al also performed SMDsimulations by pulling a chloride ion along the channelconcluding that the pore was not large enough for theconductance of chloride242 Vora et al studied ion conductancethrough MscS using the BD method also concluding that thepore in the crystal structure of MscS was not large enough forthat structure to represent a fully open conformation229

Unlike the previous studies in the all-atom MD simulationsof Spronk et al243 an external electric field was appliedmimicking the physiological transmembrane potential In thelatter study the authors observed an increase in hydration andion conduction through the channel suggesting that the crystalstructure captured a conformation close to an open stateSubsequently Sotomayer et al also reported an increase of the

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MscS pore radius upon the application of large transmembranepotential (12 V) in an all-atom MD simulation244

Recently Vasquez et al proposed fully closed and openconformations of MscS based on electron paramagneticresonance spectroscopy and all-atom MD simulations256257

In this open MscS conformation the pore diameter was sim10 Aringthroughout the channel which is large enough to yield aconductance consistent with the experimental measurementsMscS has a large balloon-like cytoplasmic domain which

might play an important role in ion conductance see Figure 4c Recently Gamini et al probed ion conductance through thepores in the cytoplasmic domain using Gluminus and K+ as modelions248 Their results suggested that the cytoplasmic domain isa molecular sieve that balances effluxes of Gluminus and K+ throughMscSThe conductance of MscS has also been modeled using

continuum electrostatics methods (see sections 41) Forexample Sotomayor et al used atomistic MD simulations togenerate multiple conformations of the channels and thecontinuum transport theory to compute the ionic current forthese conformations258586 Recently Song and Corry calculatedthe ionic currents through MscS using a simplified NernstminusPlanck (NP) theory and rather realistic BD simulations225 Thestudy has shown the ability of the NP theory to reproduce theresults of the corresponding BD simulations523 α-Hemolysin Noskov and co-workers88 explored the

currentminusvoltage relationship of the α-hemolysin channel usingGCMCBD and 3D-PNP approaches (described in sections422 and 412 respectively) One of the inputs for theGCMCBD study was the position-dependent diffusioncoefficient of each ion type To incorporate the effect of thechannel size a reduction factor for the diffusivities wascalculated as per Paine and Scherr587 The study showed theIminusV characteristic to be asymmetric with a higher current atpositive bias (with the trans-entrance at a higher potential thanthe cis) which was in qualitative agreement with experi-ments588589 The study also revealed that by switching off thecharges on the pore the asymmetry in the conductancepractically disappeared indicating that it is the chargedistribution of the pore that is responsible for the asymmetryrather than the shapeThe MD study by Aksimentiev and Schulten90 was the first

to demonstrate that atomistic simulations can be used to obtainchannel conductances with quantitative accuracy Specificallythe study found the transmembrane currents driven by anexternal electric field applied normal to the membrane to be inexcellent agreement with experiment The large pore diameterand the high salt concentration made direct comparisonbetween simulation and experiment possible A recent MDstudy by Bhattacharya et al93 probed the cation-dependentrectification of the α-hemolysin nanopore The rectification ofthe ionic current was found to be dependent on the type ofcations and increased from Li+ to Cs+ both in simulations andin experiments The MD simulations showed that the cationiccontribution to the ionic current was the dominant factorinfluencing current asymmetry The cation type-dependentasymmetry of the ionic current was explained by differentialaffinity of the cations to the charged residues at the trans-entrance of the pore which modulated the number of ionsentering the narrowest part of the pore Recent experimentalstudies using site-directed mutagenesis590 and cysteine-scanning mutagenesis347 of the α-hemolysin channel revealedthat the ion-selectivity gating and conductance properties are

significantly affected by the location and the type of charges onthe pore

524 Outer-Membrane Porins Over the past 10 yearsthere have been a number of studies addressing ion-conductance properties of various OMPs (see Table 1) Imand co-workers carried out pioneering studies of OmpF using acombination of GCMCBD6263 MD5567 and continuum55

methods These first studies of OmpF revealed asymmetriccharacter of ionic conductance and produced concentrationminusconductance relations that were in good agreement withexperiment55 OmpF was a test bed for development of theGCMCBD methodUsing the all-atom MD method Pezeshki and co-workers

explored ion conductance of two structurally similar E coliporins OmpC and OmpF over a range of temperatures pHvalues and KCl concentrations7981 The results of the MDsimulations were in good agreement with experiment at low saltconcentrations and room temperature The authors observedconsiderable differences between the simulated temperaturedependence of conductance and experiment which wasattributed to the MD force field because the latter wasoptimized for simulations at room temperature The temper-ature dependence of the channelrsquos conductance was found todiffer from that of a corresponding bulk solution indicating theimportance of ion-pore interactions Using all-atom MD Modiand co-workers investigated the temperature-dependent trans-port of the ionic liquid 1-butyl-3-methyl-imidazolium chloride(BMIM-Cl) through OmpF86 The study indicated thataqueous solution of BMIM-Cl can reduce the rate of antibioticstransport through OmpF which could lead to practicalapplications of BMIM-Cl in the field of nanopore sensorsThe transmembrane pore of OmpF contains several titratable

residues Hence its conductance can depend on the solutionpH Varma et al used all-atom MD simulations to determinepKa (see section 435) of several key residues of OmpF7071

The study has shown that the pore size and conductance ofOmpF become consistent with the X-ray structure andelectrophysiology data correspondingly only when appropriateprotonation states are assigned to the key Asp residues7071

The study of Vrouenraets and Miedema has investigated theeffect of point mutations in OmpF finding ionization states ofthe residues to be the key factor affecting the ionconductance84

53 Selective Permeability

Concentration gradients of different types of ions support avariety of intra- and intercellular signals It is therefore vital tohave membrane channels that can distinguish and selectivelyconduct ions of different types One can easily imagine anelectrostatic mechanism for regulating the flux of different ionspecies based on the ion charge but what about channels thatselect a particular ion from all ions of the same chargeExperimental studies suggesting existence of Na+ and K+

selective channels began as early as 1960591 By 1971 it hadbeen inferred that the K+ channel has a wide inner openingleading to a narrow passage which blocks the passage of largecations However the K+ channel also prefers the conductanceof K+ over Na+ and Li+ even though the latter are smaller Theldquosnug-fitrdquo explanation offered in 1972592 suggested that it isnot electrostatically favorable for a Na+ ion to enter an oxygen-lined cage unless that cage is of the same size as the Na+ ionotherwise the Na+ will not form favorable electrostatic contactscompared to its solvation shell However the ldquosnug-fitrdquo

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mechanism requires a rather rigid pore incompatible with mostprotein structures which can only be described as soft andflexible Given that sodium and potassium appear to differ onlyon a scale significantly smaller than the size of an atom it isincredible that f lexible atomic-scale structures can yieldpermeabilities for the ions that may differ by a factor of1000593 The importance of subangstrom-scale structures andthe requirement of distinguishing between various physicalfactors naturally lend the study of ion selectivity to the all-atomMD methodology531 Potassium Channels The structures of all K+

channels feature a completely conserved constriction calledthe selectivity filter which is lined with four rings of negativecarbonyl-oxygen groups The structure of KcsA revealed two K+

ions separated by a single water molecule occupying this regionIn K+ channels the selectivity filter presents a barrier to iontransport and in general the larger the barrier the slower is theexpected rate of transport Thus early MD studies have focusedon the free energy difference experienced by K+ and Na+ ions inthe selectivity filter Because of the great similarity of these ionsthe free-energy perturbation (FEP) method has been theprotocol of choice for such studiesThe FEP method introduced in section 434 can evaluate

the free energy cost of transforming one atom into anotherthrough an unphysical pathway Because the end points of thistransformation are physically meaningful the change in freeenergy is also physically meaningful when considered as a stepin a thermodynamic cycle For example the difference inbinding free energy between K+ and Na+ in an ion channelΔΔG can be found from the free energies of transforming K+

into Na+ inside the channel and of transforming Na+ to K+ in abulk solution123 Both of these terms can be obtained fromFEP however care must be taken that the FEP simulations arelong enough that the system relaxes completely and fluctuationsare fully averagedEarly FEP simulations demonstrated a preference for K+ over

Na+ in the selectivity filter of KcsA120123141594 Howeverlimited by the computational resources available at the timethese simulations also suffered from problems small systemsizes that treated the lipid bilayer protein or water inunrealistic ways subnanosecond durations of simulations ateach FEP step andor external restraints that enforced crystalstructure-like conformation on the selectivity filter Despitethese limitations the range of values for ΔΔG (5minus17 kcalmolfor a single ion) were in apparent agreement with experimentalmeasurements of relief of Ba2+ blockades by Na+ and K+Recently a combination of MD simulations and X-ray

crystallography suggested that the smaller monovalent cationsNa+ and Li+ have their own binding site in the plane of acarbonyl-oxygen ring of the selectivity filter of KcsA as depictedin Figure 10 rather than between two rings as for K+595

Subsequently one- two- three- and four-ion umbrellasampling simulations provided PMFs for a Na+ or K+ ionpermeating K+-filled selectivity filters of KcsA and Kir-Bac11191596 The authors of one study note that FEPsimulations utilizing short trajectories may not provide theion with enough opportunity to find its preferred binding siteand that such studies likely overestimate ΔΔG which theauthors estimated to be 2minus3 kcalmol596 Additional umbrellasampling simulations of a Ba2+-occupied filter demonstratedthat the results can be quantitatively reconciled with Ba2+

blockade measurements because the Na+ and K+ ions areinfluenced differently by the bound Ba2+ ion Although the

latter study596 has not yet garnered response it demonstratesthe utility of a thorough simulation for interpretation ofexperimental measurements Thus the story of potassiumchannel selectivity may still be incomplete

532 Outer-Membrane Porins Porins often exhibitselectivity toward specific molecules For instance the outer-membrane protein OprP of Pseudomonas aeruginosa ananalogue of the PhoE porin of Escherichia coli is aphosphate-selective pore What is particularly interesting isthat it is not just anion-selective but can discriminate betweenanions OprP is highly selective toward the permeation ofinorganic phosphate (Pi) over other anions from the externalenvironment to the interior of the cell597 Atomistic simulationsperformed by Pongprayoon et al80 employing constant velocitySMD and umbrella sampling demonstrated that a lysine clusternear the periplasmic end of the pore selected ions by binding Pi

with greater affinity than small anions such as Clminus Theperiplasmic mouth of the pore can accommodate a fullysolvated Clminus ion which is therefore dielectrically screened fromthe positively charged lysine cluster Pi on the other hand ispartially dehydrated when it enters the pore at the periplasmicside and therefore interacts strongly with the lysine residuesThe extracellular end of the porin however allows the passageof both Clminus and PiAnother interesting porin that has been widely studied using

computational methods is the moderately cation-selectiveOmpF trimer The IK+IClminus ratio obtained from atomisticsimulations by Pezeshki et al79 was found to be sim12 which issimilar to older estimations by Im and Roux obtained fromGCMCBD and PNP approaches55 The key to theconductance and selectivity of the porin lies in its structureOne of the loops on the extracellular side the L3 is of specialimportance as it folds back into the β-barrel constricting thechannel Positively charged arginine residues on the wall of theporin face the negatively charged residues on the loop creatinga transverse electric field in the constriction region of theOmpF This field can orient molecules and cause a separationof ion fluxes5565 Experimental as well as computationalstudies83 have shown that it is possible to alter and evenreverse the selectivity of the OmpF by mutating the chargedresidues in the constriction region (both on the L3 loop andthe pore wall)

Figure 10 Na+ (green sphere) and K+ (red spheres) ions occupydifferent binding sites in the selectivity filter of a potassium channelEarly FEP simulations indicated a large free-energy cost ΔΔG forexchanging K+ with Na+ at the K+ binding sites ΔΔG may actually besmaller if the ion is free to move to its preferred binding site Adaptedwith permission from ref 595 Copyright 2009 Macmillan PublishersLtd Nature Structural amp Molecular Biology

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54 Ion-Channel Gating and Blockages

Proper cellular function requires that ions be released at certaintimes but not at other times and this variable ion conductanceis called gating For example the mechanosensitive channels inbacteria open to prevent rupture of the cell when tension in thebilayer increases due to osmotic stress Mechanosensitivechannels also initiate the conversion of mechanical vibrationsin the inner ear into electrical signals Similarly voltage- pH-and ligand-induced gating allow signals to be initiated orpropagated depending on the cellular conditionsGating almost always involves changes in the conformation

of the channel Until very recently brute-force atomisticsimulations of such changes were not possible because of thetime-scale limitations Below we discuss exemplary studiesincluding mechanical gating of the bacterial mechanosensitivechannels of small and large conductance and voltage gating of aK+ channel Additionally we discuss blockades of ion channelscaused by neurotoxins which may have pharmacologicalsignificance541 Mechanical Gating Even though several crystal

structures of MSCs are available the gating mechanisms remainelusive Unlike ligand- or voltage-gated ion channels wheregating is triggered by a relatively local structural change gatingof mechanosensitive channels involves a global structuraltransition231232 Consequently the time scale of the gating issignificantly greater than in other channels as is the length scalethat needs to be considered222 Although the large length scaleand long time scale of the mechanosensitive gating posepractical problems in computational studies of the gatingmechanism the prokaryotic MscL and MscS channels are idealsystems to develop the computational methodology because ofthe relative simplicity of these channels that are believed to betension sensors onlyWhen only one MSC crystal structure was available (a closed

conformation of MscL from Mycobacterium tuberculosis Tb-MscL) Sukharev and co-workers proposed a gating model forEscherichia coli MscL (Ec-MscL) in which the channel opensvia an ldquoiris-likerdquo mechanism231minus233 Starting from the closedconformation they modeled the intermediate and final openconformations in atomistic detail by utilizing various exper-imental information and empirical energy functions of theCHARMM force field In the open conformation the pore sizewas predicted to be sim30 Aring while the pore size of the closedcrystal structure was only a few angstroms impermeable tosmall molecules Physiological studies provided estimates of theopen pore diameter that were close to the result of theSukharev model (eg refs 255 598 and 599)Using the gating model of Ec-MscL several groups

performed MD simulations to test the model and observe thegating transition in all-atom detail230234236minus239 Kong et alcarried out targeted MD simulations to observe the transitionfrom closed to open conformations of the Ec-MscL230

Gullingsrud et al used SMD to induce opening of the closedconformation of Ec-MscL234238 In the SMD simulations it wasassumed that the forces on the protein by membrane stretchingapply only to the residues at the waterminuslipid interface whichwas based on observations of the pressure profile in pure lipidbilayers239 The same study used the pressure-profilecalculations to estimate the magnitude of the SMD force(35minus70 pN)Other than gating by tension Elmore and Dougherty

considered the effects of point mutations and lipidcompositions on the Tb-MscL structures using MD simu-

lations235240 Later Meyer et al studied the effect of a single-tailed lipid (which has high spontaneous curvature) on thestructure of Ec-MscL249 The simulations began from amanually built dome-shaped structure containing an Ec-MscLchannel embedded at the top of the dome During a 95-nssimulation the researchers observed spontaneous restructuringof the periplasmic loops of MscL which was in agreement withexperimental observations Recently Debret et al simulated Ec-MscL embedded in a lipid bilayer whose hydrophobic thicknesswas significantly smaller than the height of Ec-MscL250 Theresearchers observed tilting of transmembrane helices suggest-ing that hydrophobic mismatch can lower the activation energyof Ec-MscL opening Another all-atom MD simulations of Tb-MscL emphasized the interplay between protein and lipidbilayer by showing that inclusion of the protein significantlyincreases the mechanical rigidity of a lipid annulus251

Despite a number of ingenious efforts gating by tension hasnot been observed in all-atom MD simulations withoutapplying artificial driving forces The main difficulty is thetime scale of the mechanical gating which is significantly longerthan the time scale of an all-atom MD simulation To overcomethe time-scale problem several researchers applied morecomputationally efficient methods at the expense of accuracyPhillips and co-workers used continuum elasticity theory toevaluate the energetics of membrane deformation by theinclusion of MscL neglecting the internal energy of MscL forsimplicity226minus228 Their analytic calculations showed that gatingof MscL proteins can be modulated by the mechanicalproperties of the membrane226227 Moreover they alsodemonstrated how the function of multiple MscL channelscan be coupled Later Chen and co-workers applied computa-tional continuum mechanics to study the gating ofMscL221minus223 In their novel approach they explicitly consideredthe conformational change of MscL by modeling the MscLstructure using a simple elastic rodlike representation of thetransmembrane helices By combining such a simple model ofMscL with a continuum model of the membrane in a finite-element framework and parametrizing the models using all-atom MD simulations they were able to observe mechanicalgating of MscL just by stretching the membraneParticle-based coarse-graining offers another route toward a

simpler model of mechanical gating In this framework groupsof atoms are represented by single interaction beads whichdramatically increases the computational efficiency of the MDsimulation The interactions between such coarse-grained beadsare calibrated to reproduce the thermodynamic properties ofmodel systems obtained from all-atom MD simulations orexperiments (eg transfer free energy of small molecules fromwater to hydrocarbon) Marrink and co-workers applied theirnovel coarse-grained model MARTINI252 to Tb-MscL253254

Specifically they were able to simulate gating of MscL just bystretching the membrane253 or pressurizing a vesicle thatcontained embedded MscL channels254

When the time scale accessible to an MD simulation issignificantly shorter than the time scale of gating one canaccelerate the simulation by applying biasing forces (egSMD) However the quality of such accelerated simulationsdepends critically on how realistic the biasing forces are In thissense combining single-molecule experiments with SMDsimulations can be very successful For example Corry et alrecently demonstrated that the distance measurements fromForster resonance energy transfer (FRET) confocal microscopycan be used as a guide for the SMD simulation255 Starting from

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a closed conformation the researchers induced a closed-to-open conformational transition by performing SMD simu-lations that utilized distance constraints derived from FRETmeasurements on an open MscL channel Because of thedistance constraints the simulations produced a reasonablestructural model of the MscL pore in an open state542 Potassium Channels Potassium channels which all

share a common sequence for the selectivity filter demonstratevoltage- pH- and Ca2+-dependent gating of an intracellulargate which limits K+ access to the selectivity filter andextracellular solution However the selectivity filter is itself afragile structure that can be inactivated Inactivation of theselectivity filter occurs more readily when the intracellular gateis open186

It may be insightful to consider purely solution-dependentinactivation and inhibition of the selectivity filter A potassiumion channel will nearly irreversibly inactivate if it is placed inelectrolyte solution of very low ion concentration All-atom MDsimulations suggested a mechanism of such inactivation bydemonstrating severe distortion of the selectivity filter when itis depleted of K+ ions that partially neutralize the negativecarbonyl-oxygens lining of this structure137143182 Similarlyconductance of K+ channels can be blocked by other ions suchas Na+ or Cs+ that bind to the selectivity channelThe Kv channels are all voltage-gated Crystallographic

studies have provided structures for several open-pore Kvchannels featuring a charged voltage-sensitive subunit sur-rounded by lipids for each monomer of the tetramer411600601

The voltage-sensitive subunits are expected to move andrearrange in response to a voltage change in such a way that asmall but measurable transient capacitative current is observedacross the membrane The associated charge is known as thegating chargeThe gating charge times the change in the potential provides

the free energy required to change conformations and gate thechannel Using all-atom simulations the gating charge can bedirectly computed by measuring the difference in the center ofcharge of the system between open and closed conforma-tions185 A more sophisticated approach allows the assessmentof each residuersquos contribution to the gating charge through thecalculation of the difference between the free-energy cost ofcharging each residue in the closed and open states185

There is currently no crystallographically obtained closed-pore structure of a voltage-gated K+ channel However in astudy that utilized 13 μs of all-atom MD simulation the open-pore structure was refined and a possible closed-pore structurefor Kv12 was obtained185 Using these structures the gatingcharge was found to be somewhat smaller than theexperimentally measured gating charge suggesting that thecomputational model represented an intermediate conforma-tion at the onset of activationVery recently special-purpose hardware enabled all-atom

simulations of a Kv12Kv21 chimera on the gating-time scaleas observed experimentally (gt300 μs)196 The simulationsdemonstrated that the crystal structure accurately representsthe functional open pore In a series of simulations differentonly by the transmembrane voltage and the initial conditionsthe channel was brought from the open state to a fully closedstate Simulations were also performed to simulate differentstages of channel activation Gating of the channel occurred bystructural rearrangements of the voltage-sensitive domains thataffected the hydrophobic cavity leading to the selectivity filterThese rearrangements caused dewetting and collapse of the

cavity The time scales of various steps during the processagreed well with available experimental measurements196

Although not based on such long simulations a study of apH-sensitive potassium channel suggested that gating for thisprotein may occur through a rather different mechanism Anarginine residue near the extracellular side of the membranewas identified through mutagenesis as providing pH-sensitiv-ity602 The PMF of K+ ions in the selectivity filter was obtainedthrough all-atom MD when the protonation state of thatarginine residue was varied The authors of this study suggestedthat the observed 3minus4 kcalmol increase in the barriers for K+

translocation accounted for gating and arose from additionalflexibility that protonation of the arginine sensors granted tothe selectivity filter602 However it should be noted thatbecause no X-ray structure is available a homology model ofthe K2P channel built from Kv12 was used for this studyThus potassium channels share a great deal of structural and

sequence similarity around the selectivity filter but can be gatedin a variety of ways All-atom simulation techniques haveprovided a great deal of insight into the structural mechanismsof the gating processes In one exemplary study196 brute-forceall-atom MD simulations described the complete gating processof a voltage-sensitive potassium channel on a time scale ofhundreds of microseconds At this time it remains to be seenwhether other potassium channels use similar mechanisms togate

543 Blockades Some toxins bind and inactivateparticular target channels The potential for specificity ofchannel-binding toxins makes them an attractive source forpharmaceutical innovation The all-atom MD methodology hasbeen used to find the standard binding free energies of manysmall ligands but only recently have researchers attempted tofind the binding free energies of large ligands In particularseveral studies demonstrated challenges and shortcuts whencomputing standard binding free energies of charbydotoxinbinding to various voltage sensitive potassium chan-nels116603604

Of greater pharmacological interest the Kv13 K+ channelhas been identified as a target treatment of multiple sclerosisand other autoimmune disorders422 In a recent study the toxinShK which blocks Kv13 but also Kv11 was docked to severalK+ channels and the binding free energy was calculated425

Surprisingly the simulations revealed different binding geo-metries to Kv13 and Kv11 but similar binding free energiesthat agree well with experimentally determined values Theauthors concluded with mutations to ShK that may enhance theselectivity of Kv13 over Kv11At present free-energy calculations require too much

computing power and are not automated enough to be usedas a predictive tool by the pharmaceutical industry Inparticular reliably docking potential drug candidates remainsa challenge Nevertheless the combination of special-purposehardware for performing MD simulations very quickly andimproved automation of tools for calculating binding freeenergies may give rise to the use of all-atom simulations inadvanced computation drug screening within the pharmaceut-ical industry

55 Biosensing with Channels

About 20 years ago Bezrukov et al605 and Kasianowicz447 andco-workers demonstrated the possibility of using ionic channelsas molecular Coulter counters to detect the presence andcharacterize the type of biomolecules The basic principle of the

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approach is the following A membrane containing a single-ionchannel separates electrolyte solution into two compartmentsconnected only through the transmembrane pore of thechannel A transmembrane bias is imposed using an externalvoltage source producing a steady ionic current through anopen pore The transmembrane bias facilitates unidirectionaltransport of charged biomolecules from one compartment tothe other Each passage is detected as transient reduction (ablockade) of the ionic current flowing through the pore Theduration and magnitude of the ionic current blockades canindicate the length and chemical composition of a nucleic acidpolymer447606minus608 suggesting the possibility of recording thenucleotide sequence of a DNA strand directly by measuring theionic current flowing through a nanoporeCritical to the success of the above approach is the lack of

spontaneous gating of the ion conductance which if presentcan easily be confused with the signal resulting from interactionof the channel with a biomolecule Because of its superiorstructural stability the α-hemolysin channel was the firstnanopore to be considered for biosensing applications447609

However other channels such as the bacterial porinMspA449minus451 and man-made silicon-based610minus612 and gra-phene613minus615 nanopores have been successfully used fordetection of biomolecules Apart from DNA sequencingnumerous other applications have been proposed for nano-pores including detection of small analytes589616617 drugdesign390618 pathogen detection619 and force spectrosco-py620minus622 Interested readers are directed to several reviews onthis subject446623minus627

Modeling and computer simulations have played a major rolein development of nanopore applications585 There have alsobeen numerous theoretical studies of various aspects ofpolymer capture and translocation through nanoporesTypically such studies involve the application of scalingconcepts of polymer physics or transport equations628minus630 toelucidate the dynamics of charged polymer capture andtranslocation All-atom simulations have been used as a kindof a computational force microscope to directly relate themicroscopic events taking place in a nanopore to the ioniccurrent blockades recorded in experiment377585

551 α-Hemolysin Among many β-barrel proteins α-hemolysin has been the channel of choice for mostexperimental studies because of its exceptional structuralstability under harsh experimental conditions The knowncrystallographic structure and relatively straightforward site-directed mutagenesis procedures permit rational engineering ofthis channel to enhance sensitivity of ionic current blockadesfor example by introducing a molecular adapter616 or othersite-specific mutations631632

The 2005 publication by Aksimentiev and Schulten90

pioneered the application of the all-atom MD method forprediction of the ionic conductance of membrane channelsThe simulations demonstrated for the first time quantitativeaccuracy of the MD method in predicting the absolute value ofthe ionic current reproducing the asymmetric currentminusvoltagedependence of α-hemolysin and characterizing the electro-osmotic effect The simulations also suggested a microscopicmechanism explaining the pH-dependence of the noise in theionic current recordings633 The study has also demonstrated amethod for computing the average distribution of theelectrostatic potential in a membrane channel directly froman all-atom MD simulation90 Following the successful study ofionic conductance through α-hemolysin the researchers were

challenged by an experimentalist (A Meller Boston University)to predict the influence of the global orientation of a DNAstrand in α-hemolysin on the velocity of DNA transport andthe ionic current blockades This was a blind test as no priorinformation about the outcome of experiments was given Tofind out the molecular origin of the observed differences MDsimulations were performed on α-hemolysin systems havingDNA threaded through in two different global orientationsfrom 3prime to 5prime and from 5prime to 3prime The outcome of the simulationsrevealed a propensity for DNA nucleotides to tilt toward their5prime-ends in confined environments which was linked toobservable differences in DNA translocation dynamics andionic current blockades97 The results of the MD simulationswere in qualitative agreement with experiment Because oflimited computational resources direct quantitative comparisonwas not possible at that timeThe α-hemolysin channel has been a test bed for developing

advanced simulation techniques The Roux group exploredpermeation of ions through the α-hemolysin channel using 3D-PNP as well as the grand canonical Monte Carlo Browniandynamics (GCMCBD) approaches88 in the absence of anyanalytes The study revealed that the asymmetric conductanceof the pore arises from the permanent charge distribution in thepore Another PNP study examined the influence of chargedresidues in α-hemolysin on the asymmetry of the currentminusvoltage dependence89100 Shilov and Kurnikova96 employedMD simulations to investigate the energetics and dynamics of aβ-cyclodextrin (βCD) molecule confined inside the α-hemolysin pore The Roux group investigated the effect ofβCD on the ion selectivity of the α-hemolysin through MDsimulations and PMF calculations94 The simulations haveshown that electrically neutral βCD enhances the concentrationof Clminus in the nanopore by causing a partial desolvation of theions which reduces the dielectric shielding by the solvent TheGCMCBD method was used to account for multi-ion effectsin a subsequent study94 Simakov and Kurnikova devised amodified PNP approach to incorporate a soft repulsion modelof short-range interactions between mobile ions and protein92

To overcome the time-scale limitation of the MD methodthe Aksimentiev group developed a method for acceleratingsimulations of DNA transport through nanopores thatpreserves all-atom features of the MD model98 The key ideaof the method dubbed grid-steered MD (G-SMD) was theselective amplification of the electrostatic potential that drivesDNA transport while maintaining all other interactionsunchanged Using G-SMD the Aksimentiev group performedmultiple simulations of DNA transport through α-hemolysinand determined the dependence of the translocation velocityon the sequence and orientation of the DNA strands98 a taskthat was considered formidable at that time634 De Biase andco-workers recently developed a theoretical framework tomodel DNA translocation across a nanopore by combining theGCMCBD algorithm with a coarse-grained polymer model forDNA102 which enabled multimicrosecond simulations at afraction of the cost of all-atom MD When applied to modeltranslocation of poly(dA) and poly(dC) strands through α-hemolysin the model yielded results in reasonable agreementwith experiments Reiner et al367 developed an elegantcontinuum theory to describe the results of nanopore massspectroscopy experiments with quantitative accuracy635 Bondet al employed all-atom MD simulations to explore thetranslocation of short strands of DNA through a simplifiedmodel of the α-hemolysin pore comprising the stem of the pore

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surrounded by a membrane mimetic slab99 The studyexamined the effect of cationic amino acids on the translocationdynamics of DNA Compared to wild type α-hemolysinarginine mutations were found to reduce the transport rate ofDNA through the pore as well as the ionic current552 MspA The long stem of α-hemolysin can

accommodate up to 12 DNA nucleotides which makes difficultthe detection of single nucleotides by measuring ionic currentThe MspA porin has recently emerged as a viable alternative toα-hemolysin on account of its superior architecture MspA has agoblet-like structure with a constriction region that is sim1 nmideal for holding just one or two nucleotides see Figure 11aButler and co-workers showed that by eliminating the negativecharge in the constriction a variant of MspA called M1MspAwas capable of detecting a single DNA strand electrophoreti-cally driven through the pore449 A series of subsequentexperimental work in the Niederweis and Gundlach groupshave since established that the current resolution of the MspAvariant is superior to that of α-hemolysin636 and that singlenucleotide substitutions can be detected on a randomheteropolymeric background using a tethered DNA451

However the primary challenge is that the translocation rateof DNA through MspA is several orders of magnitude higherthan the rate required to resolve the type of DNA nucleotidesby measuring ionic current The two main strategies to controlDNA translocation are to engineer intrinsic brakes in the MspAstructure or use an auxiliary enzyme such as DNA polymer-ase637

The first computational study of MspA was recently carriedout by Bhattacharya and co-workers348 The study reportsextensive all-atom MD simulations that explored the effect ofpositively charged arginine residues on the translocation rate ofDNA and the ionic current On account of the highcomputational overhead due to the large system size theauthors performed the majority of the simulations using a

truncated version of the pore (see Figure 11b c) Since theDNA was found to be quite mobile even when confined to thenanopore the authors adopted an ensemble approach tosample the configurational dynamics of the DNA Theensemble method was shown to be a viable alternative tofollowing a single long-time-scale trajectory which is currentlypossible only using special-purpose supercomputers such asAnton The ensemble approach allowed the use of traditionalsupercomputers to obtain combined trajectory lengths of tensof microseconds within reasonable physical time Thesimulations have shown that by introducing several arginineresidues near the constriction of MspA the DNA permeationrate can be reduced by a factor of 10minus30 due to the formationof multiple salt bridges between the DNA backbone and theguanidinium groups of the arginine substitutions as well as dueto base-stacking interactions Furthermore the simulationspredicted that such mutations would not eliminate thenucleotide sensitivity of the ionic-current blockades Thestudy explained why similar mutations introduced in α-hemolysin reduced the ionic current practically to zero638

making such mutants unsuitable for DNA sequencingapplications

553 Other Nanopore Systems Other β-barrel nano-pores have been explored for stochastic sensing applicationsFor instance an MD study of the bacterial porin OmpG wascarried out by Chen and co-workers to determine the origin ofits spontaneous gating activity77 On the basis of the simulationstudy a variant of the porin with stabilizing mutations wascreated and was used for detection of adenosine diphosphateafter inserting a cyclodextrin molecular adapter77

Using 3D-Poisson equations and linear transport theory360

Vidal and co-workers demonstrated that a nanopore in a heavilydoped silicon membrane connected to a voltage source can beused as an electrically tunable ion filter The PNP model wasused to study ion transport through synthetic nanopores in

Figure 11 (a) Cut-away view of the full-length MspA nanopore embedded in a lipid membrane with a DNA strand threaded through The MspA isrepresented by a teal molecular surface the lipid membrane is represented by purple lines and the DNA bases are shown in magenta-colored licoricerepresentation (b) Average electrostatic potentials along the symmetry axis of the full and truncated MspA nanopores at a transmembrane bias of180 mV The electrostatic potentials are computed from MD simulations of open-pore MspA nanopores (c) Cut-away view of the reduced MspAsystem The DNA is covalently joined to itself across the periodic boundary (d) The ionic current trace of a sample trajectory of a poly(dC) strandthreaded through the MspA nanopore (e) Ionic current histograms obtained from ensemble simulations of the M1MspA (yellow) and its argininevariant M1 L88RA96RS116R (blue) The overlap of the two histograms is shown in green The histograms were constructed using 100 nsaverages of the instantaneous ionic current Adapted with permission from ref 348 Copyright 2012 American Chemical Society

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several studies359363366 exploring rectification and ionselectivity A Langevin dynamics approach to study thetransport of flexible macromolecules in confined geometrieswas proposed by Peters372 Recently an atomic resolution BDmethod was developed by Comer and co-workers that was usedto study the sequence dependence of ionic current in syntheticnanopores373374 All-atom MD simulations have been usedwith considerable success to investigate nanopore transport ofDNA and ionic current blockades375376 nanopore unzipping ofDNA hairpins380 the microscopic origin of the electrophoreticforce on DNA in a nanopore378381 and the effect of electrolyteon the DNA translocation rates391 For detailed description ofthe simulation protocols interested readers are directed torecent reviews on this subject585639640

6 OUTLOOK

Advances in computational technologies and membraneprotein structure-determination methods are poised to makemodeling and simulations of ion channels an integral part offuture drug-development efforts The greatest obstacle so far isthe lack of atomic-resolution structures of the majority ofbiomedically relevant ion channels Several limitations pertainto the computational technology itself Whereas all-atommolecular dynamics simulation of an ion channel can providethe most detailed information about the microscopicmechanism of its function the method is currently limited bythe accuracy of the classical force field and the microsecondtime scale of the simulations on conventional computerclustersTremendous advances in addressing both limitations have

already been made The first computational studies of ionchannel systems using polarizable models have already beenreported277563 Thus it is very likely that a full polarizable forcefield will become available within the next 10 years Anothermajor advancement was the millisecond simulation of amembrane channel in its native environment that revealedthe microscopic details of its voltage-dependent gatingmechanism196 We hope that such a tremendous success ofspecial-purpose hardware will prompt the development ofcommodity special-purpose hardware which will make suchlong-time-scale simulations available to mainstream researchersFinally advances in computational methods will also aid thediscovery of atomic-resolution structures through either denovo structure prediction641 or refinement of low-resolution X-ray and cryo-EM structures443

It would be misleading however to think that all questionspertaining to ion channels would be answered through all-atomMD From a drug-development perspective high-throughputand accurate calculation of binding free energies of smallchemical compounds is more important than long-time-scalesimulations of a single channelrsquos action Enabling such high-throughput docking is dependent on the availability of accurategeneric force fields Furthermore as millisecond simulationsbecome more available describing possible chemical reactionsbetween components of the system will become increasinglyimportant Finally modeling a single channel in a membrane isonly a first step toward the realistic modeling of in vivoprocesses We anticipate continuum and implicit solventapproaches to play a pivotal role in the development ofdetailed quantitative models of realistic biological membranesand small organelles that incorporate an ensemble of ionchannels

AUTHOR INFORMATION

Corresponding Author

E-mail aksimentillinoisedu

Notes

The authors declare no competing financial interest

Biographies

Christopher Maffeo received his BSc in physics from the University of

California Santa Barbara in 2006 He joined the Aksimentiev group in

December 2006 After studying the structural and conductance

properties of the phospholamban pentamer he has focused his efforts

on understanding the kinetics energetics and electrostatics of various

DNAminusDNA and DNAminusprotein interactions

Swati Bhattacharya is a postdoctoral fellow in the group of Aleksei

Aksimentiev at the University of Illinois at UrbanaminusChampaign She

received her PhD in physics for work on the adsorption of polymers

at surfaces under the supervision of Thomas Vilgis in 2009 from the

Max Planck Institute for Polymer Research in Mainz Her current

research activities include computational modeling aimed at

developing applications of nanopores particularly for DNA sequencing

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from the lack of polarizability by showing that the agreementwith the experiment is significantly better when employing apolarizable model565

Motivated by the apparent limitations of the currentnonpolarizable models many research groups proposed variouspolarizable models566 However their development is still at theinitial stage and the application of polarizable models to thechannel proteins is still limited The two most practicalpolarizable models of biomolecules are the Drude oscillator andAMOEBA force fields566 Ponder and co-workers developed theAMOEBA force field in which molecular polarization can beachieved by using permanent atomic multipoles567minus569

Equipped with an analytic solution that treats intramolecularpolarization the AMOEBA force field can deal with flexiblemolecules such as peptides and lipids567 Even though theAMOEBA force field is not ready for all biomolecules (eglipid) it shows promising results for example reproducingstructural and thermodynamic data such as solvation structureand solvation free energy of small drug-like molecules569 andion solvation568

In the classical Drude oscillator model (eg ref 570)polarization is achieved by a charge harmonically bound to anatomic center In the presence of an electric field the mobilecharge oscillates around a position slightly displaced from theatomic center inducing a dipole moment By using the Drudemodel several promising results have been reported Forexample the description of monovalent and divalent cations isimproved563 and hydration free energies of small molecules canbe calculated more accurately571 However as for theAMOEBA force field the application of the Drude oscillatormodel is currently limited to small molecules in an aqueoussolution Thus the polarizable models must be furtherdeveloped and tested before they can be applied to an ion-channel systemAlthough it will take some time for the polarizable models to

replace the currently popular nonpolarizable models especiallyfor the simulations of channels there already have beenmeaningful attempts to test the polarizable models in themembrane environment For example Vorobyov et al appliedthe Drude oscillator model to calculate the transfer free energyof an arginine analogue to the lipid bilayer572 More recentlyWang et al used the Drude oscillator model in combinationwith a nonpolarizable model to study the transfer ofammonium through an ammonium transporter277 In thisstudy ammonium water and side-chains were treated usingthe polarizable model to better describe the less aqueouscharacter of the channel while the other parts were treatedusing the nonpolarizable model The successful demonstrationof such a hybrid approach is a very promising development thatwill likely grow in popularity until full polarizable simulationsbecome feasible

5 TYPICAL QUESTIONS OF INTERESTIdeally a simulation study of an ion channel would provide acomprehensive description of all aspects of the channelrsquosfunction In reality computational studies are limited by theaccuracy of the methods chosen the availability of computerresources and experimental knowledge of the system Amongthe many topics that could be probed about the function andbiological role of an ion channel we focus on the followingfour ion-binding sites and permeation pathways ionicconductance selectivity and gating The fifth subsection ofthis section details the use of computational methods in

biosensing applications of ion channels Although all five can beintegral parts of the same ion-transport mechanism suchdivision is possible in part due to the separation of the timescales Thus for some channels the time scale of 100 ns issufficient to observe selective ionic transport whereas for theother channels this time scale is barely sufficient to determinethe most probable locations of ions In general theexperimental conductance of an ion channel gives a goodestimate of the time scale of ion-permeation events and can beused to choose an adequate simulation method

51 Ion-Binding Sites and Permeation Pathways

To understand the microscopic details of ion selectivity andconductance one must know where ions are likely to be in thechannel The density of ions in a channel can be obtainedthrough all-atom simulation and is directly related to thepotential of mean force (PMF) The PMF is enormouslyvaluable because it plainly exposes the pits and barriers an ionmust traverse during its journey across a membrane The PMFmay yield significant insights into the specificity of a channel forcertain ionic species and it can support conjectures regardingthe impact of the protein structure on ionic conductanceBinding of multivalent ions can alter the structural features of amembrane channel573 and influence the outcome of structuredetermination studies574575

511 Potassium-Selective Channels Potassium ionpermeation across cell membranes has a long history ofquantitative study Hodgkin and Keynes found a relationbetween the ratio of K+ ions flowing into and out of a cell andthe voltage difference across the cell membrane that describedthe data across a wide range of intra- and extracellular K+

concentrations with only one free parameter n576 Seeking atheoretical explanation for the excellent fit of their heuristicequation they proposed the ldquoknock-onrdquo model in which K+

ions move single file through a chain of (n minus 1) K+ occupiedsites colliding with one another so they all move in a concertedfashion Hodgkin and Keynes found that the channel isoccupied by 2minus3 K+ ions Their explanation is remarkably closeto the mechanism revealed through X-ray crystallography andscores of simulation studies which showed that the selectivityfilter includes four binding sites usually occupied by two ionswith a third ion sometimes present near one of the twoopenings (see Figure 9)Simulation studies of the KcsA K+ channel have employed a

broad spectrum of methods to study occupancy of theselectivity filter by a set of ions The most used is the umbrellasampling method described in section 434The three-ion PMF for the process of ion permeation

through the KcsA filter was obtained in 2001126 The PMFallowed the authors to identify concerted transition pathwaysfor the ions demonstrating that the shallowest pathways forpermeation involved concerted motions of pairs of ionsHowever pathways involving all three ions were also observedwith barriers that were sim1 kcalmol larger than pathwaysinvolving only two ions The simulations revealed which of thebinding sites were most attractive to K+ A subsequent SMDstudy confirmed the concerted motion of pairs of K+ ions in theselectivity filter164

In 2008 a study compared several methodologies for findingthe PMF namely SMD in conjunction with the Jarzynskiequality (JE) umbrella sampling and another free-energycalculation technique called metadynamics176 Metadynamicsbelongs to a class of newer enhanced sampling protocols in

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which the system is pushed away from regions of phase spacethat have already been sampled577minus579 All of these methodsseek to map the free energy along one or more coordinatesalthough SMD is inherently one-dimensional A typical choicefor studies of single-file ion permeation is the position of one ormore ions along the pore axisThe PMFs of ion permeation through KcsA obtained from

SMD and umbrella sampling simulations were qualitativelysimilar and revealed overlapping minima and maxima176 Theresults obtained using these two methods were found to besensitive to the conformation of the residues in the filter andthe position of the ion in the cavity just outside the filter whichcould change on the time scale of the simulations The PMFsobtained using the SMD method were created by combiningdata from multiple simulations demonstrating the advantage ofincreased parallelization However for such an approach to bevalid individual simulations should be sufficiently long toaverage over conformational fluctuations Unfortunately theauthors did not sample equivalent amounts using these twomethods and thus a direct comparison could not be obtainedIn general the SMD method results in a PMF that has barriersconsiderably larger than those determined from umbrellasampling simulations512 Gramicidin A For details of the history of gramicidin

A in all-atom simulation we refer interested readers to recentreviews2139 Here we highlight the methodologies used tostudy ion channels that have been validated using gramicidin AThe first applications of quantitative MD methods to the

study of ion channels were free-energy perturbation calculations(FEP see section 434) on gramicidin A which providedsignificant insight into the ion-translocation process The firstsuch study was performed over 20 years ago and compared thesolvation free energy of a Na+ ion in gramicidin A at differentpositions in the pore to the solvation free energy in bulksolution18 The results of this study can be considered as a low-resolution PMF that indicated a series of rather large (sim5 kcalmol) pits and barriers within the channel Another FEP studydetermined the relative solvation free energy for Na+ in a singlyand doubly occupied gramicidin A relative to bulk water19 TheNa+ ions were then mutated into the other four commonmonovalent cations These calculations demonstrated thatsmall ions are less likely to doubly occupy gramicidin A

compared to large ions agreeing with experiment andsupporting the validity of the underlying model The umbrellasampling method was recently used to determine a two-ionPMF demonstrating that double occupancy in gramicidin A isnot favorable46

Single-ion permeation through gramicidin A has since beenstudied numerous times using the umbrella sampling35415051

and SMD38424348 methodologies Studies employing theumbrella sampling50 and SMD48 approaches have cautionedthat extensive simulations are needed to obtain completeconvergence using either method Sampling on the order ofhundreds of nanoseconds may be required to achieve theconvergence irrespective of the chosen method althoughunidirectional SMD simulations were found to exhibit severehysteresis in relatively short simulation when compared toumbrella sampling41

513 Others Channels PLN The uptake of Ca2+ by Ca2+-ATPase is regulated by the membrane protein phospholamban(PLN) which acts as an inhibitor Although more than 75 ofPLN in a lipid bilayer membrane is pentameric the only knownfunction of PLN ie Ca2+-ATPase inhibition involves a PLNmonomer and not a pentamer although there were a fewexperimental reports of ion conductance involving PLN580581

Using SMD330 and the umbrella sampling345 methods it wasrecently shown that the channel-like NMR model of the PLNpentamer does not conduct ions in agreement with morerecent experimental studies582

VDAC The Im group carried out all-atom MD study of thehuman VDAC1 to characterize the ion permeation andselectivity of the pore262 The study revealed that negativelycharged Asp and Glu residues serve as traps for K+ ions as theypass through the channel The one-dimensional multi-ion PMFcomputed for K+ and Clminus revealed the reason for the anionselectivity of the channel a higher free-energy barrier for K+

ions to enter the channelOmpF Im and Roux explored the ion density profiles and

the conductance of the Escherichia coli porin OmpF in adetailed study employing MD BD and PNP approaches5567

All three approaches revealed distinct ion pathways for K+ andClminus ions through the pore determined by the distribution ofcharged residues in the porin The phosphate selective porinOprP was recently studied using equilibrium SMD andumbrella sampling simulations80 The study revealed twonegatively charged phosphate-binding sites in the interior ofthe pore in close proximity to one another each with a freeenergy minimum of sim8 kBT Findings relating to thepreference of OprP for phosphate over Clminus will be discussedbelow

AmtB Luzhkov et al performed FEP and pKa calculations(see sections 434 and 435) using all-atom MD simulations tostudy the interaction of ammonium with the external bindingsites and determine the protonation states of ammonium278

They concluded that ammonium (NH4+) is dominant over

ammonia (NH3) near the external binding sites and thatdeprotonation can occur only inside the channel Bostick andco-workers also performed free-energy calculations using all-atom MD simulations275276 By calculating the transfer freeenergy of both ammonium and ammonia they showed apossible transport mechanism of ammonium through thechannel Moreover they emphasized the importance ofdehydration in the channel for the deprotonation ofammonium Most recently Wang et al used hybrid polarizablemechanicsmolecular mechanics (PMMM) simulations and

Figure 9 Selectivity filter of KcsA The system is depicted as in Figure5 but additionally with K+ ions resolved in the X-ray structure (orangespheres) In the active state the selectivity filter will always contain atleast two K+ ions separated by a single water molecule

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hybrid quantum mechanicsmolecular mechanics (QMMM)simulations to elucidate the permeation mechanism of bothammonium and protons277

ClC Cohen and Schulten260 explored the mechanism ofanion conduction across the ClC chloride channel by PMFcalculations using atomistic simulations The resulting PMFrevealed that the energy barrier for conduction of a single Clminus

ion is prohibitively high Interestingly the energy barrier wasreduced to 4 kcalmol in the presence of two Clminus ions in thepore suggesting that the incoming Clminus pushes the central ClminusSuenaga et al performed all-atom MD simulations to test thehypothesis that ClC channels are H+minusClminus exchange trans-porters Their results suggested that cations such as H+ and Na+

facilitate the channel opening and Clminus conduction261 Chungand co-workers utilized BD and MD simulations to reveal thebinding site of Clminus in the channel the electrostatic barrier ofClminus and the gating by an external Glu residue in atomisticdetail265266 Recently the first eukaryotic ClC transporter wascrystallized583 and Cheng and Coalson compared the Clminus

transport through the eukaryotic channel with that throughthe prokaryotic channel264 Their PMFs of Clminus in the channelsuggested that proper protonation of the external Glu gate iscritical for conduction

52 Ion Conductance

The force driving the permeation of ions through an ionchannel is the transmembrane potential arising from an unequaldistribution of ions on the two sides of the membrane A smallcharge imbalance in the vicinity of the pore gives rise to thepotential difference173 Explicit modeling of such chargeimbalance is difficult in all-atom MD simulations of a singlebilayer system as such simulations usually employ periodicboundary conditions so that the solution found at the two sidesof the membrane is one continuous volume One possibility isto use a single bilayer and two electrolyte compartmentsterminated by a vacuumwater interface329 An alternativeapproach is to use a twin bilayer system that includes twosolution phases584 of unequal ionic makeup that can generate atransmembrane electric field solely based on ion dynamics Inearly studies employing the twin bilayer setup the twomembranes were used to define the compartments of differention concentration A transmembrane potential was establisheddue to a small charge imbalance between the two compart-ments which was sufficient to generate short unsustained ionflux through the membrane channels To produce a continuousion flux the charge imbalance between the two compartmentshas to be maintained Kutzner et al recently demonstrated amethod to exchange ionwater pairs between the compart-ments and thus sustain the charge imbalance339 This methodwas applied to bacterial porin PorB of Neisseria meningitis todetermine the ion conductance and selectivity of the porinThe double-membrane approach however requires larger

systems which significantly increases the computationaloverhead A simpler alternative is to apply an external electricfield normal to the membrane to generate ionic flux throughthe pore Despite the apparent artificiality of the methodRoux173 provided a rigorous theoretical framework for thisstrategy An early study by Crozier et al289 in which the flow ofsodium ions was simulated through a simplified channel-membrane system under an imposed electric field demon-strated the feasibility of modeling an ionic current through amembrane In 2005 Aksimentiev and Schulten90 showed thatthe currentminusvoltage relationship of α-hemolysin could be

directly computed from all-atom MD simulations by applyingan external electric field The multinanosecond trajectoriesobtained in this 2005 study firmly established all-atom MD asthe method of choice for exploring conductance properties ofnanopores and using MD simulations to guide the developmentof nanopore sensors585 A similar approach was later applied inthe studies of MscS by Sotomayor et al244 and of Escherichiacoli porins OmpF and OmpC by Pezeshki et al7981 A recentstudy provides a detailed description of the external electricfield approach346

521 Potassium Channels MD simulations of K+

translocation through the selectivity filter of Kv12 allowedfor direct observation of the ldquoknock-onrdquo mechanism during asmall number of permeation events151 Subsequent brute-forcesimulations permitted estimation of the channelrsquos conductanceat several transmembrane biases151183 The simulated con-ductance was found to be nearly three times larger than theexperimentally measured one The discrepancy could bepartially attributed to a domain that was missing in thesimulated structure and may obstruct ion access in experimentThe simulations determined a five-step map of the trans-location cycle which was in agreement with the cyclesproposed from multi-ion free-energy calculations126 Thebrute-force approach allowed for direct observation of thekinetics between these steps identifying dehydration of theincoming K+ ion as the rate-limiting step of ion transportthrough the selectivity filter

522 Mechanosensitive Channels Among the twobacterial mechanosensitive channels with known high-reso-lution structure (MscL and MscS) MscS has been the subjectof ion conductance studies for several reasons Theconductance of the open MscL channel was experimentallydetermined to be fairly large suggesting a pore diameter of upto 30 Aring231232 Through such a wide channel small solutes canpass almost freely making the study of ion conductance lessinteresting In contrast the first MscS conformation reportedby Bass et al408 had been initially thought to capture thechannel in an open ion-conducting form However subsequentcomputational studies determined that the transmembranechannel in that MscS structure was not wide enough to furnisha fully hydrated transmembrane pore241242

Anishkin et al and Sotomayor et al performed pioneeringMD simulations of MscS241242247 In their all-atom MDsimulations they characterized the structural stability of MscSbased on the structure determined by Bass et al408 Thesimulations revealed partial collapse of the pore suggesting thatthe MscS conformation was at best partially open Thesimulations examined the distribution of water and ions in thechannel revealing dehydration of the narrowest part of thetransmembrane pore Anishkin et al also performed SMDsimulations by pulling a chloride ion along the channelconcluding that the pore was not large enough for theconductance of chloride242 Vora et al studied ion conductancethrough MscS using the BD method also concluding that thepore in the crystal structure of MscS was not large enough forthat structure to represent a fully open conformation229

Unlike the previous studies in the all-atom MD simulationsof Spronk et al243 an external electric field was appliedmimicking the physiological transmembrane potential In thelatter study the authors observed an increase in hydration andion conduction through the channel suggesting that the crystalstructure captured a conformation close to an open stateSubsequently Sotomayer et al also reported an increase of the

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MscS pore radius upon the application of large transmembranepotential (12 V) in an all-atom MD simulation244

Recently Vasquez et al proposed fully closed and openconformations of MscS based on electron paramagneticresonance spectroscopy and all-atom MD simulations256257

In this open MscS conformation the pore diameter was sim10 Aringthroughout the channel which is large enough to yield aconductance consistent with the experimental measurementsMscS has a large balloon-like cytoplasmic domain which

might play an important role in ion conductance see Figure 4c Recently Gamini et al probed ion conductance through thepores in the cytoplasmic domain using Gluminus and K+ as modelions248 Their results suggested that the cytoplasmic domain isa molecular sieve that balances effluxes of Gluminus and K+ throughMscSThe conductance of MscS has also been modeled using

continuum electrostatics methods (see sections 41) Forexample Sotomayor et al used atomistic MD simulations togenerate multiple conformations of the channels and thecontinuum transport theory to compute the ionic current forthese conformations258586 Recently Song and Corry calculatedthe ionic currents through MscS using a simplified NernstminusPlanck (NP) theory and rather realistic BD simulations225 Thestudy has shown the ability of the NP theory to reproduce theresults of the corresponding BD simulations523 α-Hemolysin Noskov and co-workers88 explored the

currentminusvoltage relationship of the α-hemolysin channel usingGCMCBD and 3D-PNP approaches (described in sections422 and 412 respectively) One of the inputs for theGCMCBD study was the position-dependent diffusioncoefficient of each ion type To incorporate the effect of thechannel size a reduction factor for the diffusivities wascalculated as per Paine and Scherr587 The study showed theIminusV characteristic to be asymmetric with a higher current atpositive bias (with the trans-entrance at a higher potential thanthe cis) which was in qualitative agreement with experi-ments588589 The study also revealed that by switching off thecharges on the pore the asymmetry in the conductancepractically disappeared indicating that it is the chargedistribution of the pore that is responsible for the asymmetryrather than the shapeThe MD study by Aksimentiev and Schulten90 was the first

to demonstrate that atomistic simulations can be used to obtainchannel conductances with quantitative accuracy Specificallythe study found the transmembrane currents driven by anexternal electric field applied normal to the membrane to be inexcellent agreement with experiment The large pore diameterand the high salt concentration made direct comparisonbetween simulation and experiment possible A recent MDstudy by Bhattacharya et al93 probed the cation-dependentrectification of the α-hemolysin nanopore The rectification ofthe ionic current was found to be dependent on the type ofcations and increased from Li+ to Cs+ both in simulations andin experiments The MD simulations showed that the cationiccontribution to the ionic current was the dominant factorinfluencing current asymmetry The cation type-dependentasymmetry of the ionic current was explained by differentialaffinity of the cations to the charged residues at the trans-entrance of the pore which modulated the number of ionsentering the narrowest part of the pore Recent experimentalstudies using site-directed mutagenesis590 and cysteine-scanning mutagenesis347 of the α-hemolysin channel revealedthat the ion-selectivity gating and conductance properties are

significantly affected by the location and the type of charges onthe pore

524 Outer-Membrane Porins Over the past 10 yearsthere have been a number of studies addressing ion-conductance properties of various OMPs (see Table 1) Imand co-workers carried out pioneering studies of OmpF using acombination of GCMCBD6263 MD5567 and continuum55

methods These first studies of OmpF revealed asymmetriccharacter of ionic conductance and produced concentrationminusconductance relations that were in good agreement withexperiment55 OmpF was a test bed for development of theGCMCBD methodUsing the all-atom MD method Pezeshki and co-workers

explored ion conductance of two structurally similar E coliporins OmpC and OmpF over a range of temperatures pHvalues and KCl concentrations7981 The results of the MDsimulations were in good agreement with experiment at low saltconcentrations and room temperature The authors observedconsiderable differences between the simulated temperaturedependence of conductance and experiment which wasattributed to the MD force field because the latter wasoptimized for simulations at room temperature The temper-ature dependence of the channelrsquos conductance was found todiffer from that of a corresponding bulk solution indicating theimportance of ion-pore interactions Using all-atom MD Modiand co-workers investigated the temperature-dependent trans-port of the ionic liquid 1-butyl-3-methyl-imidazolium chloride(BMIM-Cl) through OmpF86 The study indicated thataqueous solution of BMIM-Cl can reduce the rate of antibioticstransport through OmpF which could lead to practicalapplications of BMIM-Cl in the field of nanopore sensorsThe transmembrane pore of OmpF contains several titratable

residues Hence its conductance can depend on the solutionpH Varma et al used all-atom MD simulations to determinepKa (see section 435) of several key residues of OmpF7071

The study has shown that the pore size and conductance ofOmpF become consistent with the X-ray structure andelectrophysiology data correspondingly only when appropriateprotonation states are assigned to the key Asp residues7071

The study of Vrouenraets and Miedema has investigated theeffect of point mutations in OmpF finding ionization states ofthe residues to be the key factor affecting the ionconductance84

53 Selective Permeability

Concentration gradients of different types of ions support avariety of intra- and intercellular signals It is therefore vital tohave membrane channels that can distinguish and selectivelyconduct ions of different types One can easily imagine anelectrostatic mechanism for regulating the flux of different ionspecies based on the ion charge but what about channels thatselect a particular ion from all ions of the same chargeExperimental studies suggesting existence of Na+ and K+

selective channels began as early as 1960591 By 1971 it hadbeen inferred that the K+ channel has a wide inner openingleading to a narrow passage which blocks the passage of largecations However the K+ channel also prefers the conductanceof K+ over Na+ and Li+ even though the latter are smaller Theldquosnug-fitrdquo explanation offered in 1972592 suggested that it isnot electrostatically favorable for a Na+ ion to enter an oxygen-lined cage unless that cage is of the same size as the Na+ ionotherwise the Na+ will not form favorable electrostatic contactscompared to its solvation shell However the ldquosnug-fitrdquo

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mechanism requires a rather rigid pore incompatible with mostprotein structures which can only be described as soft andflexible Given that sodium and potassium appear to differ onlyon a scale significantly smaller than the size of an atom it isincredible that f lexible atomic-scale structures can yieldpermeabilities for the ions that may differ by a factor of1000593 The importance of subangstrom-scale structures andthe requirement of distinguishing between various physicalfactors naturally lend the study of ion selectivity to the all-atomMD methodology531 Potassium Channels The structures of all K+

channels feature a completely conserved constriction calledthe selectivity filter which is lined with four rings of negativecarbonyl-oxygen groups The structure of KcsA revealed two K+

ions separated by a single water molecule occupying this regionIn K+ channels the selectivity filter presents a barrier to iontransport and in general the larger the barrier the slower is theexpected rate of transport Thus early MD studies have focusedon the free energy difference experienced by K+ and Na+ ions inthe selectivity filter Because of the great similarity of these ionsthe free-energy perturbation (FEP) method has been theprotocol of choice for such studiesThe FEP method introduced in section 434 can evaluate

the free energy cost of transforming one atom into anotherthrough an unphysical pathway Because the end points of thistransformation are physically meaningful the change in freeenergy is also physically meaningful when considered as a stepin a thermodynamic cycle For example the difference inbinding free energy between K+ and Na+ in an ion channelΔΔG can be found from the free energies of transforming K+

into Na+ inside the channel and of transforming Na+ to K+ in abulk solution123 Both of these terms can be obtained fromFEP however care must be taken that the FEP simulations arelong enough that the system relaxes completely and fluctuationsare fully averagedEarly FEP simulations demonstrated a preference for K+ over

Na+ in the selectivity filter of KcsA120123141594 Howeverlimited by the computational resources available at the timethese simulations also suffered from problems small systemsizes that treated the lipid bilayer protein or water inunrealistic ways subnanosecond durations of simulations ateach FEP step andor external restraints that enforced crystalstructure-like conformation on the selectivity filter Despitethese limitations the range of values for ΔΔG (5minus17 kcalmolfor a single ion) were in apparent agreement with experimentalmeasurements of relief of Ba2+ blockades by Na+ and K+Recently a combination of MD simulations and X-ray

crystallography suggested that the smaller monovalent cationsNa+ and Li+ have their own binding site in the plane of acarbonyl-oxygen ring of the selectivity filter of KcsA as depictedin Figure 10 rather than between two rings as for K+595

Subsequently one- two- three- and four-ion umbrellasampling simulations provided PMFs for a Na+ or K+ ionpermeating K+-filled selectivity filters of KcsA and Kir-Bac11191596 The authors of one study note that FEPsimulations utilizing short trajectories may not provide theion with enough opportunity to find its preferred binding siteand that such studies likely overestimate ΔΔG which theauthors estimated to be 2minus3 kcalmol596 Additional umbrellasampling simulations of a Ba2+-occupied filter demonstratedthat the results can be quantitatively reconciled with Ba2+

blockade measurements because the Na+ and K+ ions areinfluenced differently by the bound Ba2+ ion Although the

latter study596 has not yet garnered response it demonstratesthe utility of a thorough simulation for interpretation ofexperimental measurements Thus the story of potassiumchannel selectivity may still be incomplete

532 Outer-Membrane Porins Porins often exhibitselectivity toward specific molecules For instance the outer-membrane protein OprP of Pseudomonas aeruginosa ananalogue of the PhoE porin of Escherichia coli is aphosphate-selective pore What is particularly interesting isthat it is not just anion-selective but can discriminate betweenanions OprP is highly selective toward the permeation ofinorganic phosphate (Pi) over other anions from the externalenvironment to the interior of the cell597 Atomistic simulationsperformed by Pongprayoon et al80 employing constant velocitySMD and umbrella sampling demonstrated that a lysine clusternear the periplasmic end of the pore selected ions by binding Pi

with greater affinity than small anions such as Clminus Theperiplasmic mouth of the pore can accommodate a fullysolvated Clminus ion which is therefore dielectrically screened fromthe positively charged lysine cluster Pi on the other hand ispartially dehydrated when it enters the pore at the periplasmicside and therefore interacts strongly with the lysine residuesThe extracellular end of the porin however allows the passageof both Clminus and PiAnother interesting porin that has been widely studied using

computational methods is the moderately cation-selectiveOmpF trimer The IK+IClminus ratio obtained from atomisticsimulations by Pezeshki et al79 was found to be sim12 which issimilar to older estimations by Im and Roux obtained fromGCMCBD and PNP approaches55 The key to theconductance and selectivity of the porin lies in its structureOne of the loops on the extracellular side the L3 is of specialimportance as it folds back into the β-barrel constricting thechannel Positively charged arginine residues on the wall of theporin face the negatively charged residues on the loop creatinga transverse electric field in the constriction region of theOmpF This field can orient molecules and cause a separationof ion fluxes5565 Experimental as well as computationalstudies83 have shown that it is possible to alter and evenreverse the selectivity of the OmpF by mutating the chargedresidues in the constriction region (both on the L3 loop andthe pore wall)

Figure 10 Na+ (green sphere) and K+ (red spheres) ions occupydifferent binding sites in the selectivity filter of a potassium channelEarly FEP simulations indicated a large free-energy cost ΔΔG forexchanging K+ with Na+ at the K+ binding sites ΔΔG may actually besmaller if the ion is free to move to its preferred binding site Adaptedwith permission from ref 595 Copyright 2009 Macmillan PublishersLtd Nature Structural amp Molecular Biology

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54 Ion-Channel Gating and Blockages

Proper cellular function requires that ions be released at certaintimes but not at other times and this variable ion conductanceis called gating For example the mechanosensitive channels inbacteria open to prevent rupture of the cell when tension in thebilayer increases due to osmotic stress Mechanosensitivechannels also initiate the conversion of mechanical vibrationsin the inner ear into electrical signals Similarly voltage- pH-and ligand-induced gating allow signals to be initiated orpropagated depending on the cellular conditionsGating almost always involves changes in the conformation

of the channel Until very recently brute-force atomisticsimulations of such changes were not possible because of thetime-scale limitations Below we discuss exemplary studiesincluding mechanical gating of the bacterial mechanosensitivechannels of small and large conductance and voltage gating of aK+ channel Additionally we discuss blockades of ion channelscaused by neurotoxins which may have pharmacologicalsignificance541 Mechanical Gating Even though several crystal

structures of MSCs are available the gating mechanisms remainelusive Unlike ligand- or voltage-gated ion channels wheregating is triggered by a relatively local structural change gatingof mechanosensitive channels involves a global structuraltransition231232 Consequently the time scale of the gating issignificantly greater than in other channels as is the length scalethat needs to be considered222 Although the large length scaleand long time scale of the mechanosensitive gating posepractical problems in computational studies of the gatingmechanism the prokaryotic MscL and MscS channels are idealsystems to develop the computational methodology because ofthe relative simplicity of these channels that are believed to betension sensors onlyWhen only one MSC crystal structure was available (a closed

conformation of MscL from Mycobacterium tuberculosis Tb-MscL) Sukharev and co-workers proposed a gating model forEscherichia coli MscL (Ec-MscL) in which the channel opensvia an ldquoiris-likerdquo mechanism231minus233 Starting from the closedconformation they modeled the intermediate and final openconformations in atomistic detail by utilizing various exper-imental information and empirical energy functions of theCHARMM force field In the open conformation the pore sizewas predicted to be sim30 Aring while the pore size of the closedcrystal structure was only a few angstroms impermeable tosmall molecules Physiological studies provided estimates of theopen pore diameter that were close to the result of theSukharev model (eg refs 255 598 and 599)Using the gating model of Ec-MscL several groups

performed MD simulations to test the model and observe thegating transition in all-atom detail230234236minus239 Kong et alcarried out targeted MD simulations to observe the transitionfrom closed to open conformations of the Ec-MscL230

Gullingsrud et al used SMD to induce opening of the closedconformation of Ec-MscL234238 In the SMD simulations it wasassumed that the forces on the protein by membrane stretchingapply only to the residues at the waterminuslipid interface whichwas based on observations of the pressure profile in pure lipidbilayers239 The same study used the pressure-profilecalculations to estimate the magnitude of the SMD force(35minus70 pN)Other than gating by tension Elmore and Dougherty

considered the effects of point mutations and lipidcompositions on the Tb-MscL structures using MD simu-

lations235240 Later Meyer et al studied the effect of a single-tailed lipid (which has high spontaneous curvature) on thestructure of Ec-MscL249 The simulations began from amanually built dome-shaped structure containing an Ec-MscLchannel embedded at the top of the dome During a 95-nssimulation the researchers observed spontaneous restructuringof the periplasmic loops of MscL which was in agreement withexperimental observations Recently Debret et al simulated Ec-MscL embedded in a lipid bilayer whose hydrophobic thicknesswas significantly smaller than the height of Ec-MscL250 Theresearchers observed tilting of transmembrane helices suggest-ing that hydrophobic mismatch can lower the activation energyof Ec-MscL opening Another all-atom MD simulations of Tb-MscL emphasized the interplay between protein and lipidbilayer by showing that inclusion of the protein significantlyincreases the mechanical rigidity of a lipid annulus251

Despite a number of ingenious efforts gating by tension hasnot been observed in all-atom MD simulations withoutapplying artificial driving forces The main difficulty is thetime scale of the mechanical gating which is significantly longerthan the time scale of an all-atom MD simulation To overcomethe time-scale problem several researchers applied morecomputationally efficient methods at the expense of accuracyPhillips and co-workers used continuum elasticity theory toevaluate the energetics of membrane deformation by theinclusion of MscL neglecting the internal energy of MscL forsimplicity226minus228 Their analytic calculations showed that gatingof MscL proteins can be modulated by the mechanicalproperties of the membrane226227 Moreover they alsodemonstrated how the function of multiple MscL channelscan be coupled Later Chen and co-workers applied computa-tional continuum mechanics to study the gating ofMscL221minus223 In their novel approach they explicitly consideredthe conformational change of MscL by modeling the MscLstructure using a simple elastic rodlike representation of thetransmembrane helices By combining such a simple model ofMscL with a continuum model of the membrane in a finite-element framework and parametrizing the models using all-atom MD simulations they were able to observe mechanicalgating of MscL just by stretching the membraneParticle-based coarse-graining offers another route toward a

simpler model of mechanical gating In this framework groupsof atoms are represented by single interaction beads whichdramatically increases the computational efficiency of the MDsimulation The interactions between such coarse-grained beadsare calibrated to reproduce the thermodynamic properties ofmodel systems obtained from all-atom MD simulations orexperiments (eg transfer free energy of small molecules fromwater to hydrocarbon) Marrink and co-workers applied theirnovel coarse-grained model MARTINI252 to Tb-MscL253254

Specifically they were able to simulate gating of MscL just bystretching the membrane253 or pressurizing a vesicle thatcontained embedded MscL channels254

When the time scale accessible to an MD simulation issignificantly shorter than the time scale of gating one canaccelerate the simulation by applying biasing forces (egSMD) However the quality of such accelerated simulationsdepends critically on how realistic the biasing forces are In thissense combining single-molecule experiments with SMDsimulations can be very successful For example Corry et alrecently demonstrated that the distance measurements fromForster resonance energy transfer (FRET) confocal microscopycan be used as a guide for the SMD simulation255 Starting from

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a closed conformation the researchers induced a closed-to-open conformational transition by performing SMD simu-lations that utilized distance constraints derived from FRETmeasurements on an open MscL channel Because of thedistance constraints the simulations produced a reasonablestructural model of the MscL pore in an open state542 Potassium Channels Potassium channels which all

share a common sequence for the selectivity filter demonstratevoltage- pH- and Ca2+-dependent gating of an intracellulargate which limits K+ access to the selectivity filter andextracellular solution However the selectivity filter is itself afragile structure that can be inactivated Inactivation of theselectivity filter occurs more readily when the intracellular gateis open186

It may be insightful to consider purely solution-dependentinactivation and inhibition of the selectivity filter A potassiumion channel will nearly irreversibly inactivate if it is placed inelectrolyte solution of very low ion concentration All-atom MDsimulations suggested a mechanism of such inactivation bydemonstrating severe distortion of the selectivity filter when itis depleted of K+ ions that partially neutralize the negativecarbonyl-oxygens lining of this structure137143182 Similarlyconductance of K+ channels can be blocked by other ions suchas Na+ or Cs+ that bind to the selectivity channelThe Kv channels are all voltage-gated Crystallographic

studies have provided structures for several open-pore Kvchannels featuring a charged voltage-sensitive subunit sur-rounded by lipids for each monomer of the tetramer411600601

The voltage-sensitive subunits are expected to move andrearrange in response to a voltage change in such a way that asmall but measurable transient capacitative current is observedacross the membrane The associated charge is known as thegating chargeThe gating charge times the change in the potential provides

the free energy required to change conformations and gate thechannel Using all-atom simulations the gating charge can bedirectly computed by measuring the difference in the center ofcharge of the system between open and closed conforma-tions185 A more sophisticated approach allows the assessmentof each residuersquos contribution to the gating charge through thecalculation of the difference between the free-energy cost ofcharging each residue in the closed and open states185

There is currently no crystallographically obtained closed-pore structure of a voltage-gated K+ channel However in astudy that utilized 13 μs of all-atom MD simulation the open-pore structure was refined and a possible closed-pore structurefor Kv12 was obtained185 Using these structures the gatingcharge was found to be somewhat smaller than theexperimentally measured gating charge suggesting that thecomputational model represented an intermediate conforma-tion at the onset of activationVery recently special-purpose hardware enabled all-atom

simulations of a Kv12Kv21 chimera on the gating-time scaleas observed experimentally (gt300 μs)196 The simulationsdemonstrated that the crystal structure accurately representsthe functional open pore In a series of simulations differentonly by the transmembrane voltage and the initial conditionsthe channel was brought from the open state to a fully closedstate Simulations were also performed to simulate differentstages of channel activation Gating of the channel occurred bystructural rearrangements of the voltage-sensitive domains thataffected the hydrophobic cavity leading to the selectivity filterThese rearrangements caused dewetting and collapse of the

cavity The time scales of various steps during the processagreed well with available experimental measurements196

Although not based on such long simulations a study of apH-sensitive potassium channel suggested that gating for thisprotein may occur through a rather different mechanism Anarginine residue near the extracellular side of the membranewas identified through mutagenesis as providing pH-sensitiv-ity602 The PMF of K+ ions in the selectivity filter was obtainedthrough all-atom MD when the protonation state of thatarginine residue was varied The authors of this study suggestedthat the observed 3minus4 kcalmol increase in the barriers for K+

translocation accounted for gating and arose from additionalflexibility that protonation of the arginine sensors granted tothe selectivity filter602 However it should be noted thatbecause no X-ray structure is available a homology model ofthe K2P channel built from Kv12 was used for this studyThus potassium channels share a great deal of structural and

sequence similarity around the selectivity filter but can be gatedin a variety of ways All-atom simulation techniques haveprovided a great deal of insight into the structural mechanismsof the gating processes In one exemplary study196 brute-forceall-atom MD simulations described the complete gating processof a voltage-sensitive potassium channel on a time scale ofhundreds of microseconds At this time it remains to be seenwhether other potassium channels use similar mechanisms togate

543 Blockades Some toxins bind and inactivateparticular target channels The potential for specificity ofchannel-binding toxins makes them an attractive source forpharmaceutical innovation The all-atom MD methodology hasbeen used to find the standard binding free energies of manysmall ligands but only recently have researchers attempted tofind the binding free energies of large ligands In particularseveral studies demonstrated challenges and shortcuts whencomputing standard binding free energies of charbydotoxinbinding to various voltage sensitive potassium chan-nels116603604

Of greater pharmacological interest the Kv13 K+ channelhas been identified as a target treatment of multiple sclerosisand other autoimmune disorders422 In a recent study the toxinShK which blocks Kv13 but also Kv11 was docked to severalK+ channels and the binding free energy was calculated425

Surprisingly the simulations revealed different binding geo-metries to Kv13 and Kv11 but similar binding free energiesthat agree well with experimentally determined values Theauthors concluded with mutations to ShK that may enhance theselectivity of Kv13 over Kv11At present free-energy calculations require too much

computing power and are not automated enough to be usedas a predictive tool by the pharmaceutical industry Inparticular reliably docking potential drug candidates remainsa challenge Nevertheless the combination of special-purposehardware for performing MD simulations very quickly andimproved automation of tools for calculating binding freeenergies may give rise to the use of all-atom simulations inadvanced computation drug screening within the pharmaceut-ical industry

55 Biosensing with Channels

About 20 years ago Bezrukov et al605 and Kasianowicz447 andco-workers demonstrated the possibility of using ionic channelsas molecular Coulter counters to detect the presence andcharacterize the type of biomolecules The basic principle of the

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approach is the following A membrane containing a single-ionchannel separates electrolyte solution into two compartmentsconnected only through the transmembrane pore of thechannel A transmembrane bias is imposed using an externalvoltage source producing a steady ionic current through anopen pore The transmembrane bias facilitates unidirectionaltransport of charged biomolecules from one compartment tothe other Each passage is detected as transient reduction (ablockade) of the ionic current flowing through the pore Theduration and magnitude of the ionic current blockades canindicate the length and chemical composition of a nucleic acidpolymer447606minus608 suggesting the possibility of recording thenucleotide sequence of a DNA strand directly by measuring theionic current flowing through a nanoporeCritical to the success of the above approach is the lack of

spontaneous gating of the ion conductance which if presentcan easily be confused with the signal resulting from interactionof the channel with a biomolecule Because of its superiorstructural stability the α-hemolysin channel was the firstnanopore to be considered for biosensing applications447609

However other channels such as the bacterial porinMspA449minus451 and man-made silicon-based610minus612 and gra-phene613minus615 nanopores have been successfully used fordetection of biomolecules Apart from DNA sequencingnumerous other applications have been proposed for nano-pores including detection of small analytes589616617 drugdesign390618 pathogen detection619 and force spectrosco-py620minus622 Interested readers are directed to several reviews onthis subject446623minus627

Modeling and computer simulations have played a major rolein development of nanopore applications585 There have alsobeen numerous theoretical studies of various aspects ofpolymer capture and translocation through nanoporesTypically such studies involve the application of scalingconcepts of polymer physics or transport equations628minus630 toelucidate the dynamics of charged polymer capture andtranslocation All-atom simulations have been used as a kindof a computational force microscope to directly relate themicroscopic events taking place in a nanopore to the ioniccurrent blockades recorded in experiment377585

551 α-Hemolysin Among many β-barrel proteins α-hemolysin has been the channel of choice for mostexperimental studies because of its exceptional structuralstability under harsh experimental conditions The knowncrystallographic structure and relatively straightforward site-directed mutagenesis procedures permit rational engineering ofthis channel to enhance sensitivity of ionic current blockadesfor example by introducing a molecular adapter616 or othersite-specific mutations631632

The 2005 publication by Aksimentiev and Schulten90

pioneered the application of the all-atom MD method forprediction of the ionic conductance of membrane channelsThe simulations demonstrated for the first time quantitativeaccuracy of the MD method in predicting the absolute value ofthe ionic current reproducing the asymmetric currentminusvoltagedependence of α-hemolysin and characterizing the electro-osmotic effect The simulations also suggested a microscopicmechanism explaining the pH-dependence of the noise in theionic current recordings633 The study has also demonstrated amethod for computing the average distribution of theelectrostatic potential in a membrane channel directly froman all-atom MD simulation90 Following the successful study ofionic conductance through α-hemolysin the researchers were

challenged by an experimentalist (A Meller Boston University)to predict the influence of the global orientation of a DNAstrand in α-hemolysin on the velocity of DNA transport andthe ionic current blockades This was a blind test as no priorinformation about the outcome of experiments was given Tofind out the molecular origin of the observed differences MDsimulations were performed on α-hemolysin systems havingDNA threaded through in two different global orientationsfrom 3prime to 5prime and from 5prime to 3prime The outcome of the simulationsrevealed a propensity for DNA nucleotides to tilt toward their5prime-ends in confined environments which was linked toobservable differences in DNA translocation dynamics andionic current blockades97 The results of the MD simulationswere in qualitative agreement with experiment Because oflimited computational resources direct quantitative comparisonwas not possible at that timeThe α-hemolysin channel has been a test bed for developing

advanced simulation techniques The Roux group exploredpermeation of ions through the α-hemolysin channel using 3D-PNP as well as the grand canonical Monte Carlo Browniandynamics (GCMCBD) approaches88 in the absence of anyanalytes The study revealed that the asymmetric conductanceof the pore arises from the permanent charge distribution in thepore Another PNP study examined the influence of chargedresidues in α-hemolysin on the asymmetry of the currentminusvoltage dependence89100 Shilov and Kurnikova96 employedMD simulations to investigate the energetics and dynamics of aβ-cyclodextrin (βCD) molecule confined inside the α-hemolysin pore The Roux group investigated the effect ofβCD on the ion selectivity of the α-hemolysin through MDsimulations and PMF calculations94 The simulations haveshown that electrically neutral βCD enhances the concentrationof Clminus in the nanopore by causing a partial desolvation of theions which reduces the dielectric shielding by the solvent TheGCMCBD method was used to account for multi-ion effectsin a subsequent study94 Simakov and Kurnikova devised amodified PNP approach to incorporate a soft repulsion modelof short-range interactions between mobile ions and protein92

To overcome the time-scale limitation of the MD methodthe Aksimentiev group developed a method for acceleratingsimulations of DNA transport through nanopores thatpreserves all-atom features of the MD model98 The key ideaof the method dubbed grid-steered MD (G-SMD) was theselective amplification of the electrostatic potential that drivesDNA transport while maintaining all other interactionsunchanged Using G-SMD the Aksimentiev group performedmultiple simulations of DNA transport through α-hemolysinand determined the dependence of the translocation velocityon the sequence and orientation of the DNA strands98 a taskthat was considered formidable at that time634 De Biase andco-workers recently developed a theoretical framework tomodel DNA translocation across a nanopore by combining theGCMCBD algorithm with a coarse-grained polymer model forDNA102 which enabled multimicrosecond simulations at afraction of the cost of all-atom MD When applied to modeltranslocation of poly(dA) and poly(dC) strands through α-hemolysin the model yielded results in reasonable agreementwith experiments Reiner et al367 developed an elegantcontinuum theory to describe the results of nanopore massspectroscopy experiments with quantitative accuracy635 Bondet al employed all-atom MD simulations to explore thetranslocation of short strands of DNA through a simplifiedmodel of the α-hemolysin pore comprising the stem of the pore

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surrounded by a membrane mimetic slab99 The studyexamined the effect of cationic amino acids on the translocationdynamics of DNA Compared to wild type α-hemolysinarginine mutations were found to reduce the transport rate ofDNA through the pore as well as the ionic current552 MspA The long stem of α-hemolysin can

accommodate up to 12 DNA nucleotides which makes difficultthe detection of single nucleotides by measuring ionic currentThe MspA porin has recently emerged as a viable alternative toα-hemolysin on account of its superior architecture MspA has agoblet-like structure with a constriction region that is sim1 nmideal for holding just one or two nucleotides see Figure 11aButler and co-workers showed that by eliminating the negativecharge in the constriction a variant of MspA called M1MspAwas capable of detecting a single DNA strand electrophoreti-cally driven through the pore449 A series of subsequentexperimental work in the Niederweis and Gundlach groupshave since established that the current resolution of the MspAvariant is superior to that of α-hemolysin636 and that singlenucleotide substitutions can be detected on a randomheteropolymeric background using a tethered DNA451

However the primary challenge is that the translocation rateof DNA through MspA is several orders of magnitude higherthan the rate required to resolve the type of DNA nucleotidesby measuring ionic current The two main strategies to controlDNA translocation are to engineer intrinsic brakes in the MspAstructure or use an auxiliary enzyme such as DNA polymer-ase637

The first computational study of MspA was recently carriedout by Bhattacharya and co-workers348 The study reportsextensive all-atom MD simulations that explored the effect ofpositively charged arginine residues on the translocation rate ofDNA and the ionic current On account of the highcomputational overhead due to the large system size theauthors performed the majority of the simulations using a

truncated version of the pore (see Figure 11b c) Since theDNA was found to be quite mobile even when confined to thenanopore the authors adopted an ensemble approach tosample the configurational dynamics of the DNA Theensemble method was shown to be a viable alternative tofollowing a single long-time-scale trajectory which is currentlypossible only using special-purpose supercomputers such asAnton The ensemble approach allowed the use of traditionalsupercomputers to obtain combined trajectory lengths of tensof microseconds within reasonable physical time Thesimulations have shown that by introducing several arginineresidues near the constriction of MspA the DNA permeationrate can be reduced by a factor of 10minus30 due to the formationof multiple salt bridges between the DNA backbone and theguanidinium groups of the arginine substitutions as well as dueto base-stacking interactions Furthermore the simulationspredicted that such mutations would not eliminate thenucleotide sensitivity of the ionic-current blockades Thestudy explained why similar mutations introduced in α-hemolysin reduced the ionic current practically to zero638

making such mutants unsuitable for DNA sequencingapplications

553 Other Nanopore Systems Other β-barrel nano-pores have been explored for stochastic sensing applicationsFor instance an MD study of the bacterial porin OmpG wascarried out by Chen and co-workers to determine the origin ofits spontaneous gating activity77 On the basis of the simulationstudy a variant of the porin with stabilizing mutations wascreated and was used for detection of adenosine diphosphateafter inserting a cyclodextrin molecular adapter77

Using 3D-Poisson equations and linear transport theory360

Vidal and co-workers demonstrated that a nanopore in a heavilydoped silicon membrane connected to a voltage source can beused as an electrically tunable ion filter The PNP model wasused to study ion transport through synthetic nanopores in

Figure 11 (a) Cut-away view of the full-length MspA nanopore embedded in a lipid membrane with a DNA strand threaded through The MspA isrepresented by a teal molecular surface the lipid membrane is represented by purple lines and the DNA bases are shown in magenta-colored licoricerepresentation (b) Average electrostatic potentials along the symmetry axis of the full and truncated MspA nanopores at a transmembrane bias of180 mV The electrostatic potentials are computed from MD simulations of open-pore MspA nanopores (c) Cut-away view of the reduced MspAsystem The DNA is covalently joined to itself across the periodic boundary (d) The ionic current trace of a sample trajectory of a poly(dC) strandthreaded through the MspA nanopore (e) Ionic current histograms obtained from ensemble simulations of the M1MspA (yellow) and its argininevariant M1 L88RA96RS116R (blue) The overlap of the two histograms is shown in green The histograms were constructed using 100 nsaverages of the instantaneous ionic current Adapted with permission from ref 348 Copyright 2012 American Chemical Society

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several studies359363366 exploring rectification and ionselectivity A Langevin dynamics approach to study thetransport of flexible macromolecules in confined geometrieswas proposed by Peters372 Recently an atomic resolution BDmethod was developed by Comer and co-workers that was usedto study the sequence dependence of ionic current in syntheticnanopores373374 All-atom MD simulations have been usedwith considerable success to investigate nanopore transport ofDNA and ionic current blockades375376 nanopore unzipping ofDNA hairpins380 the microscopic origin of the electrophoreticforce on DNA in a nanopore378381 and the effect of electrolyteon the DNA translocation rates391 For detailed description ofthe simulation protocols interested readers are directed torecent reviews on this subject585639640

6 OUTLOOK

Advances in computational technologies and membraneprotein structure-determination methods are poised to makemodeling and simulations of ion channels an integral part offuture drug-development efforts The greatest obstacle so far isthe lack of atomic-resolution structures of the majority ofbiomedically relevant ion channels Several limitations pertainto the computational technology itself Whereas all-atommolecular dynamics simulation of an ion channel can providethe most detailed information about the microscopicmechanism of its function the method is currently limited bythe accuracy of the classical force field and the microsecondtime scale of the simulations on conventional computerclustersTremendous advances in addressing both limitations have

already been made The first computational studies of ionchannel systems using polarizable models have already beenreported277563 Thus it is very likely that a full polarizable forcefield will become available within the next 10 years Anothermajor advancement was the millisecond simulation of amembrane channel in its native environment that revealedthe microscopic details of its voltage-dependent gatingmechanism196 We hope that such a tremendous success ofspecial-purpose hardware will prompt the development ofcommodity special-purpose hardware which will make suchlong-time-scale simulations available to mainstream researchersFinally advances in computational methods will also aid thediscovery of atomic-resolution structures through either denovo structure prediction641 or refinement of low-resolution X-ray and cryo-EM structures443

It would be misleading however to think that all questionspertaining to ion channels would be answered through all-atomMD From a drug-development perspective high-throughputand accurate calculation of binding free energies of smallchemical compounds is more important than long-time-scalesimulations of a single channelrsquos action Enabling such high-throughput docking is dependent on the availability of accurategeneric force fields Furthermore as millisecond simulationsbecome more available describing possible chemical reactionsbetween components of the system will become increasinglyimportant Finally modeling a single channel in a membrane isonly a first step toward the realistic modeling of in vivoprocesses We anticipate continuum and implicit solventapproaches to play a pivotal role in the development ofdetailed quantitative models of realistic biological membranesand small organelles that incorporate an ensemble of ionchannels

AUTHOR INFORMATION

Corresponding Author

E-mail aksimentillinoisedu

Notes

The authors declare no competing financial interest

Biographies

Christopher Maffeo received his BSc in physics from the University of

California Santa Barbara in 2006 He joined the Aksimentiev group in

December 2006 After studying the structural and conductance

properties of the phospholamban pentamer he has focused his efforts

on understanding the kinetics energetics and electrostatics of various

DNAminusDNA and DNAminusprotein interactions

Swati Bhattacharya is a postdoctoral fellow in the group of Aleksei

Aksimentiev at the University of Illinois at UrbanaminusChampaign She

received her PhD in physics for work on the adsorption of polymers

at surfaces under the supervision of Thomas Vilgis in 2009 from the

Max Planck Institute for Polymer Research in Mainz Her current

research activities include computational modeling aimed at

developing applications of nanopores particularly for DNA sequencing

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which the system is pushed away from regions of phase spacethat have already been sampled577minus579 All of these methodsseek to map the free energy along one or more coordinatesalthough SMD is inherently one-dimensional A typical choicefor studies of single-file ion permeation is the position of one ormore ions along the pore axisThe PMFs of ion permeation through KcsA obtained from

SMD and umbrella sampling simulations were qualitativelysimilar and revealed overlapping minima and maxima176 Theresults obtained using these two methods were found to besensitive to the conformation of the residues in the filter andthe position of the ion in the cavity just outside the filter whichcould change on the time scale of the simulations The PMFsobtained using the SMD method were created by combiningdata from multiple simulations demonstrating the advantage ofincreased parallelization However for such an approach to bevalid individual simulations should be sufficiently long toaverage over conformational fluctuations Unfortunately theauthors did not sample equivalent amounts using these twomethods and thus a direct comparison could not be obtainedIn general the SMD method results in a PMF that has barriersconsiderably larger than those determined from umbrellasampling simulations512 Gramicidin A For details of the history of gramicidin

A in all-atom simulation we refer interested readers to recentreviews2139 Here we highlight the methodologies used tostudy ion channels that have been validated using gramicidin AThe first applications of quantitative MD methods to the

study of ion channels were free-energy perturbation calculations(FEP see section 434) on gramicidin A which providedsignificant insight into the ion-translocation process The firstsuch study was performed over 20 years ago and compared thesolvation free energy of a Na+ ion in gramicidin A at differentpositions in the pore to the solvation free energy in bulksolution18 The results of this study can be considered as a low-resolution PMF that indicated a series of rather large (sim5 kcalmol) pits and barriers within the channel Another FEP studydetermined the relative solvation free energy for Na+ in a singlyand doubly occupied gramicidin A relative to bulk water19 TheNa+ ions were then mutated into the other four commonmonovalent cations These calculations demonstrated thatsmall ions are less likely to doubly occupy gramicidin A

compared to large ions agreeing with experiment andsupporting the validity of the underlying model The umbrellasampling method was recently used to determine a two-ionPMF demonstrating that double occupancy in gramicidin A isnot favorable46

Single-ion permeation through gramicidin A has since beenstudied numerous times using the umbrella sampling35415051

and SMD38424348 methodologies Studies employing theumbrella sampling50 and SMD48 approaches have cautionedthat extensive simulations are needed to obtain completeconvergence using either method Sampling on the order ofhundreds of nanoseconds may be required to achieve theconvergence irrespective of the chosen method althoughunidirectional SMD simulations were found to exhibit severehysteresis in relatively short simulation when compared toumbrella sampling41

513 Others Channels PLN The uptake of Ca2+ by Ca2+-ATPase is regulated by the membrane protein phospholamban(PLN) which acts as an inhibitor Although more than 75 ofPLN in a lipid bilayer membrane is pentameric the only knownfunction of PLN ie Ca2+-ATPase inhibition involves a PLNmonomer and not a pentamer although there were a fewexperimental reports of ion conductance involving PLN580581

Using SMD330 and the umbrella sampling345 methods it wasrecently shown that the channel-like NMR model of the PLNpentamer does not conduct ions in agreement with morerecent experimental studies582

VDAC The Im group carried out all-atom MD study of thehuman VDAC1 to characterize the ion permeation andselectivity of the pore262 The study revealed that negativelycharged Asp and Glu residues serve as traps for K+ ions as theypass through the channel The one-dimensional multi-ion PMFcomputed for K+ and Clminus revealed the reason for the anionselectivity of the channel a higher free-energy barrier for K+

ions to enter the channelOmpF Im and Roux explored the ion density profiles and

the conductance of the Escherichia coli porin OmpF in adetailed study employing MD BD and PNP approaches5567

All three approaches revealed distinct ion pathways for K+ andClminus ions through the pore determined by the distribution ofcharged residues in the porin The phosphate selective porinOprP was recently studied using equilibrium SMD andumbrella sampling simulations80 The study revealed twonegatively charged phosphate-binding sites in the interior ofthe pore in close proximity to one another each with a freeenergy minimum of sim8 kBT Findings relating to thepreference of OprP for phosphate over Clminus will be discussedbelow

AmtB Luzhkov et al performed FEP and pKa calculations(see sections 434 and 435) using all-atom MD simulations tostudy the interaction of ammonium with the external bindingsites and determine the protonation states of ammonium278

They concluded that ammonium (NH4+) is dominant over

ammonia (NH3) near the external binding sites and thatdeprotonation can occur only inside the channel Bostick andco-workers also performed free-energy calculations using all-atom MD simulations275276 By calculating the transfer freeenergy of both ammonium and ammonia they showed apossible transport mechanism of ammonium through thechannel Moreover they emphasized the importance ofdehydration in the channel for the deprotonation ofammonium Most recently Wang et al used hybrid polarizablemechanicsmolecular mechanics (PMMM) simulations and

Figure 9 Selectivity filter of KcsA The system is depicted as in Figure5 but additionally with K+ ions resolved in the X-ray structure (orangespheres) In the active state the selectivity filter will always contain atleast two K+ ions separated by a single water molecule

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hybrid quantum mechanicsmolecular mechanics (QMMM)simulations to elucidate the permeation mechanism of bothammonium and protons277

ClC Cohen and Schulten260 explored the mechanism ofanion conduction across the ClC chloride channel by PMFcalculations using atomistic simulations The resulting PMFrevealed that the energy barrier for conduction of a single Clminus

ion is prohibitively high Interestingly the energy barrier wasreduced to 4 kcalmol in the presence of two Clminus ions in thepore suggesting that the incoming Clminus pushes the central ClminusSuenaga et al performed all-atom MD simulations to test thehypothesis that ClC channels are H+minusClminus exchange trans-porters Their results suggested that cations such as H+ and Na+

facilitate the channel opening and Clminus conduction261 Chungand co-workers utilized BD and MD simulations to reveal thebinding site of Clminus in the channel the electrostatic barrier ofClminus and the gating by an external Glu residue in atomisticdetail265266 Recently the first eukaryotic ClC transporter wascrystallized583 and Cheng and Coalson compared the Clminus

transport through the eukaryotic channel with that throughthe prokaryotic channel264 Their PMFs of Clminus in the channelsuggested that proper protonation of the external Glu gate iscritical for conduction

52 Ion Conductance

The force driving the permeation of ions through an ionchannel is the transmembrane potential arising from an unequaldistribution of ions on the two sides of the membrane A smallcharge imbalance in the vicinity of the pore gives rise to thepotential difference173 Explicit modeling of such chargeimbalance is difficult in all-atom MD simulations of a singlebilayer system as such simulations usually employ periodicboundary conditions so that the solution found at the two sidesof the membrane is one continuous volume One possibility isto use a single bilayer and two electrolyte compartmentsterminated by a vacuumwater interface329 An alternativeapproach is to use a twin bilayer system that includes twosolution phases584 of unequal ionic makeup that can generate atransmembrane electric field solely based on ion dynamics Inearly studies employing the twin bilayer setup the twomembranes were used to define the compartments of differention concentration A transmembrane potential was establisheddue to a small charge imbalance between the two compart-ments which was sufficient to generate short unsustained ionflux through the membrane channels To produce a continuousion flux the charge imbalance between the two compartmentshas to be maintained Kutzner et al recently demonstrated amethod to exchange ionwater pairs between the compart-ments and thus sustain the charge imbalance339 This methodwas applied to bacterial porin PorB of Neisseria meningitis todetermine the ion conductance and selectivity of the porinThe double-membrane approach however requires larger

systems which significantly increases the computationaloverhead A simpler alternative is to apply an external electricfield normal to the membrane to generate ionic flux throughthe pore Despite the apparent artificiality of the methodRoux173 provided a rigorous theoretical framework for thisstrategy An early study by Crozier et al289 in which the flow ofsodium ions was simulated through a simplified channel-membrane system under an imposed electric field demon-strated the feasibility of modeling an ionic current through amembrane In 2005 Aksimentiev and Schulten90 showed thatthe currentminusvoltage relationship of α-hemolysin could be

directly computed from all-atom MD simulations by applyingan external electric field The multinanosecond trajectoriesobtained in this 2005 study firmly established all-atom MD asthe method of choice for exploring conductance properties ofnanopores and using MD simulations to guide the developmentof nanopore sensors585 A similar approach was later applied inthe studies of MscS by Sotomayor et al244 and of Escherichiacoli porins OmpF and OmpC by Pezeshki et al7981 A recentstudy provides a detailed description of the external electricfield approach346

521 Potassium Channels MD simulations of K+

translocation through the selectivity filter of Kv12 allowedfor direct observation of the ldquoknock-onrdquo mechanism during asmall number of permeation events151 Subsequent brute-forcesimulations permitted estimation of the channelrsquos conductanceat several transmembrane biases151183 The simulated con-ductance was found to be nearly three times larger than theexperimentally measured one The discrepancy could bepartially attributed to a domain that was missing in thesimulated structure and may obstruct ion access in experimentThe simulations determined a five-step map of the trans-location cycle which was in agreement with the cyclesproposed from multi-ion free-energy calculations126 Thebrute-force approach allowed for direct observation of thekinetics between these steps identifying dehydration of theincoming K+ ion as the rate-limiting step of ion transportthrough the selectivity filter

522 Mechanosensitive Channels Among the twobacterial mechanosensitive channels with known high-reso-lution structure (MscL and MscS) MscS has been the subjectof ion conductance studies for several reasons Theconductance of the open MscL channel was experimentallydetermined to be fairly large suggesting a pore diameter of upto 30 Aring231232 Through such a wide channel small solutes canpass almost freely making the study of ion conductance lessinteresting In contrast the first MscS conformation reportedby Bass et al408 had been initially thought to capture thechannel in an open ion-conducting form However subsequentcomputational studies determined that the transmembranechannel in that MscS structure was not wide enough to furnisha fully hydrated transmembrane pore241242

Anishkin et al and Sotomayor et al performed pioneeringMD simulations of MscS241242247 In their all-atom MDsimulations they characterized the structural stability of MscSbased on the structure determined by Bass et al408 Thesimulations revealed partial collapse of the pore suggesting thatthe MscS conformation was at best partially open Thesimulations examined the distribution of water and ions in thechannel revealing dehydration of the narrowest part of thetransmembrane pore Anishkin et al also performed SMDsimulations by pulling a chloride ion along the channelconcluding that the pore was not large enough for theconductance of chloride242 Vora et al studied ion conductancethrough MscS using the BD method also concluding that thepore in the crystal structure of MscS was not large enough forthat structure to represent a fully open conformation229

Unlike the previous studies in the all-atom MD simulationsof Spronk et al243 an external electric field was appliedmimicking the physiological transmembrane potential In thelatter study the authors observed an increase in hydration andion conduction through the channel suggesting that the crystalstructure captured a conformation close to an open stateSubsequently Sotomayer et al also reported an increase of the

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MscS pore radius upon the application of large transmembranepotential (12 V) in an all-atom MD simulation244

Recently Vasquez et al proposed fully closed and openconformations of MscS based on electron paramagneticresonance spectroscopy and all-atom MD simulations256257

In this open MscS conformation the pore diameter was sim10 Aringthroughout the channel which is large enough to yield aconductance consistent with the experimental measurementsMscS has a large balloon-like cytoplasmic domain which

might play an important role in ion conductance see Figure 4c Recently Gamini et al probed ion conductance through thepores in the cytoplasmic domain using Gluminus and K+ as modelions248 Their results suggested that the cytoplasmic domain isa molecular sieve that balances effluxes of Gluminus and K+ throughMscSThe conductance of MscS has also been modeled using

continuum electrostatics methods (see sections 41) Forexample Sotomayor et al used atomistic MD simulations togenerate multiple conformations of the channels and thecontinuum transport theory to compute the ionic current forthese conformations258586 Recently Song and Corry calculatedthe ionic currents through MscS using a simplified NernstminusPlanck (NP) theory and rather realistic BD simulations225 Thestudy has shown the ability of the NP theory to reproduce theresults of the corresponding BD simulations523 α-Hemolysin Noskov and co-workers88 explored the

currentminusvoltage relationship of the α-hemolysin channel usingGCMCBD and 3D-PNP approaches (described in sections422 and 412 respectively) One of the inputs for theGCMCBD study was the position-dependent diffusioncoefficient of each ion type To incorporate the effect of thechannel size a reduction factor for the diffusivities wascalculated as per Paine and Scherr587 The study showed theIminusV characteristic to be asymmetric with a higher current atpositive bias (with the trans-entrance at a higher potential thanthe cis) which was in qualitative agreement with experi-ments588589 The study also revealed that by switching off thecharges on the pore the asymmetry in the conductancepractically disappeared indicating that it is the chargedistribution of the pore that is responsible for the asymmetryrather than the shapeThe MD study by Aksimentiev and Schulten90 was the first

to demonstrate that atomistic simulations can be used to obtainchannel conductances with quantitative accuracy Specificallythe study found the transmembrane currents driven by anexternal electric field applied normal to the membrane to be inexcellent agreement with experiment The large pore diameterand the high salt concentration made direct comparisonbetween simulation and experiment possible A recent MDstudy by Bhattacharya et al93 probed the cation-dependentrectification of the α-hemolysin nanopore The rectification ofthe ionic current was found to be dependent on the type ofcations and increased from Li+ to Cs+ both in simulations andin experiments The MD simulations showed that the cationiccontribution to the ionic current was the dominant factorinfluencing current asymmetry The cation type-dependentasymmetry of the ionic current was explained by differentialaffinity of the cations to the charged residues at the trans-entrance of the pore which modulated the number of ionsentering the narrowest part of the pore Recent experimentalstudies using site-directed mutagenesis590 and cysteine-scanning mutagenesis347 of the α-hemolysin channel revealedthat the ion-selectivity gating and conductance properties are

significantly affected by the location and the type of charges onthe pore

524 Outer-Membrane Porins Over the past 10 yearsthere have been a number of studies addressing ion-conductance properties of various OMPs (see Table 1) Imand co-workers carried out pioneering studies of OmpF using acombination of GCMCBD6263 MD5567 and continuum55

methods These first studies of OmpF revealed asymmetriccharacter of ionic conductance and produced concentrationminusconductance relations that were in good agreement withexperiment55 OmpF was a test bed for development of theGCMCBD methodUsing the all-atom MD method Pezeshki and co-workers

explored ion conductance of two structurally similar E coliporins OmpC and OmpF over a range of temperatures pHvalues and KCl concentrations7981 The results of the MDsimulations were in good agreement with experiment at low saltconcentrations and room temperature The authors observedconsiderable differences between the simulated temperaturedependence of conductance and experiment which wasattributed to the MD force field because the latter wasoptimized for simulations at room temperature The temper-ature dependence of the channelrsquos conductance was found todiffer from that of a corresponding bulk solution indicating theimportance of ion-pore interactions Using all-atom MD Modiand co-workers investigated the temperature-dependent trans-port of the ionic liquid 1-butyl-3-methyl-imidazolium chloride(BMIM-Cl) through OmpF86 The study indicated thataqueous solution of BMIM-Cl can reduce the rate of antibioticstransport through OmpF which could lead to practicalapplications of BMIM-Cl in the field of nanopore sensorsThe transmembrane pore of OmpF contains several titratable

residues Hence its conductance can depend on the solutionpH Varma et al used all-atom MD simulations to determinepKa (see section 435) of several key residues of OmpF7071

The study has shown that the pore size and conductance ofOmpF become consistent with the X-ray structure andelectrophysiology data correspondingly only when appropriateprotonation states are assigned to the key Asp residues7071

The study of Vrouenraets and Miedema has investigated theeffect of point mutations in OmpF finding ionization states ofthe residues to be the key factor affecting the ionconductance84

53 Selective Permeability

Concentration gradients of different types of ions support avariety of intra- and intercellular signals It is therefore vital tohave membrane channels that can distinguish and selectivelyconduct ions of different types One can easily imagine anelectrostatic mechanism for regulating the flux of different ionspecies based on the ion charge but what about channels thatselect a particular ion from all ions of the same chargeExperimental studies suggesting existence of Na+ and K+

selective channels began as early as 1960591 By 1971 it hadbeen inferred that the K+ channel has a wide inner openingleading to a narrow passage which blocks the passage of largecations However the K+ channel also prefers the conductanceof K+ over Na+ and Li+ even though the latter are smaller Theldquosnug-fitrdquo explanation offered in 1972592 suggested that it isnot electrostatically favorable for a Na+ ion to enter an oxygen-lined cage unless that cage is of the same size as the Na+ ionotherwise the Na+ will not form favorable electrostatic contactscompared to its solvation shell However the ldquosnug-fitrdquo

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mechanism requires a rather rigid pore incompatible with mostprotein structures which can only be described as soft andflexible Given that sodium and potassium appear to differ onlyon a scale significantly smaller than the size of an atom it isincredible that f lexible atomic-scale structures can yieldpermeabilities for the ions that may differ by a factor of1000593 The importance of subangstrom-scale structures andthe requirement of distinguishing between various physicalfactors naturally lend the study of ion selectivity to the all-atomMD methodology531 Potassium Channels The structures of all K+

channels feature a completely conserved constriction calledthe selectivity filter which is lined with four rings of negativecarbonyl-oxygen groups The structure of KcsA revealed two K+

ions separated by a single water molecule occupying this regionIn K+ channels the selectivity filter presents a barrier to iontransport and in general the larger the barrier the slower is theexpected rate of transport Thus early MD studies have focusedon the free energy difference experienced by K+ and Na+ ions inthe selectivity filter Because of the great similarity of these ionsthe free-energy perturbation (FEP) method has been theprotocol of choice for such studiesThe FEP method introduced in section 434 can evaluate

the free energy cost of transforming one atom into anotherthrough an unphysical pathway Because the end points of thistransformation are physically meaningful the change in freeenergy is also physically meaningful when considered as a stepin a thermodynamic cycle For example the difference inbinding free energy between K+ and Na+ in an ion channelΔΔG can be found from the free energies of transforming K+

into Na+ inside the channel and of transforming Na+ to K+ in abulk solution123 Both of these terms can be obtained fromFEP however care must be taken that the FEP simulations arelong enough that the system relaxes completely and fluctuationsare fully averagedEarly FEP simulations demonstrated a preference for K+ over

Na+ in the selectivity filter of KcsA120123141594 Howeverlimited by the computational resources available at the timethese simulations also suffered from problems small systemsizes that treated the lipid bilayer protein or water inunrealistic ways subnanosecond durations of simulations ateach FEP step andor external restraints that enforced crystalstructure-like conformation on the selectivity filter Despitethese limitations the range of values for ΔΔG (5minus17 kcalmolfor a single ion) were in apparent agreement with experimentalmeasurements of relief of Ba2+ blockades by Na+ and K+Recently a combination of MD simulations and X-ray

crystallography suggested that the smaller monovalent cationsNa+ and Li+ have their own binding site in the plane of acarbonyl-oxygen ring of the selectivity filter of KcsA as depictedin Figure 10 rather than between two rings as for K+595

Subsequently one- two- three- and four-ion umbrellasampling simulations provided PMFs for a Na+ or K+ ionpermeating K+-filled selectivity filters of KcsA and Kir-Bac11191596 The authors of one study note that FEPsimulations utilizing short trajectories may not provide theion with enough opportunity to find its preferred binding siteand that such studies likely overestimate ΔΔG which theauthors estimated to be 2minus3 kcalmol596 Additional umbrellasampling simulations of a Ba2+-occupied filter demonstratedthat the results can be quantitatively reconciled with Ba2+

blockade measurements because the Na+ and K+ ions areinfluenced differently by the bound Ba2+ ion Although the

latter study596 has not yet garnered response it demonstratesthe utility of a thorough simulation for interpretation ofexperimental measurements Thus the story of potassiumchannel selectivity may still be incomplete

532 Outer-Membrane Porins Porins often exhibitselectivity toward specific molecules For instance the outer-membrane protein OprP of Pseudomonas aeruginosa ananalogue of the PhoE porin of Escherichia coli is aphosphate-selective pore What is particularly interesting isthat it is not just anion-selective but can discriminate betweenanions OprP is highly selective toward the permeation ofinorganic phosphate (Pi) over other anions from the externalenvironment to the interior of the cell597 Atomistic simulationsperformed by Pongprayoon et al80 employing constant velocitySMD and umbrella sampling demonstrated that a lysine clusternear the periplasmic end of the pore selected ions by binding Pi

with greater affinity than small anions such as Clminus Theperiplasmic mouth of the pore can accommodate a fullysolvated Clminus ion which is therefore dielectrically screened fromthe positively charged lysine cluster Pi on the other hand ispartially dehydrated when it enters the pore at the periplasmicside and therefore interacts strongly with the lysine residuesThe extracellular end of the porin however allows the passageof both Clminus and PiAnother interesting porin that has been widely studied using

computational methods is the moderately cation-selectiveOmpF trimer The IK+IClminus ratio obtained from atomisticsimulations by Pezeshki et al79 was found to be sim12 which issimilar to older estimations by Im and Roux obtained fromGCMCBD and PNP approaches55 The key to theconductance and selectivity of the porin lies in its structureOne of the loops on the extracellular side the L3 is of specialimportance as it folds back into the β-barrel constricting thechannel Positively charged arginine residues on the wall of theporin face the negatively charged residues on the loop creatinga transverse electric field in the constriction region of theOmpF This field can orient molecules and cause a separationof ion fluxes5565 Experimental as well as computationalstudies83 have shown that it is possible to alter and evenreverse the selectivity of the OmpF by mutating the chargedresidues in the constriction region (both on the L3 loop andthe pore wall)

Figure 10 Na+ (green sphere) and K+ (red spheres) ions occupydifferent binding sites in the selectivity filter of a potassium channelEarly FEP simulations indicated a large free-energy cost ΔΔG forexchanging K+ with Na+ at the K+ binding sites ΔΔG may actually besmaller if the ion is free to move to its preferred binding site Adaptedwith permission from ref 595 Copyright 2009 Macmillan PublishersLtd Nature Structural amp Molecular Biology

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54 Ion-Channel Gating and Blockages

Proper cellular function requires that ions be released at certaintimes but not at other times and this variable ion conductanceis called gating For example the mechanosensitive channels inbacteria open to prevent rupture of the cell when tension in thebilayer increases due to osmotic stress Mechanosensitivechannels also initiate the conversion of mechanical vibrationsin the inner ear into electrical signals Similarly voltage- pH-and ligand-induced gating allow signals to be initiated orpropagated depending on the cellular conditionsGating almost always involves changes in the conformation

of the channel Until very recently brute-force atomisticsimulations of such changes were not possible because of thetime-scale limitations Below we discuss exemplary studiesincluding mechanical gating of the bacterial mechanosensitivechannels of small and large conductance and voltage gating of aK+ channel Additionally we discuss blockades of ion channelscaused by neurotoxins which may have pharmacologicalsignificance541 Mechanical Gating Even though several crystal

structures of MSCs are available the gating mechanisms remainelusive Unlike ligand- or voltage-gated ion channels wheregating is triggered by a relatively local structural change gatingof mechanosensitive channels involves a global structuraltransition231232 Consequently the time scale of the gating issignificantly greater than in other channels as is the length scalethat needs to be considered222 Although the large length scaleand long time scale of the mechanosensitive gating posepractical problems in computational studies of the gatingmechanism the prokaryotic MscL and MscS channels are idealsystems to develop the computational methodology because ofthe relative simplicity of these channels that are believed to betension sensors onlyWhen only one MSC crystal structure was available (a closed

conformation of MscL from Mycobacterium tuberculosis Tb-MscL) Sukharev and co-workers proposed a gating model forEscherichia coli MscL (Ec-MscL) in which the channel opensvia an ldquoiris-likerdquo mechanism231minus233 Starting from the closedconformation they modeled the intermediate and final openconformations in atomistic detail by utilizing various exper-imental information and empirical energy functions of theCHARMM force field In the open conformation the pore sizewas predicted to be sim30 Aring while the pore size of the closedcrystal structure was only a few angstroms impermeable tosmall molecules Physiological studies provided estimates of theopen pore diameter that were close to the result of theSukharev model (eg refs 255 598 and 599)Using the gating model of Ec-MscL several groups

performed MD simulations to test the model and observe thegating transition in all-atom detail230234236minus239 Kong et alcarried out targeted MD simulations to observe the transitionfrom closed to open conformations of the Ec-MscL230

Gullingsrud et al used SMD to induce opening of the closedconformation of Ec-MscL234238 In the SMD simulations it wasassumed that the forces on the protein by membrane stretchingapply only to the residues at the waterminuslipid interface whichwas based on observations of the pressure profile in pure lipidbilayers239 The same study used the pressure-profilecalculations to estimate the magnitude of the SMD force(35minus70 pN)Other than gating by tension Elmore and Dougherty

considered the effects of point mutations and lipidcompositions on the Tb-MscL structures using MD simu-

lations235240 Later Meyer et al studied the effect of a single-tailed lipid (which has high spontaneous curvature) on thestructure of Ec-MscL249 The simulations began from amanually built dome-shaped structure containing an Ec-MscLchannel embedded at the top of the dome During a 95-nssimulation the researchers observed spontaneous restructuringof the periplasmic loops of MscL which was in agreement withexperimental observations Recently Debret et al simulated Ec-MscL embedded in a lipid bilayer whose hydrophobic thicknesswas significantly smaller than the height of Ec-MscL250 Theresearchers observed tilting of transmembrane helices suggest-ing that hydrophobic mismatch can lower the activation energyof Ec-MscL opening Another all-atom MD simulations of Tb-MscL emphasized the interplay between protein and lipidbilayer by showing that inclusion of the protein significantlyincreases the mechanical rigidity of a lipid annulus251

Despite a number of ingenious efforts gating by tension hasnot been observed in all-atom MD simulations withoutapplying artificial driving forces The main difficulty is thetime scale of the mechanical gating which is significantly longerthan the time scale of an all-atom MD simulation To overcomethe time-scale problem several researchers applied morecomputationally efficient methods at the expense of accuracyPhillips and co-workers used continuum elasticity theory toevaluate the energetics of membrane deformation by theinclusion of MscL neglecting the internal energy of MscL forsimplicity226minus228 Their analytic calculations showed that gatingof MscL proteins can be modulated by the mechanicalproperties of the membrane226227 Moreover they alsodemonstrated how the function of multiple MscL channelscan be coupled Later Chen and co-workers applied computa-tional continuum mechanics to study the gating ofMscL221minus223 In their novel approach they explicitly consideredthe conformational change of MscL by modeling the MscLstructure using a simple elastic rodlike representation of thetransmembrane helices By combining such a simple model ofMscL with a continuum model of the membrane in a finite-element framework and parametrizing the models using all-atom MD simulations they were able to observe mechanicalgating of MscL just by stretching the membraneParticle-based coarse-graining offers another route toward a

simpler model of mechanical gating In this framework groupsof atoms are represented by single interaction beads whichdramatically increases the computational efficiency of the MDsimulation The interactions between such coarse-grained beadsare calibrated to reproduce the thermodynamic properties ofmodel systems obtained from all-atom MD simulations orexperiments (eg transfer free energy of small molecules fromwater to hydrocarbon) Marrink and co-workers applied theirnovel coarse-grained model MARTINI252 to Tb-MscL253254

Specifically they were able to simulate gating of MscL just bystretching the membrane253 or pressurizing a vesicle thatcontained embedded MscL channels254

When the time scale accessible to an MD simulation issignificantly shorter than the time scale of gating one canaccelerate the simulation by applying biasing forces (egSMD) However the quality of such accelerated simulationsdepends critically on how realistic the biasing forces are In thissense combining single-molecule experiments with SMDsimulations can be very successful For example Corry et alrecently demonstrated that the distance measurements fromForster resonance energy transfer (FRET) confocal microscopycan be used as a guide for the SMD simulation255 Starting from

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a closed conformation the researchers induced a closed-to-open conformational transition by performing SMD simu-lations that utilized distance constraints derived from FRETmeasurements on an open MscL channel Because of thedistance constraints the simulations produced a reasonablestructural model of the MscL pore in an open state542 Potassium Channels Potassium channels which all

share a common sequence for the selectivity filter demonstratevoltage- pH- and Ca2+-dependent gating of an intracellulargate which limits K+ access to the selectivity filter andextracellular solution However the selectivity filter is itself afragile structure that can be inactivated Inactivation of theselectivity filter occurs more readily when the intracellular gateis open186

It may be insightful to consider purely solution-dependentinactivation and inhibition of the selectivity filter A potassiumion channel will nearly irreversibly inactivate if it is placed inelectrolyte solution of very low ion concentration All-atom MDsimulations suggested a mechanism of such inactivation bydemonstrating severe distortion of the selectivity filter when itis depleted of K+ ions that partially neutralize the negativecarbonyl-oxygens lining of this structure137143182 Similarlyconductance of K+ channels can be blocked by other ions suchas Na+ or Cs+ that bind to the selectivity channelThe Kv channels are all voltage-gated Crystallographic

studies have provided structures for several open-pore Kvchannels featuring a charged voltage-sensitive subunit sur-rounded by lipids for each monomer of the tetramer411600601

The voltage-sensitive subunits are expected to move andrearrange in response to a voltage change in such a way that asmall but measurable transient capacitative current is observedacross the membrane The associated charge is known as thegating chargeThe gating charge times the change in the potential provides

the free energy required to change conformations and gate thechannel Using all-atom simulations the gating charge can bedirectly computed by measuring the difference in the center ofcharge of the system between open and closed conforma-tions185 A more sophisticated approach allows the assessmentof each residuersquos contribution to the gating charge through thecalculation of the difference between the free-energy cost ofcharging each residue in the closed and open states185

There is currently no crystallographically obtained closed-pore structure of a voltage-gated K+ channel However in astudy that utilized 13 μs of all-atom MD simulation the open-pore structure was refined and a possible closed-pore structurefor Kv12 was obtained185 Using these structures the gatingcharge was found to be somewhat smaller than theexperimentally measured gating charge suggesting that thecomputational model represented an intermediate conforma-tion at the onset of activationVery recently special-purpose hardware enabled all-atom

simulations of a Kv12Kv21 chimera on the gating-time scaleas observed experimentally (gt300 μs)196 The simulationsdemonstrated that the crystal structure accurately representsthe functional open pore In a series of simulations differentonly by the transmembrane voltage and the initial conditionsthe channel was brought from the open state to a fully closedstate Simulations were also performed to simulate differentstages of channel activation Gating of the channel occurred bystructural rearrangements of the voltage-sensitive domains thataffected the hydrophobic cavity leading to the selectivity filterThese rearrangements caused dewetting and collapse of the

cavity The time scales of various steps during the processagreed well with available experimental measurements196

Although not based on such long simulations a study of apH-sensitive potassium channel suggested that gating for thisprotein may occur through a rather different mechanism Anarginine residue near the extracellular side of the membranewas identified through mutagenesis as providing pH-sensitiv-ity602 The PMF of K+ ions in the selectivity filter was obtainedthrough all-atom MD when the protonation state of thatarginine residue was varied The authors of this study suggestedthat the observed 3minus4 kcalmol increase in the barriers for K+

translocation accounted for gating and arose from additionalflexibility that protonation of the arginine sensors granted tothe selectivity filter602 However it should be noted thatbecause no X-ray structure is available a homology model ofthe K2P channel built from Kv12 was used for this studyThus potassium channels share a great deal of structural and

sequence similarity around the selectivity filter but can be gatedin a variety of ways All-atom simulation techniques haveprovided a great deal of insight into the structural mechanismsof the gating processes In one exemplary study196 brute-forceall-atom MD simulations described the complete gating processof a voltage-sensitive potassium channel on a time scale ofhundreds of microseconds At this time it remains to be seenwhether other potassium channels use similar mechanisms togate

543 Blockades Some toxins bind and inactivateparticular target channels The potential for specificity ofchannel-binding toxins makes them an attractive source forpharmaceutical innovation The all-atom MD methodology hasbeen used to find the standard binding free energies of manysmall ligands but only recently have researchers attempted tofind the binding free energies of large ligands In particularseveral studies demonstrated challenges and shortcuts whencomputing standard binding free energies of charbydotoxinbinding to various voltage sensitive potassium chan-nels116603604

Of greater pharmacological interest the Kv13 K+ channelhas been identified as a target treatment of multiple sclerosisand other autoimmune disorders422 In a recent study the toxinShK which blocks Kv13 but also Kv11 was docked to severalK+ channels and the binding free energy was calculated425

Surprisingly the simulations revealed different binding geo-metries to Kv13 and Kv11 but similar binding free energiesthat agree well with experimentally determined values Theauthors concluded with mutations to ShK that may enhance theselectivity of Kv13 over Kv11At present free-energy calculations require too much

computing power and are not automated enough to be usedas a predictive tool by the pharmaceutical industry Inparticular reliably docking potential drug candidates remainsa challenge Nevertheless the combination of special-purposehardware for performing MD simulations very quickly andimproved automation of tools for calculating binding freeenergies may give rise to the use of all-atom simulations inadvanced computation drug screening within the pharmaceut-ical industry

55 Biosensing with Channels

About 20 years ago Bezrukov et al605 and Kasianowicz447 andco-workers demonstrated the possibility of using ionic channelsas molecular Coulter counters to detect the presence andcharacterize the type of biomolecules The basic principle of the

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approach is the following A membrane containing a single-ionchannel separates electrolyte solution into two compartmentsconnected only through the transmembrane pore of thechannel A transmembrane bias is imposed using an externalvoltage source producing a steady ionic current through anopen pore The transmembrane bias facilitates unidirectionaltransport of charged biomolecules from one compartment tothe other Each passage is detected as transient reduction (ablockade) of the ionic current flowing through the pore Theduration and magnitude of the ionic current blockades canindicate the length and chemical composition of a nucleic acidpolymer447606minus608 suggesting the possibility of recording thenucleotide sequence of a DNA strand directly by measuring theionic current flowing through a nanoporeCritical to the success of the above approach is the lack of

spontaneous gating of the ion conductance which if presentcan easily be confused with the signal resulting from interactionof the channel with a biomolecule Because of its superiorstructural stability the α-hemolysin channel was the firstnanopore to be considered for biosensing applications447609

However other channels such as the bacterial porinMspA449minus451 and man-made silicon-based610minus612 and gra-phene613minus615 nanopores have been successfully used fordetection of biomolecules Apart from DNA sequencingnumerous other applications have been proposed for nano-pores including detection of small analytes589616617 drugdesign390618 pathogen detection619 and force spectrosco-py620minus622 Interested readers are directed to several reviews onthis subject446623minus627

Modeling and computer simulations have played a major rolein development of nanopore applications585 There have alsobeen numerous theoretical studies of various aspects ofpolymer capture and translocation through nanoporesTypically such studies involve the application of scalingconcepts of polymer physics or transport equations628minus630 toelucidate the dynamics of charged polymer capture andtranslocation All-atom simulations have been used as a kindof a computational force microscope to directly relate themicroscopic events taking place in a nanopore to the ioniccurrent blockades recorded in experiment377585

551 α-Hemolysin Among many β-barrel proteins α-hemolysin has been the channel of choice for mostexperimental studies because of its exceptional structuralstability under harsh experimental conditions The knowncrystallographic structure and relatively straightforward site-directed mutagenesis procedures permit rational engineering ofthis channel to enhance sensitivity of ionic current blockadesfor example by introducing a molecular adapter616 or othersite-specific mutations631632

The 2005 publication by Aksimentiev and Schulten90

pioneered the application of the all-atom MD method forprediction of the ionic conductance of membrane channelsThe simulations demonstrated for the first time quantitativeaccuracy of the MD method in predicting the absolute value ofthe ionic current reproducing the asymmetric currentminusvoltagedependence of α-hemolysin and characterizing the electro-osmotic effect The simulations also suggested a microscopicmechanism explaining the pH-dependence of the noise in theionic current recordings633 The study has also demonstrated amethod for computing the average distribution of theelectrostatic potential in a membrane channel directly froman all-atom MD simulation90 Following the successful study ofionic conductance through α-hemolysin the researchers were

challenged by an experimentalist (A Meller Boston University)to predict the influence of the global orientation of a DNAstrand in α-hemolysin on the velocity of DNA transport andthe ionic current blockades This was a blind test as no priorinformation about the outcome of experiments was given Tofind out the molecular origin of the observed differences MDsimulations were performed on α-hemolysin systems havingDNA threaded through in two different global orientationsfrom 3prime to 5prime and from 5prime to 3prime The outcome of the simulationsrevealed a propensity for DNA nucleotides to tilt toward their5prime-ends in confined environments which was linked toobservable differences in DNA translocation dynamics andionic current blockades97 The results of the MD simulationswere in qualitative agreement with experiment Because oflimited computational resources direct quantitative comparisonwas not possible at that timeThe α-hemolysin channel has been a test bed for developing

advanced simulation techniques The Roux group exploredpermeation of ions through the α-hemolysin channel using 3D-PNP as well as the grand canonical Monte Carlo Browniandynamics (GCMCBD) approaches88 in the absence of anyanalytes The study revealed that the asymmetric conductanceof the pore arises from the permanent charge distribution in thepore Another PNP study examined the influence of chargedresidues in α-hemolysin on the asymmetry of the currentminusvoltage dependence89100 Shilov and Kurnikova96 employedMD simulations to investigate the energetics and dynamics of aβ-cyclodextrin (βCD) molecule confined inside the α-hemolysin pore The Roux group investigated the effect ofβCD on the ion selectivity of the α-hemolysin through MDsimulations and PMF calculations94 The simulations haveshown that electrically neutral βCD enhances the concentrationof Clminus in the nanopore by causing a partial desolvation of theions which reduces the dielectric shielding by the solvent TheGCMCBD method was used to account for multi-ion effectsin a subsequent study94 Simakov and Kurnikova devised amodified PNP approach to incorporate a soft repulsion modelof short-range interactions between mobile ions and protein92

To overcome the time-scale limitation of the MD methodthe Aksimentiev group developed a method for acceleratingsimulations of DNA transport through nanopores thatpreserves all-atom features of the MD model98 The key ideaof the method dubbed grid-steered MD (G-SMD) was theselective amplification of the electrostatic potential that drivesDNA transport while maintaining all other interactionsunchanged Using G-SMD the Aksimentiev group performedmultiple simulations of DNA transport through α-hemolysinand determined the dependence of the translocation velocityon the sequence and orientation of the DNA strands98 a taskthat was considered formidable at that time634 De Biase andco-workers recently developed a theoretical framework tomodel DNA translocation across a nanopore by combining theGCMCBD algorithm with a coarse-grained polymer model forDNA102 which enabled multimicrosecond simulations at afraction of the cost of all-atom MD When applied to modeltranslocation of poly(dA) and poly(dC) strands through α-hemolysin the model yielded results in reasonable agreementwith experiments Reiner et al367 developed an elegantcontinuum theory to describe the results of nanopore massspectroscopy experiments with quantitative accuracy635 Bondet al employed all-atom MD simulations to explore thetranslocation of short strands of DNA through a simplifiedmodel of the α-hemolysin pore comprising the stem of the pore

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surrounded by a membrane mimetic slab99 The studyexamined the effect of cationic amino acids on the translocationdynamics of DNA Compared to wild type α-hemolysinarginine mutations were found to reduce the transport rate ofDNA through the pore as well as the ionic current552 MspA The long stem of α-hemolysin can

accommodate up to 12 DNA nucleotides which makes difficultthe detection of single nucleotides by measuring ionic currentThe MspA porin has recently emerged as a viable alternative toα-hemolysin on account of its superior architecture MspA has agoblet-like structure with a constriction region that is sim1 nmideal for holding just one or two nucleotides see Figure 11aButler and co-workers showed that by eliminating the negativecharge in the constriction a variant of MspA called M1MspAwas capable of detecting a single DNA strand electrophoreti-cally driven through the pore449 A series of subsequentexperimental work in the Niederweis and Gundlach groupshave since established that the current resolution of the MspAvariant is superior to that of α-hemolysin636 and that singlenucleotide substitutions can be detected on a randomheteropolymeric background using a tethered DNA451

However the primary challenge is that the translocation rateof DNA through MspA is several orders of magnitude higherthan the rate required to resolve the type of DNA nucleotidesby measuring ionic current The two main strategies to controlDNA translocation are to engineer intrinsic brakes in the MspAstructure or use an auxiliary enzyme such as DNA polymer-ase637

The first computational study of MspA was recently carriedout by Bhattacharya and co-workers348 The study reportsextensive all-atom MD simulations that explored the effect ofpositively charged arginine residues on the translocation rate ofDNA and the ionic current On account of the highcomputational overhead due to the large system size theauthors performed the majority of the simulations using a

truncated version of the pore (see Figure 11b c) Since theDNA was found to be quite mobile even when confined to thenanopore the authors adopted an ensemble approach tosample the configurational dynamics of the DNA Theensemble method was shown to be a viable alternative tofollowing a single long-time-scale trajectory which is currentlypossible only using special-purpose supercomputers such asAnton The ensemble approach allowed the use of traditionalsupercomputers to obtain combined trajectory lengths of tensof microseconds within reasonable physical time Thesimulations have shown that by introducing several arginineresidues near the constriction of MspA the DNA permeationrate can be reduced by a factor of 10minus30 due to the formationof multiple salt bridges between the DNA backbone and theguanidinium groups of the arginine substitutions as well as dueto base-stacking interactions Furthermore the simulationspredicted that such mutations would not eliminate thenucleotide sensitivity of the ionic-current blockades Thestudy explained why similar mutations introduced in α-hemolysin reduced the ionic current practically to zero638

making such mutants unsuitable for DNA sequencingapplications

553 Other Nanopore Systems Other β-barrel nano-pores have been explored for stochastic sensing applicationsFor instance an MD study of the bacterial porin OmpG wascarried out by Chen and co-workers to determine the origin ofits spontaneous gating activity77 On the basis of the simulationstudy a variant of the porin with stabilizing mutations wascreated and was used for detection of adenosine diphosphateafter inserting a cyclodextrin molecular adapter77

Using 3D-Poisson equations and linear transport theory360

Vidal and co-workers demonstrated that a nanopore in a heavilydoped silicon membrane connected to a voltage source can beused as an electrically tunable ion filter The PNP model wasused to study ion transport through synthetic nanopores in

Figure 11 (a) Cut-away view of the full-length MspA nanopore embedded in a lipid membrane with a DNA strand threaded through The MspA isrepresented by a teal molecular surface the lipid membrane is represented by purple lines and the DNA bases are shown in magenta-colored licoricerepresentation (b) Average electrostatic potentials along the symmetry axis of the full and truncated MspA nanopores at a transmembrane bias of180 mV The electrostatic potentials are computed from MD simulations of open-pore MspA nanopores (c) Cut-away view of the reduced MspAsystem The DNA is covalently joined to itself across the periodic boundary (d) The ionic current trace of a sample trajectory of a poly(dC) strandthreaded through the MspA nanopore (e) Ionic current histograms obtained from ensemble simulations of the M1MspA (yellow) and its argininevariant M1 L88RA96RS116R (blue) The overlap of the two histograms is shown in green The histograms were constructed using 100 nsaverages of the instantaneous ionic current Adapted with permission from ref 348 Copyright 2012 American Chemical Society

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several studies359363366 exploring rectification and ionselectivity A Langevin dynamics approach to study thetransport of flexible macromolecules in confined geometrieswas proposed by Peters372 Recently an atomic resolution BDmethod was developed by Comer and co-workers that was usedto study the sequence dependence of ionic current in syntheticnanopores373374 All-atom MD simulations have been usedwith considerable success to investigate nanopore transport ofDNA and ionic current blockades375376 nanopore unzipping ofDNA hairpins380 the microscopic origin of the electrophoreticforce on DNA in a nanopore378381 and the effect of electrolyteon the DNA translocation rates391 For detailed description ofthe simulation protocols interested readers are directed torecent reviews on this subject585639640

6 OUTLOOK

Advances in computational technologies and membraneprotein structure-determination methods are poised to makemodeling and simulations of ion channels an integral part offuture drug-development efforts The greatest obstacle so far isthe lack of atomic-resolution structures of the majority ofbiomedically relevant ion channels Several limitations pertainto the computational technology itself Whereas all-atommolecular dynamics simulation of an ion channel can providethe most detailed information about the microscopicmechanism of its function the method is currently limited bythe accuracy of the classical force field and the microsecondtime scale of the simulations on conventional computerclustersTremendous advances in addressing both limitations have

already been made The first computational studies of ionchannel systems using polarizable models have already beenreported277563 Thus it is very likely that a full polarizable forcefield will become available within the next 10 years Anothermajor advancement was the millisecond simulation of amembrane channel in its native environment that revealedthe microscopic details of its voltage-dependent gatingmechanism196 We hope that such a tremendous success ofspecial-purpose hardware will prompt the development ofcommodity special-purpose hardware which will make suchlong-time-scale simulations available to mainstream researchersFinally advances in computational methods will also aid thediscovery of atomic-resolution structures through either denovo structure prediction641 or refinement of low-resolution X-ray and cryo-EM structures443

It would be misleading however to think that all questionspertaining to ion channels would be answered through all-atomMD From a drug-development perspective high-throughputand accurate calculation of binding free energies of smallchemical compounds is more important than long-time-scalesimulations of a single channelrsquos action Enabling such high-throughput docking is dependent on the availability of accurategeneric force fields Furthermore as millisecond simulationsbecome more available describing possible chemical reactionsbetween components of the system will become increasinglyimportant Finally modeling a single channel in a membrane isonly a first step toward the realistic modeling of in vivoprocesses We anticipate continuum and implicit solventapproaches to play a pivotal role in the development ofdetailed quantitative models of realistic biological membranesand small organelles that incorporate an ensemble of ionchannels

AUTHOR INFORMATION

Corresponding Author

E-mail aksimentillinoisedu

Notes

The authors declare no competing financial interest

Biographies

Christopher Maffeo received his BSc in physics from the University of

California Santa Barbara in 2006 He joined the Aksimentiev group in

December 2006 After studying the structural and conductance

properties of the phospholamban pentamer he has focused his efforts

on understanding the kinetics energetics and electrostatics of various

DNAminusDNA and DNAminusprotein interactions

Swati Bhattacharya is a postdoctoral fellow in the group of Aleksei

Aksimentiev at the University of Illinois at UrbanaminusChampaign She

received her PhD in physics for work on the adsorption of polymers

at surfaces under the supervision of Thomas Vilgis in 2009 from the

Max Planck Institute for Polymer Research in Mainz Her current

research activities include computational modeling aimed at

developing applications of nanopores particularly for DNA sequencing

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hybrid quantum mechanicsmolecular mechanics (QMMM)simulations to elucidate the permeation mechanism of bothammonium and protons277

ClC Cohen and Schulten260 explored the mechanism ofanion conduction across the ClC chloride channel by PMFcalculations using atomistic simulations The resulting PMFrevealed that the energy barrier for conduction of a single Clminus

ion is prohibitively high Interestingly the energy barrier wasreduced to 4 kcalmol in the presence of two Clminus ions in thepore suggesting that the incoming Clminus pushes the central ClminusSuenaga et al performed all-atom MD simulations to test thehypothesis that ClC channels are H+minusClminus exchange trans-porters Their results suggested that cations such as H+ and Na+

facilitate the channel opening and Clminus conduction261 Chungand co-workers utilized BD and MD simulations to reveal thebinding site of Clminus in the channel the electrostatic barrier ofClminus and the gating by an external Glu residue in atomisticdetail265266 Recently the first eukaryotic ClC transporter wascrystallized583 and Cheng and Coalson compared the Clminus

transport through the eukaryotic channel with that throughthe prokaryotic channel264 Their PMFs of Clminus in the channelsuggested that proper protonation of the external Glu gate iscritical for conduction

52 Ion Conductance

The force driving the permeation of ions through an ionchannel is the transmembrane potential arising from an unequaldistribution of ions on the two sides of the membrane A smallcharge imbalance in the vicinity of the pore gives rise to thepotential difference173 Explicit modeling of such chargeimbalance is difficult in all-atom MD simulations of a singlebilayer system as such simulations usually employ periodicboundary conditions so that the solution found at the two sidesof the membrane is one continuous volume One possibility isto use a single bilayer and two electrolyte compartmentsterminated by a vacuumwater interface329 An alternativeapproach is to use a twin bilayer system that includes twosolution phases584 of unequal ionic makeup that can generate atransmembrane electric field solely based on ion dynamics Inearly studies employing the twin bilayer setup the twomembranes were used to define the compartments of differention concentration A transmembrane potential was establisheddue to a small charge imbalance between the two compart-ments which was sufficient to generate short unsustained ionflux through the membrane channels To produce a continuousion flux the charge imbalance between the two compartmentshas to be maintained Kutzner et al recently demonstrated amethod to exchange ionwater pairs between the compart-ments and thus sustain the charge imbalance339 This methodwas applied to bacterial porin PorB of Neisseria meningitis todetermine the ion conductance and selectivity of the porinThe double-membrane approach however requires larger

systems which significantly increases the computationaloverhead A simpler alternative is to apply an external electricfield normal to the membrane to generate ionic flux throughthe pore Despite the apparent artificiality of the methodRoux173 provided a rigorous theoretical framework for thisstrategy An early study by Crozier et al289 in which the flow ofsodium ions was simulated through a simplified channel-membrane system under an imposed electric field demon-strated the feasibility of modeling an ionic current through amembrane In 2005 Aksimentiev and Schulten90 showed thatthe currentminusvoltage relationship of α-hemolysin could be

directly computed from all-atom MD simulations by applyingan external electric field The multinanosecond trajectoriesobtained in this 2005 study firmly established all-atom MD asthe method of choice for exploring conductance properties ofnanopores and using MD simulations to guide the developmentof nanopore sensors585 A similar approach was later applied inthe studies of MscS by Sotomayor et al244 and of Escherichiacoli porins OmpF and OmpC by Pezeshki et al7981 A recentstudy provides a detailed description of the external electricfield approach346

521 Potassium Channels MD simulations of K+

translocation through the selectivity filter of Kv12 allowedfor direct observation of the ldquoknock-onrdquo mechanism during asmall number of permeation events151 Subsequent brute-forcesimulations permitted estimation of the channelrsquos conductanceat several transmembrane biases151183 The simulated con-ductance was found to be nearly three times larger than theexperimentally measured one The discrepancy could bepartially attributed to a domain that was missing in thesimulated structure and may obstruct ion access in experimentThe simulations determined a five-step map of the trans-location cycle which was in agreement with the cyclesproposed from multi-ion free-energy calculations126 Thebrute-force approach allowed for direct observation of thekinetics between these steps identifying dehydration of theincoming K+ ion as the rate-limiting step of ion transportthrough the selectivity filter

522 Mechanosensitive Channels Among the twobacterial mechanosensitive channels with known high-reso-lution structure (MscL and MscS) MscS has been the subjectof ion conductance studies for several reasons Theconductance of the open MscL channel was experimentallydetermined to be fairly large suggesting a pore diameter of upto 30 Aring231232 Through such a wide channel small solutes canpass almost freely making the study of ion conductance lessinteresting In contrast the first MscS conformation reportedby Bass et al408 had been initially thought to capture thechannel in an open ion-conducting form However subsequentcomputational studies determined that the transmembranechannel in that MscS structure was not wide enough to furnisha fully hydrated transmembrane pore241242

Anishkin et al and Sotomayor et al performed pioneeringMD simulations of MscS241242247 In their all-atom MDsimulations they characterized the structural stability of MscSbased on the structure determined by Bass et al408 Thesimulations revealed partial collapse of the pore suggesting thatthe MscS conformation was at best partially open Thesimulations examined the distribution of water and ions in thechannel revealing dehydration of the narrowest part of thetransmembrane pore Anishkin et al also performed SMDsimulations by pulling a chloride ion along the channelconcluding that the pore was not large enough for theconductance of chloride242 Vora et al studied ion conductancethrough MscS using the BD method also concluding that thepore in the crystal structure of MscS was not large enough forthat structure to represent a fully open conformation229

Unlike the previous studies in the all-atom MD simulationsof Spronk et al243 an external electric field was appliedmimicking the physiological transmembrane potential In thelatter study the authors observed an increase in hydration andion conduction through the channel suggesting that the crystalstructure captured a conformation close to an open stateSubsequently Sotomayer et al also reported an increase of the

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MscS pore radius upon the application of large transmembranepotential (12 V) in an all-atom MD simulation244

Recently Vasquez et al proposed fully closed and openconformations of MscS based on electron paramagneticresonance spectroscopy and all-atom MD simulations256257

In this open MscS conformation the pore diameter was sim10 Aringthroughout the channel which is large enough to yield aconductance consistent with the experimental measurementsMscS has a large balloon-like cytoplasmic domain which

might play an important role in ion conductance see Figure 4c Recently Gamini et al probed ion conductance through thepores in the cytoplasmic domain using Gluminus and K+ as modelions248 Their results suggested that the cytoplasmic domain isa molecular sieve that balances effluxes of Gluminus and K+ throughMscSThe conductance of MscS has also been modeled using

continuum electrostatics methods (see sections 41) Forexample Sotomayor et al used atomistic MD simulations togenerate multiple conformations of the channels and thecontinuum transport theory to compute the ionic current forthese conformations258586 Recently Song and Corry calculatedthe ionic currents through MscS using a simplified NernstminusPlanck (NP) theory and rather realistic BD simulations225 Thestudy has shown the ability of the NP theory to reproduce theresults of the corresponding BD simulations523 α-Hemolysin Noskov and co-workers88 explored the

currentminusvoltage relationship of the α-hemolysin channel usingGCMCBD and 3D-PNP approaches (described in sections422 and 412 respectively) One of the inputs for theGCMCBD study was the position-dependent diffusioncoefficient of each ion type To incorporate the effect of thechannel size a reduction factor for the diffusivities wascalculated as per Paine and Scherr587 The study showed theIminusV characteristic to be asymmetric with a higher current atpositive bias (with the trans-entrance at a higher potential thanthe cis) which was in qualitative agreement with experi-ments588589 The study also revealed that by switching off thecharges on the pore the asymmetry in the conductancepractically disappeared indicating that it is the chargedistribution of the pore that is responsible for the asymmetryrather than the shapeThe MD study by Aksimentiev and Schulten90 was the first

to demonstrate that atomistic simulations can be used to obtainchannel conductances with quantitative accuracy Specificallythe study found the transmembrane currents driven by anexternal electric field applied normal to the membrane to be inexcellent agreement with experiment The large pore diameterand the high salt concentration made direct comparisonbetween simulation and experiment possible A recent MDstudy by Bhattacharya et al93 probed the cation-dependentrectification of the α-hemolysin nanopore The rectification ofthe ionic current was found to be dependent on the type ofcations and increased from Li+ to Cs+ both in simulations andin experiments The MD simulations showed that the cationiccontribution to the ionic current was the dominant factorinfluencing current asymmetry The cation type-dependentasymmetry of the ionic current was explained by differentialaffinity of the cations to the charged residues at the trans-entrance of the pore which modulated the number of ionsentering the narrowest part of the pore Recent experimentalstudies using site-directed mutagenesis590 and cysteine-scanning mutagenesis347 of the α-hemolysin channel revealedthat the ion-selectivity gating and conductance properties are

significantly affected by the location and the type of charges onthe pore

524 Outer-Membrane Porins Over the past 10 yearsthere have been a number of studies addressing ion-conductance properties of various OMPs (see Table 1) Imand co-workers carried out pioneering studies of OmpF using acombination of GCMCBD6263 MD5567 and continuum55

methods These first studies of OmpF revealed asymmetriccharacter of ionic conductance and produced concentrationminusconductance relations that were in good agreement withexperiment55 OmpF was a test bed for development of theGCMCBD methodUsing the all-atom MD method Pezeshki and co-workers

explored ion conductance of two structurally similar E coliporins OmpC and OmpF over a range of temperatures pHvalues and KCl concentrations7981 The results of the MDsimulations were in good agreement with experiment at low saltconcentrations and room temperature The authors observedconsiderable differences between the simulated temperaturedependence of conductance and experiment which wasattributed to the MD force field because the latter wasoptimized for simulations at room temperature The temper-ature dependence of the channelrsquos conductance was found todiffer from that of a corresponding bulk solution indicating theimportance of ion-pore interactions Using all-atom MD Modiand co-workers investigated the temperature-dependent trans-port of the ionic liquid 1-butyl-3-methyl-imidazolium chloride(BMIM-Cl) through OmpF86 The study indicated thataqueous solution of BMIM-Cl can reduce the rate of antibioticstransport through OmpF which could lead to practicalapplications of BMIM-Cl in the field of nanopore sensorsThe transmembrane pore of OmpF contains several titratable

residues Hence its conductance can depend on the solutionpH Varma et al used all-atom MD simulations to determinepKa (see section 435) of several key residues of OmpF7071

The study has shown that the pore size and conductance ofOmpF become consistent with the X-ray structure andelectrophysiology data correspondingly only when appropriateprotonation states are assigned to the key Asp residues7071

The study of Vrouenraets and Miedema has investigated theeffect of point mutations in OmpF finding ionization states ofthe residues to be the key factor affecting the ionconductance84

53 Selective Permeability

Concentration gradients of different types of ions support avariety of intra- and intercellular signals It is therefore vital tohave membrane channels that can distinguish and selectivelyconduct ions of different types One can easily imagine anelectrostatic mechanism for regulating the flux of different ionspecies based on the ion charge but what about channels thatselect a particular ion from all ions of the same chargeExperimental studies suggesting existence of Na+ and K+

selective channels began as early as 1960591 By 1971 it hadbeen inferred that the K+ channel has a wide inner openingleading to a narrow passage which blocks the passage of largecations However the K+ channel also prefers the conductanceof K+ over Na+ and Li+ even though the latter are smaller Theldquosnug-fitrdquo explanation offered in 1972592 suggested that it isnot electrostatically favorable for a Na+ ion to enter an oxygen-lined cage unless that cage is of the same size as the Na+ ionotherwise the Na+ will not form favorable electrostatic contactscompared to its solvation shell However the ldquosnug-fitrdquo

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mechanism requires a rather rigid pore incompatible with mostprotein structures which can only be described as soft andflexible Given that sodium and potassium appear to differ onlyon a scale significantly smaller than the size of an atom it isincredible that f lexible atomic-scale structures can yieldpermeabilities for the ions that may differ by a factor of1000593 The importance of subangstrom-scale structures andthe requirement of distinguishing between various physicalfactors naturally lend the study of ion selectivity to the all-atomMD methodology531 Potassium Channels The structures of all K+

channels feature a completely conserved constriction calledthe selectivity filter which is lined with four rings of negativecarbonyl-oxygen groups The structure of KcsA revealed two K+

ions separated by a single water molecule occupying this regionIn K+ channels the selectivity filter presents a barrier to iontransport and in general the larger the barrier the slower is theexpected rate of transport Thus early MD studies have focusedon the free energy difference experienced by K+ and Na+ ions inthe selectivity filter Because of the great similarity of these ionsthe free-energy perturbation (FEP) method has been theprotocol of choice for such studiesThe FEP method introduced in section 434 can evaluate

the free energy cost of transforming one atom into anotherthrough an unphysical pathway Because the end points of thistransformation are physically meaningful the change in freeenergy is also physically meaningful when considered as a stepin a thermodynamic cycle For example the difference inbinding free energy between K+ and Na+ in an ion channelΔΔG can be found from the free energies of transforming K+

into Na+ inside the channel and of transforming Na+ to K+ in abulk solution123 Both of these terms can be obtained fromFEP however care must be taken that the FEP simulations arelong enough that the system relaxes completely and fluctuationsare fully averagedEarly FEP simulations demonstrated a preference for K+ over

Na+ in the selectivity filter of KcsA120123141594 Howeverlimited by the computational resources available at the timethese simulations also suffered from problems small systemsizes that treated the lipid bilayer protein or water inunrealistic ways subnanosecond durations of simulations ateach FEP step andor external restraints that enforced crystalstructure-like conformation on the selectivity filter Despitethese limitations the range of values for ΔΔG (5minus17 kcalmolfor a single ion) were in apparent agreement with experimentalmeasurements of relief of Ba2+ blockades by Na+ and K+Recently a combination of MD simulations and X-ray

crystallography suggested that the smaller monovalent cationsNa+ and Li+ have their own binding site in the plane of acarbonyl-oxygen ring of the selectivity filter of KcsA as depictedin Figure 10 rather than between two rings as for K+595

Subsequently one- two- three- and four-ion umbrellasampling simulations provided PMFs for a Na+ or K+ ionpermeating K+-filled selectivity filters of KcsA and Kir-Bac11191596 The authors of one study note that FEPsimulations utilizing short trajectories may not provide theion with enough opportunity to find its preferred binding siteand that such studies likely overestimate ΔΔG which theauthors estimated to be 2minus3 kcalmol596 Additional umbrellasampling simulations of a Ba2+-occupied filter demonstratedthat the results can be quantitatively reconciled with Ba2+

blockade measurements because the Na+ and K+ ions areinfluenced differently by the bound Ba2+ ion Although the

latter study596 has not yet garnered response it demonstratesthe utility of a thorough simulation for interpretation ofexperimental measurements Thus the story of potassiumchannel selectivity may still be incomplete

532 Outer-Membrane Porins Porins often exhibitselectivity toward specific molecules For instance the outer-membrane protein OprP of Pseudomonas aeruginosa ananalogue of the PhoE porin of Escherichia coli is aphosphate-selective pore What is particularly interesting isthat it is not just anion-selective but can discriminate betweenanions OprP is highly selective toward the permeation ofinorganic phosphate (Pi) over other anions from the externalenvironment to the interior of the cell597 Atomistic simulationsperformed by Pongprayoon et al80 employing constant velocitySMD and umbrella sampling demonstrated that a lysine clusternear the periplasmic end of the pore selected ions by binding Pi

with greater affinity than small anions such as Clminus Theperiplasmic mouth of the pore can accommodate a fullysolvated Clminus ion which is therefore dielectrically screened fromthe positively charged lysine cluster Pi on the other hand ispartially dehydrated when it enters the pore at the periplasmicside and therefore interacts strongly with the lysine residuesThe extracellular end of the porin however allows the passageof both Clminus and PiAnother interesting porin that has been widely studied using

computational methods is the moderately cation-selectiveOmpF trimer The IK+IClminus ratio obtained from atomisticsimulations by Pezeshki et al79 was found to be sim12 which issimilar to older estimations by Im and Roux obtained fromGCMCBD and PNP approaches55 The key to theconductance and selectivity of the porin lies in its structureOne of the loops on the extracellular side the L3 is of specialimportance as it folds back into the β-barrel constricting thechannel Positively charged arginine residues on the wall of theporin face the negatively charged residues on the loop creatinga transverse electric field in the constriction region of theOmpF This field can orient molecules and cause a separationof ion fluxes5565 Experimental as well as computationalstudies83 have shown that it is possible to alter and evenreverse the selectivity of the OmpF by mutating the chargedresidues in the constriction region (both on the L3 loop andthe pore wall)

Figure 10 Na+ (green sphere) and K+ (red spheres) ions occupydifferent binding sites in the selectivity filter of a potassium channelEarly FEP simulations indicated a large free-energy cost ΔΔG forexchanging K+ with Na+ at the K+ binding sites ΔΔG may actually besmaller if the ion is free to move to its preferred binding site Adaptedwith permission from ref 595 Copyright 2009 Macmillan PublishersLtd Nature Structural amp Molecular Biology

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54 Ion-Channel Gating and Blockages

Proper cellular function requires that ions be released at certaintimes but not at other times and this variable ion conductanceis called gating For example the mechanosensitive channels inbacteria open to prevent rupture of the cell when tension in thebilayer increases due to osmotic stress Mechanosensitivechannels also initiate the conversion of mechanical vibrationsin the inner ear into electrical signals Similarly voltage- pH-and ligand-induced gating allow signals to be initiated orpropagated depending on the cellular conditionsGating almost always involves changes in the conformation

of the channel Until very recently brute-force atomisticsimulations of such changes were not possible because of thetime-scale limitations Below we discuss exemplary studiesincluding mechanical gating of the bacterial mechanosensitivechannels of small and large conductance and voltage gating of aK+ channel Additionally we discuss blockades of ion channelscaused by neurotoxins which may have pharmacologicalsignificance541 Mechanical Gating Even though several crystal

structures of MSCs are available the gating mechanisms remainelusive Unlike ligand- or voltage-gated ion channels wheregating is triggered by a relatively local structural change gatingof mechanosensitive channels involves a global structuraltransition231232 Consequently the time scale of the gating issignificantly greater than in other channels as is the length scalethat needs to be considered222 Although the large length scaleand long time scale of the mechanosensitive gating posepractical problems in computational studies of the gatingmechanism the prokaryotic MscL and MscS channels are idealsystems to develop the computational methodology because ofthe relative simplicity of these channels that are believed to betension sensors onlyWhen only one MSC crystal structure was available (a closed

conformation of MscL from Mycobacterium tuberculosis Tb-MscL) Sukharev and co-workers proposed a gating model forEscherichia coli MscL (Ec-MscL) in which the channel opensvia an ldquoiris-likerdquo mechanism231minus233 Starting from the closedconformation they modeled the intermediate and final openconformations in atomistic detail by utilizing various exper-imental information and empirical energy functions of theCHARMM force field In the open conformation the pore sizewas predicted to be sim30 Aring while the pore size of the closedcrystal structure was only a few angstroms impermeable tosmall molecules Physiological studies provided estimates of theopen pore diameter that were close to the result of theSukharev model (eg refs 255 598 and 599)Using the gating model of Ec-MscL several groups

performed MD simulations to test the model and observe thegating transition in all-atom detail230234236minus239 Kong et alcarried out targeted MD simulations to observe the transitionfrom closed to open conformations of the Ec-MscL230

Gullingsrud et al used SMD to induce opening of the closedconformation of Ec-MscL234238 In the SMD simulations it wasassumed that the forces on the protein by membrane stretchingapply only to the residues at the waterminuslipid interface whichwas based on observations of the pressure profile in pure lipidbilayers239 The same study used the pressure-profilecalculations to estimate the magnitude of the SMD force(35minus70 pN)Other than gating by tension Elmore and Dougherty

considered the effects of point mutations and lipidcompositions on the Tb-MscL structures using MD simu-

lations235240 Later Meyer et al studied the effect of a single-tailed lipid (which has high spontaneous curvature) on thestructure of Ec-MscL249 The simulations began from amanually built dome-shaped structure containing an Ec-MscLchannel embedded at the top of the dome During a 95-nssimulation the researchers observed spontaneous restructuringof the periplasmic loops of MscL which was in agreement withexperimental observations Recently Debret et al simulated Ec-MscL embedded in a lipid bilayer whose hydrophobic thicknesswas significantly smaller than the height of Ec-MscL250 Theresearchers observed tilting of transmembrane helices suggest-ing that hydrophobic mismatch can lower the activation energyof Ec-MscL opening Another all-atom MD simulations of Tb-MscL emphasized the interplay between protein and lipidbilayer by showing that inclusion of the protein significantlyincreases the mechanical rigidity of a lipid annulus251

Despite a number of ingenious efforts gating by tension hasnot been observed in all-atom MD simulations withoutapplying artificial driving forces The main difficulty is thetime scale of the mechanical gating which is significantly longerthan the time scale of an all-atom MD simulation To overcomethe time-scale problem several researchers applied morecomputationally efficient methods at the expense of accuracyPhillips and co-workers used continuum elasticity theory toevaluate the energetics of membrane deformation by theinclusion of MscL neglecting the internal energy of MscL forsimplicity226minus228 Their analytic calculations showed that gatingof MscL proteins can be modulated by the mechanicalproperties of the membrane226227 Moreover they alsodemonstrated how the function of multiple MscL channelscan be coupled Later Chen and co-workers applied computa-tional continuum mechanics to study the gating ofMscL221minus223 In their novel approach they explicitly consideredthe conformational change of MscL by modeling the MscLstructure using a simple elastic rodlike representation of thetransmembrane helices By combining such a simple model ofMscL with a continuum model of the membrane in a finite-element framework and parametrizing the models using all-atom MD simulations they were able to observe mechanicalgating of MscL just by stretching the membraneParticle-based coarse-graining offers another route toward a

simpler model of mechanical gating In this framework groupsof atoms are represented by single interaction beads whichdramatically increases the computational efficiency of the MDsimulation The interactions between such coarse-grained beadsare calibrated to reproduce the thermodynamic properties ofmodel systems obtained from all-atom MD simulations orexperiments (eg transfer free energy of small molecules fromwater to hydrocarbon) Marrink and co-workers applied theirnovel coarse-grained model MARTINI252 to Tb-MscL253254

Specifically they were able to simulate gating of MscL just bystretching the membrane253 or pressurizing a vesicle thatcontained embedded MscL channels254

When the time scale accessible to an MD simulation issignificantly shorter than the time scale of gating one canaccelerate the simulation by applying biasing forces (egSMD) However the quality of such accelerated simulationsdepends critically on how realistic the biasing forces are In thissense combining single-molecule experiments with SMDsimulations can be very successful For example Corry et alrecently demonstrated that the distance measurements fromForster resonance energy transfer (FRET) confocal microscopycan be used as a guide for the SMD simulation255 Starting from

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a closed conformation the researchers induced a closed-to-open conformational transition by performing SMD simu-lations that utilized distance constraints derived from FRETmeasurements on an open MscL channel Because of thedistance constraints the simulations produced a reasonablestructural model of the MscL pore in an open state542 Potassium Channels Potassium channels which all

share a common sequence for the selectivity filter demonstratevoltage- pH- and Ca2+-dependent gating of an intracellulargate which limits K+ access to the selectivity filter andextracellular solution However the selectivity filter is itself afragile structure that can be inactivated Inactivation of theselectivity filter occurs more readily when the intracellular gateis open186

It may be insightful to consider purely solution-dependentinactivation and inhibition of the selectivity filter A potassiumion channel will nearly irreversibly inactivate if it is placed inelectrolyte solution of very low ion concentration All-atom MDsimulations suggested a mechanism of such inactivation bydemonstrating severe distortion of the selectivity filter when itis depleted of K+ ions that partially neutralize the negativecarbonyl-oxygens lining of this structure137143182 Similarlyconductance of K+ channels can be blocked by other ions suchas Na+ or Cs+ that bind to the selectivity channelThe Kv channels are all voltage-gated Crystallographic

studies have provided structures for several open-pore Kvchannels featuring a charged voltage-sensitive subunit sur-rounded by lipids for each monomer of the tetramer411600601

The voltage-sensitive subunits are expected to move andrearrange in response to a voltage change in such a way that asmall but measurable transient capacitative current is observedacross the membrane The associated charge is known as thegating chargeThe gating charge times the change in the potential provides

the free energy required to change conformations and gate thechannel Using all-atom simulations the gating charge can bedirectly computed by measuring the difference in the center ofcharge of the system between open and closed conforma-tions185 A more sophisticated approach allows the assessmentof each residuersquos contribution to the gating charge through thecalculation of the difference between the free-energy cost ofcharging each residue in the closed and open states185

There is currently no crystallographically obtained closed-pore structure of a voltage-gated K+ channel However in astudy that utilized 13 μs of all-atom MD simulation the open-pore structure was refined and a possible closed-pore structurefor Kv12 was obtained185 Using these structures the gatingcharge was found to be somewhat smaller than theexperimentally measured gating charge suggesting that thecomputational model represented an intermediate conforma-tion at the onset of activationVery recently special-purpose hardware enabled all-atom

simulations of a Kv12Kv21 chimera on the gating-time scaleas observed experimentally (gt300 μs)196 The simulationsdemonstrated that the crystal structure accurately representsthe functional open pore In a series of simulations differentonly by the transmembrane voltage and the initial conditionsthe channel was brought from the open state to a fully closedstate Simulations were also performed to simulate differentstages of channel activation Gating of the channel occurred bystructural rearrangements of the voltage-sensitive domains thataffected the hydrophobic cavity leading to the selectivity filterThese rearrangements caused dewetting and collapse of the

cavity The time scales of various steps during the processagreed well with available experimental measurements196

Although not based on such long simulations a study of apH-sensitive potassium channel suggested that gating for thisprotein may occur through a rather different mechanism Anarginine residue near the extracellular side of the membranewas identified through mutagenesis as providing pH-sensitiv-ity602 The PMF of K+ ions in the selectivity filter was obtainedthrough all-atom MD when the protonation state of thatarginine residue was varied The authors of this study suggestedthat the observed 3minus4 kcalmol increase in the barriers for K+

translocation accounted for gating and arose from additionalflexibility that protonation of the arginine sensors granted tothe selectivity filter602 However it should be noted thatbecause no X-ray structure is available a homology model ofthe K2P channel built from Kv12 was used for this studyThus potassium channels share a great deal of structural and

sequence similarity around the selectivity filter but can be gatedin a variety of ways All-atom simulation techniques haveprovided a great deal of insight into the structural mechanismsof the gating processes In one exemplary study196 brute-forceall-atom MD simulations described the complete gating processof a voltage-sensitive potassium channel on a time scale ofhundreds of microseconds At this time it remains to be seenwhether other potassium channels use similar mechanisms togate

543 Blockades Some toxins bind and inactivateparticular target channels The potential for specificity ofchannel-binding toxins makes them an attractive source forpharmaceutical innovation The all-atom MD methodology hasbeen used to find the standard binding free energies of manysmall ligands but only recently have researchers attempted tofind the binding free energies of large ligands In particularseveral studies demonstrated challenges and shortcuts whencomputing standard binding free energies of charbydotoxinbinding to various voltage sensitive potassium chan-nels116603604

Of greater pharmacological interest the Kv13 K+ channelhas been identified as a target treatment of multiple sclerosisand other autoimmune disorders422 In a recent study the toxinShK which blocks Kv13 but also Kv11 was docked to severalK+ channels and the binding free energy was calculated425

Surprisingly the simulations revealed different binding geo-metries to Kv13 and Kv11 but similar binding free energiesthat agree well with experimentally determined values Theauthors concluded with mutations to ShK that may enhance theselectivity of Kv13 over Kv11At present free-energy calculations require too much

computing power and are not automated enough to be usedas a predictive tool by the pharmaceutical industry Inparticular reliably docking potential drug candidates remainsa challenge Nevertheless the combination of special-purposehardware for performing MD simulations very quickly andimproved automation of tools for calculating binding freeenergies may give rise to the use of all-atom simulations inadvanced computation drug screening within the pharmaceut-ical industry

55 Biosensing with Channels

About 20 years ago Bezrukov et al605 and Kasianowicz447 andco-workers demonstrated the possibility of using ionic channelsas molecular Coulter counters to detect the presence andcharacterize the type of biomolecules The basic principle of the

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approach is the following A membrane containing a single-ionchannel separates electrolyte solution into two compartmentsconnected only through the transmembrane pore of thechannel A transmembrane bias is imposed using an externalvoltage source producing a steady ionic current through anopen pore The transmembrane bias facilitates unidirectionaltransport of charged biomolecules from one compartment tothe other Each passage is detected as transient reduction (ablockade) of the ionic current flowing through the pore Theduration and magnitude of the ionic current blockades canindicate the length and chemical composition of a nucleic acidpolymer447606minus608 suggesting the possibility of recording thenucleotide sequence of a DNA strand directly by measuring theionic current flowing through a nanoporeCritical to the success of the above approach is the lack of

spontaneous gating of the ion conductance which if presentcan easily be confused with the signal resulting from interactionof the channel with a biomolecule Because of its superiorstructural stability the α-hemolysin channel was the firstnanopore to be considered for biosensing applications447609

However other channels such as the bacterial porinMspA449minus451 and man-made silicon-based610minus612 and gra-phene613minus615 nanopores have been successfully used fordetection of biomolecules Apart from DNA sequencingnumerous other applications have been proposed for nano-pores including detection of small analytes589616617 drugdesign390618 pathogen detection619 and force spectrosco-py620minus622 Interested readers are directed to several reviews onthis subject446623minus627

Modeling and computer simulations have played a major rolein development of nanopore applications585 There have alsobeen numerous theoretical studies of various aspects ofpolymer capture and translocation through nanoporesTypically such studies involve the application of scalingconcepts of polymer physics or transport equations628minus630 toelucidate the dynamics of charged polymer capture andtranslocation All-atom simulations have been used as a kindof a computational force microscope to directly relate themicroscopic events taking place in a nanopore to the ioniccurrent blockades recorded in experiment377585

551 α-Hemolysin Among many β-barrel proteins α-hemolysin has been the channel of choice for mostexperimental studies because of its exceptional structuralstability under harsh experimental conditions The knowncrystallographic structure and relatively straightforward site-directed mutagenesis procedures permit rational engineering ofthis channel to enhance sensitivity of ionic current blockadesfor example by introducing a molecular adapter616 or othersite-specific mutations631632

The 2005 publication by Aksimentiev and Schulten90

pioneered the application of the all-atom MD method forprediction of the ionic conductance of membrane channelsThe simulations demonstrated for the first time quantitativeaccuracy of the MD method in predicting the absolute value ofthe ionic current reproducing the asymmetric currentminusvoltagedependence of α-hemolysin and characterizing the electro-osmotic effect The simulations also suggested a microscopicmechanism explaining the pH-dependence of the noise in theionic current recordings633 The study has also demonstrated amethod for computing the average distribution of theelectrostatic potential in a membrane channel directly froman all-atom MD simulation90 Following the successful study ofionic conductance through α-hemolysin the researchers were

challenged by an experimentalist (A Meller Boston University)to predict the influence of the global orientation of a DNAstrand in α-hemolysin on the velocity of DNA transport andthe ionic current blockades This was a blind test as no priorinformation about the outcome of experiments was given Tofind out the molecular origin of the observed differences MDsimulations were performed on α-hemolysin systems havingDNA threaded through in two different global orientationsfrom 3prime to 5prime and from 5prime to 3prime The outcome of the simulationsrevealed a propensity for DNA nucleotides to tilt toward their5prime-ends in confined environments which was linked toobservable differences in DNA translocation dynamics andionic current blockades97 The results of the MD simulationswere in qualitative agreement with experiment Because oflimited computational resources direct quantitative comparisonwas not possible at that timeThe α-hemolysin channel has been a test bed for developing

advanced simulation techniques The Roux group exploredpermeation of ions through the α-hemolysin channel using 3D-PNP as well as the grand canonical Monte Carlo Browniandynamics (GCMCBD) approaches88 in the absence of anyanalytes The study revealed that the asymmetric conductanceof the pore arises from the permanent charge distribution in thepore Another PNP study examined the influence of chargedresidues in α-hemolysin on the asymmetry of the currentminusvoltage dependence89100 Shilov and Kurnikova96 employedMD simulations to investigate the energetics and dynamics of aβ-cyclodextrin (βCD) molecule confined inside the α-hemolysin pore The Roux group investigated the effect ofβCD on the ion selectivity of the α-hemolysin through MDsimulations and PMF calculations94 The simulations haveshown that electrically neutral βCD enhances the concentrationof Clminus in the nanopore by causing a partial desolvation of theions which reduces the dielectric shielding by the solvent TheGCMCBD method was used to account for multi-ion effectsin a subsequent study94 Simakov and Kurnikova devised amodified PNP approach to incorporate a soft repulsion modelof short-range interactions between mobile ions and protein92

To overcome the time-scale limitation of the MD methodthe Aksimentiev group developed a method for acceleratingsimulations of DNA transport through nanopores thatpreserves all-atom features of the MD model98 The key ideaof the method dubbed grid-steered MD (G-SMD) was theselective amplification of the electrostatic potential that drivesDNA transport while maintaining all other interactionsunchanged Using G-SMD the Aksimentiev group performedmultiple simulations of DNA transport through α-hemolysinand determined the dependence of the translocation velocityon the sequence and orientation of the DNA strands98 a taskthat was considered formidable at that time634 De Biase andco-workers recently developed a theoretical framework tomodel DNA translocation across a nanopore by combining theGCMCBD algorithm with a coarse-grained polymer model forDNA102 which enabled multimicrosecond simulations at afraction of the cost of all-atom MD When applied to modeltranslocation of poly(dA) and poly(dC) strands through α-hemolysin the model yielded results in reasonable agreementwith experiments Reiner et al367 developed an elegantcontinuum theory to describe the results of nanopore massspectroscopy experiments with quantitative accuracy635 Bondet al employed all-atom MD simulations to explore thetranslocation of short strands of DNA through a simplifiedmodel of the α-hemolysin pore comprising the stem of the pore

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surrounded by a membrane mimetic slab99 The studyexamined the effect of cationic amino acids on the translocationdynamics of DNA Compared to wild type α-hemolysinarginine mutations were found to reduce the transport rate ofDNA through the pore as well as the ionic current552 MspA The long stem of α-hemolysin can

accommodate up to 12 DNA nucleotides which makes difficultthe detection of single nucleotides by measuring ionic currentThe MspA porin has recently emerged as a viable alternative toα-hemolysin on account of its superior architecture MspA has agoblet-like structure with a constriction region that is sim1 nmideal for holding just one or two nucleotides see Figure 11aButler and co-workers showed that by eliminating the negativecharge in the constriction a variant of MspA called M1MspAwas capable of detecting a single DNA strand electrophoreti-cally driven through the pore449 A series of subsequentexperimental work in the Niederweis and Gundlach groupshave since established that the current resolution of the MspAvariant is superior to that of α-hemolysin636 and that singlenucleotide substitutions can be detected on a randomheteropolymeric background using a tethered DNA451

However the primary challenge is that the translocation rateof DNA through MspA is several orders of magnitude higherthan the rate required to resolve the type of DNA nucleotidesby measuring ionic current The two main strategies to controlDNA translocation are to engineer intrinsic brakes in the MspAstructure or use an auxiliary enzyme such as DNA polymer-ase637

The first computational study of MspA was recently carriedout by Bhattacharya and co-workers348 The study reportsextensive all-atom MD simulations that explored the effect ofpositively charged arginine residues on the translocation rate ofDNA and the ionic current On account of the highcomputational overhead due to the large system size theauthors performed the majority of the simulations using a

truncated version of the pore (see Figure 11b c) Since theDNA was found to be quite mobile even when confined to thenanopore the authors adopted an ensemble approach tosample the configurational dynamics of the DNA Theensemble method was shown to be a viable alternative tofollowing a single long-time-scale trajectory which is currentlypossible only using special-purpose supercomputers such asAnton The ensemble approach allowed the use of traditionalsupercomputers to obtain combined trajectory lengths of tensof microseconds within reasonable physical time Thesimulations have shown that by introducing several arginineresidues near the constriction of MspA the DNA permeationrate can be reduced by a factor of 10minus30 due to the formationof multiple salt bridges between the DNA backbone and theguanidinium groups of the arginine substitutions as well as dueto base-stacking interactions Furthermore the simulationspredicted that such mutations would not eliminate thenucleotide sensitivity of the ionic-current blockades Thestudy explained why similar mutations introduced in α-hemolysin reduced the ionic current practically to zero638

making such mutants unsuitable for DNA sequencingapplications

553 Other Nanopore Systems Other β-barrel nano-pores have been explored for stochastic sensing applicationsFor instance an MD study of the bacterial porin OmpG wascarried out by Chen and co-workers to determine the origin ofits spontaneous gating activity77 On the basis of the simulationstudy a variant of the porin with stabilizing mutations wascreated and was used for detection of adenosine diphosphateafter inserting a cyclodextrin molecular adapter77

Using 3D-Poisson equations and linear transport theory360

Vidal and co-workers demonstrated that a nanopore in a heavilydoped silicon membrane connected to a voltage source can beused as an electrically tunable ion filter The PNP model wasused to study ion transport through synthetic nanopores in

Figure 11 (a) Cut-away view of the full-length MspA nanopore embedded in a lipid membrane with a DNA strand threaded through The MspA isrepresented by a teal molecular surface the lipid membrane is represented by purple lines and the DNA bases are shown in magenta-colored licoricerepresentation (b) Average electrostatic potentials along the symmetry axis of the full and truncated MspA nanopores at a transmembrane bias of180 mV The electrostatic potentials are computed from MD simulations of open-pore MspA nanopores (c) Cut-away view of the reduced MspAsystem The DNA is covalently joined to itself across the periodic boundary (d) The ionic current trace of a sample trajectory of a poly(dC) strandthreaded through the MspA nanopore (e) Ionic current histograms obtained from ensemble simulations of the M1MspA (yellow) and its argininevariant M1 L88RA96RS116R (blue) The overlap of the two histograms is shown in green The histograms were constructed using 100 nsaverages of the instantaneous ionic current Adapted with permission from ref 348 Copyright 2012 American Chemical Society

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several studies359363366 exploring rectification and ionselectivity A Langevin dynamics approach to study thetransport of flexible macromolecules in confined geometrieswas proposed by Peters372 Recently an atomic resolution BDmethod was developed by Comer and co-workers that was usedto study the sequence dependence of ionic current in syntheticnanopores373374 All-atom MD simulations have been usedwith considerable success to investigate nanopore transport ofDNA and ionic current blockades375376 nanopore unzipping ofDNA hairpins380 the microscopic origin of the electrophoreticforce on DNA in a nanopore378381 and the effect of electrolyteon the DNA translocation rates391 For detailed description ofthe simulation protocols interested readers are directed torecent reviews on this subject585639640

6 OUTLOOK

Advances in computational technologies and membraneprotein structure-determination methods are poised to makemodeling and simulations of ion channels an integral part offuture drug-development efforts The greatest obstacle so far isthe lack of atomic-resolution structures of the majority ofbiomedically relevant ion channels Several limitations pertainto the computational technology itself Whereas all-atommolecular dynamics simulation of an ion channel can providethe most detailed information about the microscopicmechanism of its function the method is currently limited bythe accuracy of the classical force field and the microsecondtime scale of the simulations on conventional computerclustersTremendous advances in addressing both limitations have

already been made The first computational studies of ionchannel systems using polarizable models have already beenreported277563 Thus it is very likely that a full polarizable forcefield will become available within the next 10 years Anothermajor advancement was the millisecond simulation of amembrane channel in its native environment that revealedthe microscopic details of its voltage-dependent gatingmechanism196 We hope that such a tremendous success ofspecial-purpose hardware will prompt the development ofcommodity special-purpose hardware which will make suchlong-time-scale simulations available to mainstream researchersFinally advances in computational methods will also aid thediscovery of atomic-resolution structures through either denovo structure prediction641 or refinement of low-resolution X-ray and cryo-EM structures443

It would be misleading however to think that all questionspertaining to ion channels would be answered through all-atomMD From a drug-development perspective high-throughputand accurate calculation of binding free energies of smallchemical compounds is more important than long-time-scalesimulations of a single channelrsquos action Enabling such high-throughput docking is dependent on the availability of accurategeneric force fields Furthermore as millisecond simulationsbecome more available describing possible chemical reactionsbetween components of the system will become increasinglyimportant Finally modeling a single channel in a membrane isonly a first step toward the realistic modeling of in vivoprocesses We anticipate continuum and implicit solventapproaches to play a pivotal role in the development ofdetailed quantitative models of realistic biological membranesand small organelles that incorporate an ensemble of ionchannels

AUTHOR INFORMATION

Corresponding Author

E-mail aksimentillinoisedu

Notes

The authors declare no competing financial interest

Biographies

Christopher Maffeo received his BSc in physics from the University of

California Santa Barbara in 2006 He joined the Aksimentiev group in

December 2006 After studying the structural and conductance

properties of the phospholamban pentamer he has focused his efforts

on understanding the kinetics energetics and electrostatics of various

DNAminusDNA and DNAminusprotein interactions

Swati Bhattacharya is a postdoctoral fellow in the group of Aleksei

Aksimentiev at the University of Illinois at UrbanaminusChampaign She

received her PhD in physics for work on the adsorption of polymers

at surfaces under the supervision of Thomas Vilgis in 2009 from the

Max Planck Institute for Polymer Research in Mainz Her current

research activities include computational modeling aimed at

developing applications of nanopores particularly for DNA sequencing

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MscS pore radius upon the application of large transmembranepotential (12 V) in an all-atom MD simulation244

Recently Vasquez et al proposed fully closed and openconformations of MscS based on electron paramagneticresonance spectroscopy and all-atom MD simulations256257

In this open MscS conformation the pore diameter was sim10 Aringthroughout the channel which is large enough to yield aconductance consistent with the experimental measurementsMscS has a large balloon-like cytoplasmic domain which

might play an important role in ion conductance see Figure 4c Recently Gamini et al probed ion conductance through thepores in the cytoplasmic domain using Gluminus and K+ as modelions248 Their results suggested that the cytoplasmic domain isa molecular sieve that balances effluxes of Gluminus and K+ throughMscSThe conductance of MscS has also been modeled using

continuum electrostatics methods (see sections 41) Forexample Sotomayor et al used atomistic MD simulations togenerate multiple conformations of the channels and thecontinuum transport theory to compute the ionic current forthese conformations258586 Recently Song and Corry calculatedthe ionic currents through MscS using a simplified NernstminusPlanck (NP) theory and rather realistic BD simulations225 Thestudy has shown the ability of the NP theory to reproduce theresults of the corresponding BD simulations523 α-Hemolysin Noskov and co-workers88 explored the

currentminusvoltage relationship of the α-hemolysin channel usingGCMCBD and 3D-PNP approaches (described in sections422 and 412 respectively) One of the inputs for theGCMCBD study was the position-dependent diffusioncoefficient of each ion type To incorporate the effect of thechannel size a reduction factor for the diffusivities wascalculated as per Paine and Scherr587 The study showed theIminusV characteristic to be asymmetric with a higher current atpositive bias (with the trans-entrance at a higher potential thanthe cis) which was in qualitative agreement with experi-ments588589 The study also revealed that by switching off thecharges on the pore the asymmetry in the conductancepractically disappeared indicating that it is the chargedistribution of the pore that is responsible for the asymmetryrather than the shapeThe MD study by Aksimentiev and Schulten90 was the first

to demonstrate that atomistic simulations can be used to obtainchannel conductances with quantitative accuracy Specificallythe study found the transmembrane currents driven by anexternal electric field applied normal to the membrane to be inexcellent agreement with experiment The large pore diameterand the high salt concentration made direct comparisonbetween simulation and experiment possible A recent MDstudy by Bhattacharya et al93 probed the cation-dependentrectification of the α-hemolysin nanopore The rectification ofthe ionic current was found to be dependent on the type ofcations and increased from Li+ to Cs+ both in simulations andin experiments The MD simulations showed that the cationiccontribution to the ionic current was the dominant factorinfluencing current asymmetry The cation type-dependentasymmetry of the ionic current was explained by differentialaffinity of the cations to the charged residues at the trans-entrance of the pore which modulated the number of ionsentering the narrowest part of the pore Recent experimentalstudies using site-directed mutagenesis590 and cysteine-scanning mutagenesis347 of the α-hemolysin channel revealedthat the ion-selectivity gating and conductance properties are

significantly affected by the location and the type of charges onthe pore

524 Outer-Membrane Porins Over the past 10 yearsthere have been a number of studies addressing ion-conductance properties of various OMPs (see Table 1) Imand co-workers carried out pioneering studies of OmpF using acombination of GCMCBD6263 MD5567 and continuum55

methods These first studies of OmpF revealed asymmetriccharacter of ionic conductance and produced concentrationminusconductance relations that were in good agreement withexperiment55 OmpF was a test bed for development of theGCMCBD methodUsing the all-atom MD method Pezeshki and co-workers

explored ion conductance of two structurally similar E coliporins OmpC and OmpF over a range of temperatures pHvalues and KCl concentrations7981 The results of the MDsimulations were in good agreement with experiment at low saltconcentrations and room temperature The authors observedconsiderable differences between the simulated temperaturedependence of conductance and experiment which wasattributed to the MD force field because the latter wasoptimized for simulations at room temperature The temper-ature dependence of the channelrsquos conductance was found todiffer from that of a corresponding bulk solution indicating theimportance of ion-pore interactions Using all-atom MD Modiand co-workers investigated the temperature-dependent trans-port of the ionic liquid 1-butyl-3-methyl-imidazolium chloride(BMIM-Cl) through OmpF86 The study indicated thataqueous solution of BMIM-Cl can reduce the rate of antibioticstransport through OmpF which could lead to practicalapplications of BMIM-Cl in the field of nanopore sensorsThe transmembrane pore of OmpF contains several titratable

residues Hence its conductance can depend on the solutionpH Varma et al used all-atom MD simulations to determinepKa (see section 435) of several key residues of OmpF7071

The study has shown that the pore size and conductance ofOmpF become consistent with the X-ray structure andelectrophysiology data correspondingly only when appropriateprotonation states are assigned to the key Asp residues7071

The study of Vrouenraets and Miedema has investigated theeffect of point mutations in OmpF finding ionization states ofthe residues to be the key factor affecting the ionconductance84

53 Selective Permeability

Concentration gradients of different types of ions support avariety of intra- and intercellular signals It is therefore vital tohave membrane channels that can distinguish and selectivelyconduct ions of different types One can easily imagine anelectrostatic mechanism for regulating the flux of different ionspecies based on the ion charge but what about channels thatselect a particular ion from all ions of the same chargeExperimental studies suggesting existence of Na+ and K+

selective channels began as early as 1960591 By 1971 it hadbeen inferred that the K+ channel has a wide inner openingleading to a narrow passage which blocks the passage of largecations However the K+ channel also prefers the conductanceof K+ over Na+ and Li+ even though the latter are smaller Theldquosnug-fitrdquo explanation offered in 1972592 suggested that it isnot electrostatically favorable for a Na+ ion to enter an oxygen-lined cage unless that cage is of the same size as the Na+ ionotherwise the Na+ will not form favorable electrostatic contactscompared to its solvation shell However the ldquosnug-fitrdquo

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mechanism requires a rather rigid pore incompatible with mostprotein structures which can only be described as soft andflexible Given that sodium and potassium appear to differ onlyon a scale significantly smaller than the size of an atom it isincredible that f lexible atomic-scale structures can yieldpermeabilities for the ions that may differ by a factor of1000593 The importance of subangstrom-scale structures andthe requirement of distinguishing between various physicalfactors naturally lend the study of ion selectivity to the all-atomMD methodology531 Potassium Channels The structures of all K+

channels feature a completely conserved constriction calledthe selectivity filter which is lined with four rings of negativecarbonyl-oxygen groups The structure of KcsA revealed two K+

ions separated by a single water molecule occupying this regionIn K+ channels the selectivity filter presents a barrier to iontransport and in general the larger the barrier the slower is theexpected rate of transport Thus early MD studies have focusedon the free energy difference experienced by K+ and Na+ ions inthe selectivity filter Because of the great similarity of these ionsthe free-energy perturbation (FEP) method has been theprotocol of choice for such studiesThe FEP method introduced in section 434 can evaluate

the free energy cost of transforming one atom into anotherthrough an unphysical pathway Because the end points of thistransformation are physically meaningful the change in freeenergy is also physically meaningful when considered as a stepin a thermodynamic cycle For example the difference inbinding free energy between K+ and Na+ in an ion channelΔΔG can be found from the free energies of transforming K+

into Na+ inside the channel and of transforming Na+ to K+ in abulk solution123 Both of these terms can be obtained fromFEP however care must be taken that the FEP simulations arelong enough that the system relaxes completely and fluctuationsare fully averagedEarly FEP simulations demonstrated a preference for K+ over

Na+ in the selectivity filter of KcsA120123141594 Howeverlimited by the computational resources available at the timethese simulations also suffered from problems small systemsizes that treated the lipid bilayer protein or water inunrealistic ways subnanosecond durations of simulations ateach FEP step andor external restraints that enforced crystalstructure-like conformation on the selectivity filter Despitethese limitations the range of values for ΔΔG (5minus17 kcalmolfor a single ion) were in apparent agreement with experimentalmeasurements of relief of Ba2+ blockades by Na+ and K+Recently a combination of MD simulations and X-ray

crystallography suggested that the smaller monovalent cationsNa+ and Li+ have their own binding site in the plane of acarbonyl-oxygen ring of the selectivity filter of KcsA as depictedin Figure 10 rather than between two rings as for K+595

Subsequently one- two- three- and four-ion umbrellasampling simulations provided PMFs for a Na+ or K+ ionpermeating K+-filled selectivity filters of KcsA and Kir-Bac11191596 The authors of one study note that FEPsimulations utilizing short trajectories may not provide theion with enough opportunity to find its preferred binding siteand that such studies likely overestimate ΔΔG which theauthors estimated to be 2minus3 kcalmol596 Additional umbrellasampling simulations of a Ba2+-occupied filter demonstratedthat the results can be quantitatively reconciled with Ba2+

blockade measurements because the Na+ and K+ ions areinfluenced differently by the bound Ba2+ ion Although the

latter study596 has not yet garnered response it demonstratesthe utility of a thorough simulation for interpretation ofexperimental measurements Thus the story of potassiumchannel selectivity may still be incomplete

532 Outer-Membrane Porins Porins often exhibitselectivity toward specific molecules For instance the outer-membrane protein OprP of Pseudomonas aeruginosa ananalogue of the PhoE porin of Escherichia coli is aphosphate-selective pore What is particularly interesting isthat it is not just anion-selective but can discriminate betweenanions OprP is highly selective toward the permeation ofinorganic phosphate (Pi) over other anions from the externalenvironment to the interior of the cell597 Atomistic simulationsperformed by Pongprayoon et al80 employing constant velocitySMD and umbrella sampling demonstrated that a lysine clusternear the periplasmic end of the pore selected ions by binding Pi

with greater affinity than small anions such as Clminus Theperiplasmic mouth of the pore can accommodate a fullysolvated Clminus ion which is therefore dielectrically screened fromthe positively charged lysine cluster Pi on the other hand ispartially dehydrated when it enters the pore at the periplasmicside and therefore interacts strongly with the lysine residuesThe extracellular end of the porin however allows the passageof both Clminus and PiAnother interesting porin that has been widely studied using

computational methods is the moderately cation-selectiveOmpF trimer The IK+IClminus ratio obtained from atomisticsimulations by Pezeshki et al79 was found to be sim12 which issimilar to older estimations by Im and Roux obtained fromGCMCBD and PNP approaches55 The key to theconductance and selectivity of the porin lies in its structureOne of the loops on the extracellular side the L3 is of specialimportance as it folds back into the β-barrel constricting thechannel Positively charged arginine residues on the wall of theporin face the negatively charged residues on the loop creatinga transverse electric field in the constriction region of theOmpF This field can orient molecules and cause a separationof ion fluxes5565 Experimental as well as computationalstudies83 have shown that it is possible to alter and evenreverse the selectivity of the OmpF by mutating the chargedresidues in the constriction region (both on the L3 loop andthe pore wall)

Figure 10 Na+ (green sphere) and K+ (red spheres) ions occupydifferent binding sites in the selectivity filter of a potassium channelEarly FEP simulations indicated a large free-energy cost ΔΔG forexchanging K+ with Na+ at the K+ binding sites ΔΔG may actually besmaller if the ion is free to move to its preferred binding site Adaptedwith permission from ref 595 Copyright 2009 Macmillan PublishersLtd Nature Structural amp Molecular Biology

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54 Ion-Channel Gating and Blockages

Proper cellular function requires that ions be released at certaintimes but not at other times and this variable ion conductanceis called gating For example the mechanosensitive channels inbacteria open to prevent rupture of the cell when tension in thebilayer increases due to osmotic stress Mechanosensitivechannels also initiate the conversion of mechanical vibrationsin the inner ear into electrical signals Similarly voltage- pH-and ligand-induced gating allow signals to be initiated orpropagated depending on the cellular conditionsGating almost always involves changes in the conformation

of the channel Until very recently brute-force atomisticsimulations of such changes were not possible because of thetime-scale limitations Below we discuss exemplary studiesincluding mechanical gating of the bacterial mechanosensitivechannels of small and large conductance and voltage gating of aK+ channel Additionally we discuss blockades of ion channelscaused by neurotoxins which may have pharmacologicalsignificance541 Mechanical Gating Even though several crystal

structures of MSCs are available the gating mechanisms remainelusive Unlike ligand- or voltage-gated ion channels wheregating is triggered by a relatively local structural change gatingof mechanosensitive channels involves a global structuraltransition231232 Consequently the time scale of the gating issignificantly greater than in other channels as is the length scalethat needs to be considered222 Although the large length scaleand long time scale of the mechanosensitive gating posepractical problems in computational studies of the gatingmechanism the prokaryotic MscL and MscS channels are idealsystems to develop the computational methodology because ofthe relative simplicity of these channels that are believed to betension sensors onlyWhen only one MSC crystal structure was available (a closed

conformation of MscL from Mycobacterium tuberculosis Tb-MscL) Sukharev and co-workers proposed a gating model forEscherichia coli MscL (Ec-MscL) in which the channel opensvia an ldquoiris-likerdquo mechanism231minus233 Starting from the closedconformation they modeled the intermediate and final openconformations in atomistic detail by utilizing various exper-imental information and empirical energy functions of theCHARMM force field In the open conformation the pore sizewas predicted to be sim30 Aring while the pore size of the closedcrystal structure was only a few angstroms impermeable tosmall molecules Physiological studies provided estimates of theopen pore diameter that were close to the result of theSukharev model (eg refs 255 598 and 599)Using the gating model of Ec-MscL several groups

performed MD simulations to test the model and observe thegating transition in all-atom detail230234236minus239 Kong et alcarried out targeted MD simulations to observe the transitionfrom closed to open conformations of the Ec-MscL230

Gullingsrud et al used SMD to induce opening of the closedconformation of Ec-MscL234238 In the SMD simulations it wasassumed that the forces on the protein by membrane stretchingapply only to the residues at the waterminuslipid interface whichwas based on observations of the pressure profile in pure lipidbilayers239 The same study used the pressure-profilecalculations to estimate the magnitude of the SMD force(35minus70 pN)Other than gating by tension Elmore and Dougherty

considered the effects of point mutations and lipidcompositions on the Tb-MscL structures using MD simu-

lations235240 Later Meyer et al studied the effect of a single-tailed lipid (which has high spontaneous curvature) on thestructure of Ec-MscL249 The simulations began from amanually built dome-shaped structure containing an Ec-MscLchannel embedded at the top of the dome During a 95-nssimulation the researchers observed spontaneous restructuringof the periplasmic loops of MscL which was in agreement withexperimental observations Recently Debret et al simulated Ec-MscL embedded in a lipid bilayer whose hydrophobic thicknesswas significantly smaller than the height of Ec-MscL250 Theresearchers observed tilting of transmembrane helices suggest-ing that hydrophobic mismatch can lower the activation energyof Ec-MscL opening Another all-atom MD simulations of Tb-MscL emphasized the interplay between protein and lipidbilayer by showing that inclusion of the protein significantlyincreases the mechanical rigidity of a lipid annulus251

Despite a number of ingenious efforts gating by tension hasnot been observed in all-atom MD simulations withoutapplying artificial driving forces The main difficulty is thetime scale of the mechanical gating which is significantly longerthan the time scale of an all-atom MD simulation To overcomethe time-scale problem several researchers applied morecomputationally efficient methods at the expense of accuracyPhillips and co-workers used continuum elasticity theory toevaluate the energetics of membrane deformation by theinclusion of MscL neglecting the internal energy of MscL forsimplicity226minus228 Their analytic calculations showed that gatingof MscL proteins can be modulated by the mechanicalproperties of the membrane226227 Moreover they alsodemonstrated how the function of multiple MscL channelscan be coupled Later Chen and co-workers applied computa-tional continuum mechanics to study the gating ofMscL221minus223 In their novel approach they explicitly consideredthe conformational change of MscL by modeling the MscLstructure using a simple elastic rodlike representation of thetransmembrane helices By combining such a simple model ofMscL with a continuum model of the membrane in a finite-element framework and parametrizing the models using all-atom MD simulations they were able to observe mechanicalgating of MscL just by stretching the membraneParticle-based coarse-graining offers another route toward a

simpler model of mechanical gating In this framework groupsof atoms are represented by single interaction beads whichdramatically increases the computational efficiency of the MDsimulation The interactions between such coarse-grained beadsare calibrated to reproduce the thermodynamic properties ofmodel systems obtained from all-atom MD simulations orexperiments (eg transfer free energy of small molecules fromwater to hydrocarbon) Marrink and co-workers applied theirnovel coarse-grained model MARTINI252 to Tb-MscL253254

Specifically they were able to simulate gating of MscL just bystretching the membrane253 or pressurizing a vesicle thatcontained embedded MscL channels254

When the time scale accessible to an MD simulation issignificantly shorter than the time scale of gating one canaccelerate the simulation by applying biasing forces (egSMD) However the quality of such accelerated simulationsdepends critically on how realistic the biasing forces are In thissense combining single-molecule experiments with SMDsimulations can be very successful For example Corry et alrecently demonstrated that the distance measurements fromForster resonance energy transfer (FRET) confocal microscopycan be used as a guide for the SMD simulation255 Starting from

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a closed conformation the researchers induced a closed-to-open conformational transition by performing SMD simu-lations that utilized distance constraints derived from FRETmeasurements on an open MscL channel Because of thedistance constraints the simulations produced a reasonablestructural model of the MscL pore in an open state542 Potassium Channels Potassium channels which all

share a common sequence for the selectivity filter demonstratevoltage- pH- and Ca2+-dependent gating of an intracellulargate which limits K+ access to the selectivity filter andextracellular solution However the selectivity filter is itself afragile structure that can be inactivated Inactivation of theselectivity filter occurs more readily when the intracellular gateis open186

It may be insightful to consider purely solution-dependentinactivation and inhibition of the selectivity filter A potassiumion channel will nearly irreversibly inactivate if it is placed inelectrolyte solution of very low ion concentration All-atom MDsimulations suggested a mechanism of such inactivation bydemonstrating severe distortion of the selectivity filter when itis depleted of K+ ions that partially neutralize the negativecarbonyl-oxygens lining of this structure137143182 Similarlyconductance of K+ channels can be blocked by other ions suchas Na+ or Cs+ that bind to the selectivity channelThe Kv channels are all voltage-gated Crystallographic

studies have provided structures for several open-pore Kvchannels featuring a charged voltage-sensitive subunit sur-rounded by lipids for each monomer of the tetramer411600601

The voltage-sensitive subunits are expected to move andrearrange in response to a voltage change in such a way that asmall but measurable transient capacitative current is observedacross the membrane The associated charge is known as thegating chargeThe gating charge times the change in the potential provides

the free energy required to change conformations and gate thechannel Using all-atom simulations the gating charge can bedirectly computed by measuring the difference in the center ofcharge of the system between open and closed conforma-tions185 A more sophisticated approach allows the assessmentof each residuersquos contribution to the gating charge through thecalculation of the difference between the free-energy cost ofcharging each residue in the closed and open states185

There is currently no crystallographically obtained closed-pore structure of a voltage-gated K+ channel However in astudy that utilized 13 μs of all-atom MD simulation the open-pore structure was refined and a possible closed-pore structurefor Kv12 was obtained185 Using these structures the gatingcharge was found to be somewhat smaller than theexperimentally measured gating charge suggesting that thecomputational model represented an intermediate conforma-tion at the onset of activationVery recently special-purpose hardware enabled all-atom

simulations of a Kv12Kv21 chimera on the gating-time scaleas observed experimentally (gt300 μs)196 The simulationsdemonstrated that the crystal structure accurately representsthe functional open pore In a series of simulations differentonly by the transmembrane voltage and the initial conditionsthe channel was brought from the open state to a fully closedstate Simulations were also performed to simulate differentstages of channel activation Gating of the channel occurred bystructural rearrangements of the voltage-sensitive domains thataffected the hydrophobic cavity leading to the selectivity filterThese rearrangements caused dewetting and collapse of the

cavity The time scales of various steps during the processagreed well with available experimental measurements196

Although not based on such long simulations a study of apH-sensitive potassium channel suggested that gating for thisprotein may occur through a rather different mechanism Anarginine residue near the extracellular side of the membranewas identified through mutagenesis as providing pH-sensitiv-ity602 The PMF of K+ ions in the selectivity filter was obtainedthrough all-atom MD when the protonation state of thatarginine residue was varied The authors of this study suggestedthat the observed 3minus4 kcalmol increase in the barriers for K+

translocation accounted for gating and arose from additionalflexibility that protonation of the arginine sensors granted tothe selectivity filter602 However it should be noted thatbecause no X-ray structure is available a homology model ofthe K2P channel built from Kv12 was used for this studyThus potassium channels share a great deal of structural and

sequence similarity around the selectivity filter but can be gatedin a variety of ways All-atom simulation techniques haveprovided a great deal of insight into the structural mechanismsof the gating processes In one exemplary study196 brute-forceall-atom MD simulations described the complete gating processof a voltage-sensitive potassium channel on a time scale ofhundreds of microseconds At this time it remains to be seenwhether other potassium channels use similar mechanisms togate

543 Blockades Some toxins bind and inactivateparticular target channels The potential for specificity ofchannel-binding toxins makes them an attractive source forpharmaceutical innovation The all-atom MD methodology hasbeen used to find the standard binding free energies of manysmall ligands but only recently have researchers attempted tofind the binding free energies of large ligands In particularseveral studies demonstrated challenges and shortcuts whencomputing standard binding free energies of charbydotoxinbinding to various voltage sensitive potassium chan-nels116603604

Of greater pharmacological interest the Kv13 K+ channelhas been identified as a target treatment of multiple sclerosisand other autoimmune disorders422 In a recent study the toxinShK which blocks Kv13 but also Kv11 was docked to severalK+ channels and the binding free energy was calculated425

Surprisingly the simulations revealed different binding geo-metries to Kv13 and Kv11 but similar binding free energiesthat agree well with experimentally determined values Theauthors concluded with mutations to ShK that may enhance theselectivity of Kv13 over Kv11At present free-energy calculations require too much

computing power and are not automated enough to be usedas a predictive tool by the pharmaceutical industry Inparticular reliably docking potential drug candidates remainsa challenge Nevertheless the combination of special-purposehardware for performing MD simulations very quickly andimproved automation of tools for calculating binding freeenergies may give rise to the use of all-atom simulations inadvanced computation drug screening within the pharmaceut-ical industry

55 Biosensing with Channels

About 20 years ago Bezrukov et al605 and Kasianowicz447 andco-workers demonstrated the possibility of using ionic channelsas molecular Coulter counters to detect the presence andcharacterize the type of biomolecules The basic principle of the

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approach is the following A membrane containing a single-ionchannel separates electrolyte solution into two compartmentsconnected only through the transmembrane pore of thechannel A transmembrane bias is imposed using an externalvoltage source producing a steady ionic current through anopen pore The transmembrane bias facilitates unidirectionaltransport of charged biomolecules from one compartment tothe other Each passage is detected as transient reduction (ablockade) of the ionic current flowing through the pore Theduration and magnitude of the ionic current blockades canindicate the length and chemical composition of a nucleic acidpolymer447606minus608 suggesting the possibility of recording thenucleotide sequence of a DNA strand directly by measuring theionic current flowing through a nanoporeCritical to the success of the above approach is the lack of

spontaneous gating of the ion conductance which if presentcan easily be confused with the signal resulting from interactionof the channel with a biomolecule Because of its superiorstructural stability the α-hemolysin channel was the firstnanopore to be considered for biosensing applications447609

However other channels such as the bacterial porinMspA449minus451 and man-made silicon-based610minus612 and gra-phene613minus615 nanopores have been successfully used fordetection of biomolecules Apart from DNA sequencingnumerous other applications have been proposed for nano-pores including detection of small analytes589616617 drugdesign390618 pathogen detection619 and force spectrosco-py620minus622 Interested readers are directed to several reviews onthis subject446623minus627

Modeling and computer simulations have played a major rolein development of nanopore applications585 There have alsobeen numerous theoretical studies of various aspects ofpolymer capture and translocation through nanoporesTypically such studies involve the application of scalingconcepts of polymer physics or transport equations628minus630 toelucidate the dynamics of charged polymer capture andtranslocation All-atom simulations have been used as a kindof a computational force microscope to directly relate themicroscopic events taking place in a nanopore to the ioniccurrent blockades recorded in experiment377585

551 α-Hemolysin Among many β-barrel proteins α-hemolysin has been the channel of choice for mostexperimental studies because of its exceptional structuralstability under harsh experimental conditions The knowncrystallographic structure and relatively straightforward site-directed mutagenesis procedures permit rational engineering ofthis channel to enhance sensitivity of ionic current blockadesfor example by introducing a molecular adapter616 or othersite-specific mutations631632

The 2005 publication by Aksimentiev and Schulten90

pioneered the application of the all-atom MD method forprediction of the ionic conductance of membrane channelsThe simulations demonstrated for the first time quantitativeaccuracy of the MD method in predicting the absolute value ofthe ionic current reproducing the asymmetric currentminusvoltagedependence of α-hemolysin and characterizing the electro-osmotic effect The simulations also suggested a microscopicmechanism explaining the pH-dependence of the noise in theionic current recordings633 The study has also demonstrated amethod for computing the average distribution of theelectrostatic potential in a membrane channel directly froman all-atom MD simulation90 Following the successful study ofionic conductance through α-hemolysin the researchers were

challenged by an experimentalist (A Meller Boston University)to predict the influence of the global orientation of a DNAstrand in α-hemolysin on the velocity of DNA transport andthe ionic current blockades This was a blind test as no priorinformation about the outcome of experiments was given Tofind out the molecular origin of the observed differences MDsimulations were performed on α-hemolysin systems havingDNA threaded through in two different global orientationsfrom 3prime to 5prime and from 5prime to 3prime The outcome of the simulationsrevealed a propensity for DNA nucleotides to tilt toward their5prime-ends in confined environments which was linked toobservable differences in DNA translocation dynamics andionic current blockades97 The results of the MD simulationswere in qualitative agreement with experiment Because oflimited computational resources direct quantitative comparisonwas not possible at that timeThe α-hemolysin channel has been a test bed for developing

advanced simulation techniques The Roux group exploredpermeation of ions through the α-hemolysin channel using 3D-PNP as well as the grand canonical Monte Carlo Browniandynamics (GCMCBD) approaches88 in the absence of anyanalytes The study revealed that the asymmetric conductanceof the pore arises from the permanent charge distribution in thepore Another PNP study examined the influence of chargedresidues in α-hemolysin on the asymmetry of the currentminusvoltage dependence89100 Shilov and Kurnikova96 employedMD simulations to investigate the energetics and dynamics of aβ-cyclodextrin (βCD) molecule confined inside the α-hemolysin pore The Roux group investigated the effect ofβCD on the ion selectivity of the α-hemolysin through MDsimulations and PMF calculations94 The simulations haveshown that electrically neutral βCD enhances the concentrationof Clminus in the nanopore by causing a partial desolvation of theions which reduces the dielectric shielding by the solvent TheGCMCBD method was used to account for multi-ion effectsin a subsequent study94 Simakov and Kurnikova devised amodified PNP approach to incorporate a soft repulsion modelof short-range interactions between mobile ions and protein92

To overcome the time-scale limitation of the MD methodthe Aksimentiev group developed a method for acceleratingsimulations of DNA transport through nanopores thatpreserves all-atom features of the MD model98 The key ideaof the method dubbed grid-steered MD (G-SMD) was theselective amplification of the electrostatic potential that drivesDNA transport while maintaining all other interactionsunchanged Using G-SMD the Aksimentiev group performedmultiple simulations of DNA transport through α-hemolysinand determined the dependence of the translocation velocityon the sequence and orientation of the DNA strands98 a taskthat was considered formidable at that time634 De Biase andco-workers recently developed a theoretical framework tomodel DNA translocation across a nanopore by combining theGCMCBD algorithm with a coarse-grained polymer model forDNA102 which enabled multimicrosecond simulations at afraction of the cost of all-atom MD When applied to modeltranslocation of poly(dA) and poly(dC) strands through α-hemolysin the model yielded results in reasonable agreementwith experiments Reiner et al367 developed an elegantcontinuum theory to describe the results of nanopore massspectroscopy experiments with quantitative accuracy635 Bondet al employed all-atom MD simulations to explore thetranslocation of short strands of DNA through a simplifiedmodel of the α-hemolysin pore comprising the stem of the pore

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surrounded by a membrane mimetic slab99 The studyexamined the effect of cationic amino acids on the translocationdynamics of DNA Compared to wild type α-hemolysinarginine mutations were found to reduce the transport rate ofDNA through the pore as well as the ionic current552 MspA The long stem of α-hemolysin can

accommodate up to 12 DNA nucleotides which makes difficultthe detection of single nucleotides by measuring ionic currentThe MspA porin has recently emerged as a viable alternative toα-hemolysin on account of its superior architecture MspA has agoblet-like structure with a constriction region that is sim1 nmideal for holding just one or two nucleotides see Figure 11aButler and co-workers showed that by eliminating the negativecharge in the constriction a variant of MspA called M1MspAwas capable of detecting a single DNA strand electrophoreti-cally driven through the pore449 A series of subsequentexperimental work in the Niederweis and Gundlach groupshave since established that the current resolution of the MspAvariant is superior to that of α-hemolysin636 and that singlenucleotide substitutions can be detected on a randomheteropolymeric background using a tethered DNA451

However the primary challenge is that the translocation rateof DNA through MspA is several orders of magnitude higherthan the rate required to resolve the type of DNA nucleotidesby measuring ionic current The two main strategies to controlDNA translocation are to engineer intrinsic brakes in the MspAstructure or use an auxiliary enzyme such as DNA polymer-ase637

The first computational study of MspA was recently carriedout by Bhattacharya and co-workers348 The study reportsextensive all-atom MD simulations that explored the effect ofpositively charged arginine residues on the translocation rate ofDNA and the ionic current On account of the highcomputational overhead due to the large system size theauthors performed the majority of the simulations using a

truncated version of the pore (see Figure 11b c) Since theDNA was found to be quite mobile even when confined to thenanopore the authors adopted an ensemble approach tosample the configurational dynamics of the DNA Theensemble method was shown to be a viable alternative tofollowing a single long-time-scale trajectory which is currentlypossible only using special-purpose supercomputers such asAnton The ensemble approach allowed the use of traditionalsupercomputers to obtain combined trajectory lengths of tensof microseconds within reasonable physical time Thesimulations have shown that by introducing several arginineresidues near the constriction of MspA the DNA permeationrate can be reduced by a factor of 10minus30 due to the formationof multiple salt bridges between the DNA backbone and theguanidinium groups of the arginine substitutions as well as dueto base-stacking interactions Furthermore the simulationspredicted that such mutations would not eliminate thenucleotide sensitivity of the ionic-current blockades Thestudy explained why similar mutations introduced in α-hemolysin reduced the ionic current practically to zero638

making such mutants unsuitable for DNA sequencingapplications

553 Other Nanopore Systems Other β-barrel nano-pores have been explored for stochastic sensing applicationsFor instance an MD study of the bacterial porin OmpG wascarried out by Chen and co-workers to determine the origin ofits spontaneous gating activity77 On the basis of the simulationstudy a variant of the porin with stabilizing mutations wascreated and was used for detection of adenosine diphosphateafter inserting a cyclodextrin molecular adapter77

Using 3D-Poisson equations and linear transport theory360

Vidal and co-workers demonstrated that a nanopore in a heavilydoped silicon membrane connected to a voltage source can beused as an electrically tunable ion filter The PNP model wasused to study ion transport through synthetic nanopores in

Figure 11 (a) Cut-away view of the full-length MspA nanopore embedded in a lipid membrane with a DNA strand threaded through The MspA isrepresented by a teal molecular surface the lipid membrane is represented by purple lines and the DNA bases are shown in magenta-colored licoricerepresentation (b) Average electrostatic potentials along the symmetry axis of the full and truncated MspA nanopores at a transmembrane bias of180 mV The electrostatic potentials are computed from MD simulations of open-pore MspA nanopores (c) Cut-away view of the reduced MspAsystem The DNA is covalently joined to itself across the periodic boundary (d) The ionic current trace of a sample trajectory of a poly(dC) strandthreaded through the MspA nanopore (e) Ionic current histograms obtained from ensemble simulations of the M1MspA (yellow) and its argininevariant M1 L88RA96RS116R (blue) The overlap of the two histograms is shown in green The histograms were constructed using 100 nsaverages of the instantaneous ionic current Adapted with permission from ref 348 Copyright 2012 American Chemical Society

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several studies359363366 exploring rectification and ionselectivity A Langevin dynamics approach to study thetransport of flexible macromolecules in confined geometrieswas proposed by Peters372 Recently an atomic resolution BDmethod was developed by Comer and co-workers that was usedto study the sequence dependence of ionic current in syntheticnanopores373374 All-atom MD simulations have been usedwith considerable success to investigate nanopore transport ofDNA and ionic current blockades375376 nanopore unzipping ofDNA hairpins380 the microscopic origin of the electrophoreticforce on DNA in a nanopore378381 and the effect of electrolyteon the DNA translocation rates391 For detailed description ofthe simulation protocols interested readers are directed torecent reviews on this subject585639640

6 OUTLOOK

Advances in computational technologies and membraneprotein structure-determination methods are poised to makemodeling and simulations of ion channels an integral part offuture drug-development efforts The greatest obstacle so far isthe lack of atomic-resolution structures of the majority ofbiomedically relevant ion channels Several limitations pertainto the computational technology itself Whereas all-atommolecular dynamics simulation of an ion channel can providethe most detailed information about the microscopicmechanism of its function the method is currently limited bythe accuracy of the classical force field and the microsecondtime scale of the simulations on conventional computerclustersTremendous advances in addressing both limitations have

already been made The first computational studies of ionchannel systems using polarizable models have already beenreported277563 Thus it is very likely that a full polarizable forcefield will become available within the next 10 years Anothermajor advancement was the millisecond simulation of amembrane channel in its native environment that revealedthe microscopic details of its voltage-dependent gatingmechanism196 We hope that such a tremendous success ofspecial-purpose hardware will prompt the development ofcommodity special-purpose hardware which will make suchlong-time-scale simulations available to mainstream researchersFinally advances in computational methods will also aid thediscovery of atomic-resolution structures through either denovo structure prediction641 or refinement of low-resolution X-ray and cryo-EM structures443

It would be misleading however to think that all questionspertaining to ion channels would be answered through all-atomMD From a drug-development perspective high-throughputand accurate calculation of binding free energies of smallchemical compounds is more important than long-time-scalesimulations of a single channelrsquos action Enabling such high-throughput docking is dependent on the availability of accurategeneric force fields Furthermore as millisecond simulationsbecome more available describing possible chemical reactionsbetween components of the system will become increasinglyimportant Finally modeling a single channel in a membrane isonly a first step toward the realistic modeling of in vivoprocesses We anticipate continuum and implicit solventapproaches to play a pivotal role in the development ofdetailed quantitative models of realistic biological membranesand small organelles that incorporate an ensemble of ionchannels

AUTHOR INFORMATION

Corresponding Author

E-mail aksimentillinoisedu

Notes

The authors declare no competing financial interest

Biographies

Christopher Maffeo received his BSc in physics from the University of

California Santa Barbara in 2006 He joined the Aksimentiev group in

December 2006 After studying the structural and conductance

properties of the phospholamban pentamer he has focused his efforts

on understanding the kinetics energetics and electrostatics of various

DNAminusDNA and DNAminusprotein interactions

Swati Bhattacharya is a postdoctoral fellow in the group of Aleksei

Aksimentiev at the University of Illinois at UrbanaminusChampaign She

received her PhD in physics for work on the adsorption of polymers

at surfaces under the supervision of Thomas Vilgis in 2009 from the

Max Planck Institute for Polymer Research in Mainz Her current

research activities include computational modeling aimed at

developing applications of nanopores particularly for DNA sequencing

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mechanism requires a rather rigid pore incompatible with mostprotein structures which can only be described as soft andflexible Given that sodium and potassium appear to differ onlyon a scale significantly smaller than the size of an atom it isincredible that f lexible atomic-scale structures can yieldpermeabilities for the ions that may differ by a factor of1000593 The importance of subangstrom-scale structures andthe requirement of distinguishing between various physicalfactors naturally lend the study of ion selectivity to the all-atomMD methodology531 Potassium Channels The structures of all K+

channels feature a completely conserved constriction calledthe selectivity filter which is lined with four rings of negativecarbonyl-oxygen groups The structure of KcsA revealed two K+

ions separated by a single water molecule occupying this regionIn K+ channels the selectivity filter presents a barrier to iontransport and in general the larger the barrier the slower is theexpected rate of transport Thus early MD studies have focusedon the free energy difference experienced by K+ and Na+ ions inthe selectivity filter Because of the great similarity of these ionsthe free-energy perturbation (FEP) method has been theprotocol of choice for such studiesThe FEP method introduced in section 434 can evaluate

the free energy cost of transforming one atom into anotherthrough an unphysical pathway Because the end points of thistransformation are physically meaningful the change in freeenergy is also physically meaningful when considered as a stepin a thermodynamic cycle For example the difference inbinding free energy between K+ and Na+ in an ion channelΔΔG can be found from the free energies of transforming K+

into Na+ inside the channel and of transforming Na+ to K+ in abulk solution123 Both of these terms can be obtained fromFEP however care must be taken that the FEP simulations arelong enough that the system relaxes completely and fluctuationsare fully averagedEarly FEP simulations demonstrated a preference for K+ over

Na+ in the selectivity filter of KcsA120123141594 Howeverlimited by the computational resources available at the timethese simulations also suffered from problems small systemsizes that treated the lipid bilayer protein or water inunrealistic ways subnanosecond durations of simulations ateach FEP step andor external restraints that enforced crystalstructure-like conformation on the selectivity filter Despitethese limitations the range of values for ΔΔG (5minus17 kcalmolfor a single ion) were in apparent agreement with experimentalmeasurements of relief of Ba2+ blockades by Na+ and K+Recently a combination of MD simulations and X-ray

crystallography suggested that the smaller monovalent cationsNa+ and Li+ have their own binding site in the plane of acarbonyl-oxygen ring of the selectivity filter of KcsA as depictedin Figure 10 rather than between two rings as for K+595

Subsequently one- two- three- and four-ion umbrellasampling simulations provided PMFs for a Na+ or K+ ionpermeating K+-filled selectivity filters of KcsA and Kir-Bac11191596 The authors of one study note that FEPsimulations utilizing short trajectories may not provide theion with enough opportunity to find its preferred binding siteand that such studies likely overestimate ΔΔG which theauthors estimated to be 2minus3 kcalmol596 Additional umbrellasampling simulations of a Ba2+-occupied filter demonstratedthat the results can be quantitatively reconciled with Ba2+

blockade measurements because the Na+ and K+ ions areinfluenced differently by the bound Ba2+ ion Although the

latter study596 has not yet garnered response it demonstratesthe utility of a thorough simulation for interpretation ofexperimental measurements Thus the story of potassiumchannel selectivity may still be incomplete

532 Outer-Membrane Porins Porins often exhibitselectivity toward specific molecules For instance the outer-membrane protein OprP of Pseudomonas aeruginosa ananalogue of the PhoE porin of Escherichia coli is aphosphate-selective pore What is particularly interesting isthat it is not just anion-selective but can discriminate betweenanions OprP is highly selective toward the permeation ofinorganic phosphate (Pi) over other anions from the externalenvironment to the interior of the cell597 Atomistic simulationsperformed by Pongprayoon et al80 employing constant velocitySMD and umbrella sampling demonstrated that a lysine clusternear the periplasmic end of the pore selected ions by binding Pi

with greater affinity than small anions such as Clminus Theperiplasmic mouth of the pore can accommodate a fullysolvated Clminus ion which is therefore dielectrically screened fromthe positively charged lysine cluster Pi on the other hand ispartially dehydrated when it enters the pore at the periplasmicside and therefore interacts strongly with the lysine residuesThe extracellular end of the porin however allows the passageof both Clminus and PiAnother interesting porin that has been widely studied using

computational methods is the moderately cation-selectiveOmpF trimer The IK+IClminus ratio obtained from atomisticsimulations by Pezeshki et al79 was found to be sim12 which issimilar to older estimations by Im and Roux obtained fromGCMCBD and PNP approaches55 The key to theconductance and selectivity of the porin lies in its structureOne of the loops on the extracellular side the L3 is of specialimportance as it folds back into the β-barrel constricting thechannel Positively charged arginine residues on the wall of theporin face the negatively charged residues on the loop creatinga transverse electric field in the constriction region of theOmpF This field can orient molecules and cause a separationof ion fluxes5565 Experimental as well as computationalstudies83 have shown that it is possible to alter and evenreverse the selectivity of the OmpF by mutating the chargedresidues in the constriction region (both on the L3 loop andthe pore wall)

Figure 10 Na+ (green sphere) and K+ (red spheres) ions occupydifferent binding sites in the selectivity filter of a potassium channelEarly FEP simulations indicated a large free-energy cost ΔΔG forexchanging K+ with Na+ at the K+ binding sites ΔΔG may actually besmaller if the ion is free to move to its preferred binding site Adaptedwith permission from ref 595 Copyright 2009 Macmillan PublishersLtd Nature Structural amp Molecular Biology

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dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXT

54 Ion-Channel Gating and Blockages

Proper cellular function requires that ions be released at certaintimes but not at other times and this variable ion conductanceis called gating For example the mechanosensitive channels inbacteria open to prevent rupture of the cell when tension in thebilayer increases due to osmotic stress Mechanosensitivechannels also initiate the conversion of mechanical vibrationsin the inner ear into electrical signals Similarly voltage- pH-and ligand-induced gating allow signals to be initiated orpropagated depending on the cellular conditionsGating almost always involves changes in the conformation

of the channel Until very recently brute-force atomisticsimulations of such changes were not possible because of thetime-scale limitations Below we discuss exemplary studiesincluding mechanical gating of the bacterial mechanosensitivechannels of small and large conductance and voltage gating of aK+ channel Additionally we discuss blockades of ion channelscaused by neurotoxins which may have pharmacologicalsignificance541 Mechanical Gating Even though several crystal

structures of MSCs are available the gating mechanisms remainelusive Unlike ligand- or voltage-gated ion channels wheregating is triggered by a relatively local structural change gatingof mechanosensitive channels involves a global structuraltransition231232 Consequently the time scale of the gating issignificantly greater than in other channels as is the length scalethat needs to be considered222 Although the large length scaleand long time scale of the mechanosensitive gating posepractical problems in computational studies of the gatingmechanism the prokaryotic MscL and MscS channels are idealsystems to develop the computational methodology because ofthe relative simplicity of these channels that are believed to betension sensors onlyWhen only one MSC crystal structure was available (a closed

conformation of MscL from Mycobacterium tuberculosis Tb-MscL) Sukharev and co-workers proposed a gating model forEscherichia coli MscL (Ec-MscL) in which the channel opensvia an ldquoiris-likerdquo mechanism231minus233 Starting from the closedconformation they modeled the intermediate and final openconformations in atomistic detail by utilizing various exper-imental information and empirical energy functions of theCHARMM force field In the open conformation the pore sizewas predicted to be sim30 Aring while the pore size of the closedcrystal structure was only a few angstroms impermeable tosmall molecules Physiological studies provided estimates of theopen pore diameter that were close to the result of theSukharev model (eg refs 255 598 and 599)Using the gating model of Ec-MscL several groups

performed MD simulations to test the model and observe thegating transition in all-atom detail230234236minus239 Kong et alcarried out targeted MD simulations to observe the transitionfrom closed to open conformations of the Ec-MscL230

Gullingsrud et al used SMD to induce opening of the closedconformation of Ec-MscL234238 In the SMD simulations it wasassumed that the forces on the protein by membrane stretchingapply only to the residues at the waterminuslipid interface whichwas based on observations of the pressure profile in pure lipidbilayers239 The same study used the pressure-profilecalculations to estimate the magnitude of the SMD force(35minus70 pN)Other than gating by tension Elmore and Dougherty

considered the effects of point mutations and lipidcompositions on the Tb-MscL structures using MD simu-

lations235240 Later Meyer et al studied the effect of a single-tailed lipid (which has high spontaneous curvature) on thestructure of Ec-MscL249 The simulations began from amanually built dome-shaped structure containing an Ec-MscLchannel embedded at the top of the dome During a 95-nssimulation the researchers observed spontaneous restructuringof the periplasmic loops of MscL which was in agreement withexperimental observations Recently Debret et al simulated Ec-MscL embedded in a lipid bilayer whose hydrophobic thicknesswas significantly smaller than the height of Ec-MscL250 Theresearchers observed tilting of transmembrane helices suggest-ing that hydrophobic mismatch can lower the activation energyof Ec-MscL opening Another all-atom MD simulations of Tb-MscL emphasized the interplay between protein and lipidbilayer by showing that inclusion of the protein significantlyincreases the mechanical rigidity of a lipid annulus251

Despite a number of ingenious efforts gating by tension hasnot been observed in all-atom MD simulations withoutapplying artificial driving forces The main difficulty is thetime scale of the mechanical gating which is significantly longerthan the time scale of an all-atom MD simulation To overcomethe time-scale problem several researchers applied morecomputationally efficient methods at the expense of accuracyPhillips and co-workers used continuum elasticity theory toevaluate the energetics of membrane deformation by theinclusion of MscL neglecting the internal energy of MscL forsimplicity226minus228 Their analytic calculations showed that gatingof MscL proteins can be modulated by the mechanicalproperties of the membrane226227 Moreover they alsodemonstrated how the function of multiple MscL channelscan be coupled Later Chen and co-workers applied computa-tional continuum mechanics to study the gating ofMscL221minus223 In their novel approach they explicitly consideredthe conformational change of MscL by modeling the MscLstructure using a simple elastic rodlike representation of thetransmembrane helices By combining such a simple model ofMscL with a continuum model of the membrane in a finite-element framework and parametrizing the models using all-atom MD simulations they were able to observe mechanicalgating of MscL just by stretching the membraneParticle-based coarse-graining offers another route toward a

simpler model of mechanical gating In this framework groupsof atoms are represented by single interaction beads whichdramatically increases the computational efficiency of the MDsimulation The interactions between such coarse-grained beadsare calibrated to reproduce the thermodynamic properties ofmodel systems obtained from all-atom MD simulations orexperiments (eg transfer free energy of small molecules fromwater to hydrocarbon) Marrink and co-workers applied theirnovel coarse-grained model MARTINI252 to Tb-MscL253254

Specifically they were able to simulate gating of MscL just bystretching the membrane253 or pressurizing a vesicle thatcontained embedded MscL channels254

When the time scale accessible to an MD simulation issignificantly shorter than the time scale of gating one canaccelerate the simulation by applying biasing forces (egSMD) However the quality of such accelerated simulationsdepends critically on how realistic the biasing forces are In thissense combining single-molecule experiments with SMDsimulations can be very successful For example Corry et alrecently demonstrated that the distance measurements fromForster resonance energy transfer (FRET) confocal microscopycan be used as a guide for the SMD simulation255 Starting from

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXU

a closed conformation the researchers induced a closed-to-open conformational transition by performing SMD simu-lations that utilized distance constraints derived from FRETmeasurements on an open MscL channel Because of thedistance constraints the simulations produced a reasonablestructural model of the MscL pore in an open state542 Potassium Channels Potassium channels which all

share a common sequence for the selectivity filter demonstratevoltage- pH- and Ca2+-dependent gating of an intracellulargate which limits K+ access to the selectivity filter andextracellular solution However the selectivity filter is itself afragile structure that can be inactivated Inactivation of theselectivity filter occurs more readily when the intracellular gateis open186

It may be insightful to consider purely solution-dependentinactivation and inhibition of the selectivity filter A potassiumion channel will nearly irreversibly inactivate if it is placed inelectrolyte solution of very low ion concentration All-atom MDsimulations suggested a mechanism of such inactivation bydemonstrating severe distortion of the selectivity filter when itis depleted of K+ ions that partially neutralize the negativecarbonyl-oxygens lining of this structure137143182 Similarlyconductance of K+ channels can be blocked by other ions suchas Na+ or Cs+ that bind to the selectivity channelThe Kv channels are all voltage-gated Crystallographic

studies have provided structures for several open-pore Kvchannels featuring a charged voltage-sensitive subunit sur-rounded by lipids for each monomer of the tetramer411600601

The voltage-sensitive subunits are expected to move andrearrange in response to a voltage change in such a way that asmall but measurable transient capacitative current is observedacross the membrane The associated charge is known as thegating chargeThe gating charge times the change in the potential provides

the free energy required to change conformations and gate thechannel Using all-atom simulations the gating charge can bedirectly computed by measuring the difference in the center ofcharge of the system between open and closed conforma-tions185 A more sophisticated approach allows the assessmentof each residuersquos contribution to the gating charge through thecalculation of the difference between the free-energy cost ofcharging each residue in the closed and open states185

There is currently no crystallographically obtained closed-pore structure of a voltage-gated K+ channel However in astudy that utilized 13 μs of all-atom MD simulation the open-pore structure was refined and a possible closed-pore structurefor Kv12 was obtained185 Using these structures the gatingcharge was found to be somewhat smaller than theexperimentally measured gating charge suggesting that thecomputational model represented an intermediate conforma-tion at the onset of activationVery recently special-purpose hardware enabled all-atom

simulations of a Kv12Kv21 chimera on the gating-time scaleas observed experimentally (gt300 μs)196 The simulationsdemonstrated that the crystal structure accurately representsthe functional open pore In a series of simulations differentonly by the transmembrane voltage and the initial conditionsthe channel was brought from the open state to a fully closedstate Simulations were also performed to simulate differentstages of channel activation Gating of the channel occurred bystructural rearrangements of the voltage-sensitive domains thataffected the hydrophobic cavity leading to the selectivity filterThese rearrangements caused dewetting and collapse of the

cavity The time scales of various steps during the processagreed well with available experimental measurements196

Although not based on such long simulations a study of apH-sensitive potassium channel suggested that gating for thisprotein may occur through a rather different mechanism Anarginine residue near the extracellular side of the membranewas identified through mutagenesis as providing pH-sensitiv-ity602 The PMF of K+ ions in the selectivity filter was obtainedthrough all-atom MD when the protonation state of thatarginine residue was varied The authors of this study suggestedthat the observed 3minus4 kcalmol increase in the barriers for K+

translocation accounted for gating and arose from additionalflexibility that protonation of the arginine sensors granted tothe selectivity filter602 However it should be noted thatbecause no X-ray structure is available a homology model ofthe K2P channel built from Kv12 was used for this studyThus potassium channels share a great deal of structural and

sequence similarity around the selectivity filter but can be gatedin a variety of ways All-atom simulation techniques haveprovided a great deal of insight into the structural mechanismsof the gating processes In one exemplary study196 brute-forceall-atom MD simulations described the complete gating processof a voltage-sensitive potassium channel on a time scale ofhundreds of microseconds At this time it remains to be seenwhether other potassium channels use similar mechanisms togate

543 Blockades Some toxins bind and inactivateparticular target channels The potential for specificity ofchannel-binding toxins makes them an attractive source forpharmaceutical innovation The all-atom MD methodology hasbeen used to find the standard binding free energies of manysmall ligands but only recently have researchers attempted tofind the binding free energies of large ligands In particularseveral studies demonstrated challenges and shortcuts whencomputing standard binding free energies of charbydotoxinbinding to various voltage sensitive potassium chan-nels116603604

Of greater pharmacological interest the Kv13 K+ channelhas been identified as a target treatment of multiple sclerosisand other autoimmune disorders422 In a recent study the toxinShK which blocks Kv13 but also Kv11 was docked to severalK+ channels and the binding free energy was calculated425

Surprisingly the simulations revealed different binding geo-metries to Kv13 and Kv11 but similar binding free energiesthat agree well with experimentally determined values Theauthors concluded with mutations to ShK that may enhance theselectivity of Kv13 over Kv11At present free-energy calculations require too much

computing power and are not automated enough to be usedas a predictive tool by the pharmaceutical industry Inparticular reliably docking potential drug candidates remainsa challenge Nevertheless the combination of special-purposehardware for performing MD simulations very quickly andimproved automation of tools for calculating binding freeenergies may give rise to the use of all-atom simulations inadvanced computation drug screening within the pharmaceut-ical industry

55 Biosensing with Channels

About 20 years ago Bezrukov et al605 and Kasianowicz447 andco-workers demonstrated the possibility of using ionic channelsas molecular Coulter counters to detect the presence andcharacterize the type of biomolecules The basic principle of the

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dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXV

approach is the following A membrane containing a single-ionchannel separates electrolyte solution into two compartmentsconnected only through the transmembrane pore of thechannel A transmembrane bias is imposed using an externalvoltage source producing a steady ionic current through anopen pore The transmembrane bias facilitates unidirectionaltransport of charged biomolecules from one compartment tothe other Each passage is detected as transient reduction (ablockade) of the ionic current flowing through the pore Theduration and magnitude of the ionic current blockades canindicate the length and chemical composition of a nucleic acidpolymer447606minus608 suggesting the possibility of recording thenucleotide sequence of a DNA strand directly by measuring theionic current flowing through a nanoporeCritical to the success of the above approach is the lack of

spontaneous gating of the ion conductance which if presentcan easily be confused with the signal resulting from interactionof the channel with a biomolecule Because of its superiorstructural stability the α-hemolysin channel was the firstnanopore to be considered for biosensing applications447609

However other channels such as the bacterial porinMspA449minus451 and man-made silicon-based610minus612 and gra-phene613minus615 nanopores have been successfully used fordetection of biomolecules Apart from DNA sequencingnumerous other applications have been proposed for nano-pores including detection of small analytes589616617 drugdesign390618 pathogen detection619 and force spectrosco-py620minus622 Interested readers are directed to several reviews onthis subject446623minus627

Modeling and computer simulations have played a major rolein development of nanopore applications585 There have alsobeen numerous theoretical studies of various aspects ofpolymer capture and translocation through nanoporesTypically such studies involve the application of scalingconcepts of polymer physics or transport equations628minus630 toelucidate the dynamics of charged polymer capture andtranslocation All-atom simulations have been used as a kindof a computational force microscope to directly relate themicroscopic events taking place in a nanopore to the ioniccurrent blockades recorded in experiment377585

551 α-Hemolysin Among many β-barrel proteins α-hemolysin has been the channel of choice for mostexperimental studies because of its exceptional structuralstability under harsh experimental conditions The knowncrystallographic structure and relatively straightforward site-directed mutagenesis procedures permit rational engineering ofthis channel to enhance sensitivity of ionic current blockadesfor example by introducing a molecular adapter616 or othersite-specific mutations631632

The 2005 publication by Aksimentiev and Schulten90

pioneered the application of the all-atom MD method forprediction of the ionic conductance of membrane channelsThe simulations demonstrated for the first time quantitativeaccuracy of the MD method in predicting the absolute value ofthe ionic current reproducing the asymmetric currentminusvoltagedependence of α-hemolysin and characterizing the electro-osmotic effect The simulations also suggested a microscopicmechanism explaining the pH-dependence of the noise in theionic current recordings633 The study has also demonstrated amethod for computing the average distribution of theelectrostatic potential in a membrane channel directly froman all-atom MD simulation90 Following the successful study ofionic conductance through α-hemolysin the researchers were

challenged by an experimentalist (A Meller Boston University)to predict the influence of the global orientation of a DNAstrand in α-hemolysin on the velocity of DNA transport andthe ionic current blockades This was a blind test as no priorinformation about the outcome of experiments was given Tofind out the molecular origin of the observed differences MDsimulations were performed on α-hemolysin systems havingDNA threaded through in two different global orientationsfrom 3prime to 5prime and from 5prime to 3prime The outcome of the simulationsrevealed a propensity for DNA nucleotides to tilt toward their5prime-ends in confined environments which was linked toobservable differences in DNA translocation dynamics andionic current blockades97 The results of the MD simulationswere in qualitative agreement with experiment Because oflimited computational resources direct quantitative comparisonwas not possible at that timeThe α-hemolysin channel has been a test bed for developing

advanced simulation techniques The Roux group exploredpermeation of ions through the α-hemolysin channel using 3D-PNP as well as the grand canonical Monte Carlo Browniandynamics (GCMCBD) approaches88 in the absence of anyanalytes The study revealed that the asymmetric conductanceof the pore arises from the permanent charge distribution in thepore Another PNP study examined the influence of chargedresidues in α-hemolysin on the asymmetry of the currentminusvoltage dependence89100 Shilov and Kurnikova96 employedMD simulations to investigate the energetics and dynamics of aβ-cyclodextrin (βCD) molecule confined inside the α-hemolysin pore The Roux group investigated the effect ofβCD on the ion selectivity of the α-hemolysin through MDsimulations and PMF calculations94 The simulations haveshown that electrically neutral βCD enhances the concentrationof Clminus in the nanopore by causing a partial desolvation of theions which reduces the dielectric shielding by the solvent TheGCMCBD method was used to account for multi-ion effectsin a subsequent study94 Simakov and Kurnikova devised amodified PNP approach to incorporate a soft repulsion modelof short-range interactions between mobile ions and protein92

To overcome the time-scale limitation of the MD methodthe Aksimentiev group developed a method for acceleratingsimulations of DNA transport through nanopores thatpreserves all-atom features of the MD model98 The key ideaof the method dubbed grid-steered MD (G-SMD) was theselective amplification of the electrostatic potential that drivesDNA transport while maintaining all other interactionsunchanged Using G-SMD the Aksimentiev group performedmultiple simulations of DNA transport through α-hemolysinand determined the dependence of the translocation velocityon the sequence and orientation of the DNA strands98 a taskthat was considered formidable at that time634 De Biase andco-workers recently developed a theoretical framework tomodel DNA translocation across a nanopore by combining theGCMCBD algorithm with a coarse-grained polymer model forDNA102 which enabled multimicrosecond simulations at afraction of the cost of all-atom MD When applied to modeltranslocation of poly(dA) and poly(dC) strands through α-hemolysin the model yielded results in reasonable agreementwith experiments Reiner et al367 developed an elegantcontinuum theory to describe the results of nanopore massspectroscopy experiments with quantitative accuracy635 Bondet al employed all-atom MD simulations to explore thetranslocation of short strands of DNA through a simplifiedmodel of the α-hemolysin pore comprising the stem of the pore

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXW

surrounded by a membrane mimetic slab99 The studyexamined the effect of cationic amino acids on the translocationdynamics of DNA Compared to wild type α-hemolysinarginine mutations were found to reduce the transport rate ofDNA through the pore as well as the ionic current552 MspA The long stem of α-hemolysin can

accommodate up to 12 DNA nucleotides which makes difficultthe detection of single nucleotides by measuring ionic currentThe MspA porin has recently emerged as a viable alternative toα-hemolysin on account of its superior architecture MspA has agoblet-like structure with a constriction region that is sim1 nmideal for holding just one or two nucleotides see Figure 11aButler and co-workers showed that by eliminating the negativecharge in the constriction a variant of MspA called M1MspAwas capable of detecting a single DNA strand electrophoreti-cally driven through the pore449 A series of subsequentexperimental work in the Niederweis and Gundlach groupshave since established that the current resolution of the MspAvariant is superior to that of α-hemolysin636 and that singlenucleotide substitutions can be detected on a randomheteropolymeric background using a tethered DNA451

However the primary challenge is that the translocation rateof DNA through MspA is several orders of magnitude higherthan the rate required to resolve the type of DNA nucleotidesby measuring ionic current The two main strategies to controlDNA translocation are to engineer intrinsic brakes in the MspAstructure or use an auxiliary enzyme such as DNA polymer-ase637

The first computational study of MspA was recently carriedout by Bhattacharya and co-workers348 The study reportsextensive all-atom MD simulations that explored the effect ofpositively charged arginine residues on the translocation rate ofDNA and the ionic current On account of the highcomputational overhead due to the large system size theauthors performed the majority of the simulations using a

truncated version of the pore (see Figure 11b c) Since theDNA was found to be quite mobile even when confined to thenanopore the authors adopted an ensemble approach tosample the configurational dynamics of the DNA Theensemble method was shown to be a viable alternative tofollowing a single long-time-scale trajectory which is currentlypossible only using special-purpose supercomputers such asAnton The ensemble approach allowed the use of traditionalsupercomputers to obtain combined trajectory lengths of tensof microseconds within reasonable physical time Thesimulations have shown that by introducing several arginineresidues near the constriction of MspA the DNA permeationrate can be reduced by a factor of 10minus30 due to the formationof multiple salt bridges between the DNA backbone and theguanidinium groups of the arginine substitutions as well as dueto base-stacking interactions Furthermore the simulationspredicted that such mutations would not eliminate thenucleotide sensitivity of the ionic-current blockades Thestudy explained why similar mutations introduced in α-hemolysin reduced the ionic current practically to zero638

making such mutants unsuitable for DNA sequencingapplications

553 Other Nanopore Systems Other β-barrel nano-pores have been explored for stochastic sensing applicationsFor instance an MD study of the bacterial porin OmpG wascarried out by Chen and co-workers to determine the origin ofits spontaneous gating activity77 On the basis of the simulationstudy a variant of the porin with stabilizing mutations wascreated and was used for detection of adenosine diphosphateafter inserting a cyclodextrin molecular adapter77

Using 3D-Poisson equations and linear transport theory360

Vidal and co-workers demonstrated that a nanopore in a heavilydoped silicon membrane connected to a voltage source can beused as an electrically tunable ion filter The PNP model wasused to study ion transport through synthetic nanopores in

Figure 11 (a) Cut-away view of the full-length MspA nanopore embedded in a lipid membrane with a DNA strand threaded through The MspA isrepresented by a teal molecular surface the lipid membrane is represented by purple lines and the DNA bases are shown in magenta-colored licoricerepresentation (b) Average electrostatic potentials along the symmetry axis of the full and truncated MspA nanopores at a transmembrane bias of180 mV The electrostatic potentials are computed from MD simulations of open-pore MspA nanopores (c) Cut-away view of the reduced MspAsystem The DNA is covalently joined to itself across the periodic boundary (d) The ionic current trace of a sample trajectory of a poly(dC) strandthreaded through the MspA nanopore (e) Ionic current histograms obtained from ensemble simulations of the M1MspA (yellow) and its argininevariant M1 L88RA96RS116R (blue) The overlap of the two histograms is shown in green The histograms were constructed using 100 nsaverages of the instantaneous ionic current Adapted with permission from ref 348 Copyright 2012 American Chemical Society

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXX

several studies359363366 exploring rectification and ionselectivity A Langevin dynamics approach to study thetransport of flexible macromolecules in confined geometrieswas proposed by Peters372 Recently an atomic resolution BDmethod was developed by Comer and co-workers that was usedto study the sequence dependence of ionic current in syntheticnanopores373374 All-atom MD simulations have been usedwith considerable success to investigate nanopore transport ofDNA and ionic current blockades375376 nanopore unzipping ofDNA hairpins380 the microscopic origin of the electrophoreticforce on DNA in a nanopore378381 and the effect of electrolyteon the DNA translocation rates391 For detailed description ofthe simulation protocols interested readers are directed torecent reviews on this subject585639640

6 OUTLOOK

Advances in computational technologies and membraneprotein structure-determination methods are poised to makemodeling and simulations of ion channels an integral part offuture drug-development efforts The greatest obstacle so far isthe lack of atomic-resolution structures of the majority ofbiomedically relevant ion channels Several limitations pertainto the computational technology itself Whereas all-atommolecular dynamics simulation of an ion channel can providethe most detailed information about the microscopicmechanism of its function the method is currently limited bythe accuracy of the classical force field and the microsecondtime scale of the simulations on conventional computerclustersTremendous advances in addressing both limitations have

already been made The first computational studies of ionchannel systems using polarizable models have already beenreported277563 Thus it is very likely that a full polarizable forcefield will become available within the next 10 years Anothermajor advancement was the millisecond simulation of amembrane channel in its native environment that revealedthe microscopic details of its voltage-dependent gatingmechanism196 We hope that such a tremendous success ofspecial-purpose hardware will prompt the development ofcommodity special-purpose hardware which will make suchlong-time-scale simulations available to mainstream researchersFinally advances in computational methods will also aid thediscovery of atomic-resolution structures through either denovo structure prediction641 or refinement of low-resolution X-ray and cryo-EM structures443

It would be misleading however to think that all questionspertaining to ion channels would be answered through all-atomMD From a drug-development perspective high-throughputand accurate calculation of binding free energies of smallchemical compounds is more important than long-time-scalesimulations of a single channelrsquos action Enabling such high-throughput docking is dependent on the availability of accurategeneric force fields Furthermore as millisecond simulationsbecome more available describing possible chemical reactionsbetween components of the system will become increasinglyimportant Finally modeling a single channel in a membrane isonly a first step toward the realistic modeling of in vivoprocesses We anticipate continuum and implicit solventapproaches to play a pivotal role in the development ofdetailed quantitative models of realistic biological membranesand small organelles that incorporate an ensemble of ionchannels

AUTHOR INFORMATION

Corresponding Author

E-mail aksimentillinoisedu

Notes

The authors declare no competing financial interest

Biographies

Christopher Maffeo received his BSc in physics from the University of

California Santa Barbara in 2006 He joined the Aksimentiev group in

December 2006 After studying the structural and conductance

properties of the phospholamban pentamer he has focused his efforts

on understanding the kinetics energetics and electrostatics of various

DNAminusDNA and DNAminusprotein interactions

Swati Bhattacharya is a postdoctoral fellow in the group of Aleksei

Aksimentiev at the University of Illinois at UrbanaminusChampaign She

received her PhD in physics for work on the adsorption of polymers

at surfaces under the supervision of Thomas Vilgis in 2009 from the

Max Planck Institute for Polymer Research in Mainz Her current

research activities include computational modeling aimed at

developing applications of nanopores particularly for DNA sequencing

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXY

54 Ion-Channel Gating and Blockages

Proper cellular function requires that ions be released at certaintimes but not at other times and this variable ion conductanceis called gating For example the mechanosensitive channels inbacteria open to prevent rupture of the cell when tension in thebilayer increases due to osmotic stress Mechanosensitivechannels also initiate the conversion of mechanical vibrationsin the inner ear into electrical signals Similarly voltage- pH-and ligand-induced gating allow signals to be initiated orpropagated depending on the cellular conditionsGating almost always involves changes in the conformation

of the channel Until very recently brute-force atomisticsimulations of such changes were not possible because of thetime-scale limitations Below we discuss exemplary studiesincluding mechanical gating of the bacterial mechanosensitivechannels of small and large conductance and voltage gating of aK+ channel Additionally we discuss blockades of ion channelscaused by neurotoxins which may have pharmacologicalsignificance541 Mechanical Gating Even though several crystal

structures of MSCs are available the gating mechanisms remainelusive Unlike ligand- or voltage-gated ion channels wheregating is triggered by a relatively local structural change gatingof mechanosensitive channels involves a global structuraltransition231232 Consequently the time scale of the gating issignificantly greater than in other channels as is the length scalethat needs to be considered222 Although the large length scaleand long time scale of the mechanosensitive gating posepractical problems in computational studies of the gatingmechanism the prokaryotic MscL and MscS channels are idealsystems to develop the computational methodology because ofthe relative simplicity of these channels that are believed to betension sensors onlyWhen only one MSC crystal structure was available (a closed

conformation of MscL from Mycobacterium tuberculosis Tb-MscL) Sukharev and co-workers proposed a gating model forEscherichia coli MscL (Ec-MscL) in which the channel opensvia an ldquoiris-likerdquo mechanism231minus233 Starting from the closedconformation they modeled the intermediate and final openconformations in atomistic detail by utilizing various exper-imental information and empirical energy functions of theCHARMM force field In the open conformation the pore sizewas predicted to be sim30 Aring while the pore size of the closedcrystal structure was only a few angstroms impermeable tosmall molecules Physiological studies provided estimates of theopen pore diameter that were close to the result of theSukharev model (eg refs 255 598 and 599)Using the gating model of Ec-MscL several groups

performed MD simulations to test the model and observe thegating transition in all-atom detail230234236minus239 Kong et alcarried out targeted MD simulations to observe the transitionfrom closed to open conformations of the Ec-MscL230

Gullingsrud et al used SMD to induce opening of the closedconformation of Ec-MscL234238 In the SMD simulations it wasassumed that the forces on the protein by membrane stretchingapply only to the residues at the waterminuslipid interface whichwas based on observations of the pressure profile in pure lipidbilayers239 The same study used the pressure-profilecalculations to estimate the magnitude of the SMD force(35minus70 pN)Other than gating by tension Elmore and Dougherty

considered the effects of point mutations and lipidcompositions on the Tb-MscL structures using MD simu-

lations235240 Later Meyer et al studied the effect of a single-tailed lipid (which has high spontaneous curvature) on thestructure of Ec-MscL249 The simulations began from amanually built dome-shaped structure containing an Ec-MscLchannel embedded at the top of the dome During a 95-nssimulation the researchers observed spontaneous restructuringof the periplasmic loops of MscL which was in agreement withexperimental observations Recently Debret et al simulated Ec-MscL embedded in a lipid bilayer whose hydrophobic thicknesswas significantly smaller than the height of Ec-MscL250 Theresearchers observed tilting of transmembrane helices suggest-ing that hydrophobic mismatch can lower the activation energyof Ec-MscL opening Another all-atom MD simulations of Tb-MscL emphasized the interplay between protein and lipidbilayer by showing that inclusion of the protein significantlyincreases the mechanical rigidity of a lipid annulus251

Despite a number of ingenious efforts gating by tension hasnot been observed in all-atom MD simulations withoutapplying artificial driving forces The main difficulty is thetime scale of the mechanical gating which is significantly longerthan the time scale of an all-atom MD simulation To overcomethe time-scale problem several researchers applied morecomputationally efficient methods at the expense of accuracyPhillips and co-workers used continuum elasticity theory toevaluate the energetics of membrane deformation by theinclusion of MscL neglecting the internal energy of MscL forsimplicity226minus228 Their analytic calculations showed that gatingof MscL proteins can be modulated by the mechanicalproperties of the membrane226227 Moreover they alsodemonstrated how the function of multiple MscL channelscan be coupled Later Chen and co-workers applied computa-tional continuum mechanics to study the gating ofMscL221minus223 In their novel approach they explicitly consideredthe conformational change of MscL by modeling the MscLstructure using a simple elastic rodlike representation of thetransmembrane helices By combining such a simple model ofMscL with a continuum model of the membrane in a finite-element framework and parametrizing the models using all-atom MD simulations they were able to observe mechanicalgating of MscL just by stretching the membraneParticle-based coarse-graining offers another route toward a

simpler model of mechanical gating In this framework groupsof atoms are represented by single interaction beads whichdramatically increases the computational efficiency of the MDsimulation The interactions between such coarse-grained beadsare calibrated to reproduce the thermodynamic properties ofmodel systems obtained from all-atom MD simulations orexperiments (eg transfer free energy of small molecules fromwater to hydrocarbon) Marrink and co-workers applied theirnovel coarse-grained model MARTINI252 to Tb-MscL253254

Specifically they were able to simulate gating of MscL just bystretching the membrane253 or pressurizing a vesicle thatcontained embedded MscL channels254

When the time scale accessible to an MD simulation issignificantly shorter than the time scale of gating one canaccelerate the simulation by applying biasing forces (egSMD) However the quality of such accelerated simulationsdepends critically on how realistic the biasing forces are In thissense combining single-molecule experiments with SMDsimulations can be very successful For example Corry et alrecently demonstrated that the distance measurements fromForster resonance energy transfer (FRET) confocal microscopycan be used as a guide for the SMD simulation255 Starting from

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXU

a closed conformation the researchers induced a closed-to-open conformational transition by performing SMD simu-lations that utilized distance constraints derived from FRETmeasurements on an open MscL channel Because of thedistance constraints the simulations produced a reasonablestructural model of the MscL pore in an open state542 Potassium Channels Potassium channels which all

share a common sequence for the selectivity filter demonstratevoltage- pH- and Ca2+-dependent gating of an intracellulargate which limits K+ access to the selectivity filter andextracellular solution However the selectivity filter is itself afragile structure that can be inactivated Inactivation of theselectivity filter occurs more readily when the intracellular gateis open186

It may be insightful to consider purely solution-dependentinactivation and inhibition of the selectivity filter A potassiumion channel will nearly irreversibly inactivate if it is placed inelectrolyte solution of very low ion concentration All-atom MDsimulations suggested a mechanism of such inactivation bydemonstrating severe distortion of the selectivity filter when itis depleted of K+ ions that partially neutralize the negativecarbonyl-oxygens lining of this structure137143182 Similarlyconductance of K+ channels can be blocked by other ions suchas Na+ or Cs+ that bind to the selectivity channelThe Kv channels are all voltage-gated Crystallographic

studies have provided structures for several open-pore Kvchannels featuring a charged voltage-sensitive subunit sur-rounded by lipids for each monomer of the tetramer411600601

The voltage-sensitive subunits are expected to move andrearrange in response to a voltage change in such a way that asmall but measurable transient capacitative current is observedacross the membrane The associated charge is known as thegating chargeThe gating charge times the change in the potential provides

the free energy required to change conformations and gate thechannel Using all-atom simulations the gating charge can bedirectly computed by measuring the difference in the center ofcharge of the system between open and closed conforma-tions185 A more sophisticated approach allows the assessmentof each residuersquos contribution to the gating charge through thecalculation of the difference between the free-energy cost ofcharging each residue in the closed and open states185

There is currently no crystallographically obtained closed-pore structure of a voltage-gated K+ channel However in astudy that utilized 13 μs of all-atom MD simulation the open-pore structure was refined and a possible closed-pore structurefor Kv12 was obtained185 Using these structures the gatingcharge was found to be somewhat smaller than theexperimentally measured gating charge suggesting that thecomputational model represented an intermediate conforma-tion at the onset of activationVery recently special-purpose hardware enabled all-atom

simulations of a Kv12Kv21 chimera on the gating-time scaleas observed experimentally (gt300 μs)196 The simulationsdemonstrated that the crystal structure accurately representsthe functional open pore In a series of simulations differentonly by the transmembrane voltage and the initial conditionsthe channel was brought from the open state to a fully closedstate Simulations were also performed to simulate differentstages of channel activation Gating of the channel occurred bystructural rearrangements of the voltage-sensitive domains thataffected the hydrophobic cavity leading to the selectivity filterThese rearrangements caused dewetting and collapse of the

cavity The time scales of various steps during the processagreed well with available experimental measurements196

Although not based on such long simulations a study of apH-sensitive potassium channel suggested that gating for thisprotein may occur through a rather different mechanism Anarginine residue near the extracellular side of the membranewas identified through mutagenesis as providing pH-sensitiv-ity602 The PMF of K+ ions in the selectivity filter was obtainedthrough all-atom MD when the protonation state of thatarginine residue was varied The authors of this study suggestedthat the observed 3minus4 kcalmol increase in the barriers for K+

translocation accounted for gating and arose from additionalflexibility that protonation of the arginine sensors granted tothe selectivity filter602 However it should be noted thatbecause no X-ray structure is available a homology model ofthe K2P channel built from Kv12 was used for this studyThus potassium channels share a great deal of structural and

sequence similarity around the selectivity filter but can be gatedin a variety of ways All-atom simulation techniques haveprovided a great deal of insight into the structural mechanismsof the gating processes In one exemplary study196 brute-forceall-atom MD simulations described the complete gating processof a voltage-sensitive potassium channel on a time scale ofhundreds of microseconds At this time it remains to be seenwhether other potassium channels use similar mechanisms togate

543 Blockades Some toxins bind and inactivateparticular target channels The potential for specificity ofchannel-binding toxins makes them an attractive source forpharmaceutical innovation The all-atom MD methodology hasbeen used to find the standard binding free energies of manysmall ligands but only recently have researchers attempted tofind the binding free energies of large ligands In particularseveral studies demonstrated challenges and shortcuts whencomputing standard binding free energies of charbydotoxinbinding to various voltage sensitive potassium chan-nels116603604

Of greater pharmacological interest the Kv13 K+ channelhas been identified as a target treatment of multiple sclerosisand other autoimmune disorders422 In a recent study the toxinShK which blocks Kv13 but also Kv11 was docked to severalK+ channels and the binding free energy was calculated425

Surprisingly the simulations revealed different binding geo-metries to Kv13 and Kv11 but similar binding free energiesthat agree well with experimentally determined values Theauthors concluded with mutations to ShK that may enhance theselectivity of Kv13 over Kv11At present free-energy calculations require too much

computing power and are not automated enough to be usedas a predictive tool by the pharmaceutical industry Inparticular reliably docking potential drug candidates remainsa challenge Nevertheless the combination of special-purposehardware for performing MD simulations very quickly andimproved automation of tools for calculating binding freeenergies may give rise to the use of all-atom simulations inadvanced computation drug screening within the pharmaceut-ical industry

55 Biosensing with Channels

About 20 years ago Bezrukov et al605 and Kasianowicz447 andco-workers demonstrated the possibility of using ionic channelsas molecular Coulter counters to detect the presence andcharacterize the type of biomolecules The basic principle of the

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXV

approach is the following A membrane containing a single-ionchannel separates electrolyte solution into two compartmentsconnected only through the transmembrane pore of thechannel A transmembrane bias is imposed using an externalvoltage source producing a steady ionic current through anopen pore The transmembrane bias facilitates unidirectionaltransport of charged biomolecules from one compartment tothe other Each passage is detected as transient reduction (ablockade) of the ionic current flowing through the pore Theduration and magnitude of the ionic current blockades canindicate the length and chemical composition of a nucleic acidpolymer447606minus608 suggesting the possibility of recording thenucleotide sequence of a DNA strand directly by measuring theionic current flowing through a nanoporeCritical to the success of the above approach is the lack of

spontaneous gating of the ion conductance which if presentcan easily be confused with the signal resulting from interactionof the channel with a biomolecule Because of its superiorstructural stability the α-hemolysin channel was the firstnanopore to be considered for biosensing applications447609

However other channels such as the bacterial porinMspA449minus451 and man-made silicon-based610minus612 and gra-phene613minus615 nanopores have been successfully used fordetection of biomolecules Apart from DNA sequencingnumerous other applications have been proposed for nano-pores including detection of small analytes589616617 drugdesign390618 pathogen detection619 and force spectrosco-py620minus622 Interested readers are directed to several reviews onthis subject446623minus627

Modeling and computer simulations have played a major rolein development of nanopore applications585 There have alsobeen numerous theoretical studies of various aspects ofpolymer capture and translocation through nanoporesTypically such studies involve the application of scalingconcepts of polymer physics or transport equations628minus630 toelucidate the dynamics of charged polymer capture andtranslocation All-atom simulations have been used as a kindof a computational force microscope to directly relate themicroscopic events taking place in a nanopore to the ioniccurrent blockades recorded in experiment377585

551 α-Hemolysin Among many β-barrel proteins α-hemolysin has been the channel of choice for mostexperimental studies because of its exceptional structuralstability under harsh experimental conditions The knowncrystallographic structure and relatively straightforward site-directed mutagenesis procedures permit rational engineering ofthis channel to enhance sensitivity of ionic current blockadesfor example by introducing a molecular adapter616 or othersite-specific mutations631632

The 2005 publication by Aksimentiev and Schulten90

pioneered the application of the all-atom MD method forprediction of the ionic conductance of membrane channelsThe simulations demonstrated for the first time quantitativeaccuracy of the MD method in predicting the absolute value ofthe ionic current reproducing the asymmetric currentminusvoltagedependence of α-hemolysin and characterizing the electro-osmotic effect The simulations also suggested a microscopicmechanism explaining the pH-dependence of the noise in theionic current recordings633 The study has also demonstrated amethod for computing the average distribution of theelectrostatic potential in a membrane channel directly froman all-atom MD simulation90 Following the successful study ofionic conductance through α-hemolysin the researchers were

challenged by an experimentalist (A Meller Boston University)to predict the influence of the global orientation of a DNAstrand in α-hemolysin on the velocity of DNA transport andthe ionic current blockades This was a blind test as no priorinformation about the outcome of experiments was given Tofind out the molecular origin of the observed differences MDsimulations were performed on α-hemolysin systems havingDNA threaded through in two different global orientationsfrom 3prime to 5prime and from 5prime to 3prime The outcome of the simulationsrevealed a propensity for DNA nucleotides to tilt toward their5prime-ends in confined environments which was linked toobservable differences in DNA translocation dynamics andionic current blockades97 The results of the MD simulationswere in qualitative agreement with experiment Because oflimited computational resources direct quantitative comparisonwas not possible at that timeThe α-hemolysin channel has been a test bed for developing

advanced simulation techniques The Roux group exploredpermeation of ions through the α-hemolysin channel using 3D-PNP as well as the grand canonical Monte Carlo Browniandynamics (GCMCBD) approaches88 in the absence of anyanalytes The study revealed that the asymmetric conductanceof the pore arises from the permanent charge distribution in thepore Another PNP study examined the influence of chargedresidues in α-hemolysin on the asymmetry of the currentminusvoltage dependence89100 Shilov and Kurnikova96 employedMD simulations to investigate the energetics and dynamics of aβ-cyclodextrin (βCD) molecule confined inside the α-hemolysin pore The Roux group investigated the effect ofβCD on the ion selectivity of the α-hemolysin through MDsimulations and PMF calculations94 The simulations haveshown that electrically neutral βCD enhances the concentrationof Clminus in the nanopore by causing a partial desolvation of theions which reduces the dielectric shielding by the solvent TheGCMCBD method was used to account for multi-ion effectsin a subsequent study94 Simakov and Kurnikova devised amodified PNP approach to incorporate a soft repulsion modelof short-range interactions between mobile ions and protein92

To overcome the time-scale limitation of the MD methodthe Aksimentiev group developed a method for acceleratingsimulations of DNA transport through nanopores thatpreserves all-atom features of the MD model98 The key ideaof the method dubbed grid-steered MD (G-SMD) was theselective amplification of the electrostatic potential that drivesDNA transport while maintaining all other interactionsunchanged Using G-SMD the Aksimentiev group performedmultiple simulations of DNA transport through α-hemolysinand determined the dependence of the translocation velocityon the sequence and orientation of the DNA strands98 a taskthat was considered formidable at that time634 De Biase andco-workers recently developed a theoretical framework tomodel DNA translocation across a nanopore by combining theGCMCBD algorithm with a coarse-grained polymer model forDNA102 which enabled multimicrosecond simulations at afraction of the cost of all-atom MD When applied to modeltranslocation of poly(dA) and poly(dC) strands through α-hemolysin the model yielded results in reasonable agreementwith experiments Reiner et al367 developed an elegantcontinuum theory to describe the results of nanopore massspectroscopy experiments with quantitative accuracy635 Bondet al employed all-atom MD simulations to explore thetranslocation of short strands of DNA through a simplifiedmodel of the α-hemolysin pore comprising the stem of the pore

Chemical Reviews Review

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surrounded by a membrane mimetic slab99 The studyexamined the effect of cationic amino acids on the translocationdynamics of DNA Compared to wild type α-hemolysinarginine mutations were found to reduce the transport rate ofDNA through the pore as well as the ionic current552 MspA The long stem of α-hemolysin can

accommodate up to 12 DNA nucleotides which makes difficultthe detection of single nucleotides by measuring ionic currentThe MspA porin has recently emerged as a viable alternative toα-hemolysin on account of its superior architecture MspA has agoblet-like structure with a constriction region that is sim1 nmideal for holding just one or two nucleotides see Figure 11aButler and co-workers showed that by eliminating the negativecharge in the constriction a variant of MspA called M1MspAwas capable of detecting a single DNA strand electrophoreti-cally driven through the pore449 A series of subsequentexperimental work in the Niederweis and Gundlach groupshave since established that the current resolution of the MspAvariant is superior to that of α-hemolysin636 and that singlenucleotide substitutions can be detected on a randomheteropolymeric background using a tethered DNA451

However the primary challenge is that the translocation rateof DNA through MspA is several orders of magnitude higherthan the rate required to resolve the type of DNA nucleotidesby measuring ionic current The two main strategies to controlDNA translocation are to engineer intrinsic brakes in the MspAstructure or use an auxiliary enzyme such as DNA polymer-ase637

The first computational study of MspA was recently carriedout by Bhattacharya and co-workers348 The study reportsextensive all-atom MD simulations that explored the effect ofpositively charged arginine residues on the translocation rate ofDNA and the ionic current On account of the highcomputational overhead due to the large system size theauthors performed the majority of the simulations using a

truncated version of the pore (see Figure 11b c) Since theDNA was found to be quite mobile even when confined to thenanopore the authors adopted an ensemble approach tosample the configurational dynamics of the DNA Theensemble method was shown to be a viable alternative tofollowing a single long-time-scale trajectory which is currentlypossible only using special-purpose supercomputers such asAnton The ensemble approach allowed the use of traditionalsupercomputers to obtain combined trajectory lengths of tensof microseconds within reasonable physical time Thesimulations have shown that by introducing several arginineresidues near the constriction of MspA the DNA permeationrate can be reduced by a factor of 10minus30 due to the formationof multiple salt bridges between the DNA backbone and theguanidinium groups of the arginine substitutions as well as dueto base-stacking interactions Furthermore the simulationspredicted that such mutations would not eliminate thenucleotide sensitivity of the ionic-current blockades Thestudy explained why similar mutations introduced in α-hemolysin reduced the ionic current practically to zero638

making such mutants unsuitable for DNA sequencingapplications

553 Other Nanopore Systems Other β-barrel nano-pores have been explored for stochastic sensing applicationsFor instance an MD study of the bacterial porin OmpG wascarried out by Chen and co-workers to determine the origin ofits spontaneous gating activity77 On the basis of the simulationstudy a variant of the porin with stabilizing mutations wascreated and was used for detection of adenosine diphosphateafter inserting a cyclodextrin molecular adapter77

Using 3D-Poisson equations and linear transport theory360

Vidal and co-workers demonstrated that a nanopore in a heavilydoped silicon membrane connected to a voltage source can beused as an electrically tunable ion filter The PNP model wasused to study ion transport through synthetic nanopores in

Figure 11 (a) Cut-away view of the full-length MspA nanopore embedded in a lipid membrane with a DNA strand threaded through The MspA isrepresented by a teal molecular surface the lipid membrane is represented by purple lines and the DNA bases are shown in magenta-colored licoricerepresentation (b) Average electrostatic potentials along the symmetry axis of the full and truncated MspA nanopores at a transmembrane bias of180 mV The electrostatic potentials are computed from MD simulations of open-pore MspA nanopores (c) Cut-away view of the reduced MspAsystem The DNA is covalently joined to itself across the periodic boundary (d) The ionic current trace of a sample trajectory of a poly(dC) strandthreaded through the MspA nanopore (e) Ionic current histograms obtained from ensemble simulations of the M1MspA (yellow) and its argininevariant M1 L88RA96RS116R (blue) The overlap of the two histograms is shown in green The histograms were constructed using 100 nsaverages of the instantaneous ionic current Adapted with permission from ref 348 Copyright 2012 American Chemical Society

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXX

several studies359363366 exploring rectification and ionselectivity A Langevin dynamics approach to study thetransport of flexible macromolecules in confined geometrieswas proposed by Peters372 Recently an atomic resolution BDmethod was developed by Comer and co-workers that was usedto study the sequence dependence of ionic current in syntheticnanopores373374 All-atom MD simulations have been usedwith considerable success to investigate nanopore transport ofDNA and ionic current blockades375376 nanopore unzipping ofDNA hairpins380 the microscopic origin of the electrophoreticforce on DNA in a nanopore378381 and the effect of electrolyteon the DNA translocation rates391 For detailed description ofthe simulation protocols interested readers are directed torecent reviews on this subject585639640

6 OUTLOOK

Advances in computational technologies and membraneprotein structure-determination methods are poised to makemodeling and simulations of ion channels an integral part offuture drug-development efforts The greatest obstacle so far isthe lack of atomic-resolution structures of the majority ofbiomedically relevant ion channels Several limitations pertainto the computational technology itself Whereas all-atommolecular dynamics simulation of an ion channel can providethe most detailed information about the microscopicmechanism of its function the method is currently limited bythe accuracy of the classical force field and the microsecondtime scale of the simulations on conventional computerclustersTremendous advances in addressing both limitations have

already been made The first computational studies of ionchannel systems using polarizable models have already beenreported277563 Thus it is very likely that a full polarizable forcefield will become available within the next 10 years Anothermajor advancement was the millisecond simulation of amembrane channel in its native environment that revealedthe microscopic details of its voltage-dependent gatingmechanism196 We hope that such a tremendous success ofspecial-purpose hardware will prompt the development ofcommodity special-purpose hardware which will make suchlong-time-scale simulations available to mainstream researchersFinally advances in computational methods will also aid thediscovery of atomic-resolution structures through either denovo structure prediction641 or refinement of low-resolution X-ray and cryo-EM structures443

It would be misleading however to think that all questionspertaining to ion channels would be answered through all-atomMD From a drug-development perspective high-throughputand accurate calculation of binding free energies of smallchemical compounds is more important than long-time-scalesimulations of a single channelrsquos action Enabling such high-throughput docking is dependent on the availability of accurategeneric force fields Furthermore as millisecond simulationsbecome more available describing possible chemical reactionsbetween components of the system will become increasinglyimportant Finally modeling a single channel in a membrane isonly a first step toward the realistic modeling of in vivoprocesses We anticipate continuum and implicit solventapproaches to play a pivotal role in the development ofdetailed quantitative models of realistic biological membranesand small organelles that incorporate an ensemble of ionchannels

AUTHOR INFORMATION

Corresponding Author

E-mail aksimentillinoisedu

Notes

The authors declare no competing financial interest

Biographies

Christopher Maffeo received his BSc in physics from the University of

California Santa Barbara in 2006 He joined the Aksimentiev group in

December 2006 After studying the structural and conductance

properties of the phospholamban pentamer he has focused his efforts

on understanding the kinetics energetics and electrostatics of various

DNAminusDNA and DNAminusprotein interactions

Swati Bhattacharya is a postdoctoral fellow in the group of Aleksei

Aksimentiev at the University of Illinois at UrbanaminusChampaign She

received her PhD in physics for work on the adsorption of polymers

at surfaces under the supervision of Thomas Vilgis in 2009 from the

Max Planck Institute for Polymer Research in Mainz Her current

research activities include computational modeling aimed at

developing applications of nanopores particularly for DNA sequencing

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXY

a closed conformation the researchers induced a closed-to-open conformational transition by performing SMD simu-lations that utilized distance constraints derived from FRETmeasurements on an open MscL channel Because of thedistance constraints the simulations produced a reasonablestructural model of the MscL pore in an open state542 Potassium Channels Potassium channels which all

share a common sequence for the selectivity filter demonstratevoltage- pH- and Ca2+-dependent gating of an intracellulargate which limits K+ access to the selectivity filter andextracellular solution However the selectivity filter is itself afragile structure that can be inactivated Inactivation of theselectivity filter occurs more readily when the intracellular gateis open186

It may be insightful to consider purely solution-dependentinactivation and inhibition of the selectivity filter A potassiumion channel will nearly irreversibly inactivate if it is placed inelectrolyte solution of very low ion concentration All-atom MDsimulations suggested a mechanism of such inactivation bydemonstrating severe distortion of the selectivity filter when itis depleted of K+ ions that partially neutralize the negativecarbonyl-oxygens lining of this structure137143182 Similarlyconductance of K+ channels can be blocked by other ions suchas Na+ or Cs+ that bind to the selectivity channelThe Kv channels are all voltage-gated Crystallographic

studies have provided structures for several open-pore Kvchannels featuring a charged voltage-sensitive subunit sur-rounded by lipids for each monomer of the tetramer411600601

The voltage-sensitive subunits are expected to move andrearrange in response to a voltage change in such a way that asmall but measurable transient capacitative current is observedacross the membrane The associated charge is known as thegating chargeThe gating charge times the change in the potential provides

the free energy required to change conformations and gate thechannel Using all-atom simulations the gating charge can bedirectly computed by measuring the difference in the center ofcharge of the system between open and closed conforma-tions185 A more sophisticated approach allows the assessmentof each residuersquos contribution to the gating charge through thecalculation of the difference between the free-energy cost ofcharging each residue in the closed and open states185

There is currently no crystallographically obtained closed-pore structure of a voltage-gated K+ channel However in astudy that utilized 13 μs of all-atom MD simulation the open-pore structure was refined and a possible closed-pore structurefor Kv12 was obtained185 Using these structures the gatingcharge was found to be somewhat smaller than theexperimentally measured gating charge suggesting that thecomputational model represented an intermediate conforma-tion at the onset of activationVery recently special-purpose hardware enabled all-atom

simulations of a Kv12Kv21 chimera on the gating-time scaleas observed experimentally (gt300 μs)196 The simulationsdemonstrated that the crystal structure accurately representsthe functional open pore In a series of simulations differentonly by the transmembrane voltage and the initial conditionsthe channel was brought from the open state to a fully closedstate Simulations were also performed to simulate differentstages of channel activation Gating of the channel occurred bystructural rearrangements of the voltage-sensitive domains thataffected the hydrophobic cavity leading to the selectivity filterThese rearrangements caused dewetting and collapse of the

cavity The time scales of various steps during the processagreed well with available experimental measurements196

Although not based on such long simulations a study of apH-sensitive potassium channel suggested that gating for thisprotein may occur through a rather different mechanism Anarginine residue near the extracellular side of the membranewas identified through mutagenesis as providing pH-sensitiv-ity602 The PMF of K+ ions in the selectivity filter was obtainedthrough all-atom MD when the protonation state of thatarginine residue was varied The authors of this study suggestedthat the observed 3minus4 kcalmol increase in the barriers for K+

translocation accounted for gating and arose from additionalflexibility that protonation of the arginine sensors granted tothe selectivity filter602 However it should be noted thatbecause no X-ray structure is available a homology model ofthe K2P channel built from Kv12 was used for this studyThus potassium channels share a great deal of structural and

sequence similarity around the selectivity filter but can be gatedin a variety of ways All-atom simulation techniques haveprovided a great deal of insight into the structural mechanismsof the gating processes In one exemplary study196 brute-forceall-atom MD simulations described the complete gating processof a voltage-sensitive potassium channel on a time scale ofhundreds of microseconds At this time it remains to be seenwhether other potassium channels use similar mechanisms togate

543 Blockades Some toxins bind and inactivateparticular target channels The potential for specificity ofchannel-binding toxins makes them an attractive source forpharmaceutical innovation The all-atom MD methodology hasbeen used to find the standard binding free energies of manysmall ligands but only recently have researchers attempted tofind the binding free energies of large ligands In particularseveral studies demonstrated challenges and shortcuts whencomputing standard binding free energies of charbydotoxinbinding to various voltage sensitive potassium chan-nels116603604

Of greater pharmacological interest the Kv13 K+ channelhas been identified as a target treatment of multiple sclerosisand other autoimmune disorders422 In a recent study the toxinShK which blocks Kv13 but also Kv11 was docked to severalK+ channels and the binding free energy was calculated425

Surprisingly the simulations revealed different binding geo-metries to Kv13 and Kv11 but similar binding free energiesthat agree well with experimentally determined values Theauthors concluded with mutations to ShK that may enhance theselectivity of Kv13 over Kv11At present free-energy calculations require too much

computing power and are not automated enough to be usedas a predictive tool by the pharmaceutical industry Inparticular reliably docking potential drug candidates remainsa challenge Nevertheless the combination of special-purposehardware for performing MD simulations very quickly andimproved automation of tools for calculating binding freeenergies may give rise to the use of all-atom simulations inadvanced computation drug screening within the pharmaceut-ical industry

55 Biosensing with Channels

About 20 years ago Bezrukov et al605 and Kasianowicz447 andco-workers demonstrated the possibility of using ionic channelsas molecular Coulter counters to detect the presence andcharacterize the type of biomolecules The basic principle of the

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXV

approach is the following A membrane containing a single-ionchannel separates electrolyte solution into two compartmentsconnected only through the transmembrane pore of thechannel A transmembrane bias is imposed using an externalvoltage source producing a steady ionic current through anopen pore The transmembrane bias facilitates unidirectionaltransport of charged biomolecules from one compartment tothe other Each passage is detected as transient reduction (ablockade) of the ionic current flowing through the pore Theduration and magnitude of the ionic current blockades canindicate the length and chemical composition of a nucleic acidpolymer447606minus608 suggesting the possibility of recording thenucleotide sequence of a DNA strand directly by measuring theionic current flowing through a nanoporeCritical to the success of the above approach is the lack of

spontaneous gating of the ion conductance which if presentcan easily be confused with the signal resulting from interactionof the channel with a biomolecule Because of its superiorstructural stability the α-hemolysin channel was the firstnanopore to be considered for biosensing applications447609

However other channels such as the bacterial porinMspA449minus451 and man-made silicon-based610minus612 and gra-phene613minus615 nanopores have been successfully used fordetection of biomolecules Apart from DNA sequencingnumerous other applications have been proposed for nano-pores including detection of small analytes589616617 drugdesign390618 pathogen detection619 and force spectrosco-py620minus622 Interested readers are directed to several reviews onthis subject446623minus627

Modeling and computer simulations have played a major rolein development of nanopore applications585 There have alsobeen numerous theoretical studies of various aspects ofpolymer capture and translocation through nanoporesTypically such studies involve the application of scalingconcepts of polymer physics or transport equations628minus630 toelucidate the dynamics of charged polymer capture andtranslocation All-atom simulations have been used as a kindof a computational force microscope to directly relate themicroscopic events taking place in a nanopore to the ioniccurrent blockades recorded in experiment377585

551 α-Hemolysin Among many β-barrel proteins α-hemolysin has been the channel of choice for mostexperimental studies because of its exceptional structuralstability under harsh experimental conditions The knowncrystallographic structure and relatively straightforward site-directed mutagenesis procedures permit rational engineering ofthis channel to enhance sensitivity of ionic current blockadesfor example by introducing a molecular adapter616 or othersite-specific mutations631632

The 2005 publication by Aksimentiev and Schulten90

pioneered the application of the all-atom MD method forprediction of the ionic conductance of membrane channelsThe simulations demonstrated for the first time quantitativeaccuracy of the MD method in predicting the absolute value ofthe ionic current reproducing the asymmetric currentminusvoltagedependence of α-hemolysin and characterizing the electro-osmotic effect The simulations also suggested a microscopicmechanism explaining the pH-dependence of the noise in theionic current recordings633 The study has also demonstrated amethod for computing the average distribution of theelectrostatic potential in a membrane channel directly froman all-atom MD simulation90 Following the successful study ofionic conductance through α-hemolysin the researchers were

challenged by an experimentalist (A Meller Boston University)to predict the influence of the global orientation of a DNAstrand in α-hemolysin on the velocity of DNA transport andthe ionic current blockades This was a blind test as no priorinformation about the outcome of experiments was given Tofind out the molecular origin of the observed differences MDsimulations were performed on α-hemolysin systems havingDNA threaded through in two different global orientationsfrom 3prime to 5prime and from 5prime to 3prime The outcome of the simulationsrevealed a propensity for DNA nucleotides to tilt toward their5prime-ends in confined environments which was linked toobservable differences in DNA translocation dynamics andionic current blockades97 The results of the MD simulationswere in qualitative agreement with experiment Because oflimited computational resources direct quantitative comparisonwas not possible at that timeThe α-hemolysin channel has been a test bed for developing

advanced simulation techniques The Roux group exploredpermeation of ions through the α-hemolysin channel using 3D-PNP as well as the grand canonical Monte Carlo Browniandynamics (GCMCBD) approaches88 in the absence of anyanalytes The study revealed that the asymmetric conductanceof the pore arises from the permanent charge distribution in thepore Another PNP study examined the influence of chargedresidues in α-hemolysin on the asymmetry of the currentminusvoltage dependence89100 Shilov and Kurnikova96 employedMD simulations to investigate the energetics and dynamics of aβ-cyclodextrin (βCD) molecule confined inside the α-hemolysin pore The Roux group investigated the effect ofβCD on the ion selectivity of the α-hemolysin through MDsimulations and PMF calculations94 The simulations haveshown that electrically neutral βCD enhances the concentrationof Clminus in the nanopore by causing a partial desolvation of theions which reduces the dielectric shielding by the solvent TheGCMCBD method was used to account for multi-ion effectsin a subsequent study94 Simakov and Kurnikova devised amodified PNP approach to incorporate a soft repulsion modelof short-range interactions between mobile ions and protein92

To overcome the time-scale limitation of the MD methodthe Aksimentiev group developed a method for acceleratingsimulations of DNA transport through nanopores thatpreserves all-atom features of the MD model98 The key ideaof the method dubbed grid-steered MD (G-SMD) was theselective amplification of the electrostatic potential that drivesDNA transport while maintaining all other interactionsunchanged Using G-SMD the Aksimentiev group performedmultiple simulations of DNA transport through α-hemolysinand determined the dependence of the translocation velocityon the sequence and orientation of the DNA strands98 a taskthat was considered formidable at that time634 De Biase andco-workers recently developed a theoretical framework tomodel DNA translocation across a nanopore by combining theGCMCBD algorithm with a coarse-grained polymer model forDNA102 which enabled multimicrosecond simulations at afraction of the cost of all-atom MD When applied to modeltranslocation of poly(dA) and poly(dC) strands through α-hemolysin the model yielded results in reasonable agreementwith experiments Reiner et al367 developed an elegantcontinuum theory to describe the results of nanopore massspectroscopy experiments with quantitative accuracy635 Bondet al employed all-atom MD simulations to explore thetranslocation of short strands of DNA through a simplifiedmodel of the α-hemolysin pore comprising the stem of the pore

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXW

surrounded by a membrane mimetic slab99 The studyexamined the effect of cationic amino acids on the translocationdynamics of DNA Compared to wild type α-hemolysinarginine mutations were found to reduce the transport rate ofDNA through the pore as well as the ionic current552 MspA The long stem of α-hemolysin can

accommodate up to 12 DNA nucleotides which makes difficultthe detection of single nucleotides by measuring ionic currentThe MspA porin has recently emerged as a viable alternative toα-hemolysin on account of its superior architecture MspA has agoblet-like structure with a constriction region that is sim1 nmideal for holding just one or two nucleotides see Figure 11aButler and co-workers showed that by eliminating the negativecharge in the constriction a variant of MspA called M1MspAwas capable of detecting a single DNA strand electrophoreti-cally driven through the pore449 A series of subsequentexperimental work in the Niederweis and Gundlach groupshave since established that the current resolution of the MspAvariant is superior to that of α-hemolysin636 and that singlenucleotide substitutions can be detected on a randomheteropolymeric background using a tethered DNA451

However the primary challenge is that the translocation rateof DNA through MspA is several orders of magnitude higherthan the rate required to resolve the type of DNA nucleotidesby measuring ionic current The two main strategies to controlDNA translocation are to engineer intrinsic brakes in the MspAstructure or use an auxiliary enzyme such as DNA polymer-ase637

The first computational study of MspA was recently carriedout by Bhattacharya and co-workers348 The study reportsextensive all-atom MD simulations that explored the effect ofpositively charged arginine residues on the translocation rate ofDNA and the ionic current On account of the highcomputational overhead due to the large system size theauthors performed the majority of the simulations using a

truncated version of the pore (see Figure 11b c) Since theDNA was found to be quite mobile even when confined to thenanopore the authors adopted an ensemble approach tosample the configurational dynamics of the DNA Theensemble method was shown to be a viable alternative tofollowing a single long-time-scale trajectory which is currentlypossible only using special-purpose supercomputers such asAnton The ensemble approach allowed the use of traditionalsupercomputers to obtain combined trajectory lengths of tensof microseconds within reasonable physical time Thesimulations have shown that by introducing several arginineresidues near the constriction of MspA the DNA permeationrate can be reduced by a factor of 10minus30 due to the formationof multiple salt bridges between the DNA backbone and theguanidinium groups of the arginine substitutions as well as dueto base-stacking interactions Furthermore the simulationspredicted that such mutations would not eliminate thenucleotide sensitivity of the ionic-current blockades Thestudy explained why similar mutations introduced in α-hemolysin reduced the ionic current practically to zero638

making such mutants unsuitable for DNA sequencingapplications

553 Other Nanopore Systems Other β-barrel nano-pores have been explored for stochastic sensing applicationsFor instance an MD study of the bacterial porin OmpG wascarried out by Chen and co-workers to determine the origin ofits spontaneous gating activity77 On the basis of the simulationstudy a variant of the porin with stabilizing mutations wascreated and was used for detection of adenosine diphosphateafter inserting a cyclodextrin molecular adapter77

Using 3D-Poisson equations and linear transport theory360

Vidal and co-workers demonstrated that a nanopore in a heavilydoped silicon membrane connected to a voltage source can beused as an electrically tunable ion filter The PNP model wasused to study ion transport through synthetic nanopores in

Figure 11 (a) Cut-away view of the full-length MspA nanopore embedded in a lipid membrane with a DNA strand threaded through The MspA isrepresented by a teal molecular surface the lipid membrane is represented by purple lines and the DNA bases are shown in magenta-colored licoricerepresentation (b) Average electrostatic potentials along the symmetry axis of the full and truncated MspA nanopores at a transmembrane bias of180 mV The electrostatic potentials are computed from MD simulations of open-pore MspA nanopores (c) Cut-away view of the reduced MspAsystem The DNA is covalently joined to itself across the periodic boundary (d) The ionic current trace of a sample trajectory of a poly(dC) strandthreaded through the MspA nanopore (e) Ionic current histograms obtained from ensemble simulations of the M1MspA (yellow) and its argininevariant M1 L88RA96RS116R (blue) The overlap of the two histograms is shown in green The histograms were constructed using 100 nsaverages of the instantaneous ionic current Adapted with permission from ref 348 Copyright 2012 American Chemical Society

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXX

several studies359363366 exploring rectification and ionselectivity A Langevin dynamics approach to study thetransport of flexible macromolecules in confined geometrieswas proposed by Peters372 Recently an atomic resolution BDmethod was developed by Comer and co-workers that was usedto study the sequence dependence of ionic current in syntheticnanopores373374 All-atom MD simulations have been usedwith considerable success to investigate nanopore transport ofDNA and ionic current blockades375376 nanopore unzipping ofDNA hairpins380 the microscopic origin of the electrophoreticforce on DNA in a nanopore378381 and the effect of electrolyteon the DNA translocation rates391 For detailed description ofthe simulation protocols interested readers are directed torecent reviews on this subject585639640

6 OUTLOOK

Advances in computational technologies and membraneprotein structure-determination methods are poised to makemodeling and simulations of ion channels an integral part offuture drug-development efforts The greatest obstacle so far isthe lack of atomic-resolution structures of the majority ofbiomedically relevant ion channels Several limitations pertainto the computational technology itself Whereas all-atommolecular dynamics simulation of an ion channel can providethe most detailed information about the microscopicmechanism of its function the method is currently limited bythe accuracy of the classical force field and the microsecondtime scale of the simulations on conventional computerclustersTremendous advances in addressing both limitations have

already been made The first computational studies of ionchannel systems using polarizable models have already beenreported277563 Thus it is very likely that a full polarizable forcefield will become available within the next 10 years Anothermajor advancement was the millisecond simulation of amembrane channel in its native environment that revealedthe microscopic details of its voltage-dependent gatingmechanism196 We hope that such a tremendous success ofspecial-purpose hardware will prompt the development ofcommodity special-purpose hardware which will make suchlong-time-scale simulations available to mainstream researchersFinally advances in computational methods will also aid thediscovery of atomic-resolution structures through either denovo structure prediction641 or refinement of low-resolution X-ray and cryo-EM structures443

It would be misleading however to think that all questionspertaining to ion channels would be answered through all-atomMD From a drug-development perspective high-throughputand accurate calculation of binding free energies of smallchemical compounds is more important than long-time-scalesimulations of a single channelrsquos action Enabling such high-throughput docking is dependent on the availability of accurategeneric force fields Furthermore as millisecond simulationsbecome more available describing possible chemical reactionsbetween components of the system will become increasinglyimportant Finally modeling a single channel in a membrane isonly a first step toward the realistic modeling of in vivoprocesses We anticipate continuum and implicit solventapproaches to play a pivotal role in the development ofdetailed quantitative models of realistic biological membranesand small organelles that incorporate an ensemble of ionchannels

AUTHOR INFORMATION

Corresponding Author

E-mail aksimentillinoisedu

Notes

The authors declare no competing financial interest

Biographies

Christopher Maffeo received his BSc in physics from the University of

California Santa Barbara in 2006 He joined the Aksimentiev group in

December 2006 After studying the structural and conductance

properties of the phospholamban pentamer he has focused his efforts

on understanding the kinetics energetics and electrostatics of various

DNAminusDNA and DNAminusprotein interactions

Swati Bhattacharya is a postdoctoral fellow in the group of Aleksei

Aksimentiev at the University of Illinois at UrbanaminusChampaign She

received her PhD in physics for work on the adsorption of polymers

at surfaces under the supervision of Thomas Vilgis in 2009 from the

Max Planck Institute for Polymer Research in Mainz Her current

research activities include computational modeling aimed at

developing applications of nanopores particularly for DNA sequencing

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXY

approach is the following A membrane containing a single-ionchannel separates electrolyte solution into two compartmentsconnected only through the transmembrane pore of thechannel A transmembrane bias is imposed using an externalvoltage source producing a steady ionic current through anopen pore The transmembrane bias facilitates unidirectionaltransport of charged biomolecules from one compartment tothe other Each passage is detected as transient reduction (ablockade) of the ionic current flowing through the pore Theduration and magnitude of the ionic current blockades canindicate the length and chemical composition of a nucleic acidpolymer447606minus608 suggesting the possibility of recording thenucleotide sequence of a DNA strand directly by measuring theionic current flowing through a nanoporeCritical to the success of the above approach is the lack of

spontaneous gating of the ion conductance which if presentcan easily be confused with the signal resulting from interactionof the channel with a biomolecule Because of its superiorstructural stability the α-hemolysin channel was the firstnanopore to be considered for biosensing applications447609

However other channels such as the bacterial porinMspA449minus451 and man-made silicon-based610minus612 and gra-phene613minus615 nanopores have been successfully used fordetection of biomolecules Apart from DNA sequencingnumerous other applications have been proposed for nano-pores including detection of small analytes589616617 drugdesign390618 pathogen detection619 and force spectrosco-py620minus622 Interested readers are directed to several reviews onthis subject446623minus627

Modeling and computer simulations have played a major rolein development of nanopore applications585 There have alsobeen numerous theoretical studies of various aspects ofpolymer capture and translocation through nanoporesTypically such studies involve the application of scalingconcepts of polymer physics or transport equations628minus630 toelucidate the dynamics of charged polymer capture andtranslocation All-atom simulations have been used as a kindof a computational force microscope to directly relate themicroscopic events taking place in a nanopore to the ioniccurrent blockades recorded in experiment377585

551 α-Hemolysin Among many β-barrel proteins α-hemolysin has been the channel of choice for mostexperimental studies because of its exceptional structuralstability under harsh experimental conditions The knowncrystallographic structure and relatively straightforward site-directed mutagenesis procedures permit rational engineering ofthis channel to enhance sensitivity of ionic current blockadesfor example by introducing a molecular adapter616 or othersite-specific mutations631632

The 2005 publication by Aksimentiev and Schulten90

pioneered the application of the all-atom MD method forprediction of the ionic conductance of membrane channelsThe simulations demonstrated for the first time quantitativeaccuracy of the MD method in predicting the absolute value ofthe ionic current reproducing the asymmetric currentminusvoltagedependence of α-hemolysin and characterizing the electro-osmotic effect The simulations also suggested a microscopicmechanism explaining the pH-dependence of the noise in theionic current recordings633 The study has also demonstrated amethod for computing the average distribution of theelectrostatic potential in a membrane channel directly froman all-atom MD simulation90 Following the successful study ofionic conductance through α-hemolysin the researchers were

challenged by an experimentalist (A Meller Boston University)to predict the influence of the global orientation of a DNAstrand in α-hemolysin on the velocity of DNA transport andthe ionic current blockades This was a blind test as no priorinformation about the outcome of experiments was given Tofind out the molecular origin of the observed differences MDsimulations were performed on α-hemolysin systems havingDNA threaded through in two different global orientationsfrom 3prime to 5prime and from 5prime to 3prime The outcome of the simulationsrevealed a propensity for DNA nucleotides to tilt toward their5prime-ends in confined environments which was linked toobservable differences in DNA translocation dynamics andionic current blockades97 The results of the MD simulationswere in qualitative agreement with experiment Because oflimited computational resources direct quantitative comparisonwas not possible at that timeThe α-hemolysin channel has been a test bed for developing

advanced simulation techniques The Roux group exploredpermeation of ions through the α-hemolysin channel using 3D-PNP as well as the grand canonical Monte Carlo Browniandynamics (GCMCBD) approaches88 in the absence of anyanalytes The study revealed that the asymmetric conductanceof the pore arises from the permanent charge distribution in thepore Another PNP study examined the influence of chargedresidues in α-hemolysin on the asymmetry of the currentminusvoltage dependence89100 Shilov and Kurnikova96 employedMD simulations to investigate the energetics and dynamics of aβ-cyclodextrin (βCD) molecule confined inside the α-hemolysin pore The Roux group investigated the effect ofβCD on the ion selectivity of the α-hemolysin through MDsimulations and PMF calculations94 The simulations haveshown that electrically neutral βCD enhances the concentrationof Clminus in the nanopore by causing a partial desolvation of theions which reduces the dielectric shielding by the solvent TheGCMCBD method was used to account for multi-ion effectsin a subsequent study94 Simakov and Kurnikova devised amodified PNP approach to incorporate a soft repulsion modelof short-range interactions between mobile ions and protein92

To overcome the time-scale limitation of the MD methodthe Aksimentiev group developed a method for acceleratingsimulations of DNA transport through nanopores thatpreserves all-atom features of the MD model98 The key ideaof the method dubbed grid-steered MD (G-SMD) was theselective amplification of the electrostatic potential that drivesDNA transport while maintaining all other interactionsunchanged Using G-SMD the Aksimentiev group performedmultiple simulations of DNA transport through α-hemolysinand determined the dependence of the translocation velocityon the sequence and orientation of the DNA strands98 a taskthat was considered formidable at that time634 De Biase andco-workers recently developed a theoretical framework tomodel DNA translocation across a nanopore by combining theGCMCBD algorithm with a coarse-grained polymer model forDNA102 which enabled multimicrosecond simulations at afraction of the cost of all-atom MD When applied to modeltranslocation of poly(dA) and poly(dC) strands through α-hemolysin the model yielded results in reasonable agreementwith experiments Reiner et al367 developed an elegantcontinuum theory to describe the results of nanopore massspectroscopy experiments with quantitative accuracy635 Bondet al employed all-atom MD simulations to explore thetranslocation of short strands of DNA through a simplifiedmodel of the α-hemolysin pore comprising the stem of the pore

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXW

surrounded by a membrane mimetic slab99 The studyexamined the effect of cationic amino acids on the translocationdynamics of DNA Compared to wild type α-hemolysinarginine mutations were found to reduce the transport rate ofDNA through the pore as well as the ionic current552 MspA The long stem of α-hemolysin can

accommodate up to 12 DNA nucleotides which makes difficultthe detection of single nucleotides by measuring ionic currentThe MspA porin has recently emerged as a viable alternative toα-hemolysin on account of its superior architecture MspA has agoblet-like structure with a constriction region that is sim1 nmideal for holding just one or two nucleotides see Figure 11aButler and co-workers showed that by eliminating the negativecharge in the constriction a variant of MspA called M1MspAwas capable of detecting a single DNA strand electrophoreti-cally driven through the pore449 A series of subsequentexperimental work in the Niederweis and Gundlach groupshave since established that the current resolution of the MspAvariant is superior to that of α-hemolysin636 and that singlenucleotide substitutions can be detected on a randomheteropolymeric background using a tethered DNA451

However the primary challenge is that the translocation rateof DNA through MspA is several orders of magnitude higherthan the rate required to resolve the type of DNA nucleotidesby measuring ionic current The two main strategies to controlDNA translocation are to engineer intrinsic brakes in the MspAstructure or use an auxiliary enzyme such as DNA polymer-ase637

The first computational study of MspA was recently carriedout by Bhattacharya and co-workers348 The study reportsextensive all-atom MD simulations that explored the effect ofpositively charged arginine residues on the translocation rate ofDNA and the ionic current On account of the highcomputational overhead due to the large system size theauthors performed the majority of the simulations using a

truncated version of the pore (see Figure 11b c) Since theDNA was found to be quite mobile even when confined to thenanopore the authors adopted an ensemble approach tosample the configurational dynamics of the DNA Theensemble method was shown to be a viable alternative tofollowing a single long-time-scale trajectory which is currentlypossible only using special-purpose supercomputers such asAnton The ensemble approach allowed the use of traditionalsupercomputers to obtain combined trajectory lengths of tensof microseconds within reasonable physical time Thesimulations have shown that by introducing several arginineresidues near the constriction of MspA the DNA permeationrate can be reduced by a factor of 10minus30 due to the formationof multiple salt bridges between the DNA backbone and theguanidinium groups of the arginine substitutions as well as dueto base-stacking interactions Furthermore the simulationspredicted that such mutations would not eliminate thenucleotide sensitivity of the ionic-current blockades Thestudy explained why similar mutations introduced in α-hemolysin reduced the ionic current practically to zero638

making such mutants unsuitable for DNA sequencingapplications

553 Other Nanopore Systems Other β-barrel nano-pores have been explored for stochastic sensing applicationsFor instance an MD study of the bacterial porin OmpG wascarried out by Chen and co-workers to determine the origin ofits spontaneous gating activity77 On the basis of the simulationstudy a variant of the porin with stabilizing mutations wascreated and was used for detection of adenosine diphosphateafter inserting a cyclodextrin molecular adapter77

Using 3D-Poisson equations and linear transport theory360

Vidal and co-workers demonstrated that a nanopore in a heavilydoped silicon membrane connected to a voltage source can beused as an electrically tunable ion filter The PNP model wasused to study ion transport through synthetic nanopores in

Figure 11 (a) Cut-away view of the full-length MspA nanopore embedded in a lipid membrane with a DNA strand threaded through The MspA isrepresented by a teal molecular surface the lipid membrane is represented by purple lines and the DNA bases are shown in magenta-colored licoricerepresentation (b) Average electrostatic potentials along the symmetry axis of the full and truncated MspA nanopores at a transmembrane bias of180 mV The electrostatic potentials are computed from MD simulations of open-pore MspA nanopores (c) Cut-away view of the reduced MspAsystem The DNA is covalently joined to itself across the periodic boundary (d) The ionic current trace of a sample trajectory of a poly(dC) strandthreaded through the MspA nanopore (e) Ionic current histograms obtained from ensemble simulations of the M1MspA (yellow) and its argininevariant M1 L88RA96RS116R (blue) The overlap of the two histograms is shown in green The histograms were constructed using 100 nsaverages of the instantaneous ionic current Adapted with permission from ref 348 Copyright 2012 American Chemical Society

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXX

several studies359363366 exploring rectification and ionselectivity A Langevin dynamics approach to study thetransport of flexible macromolecules in confined geometrieswas proposed by Peters372 Recently an atomic resolution BDmethod was developed by Comer and co-workers that was usedto study the sequence dependence of ionic current in syntheticnanopores373374 All-atom MD simulations have been usedwith considerable success to investigate nanopore transport ofDNA and ionic current blockades375376 nanopore unzipping ofDNA hairpins380 the microscopic origin of the electrophoreticforce on DNA in a nanopore378381 and the effect of electrolyteon the DNA translocation rates391 For detailed description ofthe simulation protocols interested readers are directed torecent reviews on this subject585639640

6 OUTLOOK

Advances in computational technologies and membraneprotein structure-determination methods are poised to makemodeling and simulations of ion channels an integral part offuture drug-development efforts The greatest obstacle so far isthe lack of atomic-resolution structures of the majority ofbiomedically relevant ion channels Several limitations pertainto the computational technology itself Whereas all-atommolecular dynamics simulation of an ion channel can providethe most detailed information about the microscopicmechanism of its function the method is currently limited bythe accuracy of the classical force field and the microsecondtime scale of the simulations on conventional computerclustersTremendous advances in addressing both limitations have

already been made The first computational studies of ionchannel systems using polarizable models have already beenreported277563 Thus it is very likely that a full polarizable forcefield will become available within the next 10 years Anothermajor advancement was the millisecond simulation of amembrane channel in its native environment that revealedthe microscopic details of its voltage-dependent gatingmechanism196 We hope that such a tremendous success ofspecial-purpose hardware will prompt the development ofcommodity special-purpose hardware which will make suchlong-time-scale simulations available to mainstream researchersFinally advances in computational methods will also aid thediscovery of atomic-resolution structures through either denovo structure prediction641 or refinement of low-resolution X-ray and cryo-EM structures443

It would be misleading however to think that all questionspertaining to ion channels would be answered through all-atomMD From a drug-development perspective high-throughputand accurate calculation of binding free energies of smallchemical compounds is more important than long-time-scalesimulations of a single channelrsquos action Enabling such high-throughput docking is dependent on the availability of accurategeneric force fields Furthermore as millisecond simulationsbecome more available describing possible chemical reactionsbetween components of the system will become increasinglyimportant Finally modeling a single channel in a membrane isonly a first step toward the realistic modeling of in vivoprocesses We anticipate continuum and implicit solventapproaches to play a pivotal role in the development ofdetailed quantitative models of realistic biological membranesand small organelles that incorporate an ensemble of ionchannels

AUTHOR INFORMATION

Corresponding Author

E-mail aksimentillinoisedu

Notes

The authors declare no competing financial interest

Biographies

Christopher Maffeo received his BSc in physics from the University of

California Santa Barbara in 2006 He joined the Aksimentiev group in

December 2006 After studying the structural and conductance

properties of the phospholamban pentamer he has focused his efforts

on understanding the kinetics energetics and electrostatics of various

DNAminusDNA and DNAminusprotein interactions

Swati Bhattacharya is a postdoctoral fellow in the group of Aleksei

Aksimentiev at the University of Illinois at UrbanaminusChampaign She

received her PhD in physics for work on the adsorption of polymers

at surfaces under the supervision of Thomas Vilgis in 2009 from the

Max Planck Institute for Polymer Research in Mainz Her current

research activities include computational modeling aimed at

developing applications of nanopores particularly for DNA sequencing

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXY

surrounded by a membrane mimetic slab99 The studyexamined the effect of cationic amino acids on the translocationdynamics of DNA Compared to wild type α-hemolysinarginine mutations were found to reduce the transport rate ofDNA through the pore as well as the ionic current552 MspA The long stem of α-hemolysin can

accommodate up to 12 DNA nucleotides which makes difficultthe detection of single nucleotides by measuring ionic currentThe MspA porin has recently emerged as a viable alternative toα-hemolysin on account of its superior architecture MspA has agoblet-like structure with a constriction region that is sim1 nmideal for holding just one or two nucleotides see Figure 11aButler and co-workers showed that by eliminating the negativecharge in the constriction a variant of MspA called M1MspAwas capable of detecting a single DNA strand electrophoreti-cally driven through the pore449 A series of subsequentexperimental work in the Niederweis and Gundlach groupshave since established that the current resolution of the MspAvariant is superior to that of α-hemolysin636 and that singlenucleotide substitutions can be detected on a randomheteropolymeric background using a tethered DNA451

However the primary challenge is that the translocation rateof DNA through MspA is several orders of magnitude higherthan the rate required to resolve the type of DNA nucleotidesby measuring ionic current The two main strategies to controlDNA translocation are to engineer intrinsic brakes in the MspAstructure or use an auxiliary enzyme such as DNA polymer-ase637

The first computational study of MspA was recently carriedout by Bhattacharya and co-workers348 The study reportsextensive all-atom MD simulations that explored the effect ofpositively charged arginine residues on the translocation rate ofDNA and the ionic current On account of the highcomputational overhead due to the large system size theauthors performed the majority of the simulations using a

truncated version of the pore (see Figure 11b c) Since theDNA was found to be quite mobile even when confined to thenanopore the authors adopted an ensemble approach tosample the configurational dynamics of the DNA Theensemble method was shown to be a viable alternative tofollowing a single long-time-scale trajectory which is currentlypossible only using special-purpose supercomputers such asAnton The ensemble approach allowed the use of traditionalsupercomputers to obtain combined trajectory lengths of tensof microseconds within reasonable physical time Thesimulations have shown that by introducing several arginineresidues near the constriction of MspA the DNA permeationrate can be reduced by a factor of 10minus30 due to the formationof multiple salt bridges between the DNA backbone and theguanidinium groups of the arginine substitutions as well as dueto base-stacking interactions Furthermore the simulationspredicted that such mutations would not eliminate thenucleotide sensitivity of the ionic-current blockades Thestudy explained why similar mutations introduced in α-hemolysin reduced the ionic current practically to zero638

making such mutants unsuitable for DNA sequencingapplications

553 Other Nanopore Systems Other β-barrel nano-pores have been explored for stochastic sensing applicationsFor instance an MD study of the bacterial porin OmpG wascarried out by Chen and co-workers to determine the origin ofits spontaneous gating activity77 On the basis of the simulationstudy a variant of the porin with stabilizing mutations wascreated and was used for detection of adenosine diphosphateafter inserting a cyclodextrin molecular adapter77

Using 3D-Poisson equations and linear transport theory360

Vidal and co-workers demonstrated that a nanopore in a heavilydoped silicon membrane connected to a voltage source can beused as an electrically tunable ion filter The PNP model wasused to study ion transport through synthetic nanopores in

Figure 11 (a) Cut-away view of the full-length MspA nanopore embedded in a lipid membrane with a DNA strand threaded through The MspA isrepresented by a teal molecular surface the lipid membrane is represented by purple lines and the DNA bases are shown in magenta-colored licoricerepresentation (b) Average electrostatic potentials along the symmetry axis of the full and truncated MspA nanopores at a transmembrane bias of180 mV The electrostatic potentials are computed from MD simulations of open-pore MspA nanopores (c) Cut-away view of the reduced MspAsystem The DNA is covalently joined to itself across the periodic boundary (d) The ionic current trace of a sample trajectory of a poly(dC) strandthreaded through the MspA nanopore (e) Ionic current histograms obtained from ensemble simulations of the M1MspA (yellow) and its argininevariant M1 L88RA96RS116R (blue) The overlap of the two histograms is shown in green The histograms were constructed using 100 nsaverages of the instantaneous ionic current Adapted with permission from ref 348 Copyright 2012 American Chemical Society

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXX

several studies359363366 exploring rectification and ionselectivity A Langevin dynamics approach to study thetransport of flexible macromolecules in confined geometrieswas proposed by Peters372 Recently an atomic resolution BDmethod was developed by Comer and co-workers that was usedto study the sequence dependence of ionic current in syntheticnanopores373374 All-atom MD simulations have been usedwith considerable success to investigate nanopore transport ofDNA and ionic current blockades375376 nanopore unzipping ofDNA hairpins380 the microscopic origin of the electrophoreticforce on DNA in a nanopore378381 and the effect of electrolyteon the DNA translocation rates391 For detailed description ofthe simulation protocols interested readers are directed torecent reviews on this subject585639640

6 OUTLOOK

Advances in computational technologies and membraneprotein structure-determination methods are poised to makemodeling and simulations of ion channels an integral part offuture drug-development efforts The greatest obstacle so far isthe lack of atomic-resolution structures of the majority ofbiomedically relevant ion channels Several limitations pertainto the computational technology itself Whereas all-atommolecular dynamics simulation of an ion channel can providethe most detailed information about the microscopicmechanism of its function the method is currently limited bythe accuracy of the classical force field and the microsecondtime scale of the simulations on conventional computerclustersTremendous advances in addressing both limitations have

already been made The first computational studies of ionchannel systems using polarizable models have already beenreported277563 Thus it is very likely that a full polarizable forcefield will become available within the next 10 years Anothermajor advancement was the millisecond simulation of amembrane channel in its native environment that revealedthe microscopic details of its voltage-dependent gatingmechanism196 We hope that such a tremendous success ofspecial-purpose hardware will prompt the development ofcommodity special-purpose hardware which will make suchlong-time-scale simulations available to mainstream researchersFinally advances in computational methods will also aid thediscovery of atomic-resolution structures through either denovo structure prediction641 or refinement of low-resolution X-ray and cryo-EM structures443

It would be misleading however to think that all questionspertaining to ion channels would be answered through all-atomMD From a drug-development perspective high-throughputand accurate calculation of binding free energies of smallchemical compounds is more important than long-time-scalesimulations of a single channelrsquos action Enabling such high-throughput docking is dependent on the availability of accurategeneric force fields Furthermore as millisecond simulationsbecome more available describing possible chemical reactionsbetween components of the system will become increasinglyimportant Finally modeling a single channel in a membrane isonly a first step toward the realistic modeling of in vivoprocesses We anticipate continuum and implicit solventapproaches to play a pivotal role in the development ofdetailed quantitative models of realistic biological membranesand small organelles that incorporate an ensemble of ionchannels

AUTHOR INFORMATION

Corresponding Author

E-mail aksimentillinoisedu

Notes

The authors declare no competing financial interest

Biographies

Christopher Maffeo received his BSc in physics from the University of

California Santa Barbara in 2006 He joined the Aksimentiev group in

December 2006 After studying the structural and conductance

properties of the phospholamban pentamer he has focused his efforts

on understanding the kinetics energetics and electrostatics of various

DNAminusDNA and DNAminusprotein interactions

Swati Bhattacharya is a postdoctoral fellow in the group of Aleksei

Aksimentiev at the University of Illinois at UrbanaminusChampaign She

received her PhD in physics for work on the adsorption of polymers

at surfaces under the supervision of Thomas Vilgis in 2009 from the

Max Planck Institute for Polymer Research in Mainz Her current

research activities include computational modeling aimed at

developing applications of nanopores particularly for DNA sequencing

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXY

several studies359363366 exploring rectification and ionselectivity A Langevin dynamics approach to study thetransport of flexible macromolecules in confined geometrieswas proposed by Peters372 Recently an atomic resolution BDmethod was developed by Comer and co-workers that was usedto study the sequence dependence of ionic current in syntheticnanopores373374 All-atom MD simulations have been usedwith considerable success to investigate nanopore transport ofDNA and ionic current blockades375376 nanopore unzipping ofDNA hairpins380 the microscopic origin of the electrophoreticforce on DNA in a nanopore378381 and the effect of electrolyteon the DNA translocation rates391 For detailed description ofthe simulation protocols interested readers are directed torecent reviews on this subject585639640

6 OUTLOOK

Advances in computational technologies and membraneprotein structure-determination methods are poised to makemodeling and simulations of ion channels an integral part offuture drug-development efforts The greatest obstacle so far isthe lack of atomic-resolution structures of the majority ofbiomedically relevant ion channels Several limitations pertainto the computational technology itself Whereas all-atommolecular dynamics simulation of an ion channel can providethe most detailed information about the microscopicmechanism of its function the method is currently limited bythe accuracy of the classical force field and the microsecondtime scale of the simulations on conventional computerclustersTremendous advances in addressing both limitations have

already been made The first computational studies of ionchannel systems using polarizable models have already beenreported277563 Thus it is very likely that a full polarizable forcefield will become available within the next 10 years Anothermajor advancement was the millisecond simulation of amembrane channel in its native environment that revealedthe microscopic details of its voltage-dependent gatingmechanism196 We hope that such a tremendous success ofspecial-purpose hardware will prompt the development ofcommodity special-purpose hardware which will make suchlong-time-scale simulations available to mainstream researchersFinally advances in computational methods will also aid thediscovery of atomic-resolution structures through either denovo structure prediction641 or refinement of low-resolution X-ray and cryo-EM structures443

It would be misleading however to think that all questionspertaining to ion channels would be answered through all-atomMD From a drug-development perspective high-throughputand accurate calculation of binding free energies of smallchemical compounds is more important than long-time-scalesimulations of a single channelrsquos action Enabling such high-throughput docking is dependent on the availability of accurategeneric force fields Furthermore as millisecond simulationsbecome more available describing possible chemical reactionsbetween components of the system will become increasinglyimportant Finally modeling a single channel in a membrane isonly a first step toward the realistic modeling of in vivoprocesses We anticipate continuum and implicit solventapproaches to play a pivotal role in the development ofdetailed quantitative models of realistic biological membranesand small organelles that incorporate an ensemble of ionchannels

AUTHOR INFORMATION

Corresponding Author

E-mail aksimentillinoisedu

Notes

The authors declare no competing financial interest

Biographies

Christopher Maffeo received his BSc in physics from the University of

California Santa Barbara in 2006 He joined the Aksimentiev group in

December 2006 After studying the structural and conductance

properties of the phospholamban pentamer he has focused his efforts

on understanding the kinetics energetics and electrostatics of various

DNAminusDNA and DNAminusprotein interactions

Swati Bhattacharya is a postdoctoral fellow in the group of Aleksei

Aksimentiev at the University of Illinois at UrbanaminusChampaign She

received her PhD in physics for work on the adsorption of polymers

at surfaces under the supervision of Thomas Vilgis in 2009 from the

Max Planck Institute for Polymer Research in Mainz Her current

research activities include computational modeling aimed at

developing applications of nanopores particularly for DNA sequencing

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXY

Jejoong Yoo received his BSc in Physics and Molecular Biology fromSeoul National University (SNU) in 2001 and a PhD in Biophysicsfrom University of WisconsinMadison under the guidance of ProfQiang Cui for his study of membranes and membrane proteins usingmolecular dynamics simulations in 2005minus2010 In 2010 he joined theAksimentiev group in the Department of Physics at University ofIllinois at UrbanaminusChampaign as a postdoctoral fellow in Center forthe Physics of Living Cells He is currently interested in understandinghow the structural and dynamical properties of nucleic acid systems areeffectively modulated by various types of cations

David Wells received his BSc in Physics at the University ofWashington in 2005 He joined Professor Aksimentievrsquos group in 2006and has since performed MD simulation studies of proteins DNA andsynthetic nanopores He earned his PhD in physics from theUniversity of Illinois at UrbanaminusChampaign during the summer of2012

Aleksei Aksimentiev received his Masterrsquos degree in physics from theIvan Franko Lviv State University Lviv Ukraine and his PhD inchemistry from the Institute of Physical Chemistry Warsaw Poland

After a brief postdoctoral training at Mitsui Chemicals Japan hejoined the Theoretical and Computational Biophysics Group UrbanaIL as a Postdoctoral Research Associate In 2005 he became a FacultyMember of the Physics Department at the University of Illinois wherehe is currently a Professor of physics His research interests includesystems that combine biological macromolecules and man-madenanostructures membrane proteins and molecular machinery of DNAreplication

ACKNOWLEDGMENTS

This work was supported by the grants from the NationalScience Foundation (DMR-0955959 and PHY-0822613) andthe National Institutes of Health (R01-HG005115 and P41-RR005969) The authors gladly acknowledge supercomputertime provided through XSEDE Allocation Grant MCA05S028Department of Energy INCITE program the NationalResource for Biomedical Supercomputing at the DESRESsupercomputer Anton at the Pittsburgh SupercomputingCenter (PSCA00052) and the Taub Cluster (UIUC) AAwould like to thank the Department of Bionanosciences at DelftUniversity of Technology for hospitality and support from TheNetherlands Organisation for Scientific Research (NWO)

REFERENCES(1) Doyle D A Morais Cabral J Pfuetzner R A Kuo A GulbisJ M Cohen S L Chait B T MacKinnon R Science 1998 280 69(2) Jiang Y Lee A Chen J Ruta V Cadene M Chait B TMacKinnon R Nature 2003 423 33(3) Payandeh J Scheuer T Zheng N Catterall W Nature 2011475 353(4) Cha A Snyder G E Selvin P R Bezanilla F Nature 1999402 809(5) Glauner K Mannuzzu L Gandhi C Isacoff E Nature 1999402 813(6) Posson D Ge P Miller C Bezanilla F Selvin P Nature2005 436 848(7) Posson D J Selvin P R Neuron 2008 59 98(8) Kurnikova M G Coalson R D Graf P Nitzan A Biophys J1999 76 642(9) Hess K Ravaioli U Gupta M Aluru N Eisenberg R S VLSIDes 2001 13 179(10) Edwards S Corry B Kuyucak S Chung S-H Biophys J2002 83 1348(11) Nadler B Hollerbach U Eisenberg R Phys Rev E 2003 68021905(12) Coalson R D Kurnikova M G IEEE Trans Nanobiosci 20054 81(13) Cardenas A E Coalson R D Kurnikova M G Biophys J2000 79 80(14) Zheng Q Chen D Wei G-W J Comput Phys 2011 2305239(15) Zheng Q Wei G-W J Chem Phys 2011 134 194101(16) Bransburg-Zabary S Kessel A Gutman M Ben-Tal NBiochemistry 2002 41 6946(17) Krishnamurthy V Chung S-H IEEE Trans Nanobiosci 20065 126(18) Aringqvist J Warshel A Biophys J 1989 56 171(19) Roux B Prodrsquohom B Karplus M Biophys J 1995 68 876(20) Schumaker M F Pomes R Roux B Biophys J 2000 792840(21) Roux B Acc Chem Res 2002 35 366(22) Pomes R Roux B Biophys J 2002 82 2304(23) de Groot B L Tieleman D P Pohl P Grubmuller HBiophys J 2002 82 2934(24) Siva K Elber R Proteins Struct Funct Genet 2003 80 63

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXZ

(25) Bingham N C Smith N E C Cross T A Busath D DBiopolymers 2003 71 593(26) Yu C-H Pomes R J Am Chem Soc 2003 125 13890(27) Yu C-H Cukierman S Pomes R Biophys J 2003 84 816(28) Allen T W Andersen O S Roux B J Am Chem Soc 2003125 9868(29) Allen T W Andersen O S Roux B J Gen Physiol 2004124 679(30) Allen T W Andersen O S Roux B Proc Natl Acad SciUSA 2004 101 117(31) Liu Z Xu Y Tang P Biophys J 2005 88 3784(32) Corry B Chung S-H Eur Biophys J 2005 34 208(33) Bastug T Kuyucak S Eur Biophys J 2005 34 377(34) Bastug T Gray-Weale A Patra S M Kuyucak S Biophys J2006 90 2285(35) Allen T W Andersen O S Roux B Biophys Chem 2006124 251(36) Allen T W Andersen O S Roux B Biophys J 2006 903447(37) Mamonov A B Kurnikova M G Coalson R D BiophysChem 2006 124 268(38) Liu Z Xu Y Tang P J Phys Chem B 2006 110 12789(39) Kelkar D A Chattopadhyay A Biochim Biophys ActaBioenerg 2007 1768 2011(40) Bastug T Kuyucak S J Chem Phys 2007 126 105103(41) Bastug T Chen P-C Patra S M Kuyucak S J Chem Phys2008 128 155104(42) De Fabritiis G Coveney P V Villa-Freixa J Proteins StructFunct Bioinf 2008 73 185(43) Forney M Janosi L Kosztin I Phys Rev E 2008 78 1(44) Patel S Davis J E Bauer B A J Am Chem Soc 2009 13113890(45) Dryga A Warshel A J Phys Chem B 2010 114 12720(46) Li Y Andersen O S Roux B J Phys Chem B 2010 11413881(47) Balme S Janot J-m Berardo L Bonhenry D KraszewskiS Picaud F Ramseyer C Gerhardt I C Eug P Nano Lett 201111 712(48) Giorgino T De Fabritiis G J Chem Theory Comput 2011 71943(49) Kim T Lee K Morris P Pastor R Andersen O Im WBiophys J 2012 102 1551(50) Kato M Warshel A J Phys Chem B 2005 109 19516(51) Gordon D Krishnamurthy V Chung S-H J Chem Phys2009 131 134102(52) Mamonov A B Coalson R D Nitzan A Kurnikova M GBiophys J 2003 84 3646(53) Dorman V L Jordan P C Biophys J 2004 86 3529(54) Chen D Wei G-W J Chem Phys 2012 136 134109(55) Im W J Mol Biol 2002 322 851(56) Miedema H Meter-Arkema A Wierenga J Tang JEisenberg B Nonner W Hektor H Gillespie D Meijberg WBiophys J 2004 87 3137(57) Miedema H Vrouenraets M Wierenga J Gillespie DEisenberg B Meijberg W Nonner W Biophys J 2006 91 4392(58) Aguilella-Arzo M Garca-Celma J J Cervera J Alcaraz AAguilella V M Bioelectrochemistry 2007 70 320(59) Aguilella-Arzo M Andrio A Aguilella V M Alcaraz A PhysChem Chem Phys 2009 11 358(60) Garca-Gimenez E Lopez M L Aguilella V M Alcaraz ABiochem Biophys Res Commun 2011 404 330(61) Aguilella V M Queralt-Martn M Aguilella-Arzo M AlcarazA Integr Biol 2011 3 159(62) Im W Seefeld S Roux B Biophys J 2000 79 788(63) Im W Roux B J Chem Phys 2001 115 4850(64) Marreiro D Saraniti M Aboud S J Phys Condens Matter2007 19 215203(65) Tieleman T Berendsen B Biophys J 1998 74 2786

(66) Bond P J Faraldo-Gomez J D Sansom M S P Biophys J2002 83 763(67) Im W Roux B J Mol Biol 2002 319 1177(68) Zachariae U Helms V Engelhardt H Biophys J 2003 85954(69) Danelon C Suenaga A Winterhalter M Yamato I BiophysChem 2003 104 591(70) Varma S Jakobsson E Biophys J 2004 86 690(71) Varma S Chiu S-W W Jakobsson E Biophys J 2006 90112(72) Zachariae U Kluhspies T De S Engelhardt H Zeth K JBiol Chem 2006 281 7413(73) Khalid S Bond P J Deol S S Sansom M S P ProteinsStruct Funct Bioinf 2006 63 6(74) Bond P J Sansom M S P J Am Chem Soc 2006 128 2697(75) van Hijkoop V J Dammers A J Malek K Coppens M-O JChem Phys 2007 127 085101(76) Bond P J Derrick J P Sansom M S P Biophys J 2007 92L23(77) Chen M Khalid S Sansom M S P Bayley H Proc NatlAcad Sci USA 2008 105 6272(78) Chimerel C Movileanu L Pezeshki S Winterhalter MKleinekathofer U Eur Biophys J 2008 38 121(79) Pezeshki S Chimerel C Bessonov A N Winterhalter MKleinekathofer U Biophys J 2009 97 1898(80) Pongprayoon P Beckstein O Wee C L Sansom M S PProc Natl Acad Sci USA 2009 106 21614(81) Biro I Pezeshki S Weingart H Winterhalter MKleinekathofer U Biophys J 2010 98 1830(82) Kumar A Hajjar E Ruggerone P Ceccarelli M J PhysCondens Matter 2010 22 454125(83) Faraudo J Calero C Aguilella-Arzo M Biophys J 2010 992107(84) Vrouenraets M Miedema H Eur Biophys J 2010 39 1563(85) Calero C Faraudo J Aguilella-Arzo M Phys Rev E 2011 831(86) Modi N Singh P R Mahendran K R Schulz RWinterhalter M Kleinekath U J Phys Chem Lett 2011 2 2331(87) Singh P R Ceccarelli M Lovelle M Winterhalter MMahendran K R J Phys Chem B 2012 116 4433(88) Noskov S Y Im W Roux B Biophys J 2004 87 2299(89) Misakian M Kasianowicz J J J Membr Biol 2003 195 137(90) Aksimentiev A Schulten K Biophys J 2005 88 3745(91) Aguilella-Arzo M Aguilella V M Eur Phys J E 2010 31 429(92) Simakov N A Kurnikova M G J Phys Chem B 2010 11415180(93) Bhattacharya S Muzard J Payet L Bockelman UAksimentiev A Viasnoff V J Phys Chem C 2011 115 4255(94) Egwolf B Roux B J Mol Biol 2010 401 831(95) Egwolf B Luo Y Walters D E Roux B J Phys Chem B2010 114 2901(96) Shilov I Y Kurnikova M G J Phys Chem B 2003 107 7189(97) Mathe J Aksimentiev A Nelson D R Schulten K MellerA Proc Natl Acad Sci USA 2005 102 12377(98) Wells D B Abramkina V Aksimentiev A J Chem Phys2007 127 125101(99) Bond P J Guy A T Heron A J Bayley H Khalid SBiochemistry 2011 50 3777(100) OrsquoKeeffe J Cozmuta I Bose D Stolc V Chem Phys 2007342 25(101) Luo Y Egwolf B Walters D E Roux B J Phys Chem B2010 114 952(102) De Biase P M Solano C J F Markosyan S Czapla LNoskov S Y J Chem Theory Comput 2012 8 2540(103) Roux B Berneche S Im W Biochemistry 2000 39 13295(104) Grabe M Lecar H Jan Y N Jan L Y Proc Natl Acad SciUSA 2004 101 17640(105) Jogini V Roux B J Mol Biol 2005 354 272

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAA

(106) Robertson J L Palmer L G Roux B J Gen Physiol 2008132 613(107) Jung Y-W Lu B Mascagni M J Chem Phys 2009 131215101(108) Nekouzadeh A Rudy Y PLoS ONE 2011 6 e20186(109) Gardner C L Jones J R J Theor Biol 2011 291 10(110) Allen T W Chung S H Biochim Biophys Acta 2001 151583(111) Chung S-H Allen T W Kuyucak S Biophys J 2002 82628(112) Burykin A Kato M Warshel A Proteins Struct FunctGenet 2003 52 412(113) Berneche S Roux B Proc Natl Acad Sci USA 2003 1008644(114) Chung S-H Corry B Biophys J 2007 93 44(115) Hoyles M Krishnamurthy V Siksik M Chung S-HBiophys J 2008 94 366(116) Gordon D Chung S-H Biophys J 2011 101 2671(117) Gordon D Chen R Ho J Coote M L Chung S-H JPhys Chem B 2012 116 1933(118) Luzhkov V B Aringqvist J Biochim Biophys Acta 2000 1481360(119) Berneche S Roux B Biophys J 2000 78 2900(120) Aringqvist J Luzhkov V Nature 2000 404 881(121) Shrivastava I H Sansom M S Biophys J 2000 78 557(122) Luzhkov V B Aringqvist J FEBS Lett 2001 495 191(123) Luzhkov V B Aringqvist J Biochim Biophys Acta 2001 1548194(124) Ranatunga K M Shrivastava I H Smith G R Sansom MS Biophys J 2001 80 1210(125) Isralewitz B Baudry J Gullingsrud J Kosztin D SchultenK J Mol Graphics Modell 2001 19 13(126) Berneche S Roux B Nature 2001 414 73(127) Berneche S Roux B Biophys J 2002 82 772(128) Biggin P C Smith G R Shrivastava I Choe S SansomM S Biochim Biophys Acta 2001 1510 1(129) Capener C E Sansom M S P J Phys Chem B 2002 1064543(130) Sansom M S P Shrivastava I H Curr Biol 2002 12 R65(131) Bright J N Shrivastava I H Cordes F S Sansom M S PBiopolymers 2002 64 303(132) Shrivastava I H Peter Tieleman D Biggin P C SansomM S Biophys J 2002 83 633(133) Faraldo-Gomez J D Smith G R Sansom M S P EurBiophys J 2002 31 217(134) Shrivastava I H Sansom M S P Eur Biophys J 2002 31207(135) Sansom M S P Shrivastava I H Bright J N Tate JCapener C E Biggin P C Biochim Biophys Acta 2002 1565 294(136) Eriksson M A L Roux B Biophys J 2002 83 2595(137) Domene C Sansom M S P Biophys J 2003 85 2787(138) Luzhkov V B Osterberg F Aringqvist J FEBS Lett 2003 554159(139) Luzhkov V B Nilsson J Aringrhem P Aringqvist J BiochimBiophys Acta 2003 1652 35(140) Beckstein O Biggin P C Bond P Bright J N DomeneC Grottesi A Holyoake J Sansom M S FEBS Lett 2003 555 85(141) Noskov S Y Berneche S Roux B Nature 2004 431 830(142) Miloshevsky G V Jordan P C Trends Neurosci 2004 27308(143) Domene C Grottesi A Sansom M S P Biophys J 200487 256(144) Tieleman D P Robertson K M Maccallum J LMonticelli L Int J Quantum Chem 2004 100 1071(145) Monticelli L Robertson K M MacCallum J L TielemanD P FEBS Lett 2004 564 325(146) Treptow W Maigret B Chipot C Tarek M Biophys J2004 87 2365(147) Osterberg F Aringqvist J FEBS Lett 2005 579 2939

(148) Roux B Annu Rev Biophys Biomol Struct 2005 34 153(149) Luzhkov V B Aringqvist J Biochim Biophys Acta 2005 1747109(150) Sansom M S P Bond P J Deol S S Grottesi A HaiderS Sands Z A Biochem Soc Trans 2005 33 916(151) Khalili-Araghi F Tajkhorshid E Schulten K Biophys J2006 91 L72(152) Sands Z A Grottesi A Sansom M S P Biophys J 2006 901598(153) Hellgren M Sandberg L Edholm O Biophys Chem 2006120 1(154) Tieleman D P Clin Exp Pharmacol Physiol 2006 33 893(155) Freites J A Tobias D J White S H Biophys J 2006 91L90(156) Treptow W Tarek M Biophys J 2006 91 L81(157) Treptow W Tarek M Biophys J 2006 90 L64(158) Boiteux C Kraszewski S Ramseyer C Girardet C J MolModel 2007 13 699(159) Faraldo-Gomez J D Kutluay E Jogini V Zhao YHeginbotham L Roux B J Mol Biol 2007 365 649(160) Haider S Khalid S Tucker S J Ashcroft F M SansomM S P Biochemistry 2007 46 3643(161) Kona J Minozzi M Torre V Carloni P Theor Chem Acc2007 117 1121(162) Sands Z A Sansom M S P Structure 2007 15 235(163) Bostick D L Brooks C L Proc Natl Acad Sci USA 2007104 9260(164) Gwan J-F Baumgaertner A J Chem Phys 2007 127045103(165) Bond P J Sansom M Proc Natl Acad Sci USA 2007 1042631(166) Kutteh R Vandenberg J I Kuyucak S J Phys Chem B2007 111 1090(167) Pathak M M Yarov-Yarovoy V Agarwal G Roux BBarth P Kohout S Tombola F Isacoff E Y Neuron 2007 56 124(168) Noskov S Y Roux B Biophys Chem 2006 124 279(169) Domene C Cent Eur J Chem 2007 5 635(170) Tayefeh S Kloss T Thiel G Hertel B Moroni A Kast SM Biochemistry 2007 46 4826(171) Lindahl E Sansom M S P Curr Opin Struct Biol 2008 18425(172) Han M Zhang J Z H J Phys Chem B 2008 112 16966(173) Roux B Biophys J 2008 95 4205(174) Fowler P W Tai K Sansom M S P Biophys J 2008 955062(175) Recanatini M Cavalli A Masetti M ChemMedChem 20083 523(176) Piccinini E Ceccarelli M Affinito F Brunetti R BolognaI Fisica D Monserrato C Ca I-M Fisica D Methods 2008 173minus183(177) Sompornpisut P Roux B Perozo E Biophys J 2008 955349(178) Bjelkmar P Niemela P S Vattulainen I Lindahl E PLoSComput Biol 2009 5 e1000289(179) Treptow W Tarek M Klein M L J Am Chem Soc 2009131 2107(180) Domene C Furini S J Mol Biol 2009 389 637(181) Furini S Beckstein O Domene C Proteins Struct FunctBioinf 2009 74 437(182) Furini S Domene C Proc Natl Acad Sci USA 2009 10616074(183) Jensen M O Borhani D W Lindorff-Larsen K MaragakisP Jogini V Eastwood M P Dror R O Shaw D E Proc NatlAcad Sci USA 2010 107 5833(184) Anishkin A Milac A L Guy H R Proteins Struct FunctBioinf 2010 78 932(185) Khalili-Araghi F Jogini V Yarov-Yarovoy V TajkhorshidE Roux B Schulten K Biophys J 2010 98 2189

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAB

(186) Pan A C Cuello L G Perozo E Roux B J Gen Physiol2011 138 571(187) Bastug T Kuyucak S Biophys J 2011 100 629(188) Schiesaro A Ecker G F Prediction of hERG ChannelInhibition Using In Silico Techniques In Ion Channels and TheirInhibitors Gupta S P Ed Springer-Verlag BerlinHeidelberg 2011pp 191minus239(189) Delemotte L Tarek M Klein M L Amaral C TreptowW Proc Natl Acad Sci USA 2011 108 6109(190) Chakrapani S Cordero-Morales J F Jogini V Pan A CCortes D M Roux B Perozo E Nat Struct Mol Biol 2011 18 67(191) Furini S Domene C J Mol Biol 2011 409 867(192) Khalili-Araghi F Tajkhorshid E Roux B Schulten KBiophys J 2012 102 258(193) Knape K Linder T Wolschann P Beyer A Stary-Weinzinger A PLoS ONE 2011 6 e28778(194) Domene C Furini S Biochemistry 2012 51 1559(195) Yang H Gao Z Li P Yu K Yu Y Xu T-L Li M JiangH Biophys J 2012 102 1815(196) Jensen M O Jogini V Borhani D W Leffler A E DrorR O Shaw D E Science 2012 336 229(197) Treptow W Klein M L J Phys Chem Lett 2012 3 1017(198) Garofoli S Jordan P C Biophys J 2003 84 2814(199) Corry B Vora T Chung S-H Biochim Biophys Acta 20051711 72(200) Huetz P Boiteux C Compoint M Ramseyer C GirardetC J Chem Phys 2006 124 044703(201) Bisset D Chung S-H Biochim Biophys Acta 2008 17782273(202) Wee C L Gavaghan D Sansom M S P Biophys J 201098 1558(203) Mafe S Pellicer J Cervera J J Chem Phys 2005 122204712(204) Treptow W Marrink S-J Tarek M J Phys Chem B 2008112 3277(205) Dryga A Chakrabarty S Vicatos S Warshel A Proc NatlAcad Sci USA 2012 109 3335(206) Dryga A Chakrabarty S Vicatos S Warshel A BiochimBiophys Acta 2012 1818 303(207) Guidoni L Carloni P Biochim Biophys Acta 2002 1563 1(208) Bucher D Raugei S Guidoni L Dal Peraro MRothlisberger U Carloni P Klein M L Biophys Chem 2006124 292(209) Kariev A M Znamenskiy V S Green M E BiochimBiophys Acta 2007 1768 1218(210) Bucher D Guidoni L Maurer P Rothlisberger U J ChemTheory Comput 2009 5 2173(211) Bucher D Rothlisberger U J Gen Physiol 2010 135 549(212) Hung A Tai K Sansom M S P Biophys J 2005 88 3321(213) Law R J Henchman R H McCammon J A Proc NatlAcad Sci USA 2005 102 6813(214) Gao M Schulten K Biophys J 2006 90 3267(215) Xu Y Barrantes F J Luo X Chen K Shen J Jiang H JAm Chem Soc 2005 127 1291(216) Xu Y Barrantes F J Shen J Luo X Zhu W Chen KJiang H J Phys Chem B 2006 110 20640(217) Cheng X Wang H Grant B Sine S M McCammon J APLoS Comput Biol 2006 2 e134(218) Law R J Lightstone F C Biophys J 2009 97 1586(219) Brannigan G Lebard D N Henin J Eckenhoff R GKlein M L Proc Natl Acad Sci USA 2010 107 14122(220) Dimitropoulos N Papakyriakou A Dalkas G A ChasapisC T Poulas K Spyroulias G A Proteins Struct Funct Bioinf 201179 142(221) Chen X Cui Q Tang Y Yoo J Yethiraj A Biophys J2008 95 563(222) Tang Y Cao G Chen X Yoo J Yethiraj A Cui QBiophys J 2006 91 1248

(223) Tang Y Yoo J Yethiraj A Cui Q Chen X Biophys J2008 95 581(224) Li S Zhang X Wang W J Phys Chem B 2009 113 14431(225) Song C Corry B PLoS ONE 2011 6 e21204(226) Wiggins P Phillips R Proc Natl Acad Sci USA 2004 1014071(227) Wiggins P Phillips R Biophys J 2005 88 880(228) Ursell T Huang K C Peterson E Phillips R PLoSComput Biol 2007 3 e81(229) Vora T Corry B Chung S-H Biochim Biophys Acta 20061758 730(230) Kong Y Shen Y Warth T E Ma J Proc Natl Acad SciUSA 2002 99 5999(231) Sukharev S Durell S R Guy H R Biophys J 2001 81 917(232) Sukharev S Betanzos M Chiang C-S S Guy H RNature 2001 409 720(233) Betanzos M Chiang C-S S Guy H R Sukharev S NatStruct Biol 2002 9 704(234) Gullingsrud J Kosztin D Schulten K Biophys J 2001 802074(235) Elmore D E Dougherty D A Biophys J 2001 81 1345(236) Bilston L E Mylvaganam K FEBS Lett 2002 512 185(237) Colombo G Marrink S J Mark A E Biophys J 2003 842331(238) Gullingsrud J Schulten K Biophys J 2003 85 2087(239) Gullingsrud J Schulten K Biophys J 2004 86 3496(240) Elmore D E Dougherty D A Biophys J 2003 85 1512(241) Sotomayor M Schulten K Biophys J 2004 87 3050(242) Anishkin A Sukharev S Biophys J 2004 86 2883(243) Spronk S A Elmore D E Dougherty D A Biophys J 200690 3555(244) Sotomayor M Vasquez V Perozo E Schulten K Biophys J2007 92 886(245) Corry B Martinac B Biochim Biophys Acta 2008 17781859(246) Corry B Jayatilaka D Biophys J 2008 95 2711(247) Anishkin A Akitake B Kamaraju K Chiang C-SSukharev S J Phys Condens Matter 2010 22 454120(248) Gamini R Sotomayor M Chipot C Schulten K Biophys J2011 101 80(249) Meyer G R Gullingsrud J Schulten K Martinac BBiophys J 2006 91 1630(250) Debret G Valadie H Stadler A M Etchebest C ProteinsStruct Funct Genet 2008 71 1183(251) Jeon J Voth G A Biophys J 2008 94 3497(252) Monticelli L Kandasamy S Periole X Larson RTieleman D P Marrink S J J Chem Theory Comput 2008 4 819(253) Yefimov S van der Giessen E Onck P Marrink S JBiophys J 2008 94 2994(254) Louhivuori M Risselada H J van der Giessen E MarrinkS J Proc Natl Acad Sci USA 2010 107 19856(255) Corry B Hurst A C Pal P Nomura T Rigby PMartinac B J Gen Physiol 2010 136 483(256) Vasquez V Sotomayor M Cordero-Morales J Schulten KPerozo E Science 2008 321 1210(257) Vasquez V Sotomayor M Cortes D M Roux B SchultenK Perozo E J Mol Biol 2008 378 55(258) Sotomayor M van der Straaten T A Ravaioli U SchultenK Biophys J 2006 90 3496(259) Choudhary O P Ujwal R Kowallis W Coalson RAbramson J Grabe M J Mol Biol 2010 396 580(260) Cohen J Schulten K Biophys J 2004 86 836(261) Suenaga A Yeh J Z Taiji M Toyama A Takeuchi HSon M Takayama K Iwamoto M Sato I Narahashi TKonagaya A Goto K Biophys Chem 2006 120 36(262) Rui H Lee K I Pastor R W Im W Biophys J 2011 100602(263) Krammer E-M Homble F Prevost M PLoS One 2011 6e27994

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAC

(264) Cheng M H Coalson R D Biophys J 2012 102 1363(265) Corry B OrsquoMara M Chung S-H Biophys J 2004 86 846(266) Bisset D Corry B Chung S-H Biophys J 2005 89 179(267) Cheng M H Mamonov A B Dukes J W Coalson R D JPhys Chem B 2007 111 5956(268) Lee K I Rui H Pastor R W Im W Biophys J 2011 100611(269) Burykin A Warshel A Biophys J 2003 85 3696(270) Stroud R M Savage D Miercke L J Lee J K KhademiS Harries W FEBS Lett 2003 555 79(271) Jensen M O Tajkhorshid E Schulten K Biophys J 200385 2884(272) de Groot B L Frigato T Helms V Grubmuller H J MolBiol 2003 333 279(273) Chen H Wu Y Voth G A Biophys J 2006 90 L73(274) Wang Y Tajkhorshid E J Nutr 2007 137 1509S(275) Bostick D L Brooks C L PLoS Comput Biol 2007 3 e22(276) Bostick D L Charles L L B Biophys J 2007 92 L103(277) Wang S Orabi E A Baday S Berneche S Lamoureux GJ Am Chem Soc 2012 134 10419(278) Luzhkov V B Almlof M Nervall M Aringqvist J Biochemistry2006 45 10807(279) Levitt D G Biophys J 1991 59 271(280) Barcilon V Chen D-P Eisenberg R SIAM J App Math1992 52 1405(281) Chen D P Barcilon V Eisenberg R S Biophys J 1992 611372(282) Chen D Eisenberg R Biophys J 1993 64 1405(283) Chen D P Eisenberg R S Biophys J 1993 65 727(284) Chen D Xu L Tripathy a Meissner G Eisenberg BBiophys J 1997 73 1337(285) Chen D Lear J Eisenberg B Biophys J 1997 72 97(286) Syganow A von Kitzing E J Phys Chem 1995 99 12030(287) Moy G Corry B Kuyucak S Chung S-H Biophys J 200078 2349(288) Corry B Kuyucak S Chung S H Biophys J 2000 78 2364(289) Crozier P Rowley R Holladay N Henderson D BusathD Phys Rev Lett 2001 86 2467(290) Gillespie D Nonner W Eisenberg R S J Phys CondensMatter 2002 14 12129(291) Gillespie D Nonner W Eisenberg R Phys Rev E 2003 681(292) Koumanov A Zachariae U Engelhardt H Karshikoff AEur Biophys J 2003 32 689(293) Kuyucak S Bastug T J Biophys 2003 29 429(294) Corry B Kuyucak S Chung S-H Biophys J 2003 84 3594(295) Beckstein O Tai K Sansom M S P J Am Chem Soc 2004126 14694(296) Graf P Kurnikova M G Coalson R D Nitzan A J PhysChem B 2004 108 2006(297) Kessel A Tieleman D P Ben-Tal N Eur Biophys J 200433 16(298) Baumgartner W Comput Biol Chem 2004 28 67(299) Roux B Allen T Bernche S Im W Q Rev Biophys 200437 15(300) Gillespie D Xu L Wang Y Meissner G J Phys Chem B2005 109 15598(301) Aguilella-Arzo M Aguilella V M Eisenberg R S EurBiophys J 2005 34 314(302) Cheng M H Coalson R D J Phys Chem B 2005 109 488(303) Hwang H Schatz G C Ratner M A J Phys Chem B 2006110 6999(304) Kandt C Ash W L Tieleman D P Methods 2007 41 475(305) Singer A Norbury J SIAM J Appl Math 2009 70 949(306) Bolintineanu D S Sayyed-Ahmad A Davis H T KaznessisY N PLoS Comput Biol 2009 5 e1000277(307) Eisenberg B J Phys Chem C 2010 114 20719(308) Eisenberg B Chem Phys Lett 2011 511 1(309) Lu B Zhou Y Biophys J 2011 100 2475

(310) Eisenberg B Adv Chem Phys 2012 77minus223(311) Krishnamurthy V Chung S-H IEEE Trans Nanobiosci 20054 102(312) Vora T Bisset D Chung S-H Biophys J 2008 95 1600(313) Gordon D Krishnamurthy V Chung S-H Mol Phys 2008106 1353(314) Vora T Corry B Chung S-H Eur Biophys J 2008 38 45(315) Song C Corry B Biophys J 2010 98 404(316) Krishnamurthy V Luk K Y IEEEACM Trans Comput BiolBioinf 2011 8 273(317) Lee K I Jo S Rui H Egwolf B Roux B Pastor R WIm W J Comput Chem 2012 33 331(318) Csanyi E Boda D Gillespie D Kristof T Biochim BiophysActa 2012 1818 592(319) Smondyrev A M Voth G A Biophys J 2002 83 1987(320) Domene C Bond P J Sansom M S P Adv Protein Chem2003 66 159(321) Tarek M Maigret B Chipot C Biophys J 2003 85 2287(322) Biggin P C Grottesi A Sansom M S P From Prokaryotesto Eukaryotes Molecular Modeling and Simulation Studies of IonChannels In Bacterial Ion Channels And Their Eukaryotic HomologsKubalski A Martinac B Eds ASM Press Washington DC 2005pp 133minus152(323) Tajkhorshid E Cohen J Aksimentiev A Sotomayor MSchulten K Towards an Understanding of Membrane Channels InBacterial Ion Channels And Their Eukaryotic Homologs Kubalski AMartinac B Eds ASM Press Washington DC 2005 pp 133minus152(324) Gumbart J Wang Y Aksimentiev A Tajkhorshid ESchulten K Curr Opin Struct Biol 2005 15 423(325) Hwang H Schatz G C Ratner M A J Phys Chem B 2006110 26448(326) Carpenter T Bond P J Khalid S Sansom M S P BiophysJ 2008 95 3790(327) Shaikh S A Tajkhorshid E Biophys J 2008 95 5153(328) Pietra F J Phys Org Chem 2008 21 997(329) Delemotte L Dehez F Treptow W Tarek M J PhysChem B 2008 112 5547(330) Maffeo C Aksimentiev A Biophys J 2009 96 4853(331) Patargias G Martay H Fischer W B J Biomol Struct Dyn2009 27 1(332) Mustafa M Henderson D J Busath D D Proteins StructFunct Bioinf 2009 76 794(333) Khalili-Araghi F Gumbart J Wen P-C Sotomayor MTajkhorshid E Schulten K Curr Opin Struct Biol 2009 19 128(334) Khurana E Dal Peraro M DeVane R Vemparala SDeGrado W F Klein M L Proc Natl Acad Sci USA 2009 1061069(335) Pan J Tieleman D P Nagle J F Kucerka N Tristram-Nagle S Biochim Biophys Acta 2009 1788 1387(336) Nury H Poitevin F Van Renterghem C Changeux J-PCorringer P-J Delarue M Baaden M Proc Natl Acad Sci USA2010 107 6275(337) Cheng M H Coalson R D Tang P J Am Chem Soc 2010132 16442(338) Zhu F Hummer G Proc Natl Acad Sci USA 2010 10719814(339) Kutzner C Grubmuller H de Groot B L Zachariae UBiophys J 2011 101 809(340) Wilson M A Wei C Bjelkmar P Wallace B A PohorilleA Biophys J 2011 100 2394(341) Stansfeld P J Sansom M S P Structure 2011 19 1562(342) Chen C-C Kruger J Sramala I Hsu H-J Henklein PChen Y-M A Fischer W B Biochim Biophys Acta 2011 1808 572(343) Raunest M Kandt C Biochemistry 2012 51 1719(344) Furini S Domene C PLoS Comput Biol 2012 8 e1002476(345) Becucci L Cembran A Karim C B Thomas D DGuidelli R Gao J Veglia G Biophys J 2009 96 L60(346) Gumbart J Khalili-Araghi F Sotomayor M Roux BBiochim Biophys Acta 2011 1818 294

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAD

(347) Carnevale V Treptow W Klein M L J Phys Chem Lett2011 2 2504(348) Bhattacharya S Derrington I M Pavlenok M NiederweisM Gundlach J H Aksimentiev A ACS Nano 2012 6 6960(349) Graf P Nitzan A Kurnikova M G Coalson R D J PhysChem B 2000 104 12324(350) Peter C Hummer G Biophys J 2005 89 2222(351) Boda D Valisko M Eisenberg B Nonner W HendersonD Gillespie D Phys Rev Lett 2007 98 1(352) Thoslashgersen L Schioslashtt B Vosegaard T Nielsen N CTajkhorshid E Biophys J 2008 95 4337(353) Plank G Zhou L Greenstein J L Cortassa S Winslow RL OrsquoRourke B Trayanova N A Philos Trans R Soc A 2008 3663381(354) Eisenberg B Hyon Y Liu C J Chem Phys 2010 133104104(355) Hannongbua S Treesuwan W Boonyarat W AdvancedMolecular Modeling Techniques Applied to Ion Channels Blockers InIon Channels and Their Inhibitors Gupta S P Ed Springer-VerlagBerlinHeidelberg 2011 pp 53minus78(356) Zheng W Auerbach A PLoS Comput Biol 2011 7e1001046(357) Boda D Busath D D Eisenberg B Henderson DNonner W Phys Chem Chem Phys 2002 4 5154(358) Boda D Henderson D Busath D D Mol Phys 2002 1002361(359) Cervera J Schiedt B Ramirez P Europhys Lett 2005 7135(360) Vidal J Gracheva M E Leburton J-P Nanoscale Res Lett2006 2 61(361) Gracheva M Leburton J-P Nanotechnology 2007 18145704(362) Vidal J Gracheva M Leburton J-P Nanoscale Res Lett2007 2 61(363) Cervera J Alcaraz A Schiedt B Neumann R Ramirez PJ Phys Chem C 2007 111 12265(364) Vlassiouk I Smirnov S Siwy Z Nano Lett 2008 8 1978(365) Gillespie D Boda D He Y Apel P Siwy Z S Biophys J2008 95 609(366) Kosin ska I D Hanggi P Phys Rev E 2008 77 1(367) Reiner J E Kasianowicz J J Nablo B J Robertson J W FProc Natl Acad Sci USA 2010 107 12080(368) Zhang Y Voth G A J Chem Theory Comput 2011 7 2277(369) Zhang M Yeh L Qian S Hsu J J Phys Chem C 2012116 4793(370) Yeh L-h Zhang M Qian S Hsu J-p Tseng S J PhysChem C 2012 116 8672(371) Carr R Comer J Ginsberg M Aksimentiev A Lab Chip2011 11 3766(372) Peters M H J Chem Phys 2011 134 025105(373) Comer J Aksimentiev A J Phys Chem C 2012 116 3376(374) Timp W Comer J Aksimentiev A Biophys J 2012 102L37(375) Aksimentiev A Heng J B Timp G Schulten K Biophys J2004 87 2086(376) Heng J B Aksimentiev A Ho C Marks P Grinkova YV Sligar S Schulten K Timp G Biophys J 2006 90 1098(377) Lu D Aksimentiev A Shih A Y Cruz-Chu E FreddolinoP L Arkhipov A Schulten K Phys Bio 2006 3 S40(378) Luan B Aksimentiev A Phys Rev E 2008 78 021912(379) Carr R Weinstock I A Sivaprasadarao A Muller AAksimentiev A Nano Lett 2008 8 3916(380) Comer J Dimitrov V Zhao Q Timp G Aksimentiev ABiophys J 2009 96 593(381) Luan B Aksimentiev A J Phys Condens Matter 2010 22454123(382) Gracheva M Xiong A Aksimentiev A Schulten K TimpG Leburton J-P Nanotechnology 2006 17 622

(383) Gracheva M Aksimentiev A Leburton J-P Nanotechnology2006 17 3160(384) Sigalov G Comer J Timp G Aksimentiev A Nano Lett2008 8 56(385) Cruz-Chu E R Aksimentiev A Schulten K J Phys Chem C2009 113 1850(386) Dorvel B Sigalov G Zhao Q Comer J Dimitrov VMirsaidov U Aksimentiev A Timp G Nucleic Acids Res 2009 374170(387) Wang D Timp W Shim J Mirsaidov U Comer JAksimentiev A Timp G Biophys J 2010 98 599a(388) Comer J Aksimentiev A Nanopore Force SpectroscopyInsights from Molecular Dynamics Simulations In Nanopores Sensingand Fundamental Biological Interactions Bashir R Iqbal S EdsSpringer Science and Business Media LLC New York 2011 Chapter14 pp 335minus356(389) Sathe C Zou X Leburton J-P Schulten K ACS Nano2011 5 8842(390) Wanunu M Bhattacharya S Xie Y Tor Y AksimentievA Drndic M ACS Nano 2011 5 9345(391) Kowalczyk S W Wells D B Aksimentiev A Dekker CNano Lett 2012 12 1038(392) Wells D B Belkin M Comer J Aksimentiev A Nano Lett2012 8 4117(393) Edmonds C M Hudiono Y C Ahmadi A G Hesketh PJ Nair S J Chem Phys 2012 136 065105(394) Saha K K Drndic M Nikolic B K Nano Lett 2012 12 50(395) Hille B Ionic channels of excitable membranes 3rd ed SinauerAssociates Sunderland MA 2001(396) Hodgkin A L Huxley A F J Physiol 1952 117 500(397) Hodgkin A L Huxley A F J Physiol 1952 117 500(398) Alberts B Johnson A Lewis J Raff M Roberts K WalterP Molecular Biology of The Cell 5th ed Garland Science New York ampLondon 2007(399) Watanabe H Sugiura S Kafuku H Hisada T Biophys J2004 87 2074(400) Wong J Goktepe S Kuhl E Comput Methods Appl MechEngrg 2011 200 3139(401) Rowat P Neur Comp 2007 19 1215(402) Tuckwell H C Jost J Physica A 2009 388 4115(403) Linaro D Storace M Giugliano M PLoS Comput Biol2011 7 e1001102(404) Che Y-Q Wang J Zhou S-S Deng B Chaos SolitonsFractals 2009 40 1588(405) Beard D A PLoS Comput Biol 2005 1 e36(406) Townsley L E Tucker W A Sham S Hinton J FBiochemistry 2001 40 11676(407) Chang G Spencer R H Lee A T Barclay M T Rees DC Science 1998 282 2220(408) Bass R B Strop P Barclay M Rees D C Science 2002298 1582(409) Conroy M J Durand A Lupo D Li X-D D BulloughP A Winkler F K Merrick M Proc Natl Acad Sci USA 2007104 1213(410) Uysal S Vasquez V Tereshko V Esaki K Fellouse FSidhu S Koide S Perozo E Kossiakoff A Proc Natl Acad SciUSA 2009 106 6644(411) Long S B Tao X Campbell E B MacKinnon R Nature2007 450 376(412) Gonen T Cheng Y Sliz P Hiroaki Y Fujiyoshi YHarrison S C Walz T Nature 2005 438 633(413) Miyazawa A Fujiyoshi Y Unwin N Nature 2003 423 949(414) Unwin N J Mol Biol 2005 346 967(415) Cowan S Schirmer T Rummel G Steiert M Ghosh RPauptit R Jansonius J Rosenbusch J Nature 1992 358 727(416) Dutzler R Campbell E B MacKinnon R Science 2003 300108(417) Song L Hobaugh M R Shustak C Cheley S Bayley HGouaux J E Science 1996 274 1859

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAE

(418) Malasics A Gillespie D Nonner W Henderson DEisenberg B Boda D Biochim Biophys Acta Biomembr 2009 17882471(419) Giri J Fonseca J Boda D Henderson D Eisenberg BPhys Bio 2011 8 026004(420) Mackay D H Berens P H Wilson K R Hagler A TBiophys J 1984 46 229(421) Morais-Cabral J H Zhou Y MacKinnon R Nature 2001414 37(422) Wulff H Calabresi P A Allie R Yun S Pennington MBeeton C Chandy K G J Clin Invest 2003 111 1703(423) Judge S I V Bever C T Pharmacol Ther 2006 111 224(424) Parsegian A Nature 1969 221 844(425) Rashid M H Kuyucak S J Phys Chem B 2012 116 4812(426) Kung C Nature 2005 436 647(427) Kung C Martinac B Sukharev S Annu Rev Microbiol2010 64 313(428) Sukharev S I Blount P Martinac B Blattner F R KungC Nature 1994 368 265(429) Levina N Totemeyer S Stokes N R Louis P Jones MA Booth I R EMBO J 1999 18 1730(430) Wang W Black S S Edwards M D Miller S Morrison EL Bartlett W Dong C Naismith J H Booth I R Science 2008321 1179(431) Liu Z Gandhi C S Rees D C Nature 2009 461 120(432) Martinac B Buechner M Delcour A H Adler J Kung CProc Natl Acad Sci USA 1987 84 2297(433) Weiss M S Schulz G E J Mol Biol 1992 227 493(434) Kreusch A Schulz G J Mol Biol 1994 243 891(435) Cowan S W Garavito R M Jansonius J N Jenkins J AKarlsson R Konig N Pai E F Pauptit R A Rizkallah P JRosenbusch J P Structure 1995 3 1041(436) Schirmer T Keller T A Wang Y F Rosenbusch J PScience 1995 267 512(437) Dutzler R Rummel G Albert S Hernandez-Alles S PhaleP Rosenbusch J Bened V Schirmer T Structure 1999 7 425(438) Moraes T F Bains M Hancock R E W Strynadka N CJ Nat Struct Mol Biol 2007 14 85(439) Biswas S Mohammad M M Movileanu L van der Berg BStructure 2008 16 1027(440) Tamber S Hancock R E W FEMS Microbiol Lett 2006260 23(441) Liu J Eren E Vijayaraghavan J Cheneke B R Indic Mvan den Berg B Movileanu L Biochemistry 2012 51 2319(442) Cheneke B R van der Berg B Movileanu L Biochemistry2011 50 4987(443) Cheneke B R Indic M van den Berg B Movileanu LBiochemistry 2012 51 5348(444) Vila J Mart S Sanchez-Cespedes J J Antimicrob Chemother2007 59 1210(445) Song L Hobaugh M R Shustak C Cheley S Bayley HGouaux J E Science 1996 274 1859(446) Kasianowicz J Robertson J W F Chan E R Reiner J EStanford V M Annu Rev Anal Chem 2008 1 737(447) Kasianowicz J J Brandin E Branton D Deamer D WProc Natl Acad Sci USA 1996 93 13770(448) Faller R Neiderweis M Schulz G E Science 2004 3031189(449) Butler T Pavlenok M Derrington I Niederweis MGundlach J Proc Natl Acad Sci USA 2008 105 20647(450) Derrington I M Collins M D Pavlenok M NiederweisM Gundlach J H Biophys J 2010 98 422a(451) Manrao E Derrington I Pavlenok M Niederweis MGundlach J PLoS One 2011 6 e25723(452) Roos N Benz R Brdiczka D Biochim Biophys Acta 1982686 204(453) Hiller S Garces R G Malia T J Orekhov V YColombini M Wagner G Science 2008 321 1206

(454) Ujwal R Cascio D Colletier J-P Faham S Zhang JToro L Ping P Proc Natl Acad Sci USA 2008 105 2(455) Bayrhuber M Meins T Habeck M Becker S Giller KVillinger S Vonrhein C Griesinger C Zweckstetter M Zeth KProc Natl Acad Sci USA 2008 105 15370(456) Colombini M Trends Biochem Sci 2009 34 382(457) Hiller S Abramson J Mannella C Wagner G Zeth KTrends Biochem Sci 2010 35 514(458) Hiller S Raschle T Yu T-Y Rice A J Walz T WagnerG Biochim Biophys Acta Bioenerg 2010 1797 66(459) Chen T-Y Annu Rev Physiol 2005 67 809(460) Dutzler R Campbell E B Cadene M Chait B TMacKinnon R Nature 2002 415 287(461) Accardi A Miller C Nature 2004 427 803(462) Steinlein O K Bertrand D Biochem Pharmacol 2008 761175(463) Rose J E Biochem Pharmacol 2007 74 1263(464) Marini A M Soussi-Boudekou S Vissers S Andre B MolCell Biol 1997 17 4282(465) Ninnemann O Jauniaux J C Frommer W B EMBO J1994 13 3464(466) Marini A M Vissers S Urrestarazu A Andre B EMBO J1994 13 3456(467) Khademi S OrsquoConnell J Remis J Robles-Colmenares YMiercke L J W Stroud R M Science 2004 305 1587(468) Javelle A Lupo D Ripoche P Fulford T Merrick MWinkler F K Proc Natl Acad Sci USA 2008 105 5040(469) Gruswitz F OrsquoConnell J Stroud R M Proc Natl Acad SciUSA 2007 104 42(470) Javelle A Lupo D Zheng L Li X-D D Winkler F KMerrick M J Biol Chem 2006 281 39492(471) Gao J Truhlar D G Annu Rev Phys Chem 2002 53 467(472) Kamerlin S C L Vicatos S Dryga A Warshel A AnnuRev Phys Chem 2011 62 41(473) Modi N Winterhalter M Kleinekathofer U Nanoscale2012 4 6166(474) Maffeo C Schopflin R Brutzer H Stehr R AksimentievA Wedemann G Seidel R Phys Rev Lett 2010 105 158101(475) Simonson T Carlsson J Case D A J Am Chem Soc 2004126 4167(476) Rocchia W Alxov E Honig B J Phys Chem B 2001 1056507(477) Baker N Sept D Joseph S Hoist M McCammon J ProcNatl Acad Sci USA 2001 98 10037(478) Ramrez P Aguilella-Arzo M Alcaraz A Cervera JAguilella V M Cell Biochem Biophys 2006 44 287(479) Woolley G Biggin P Schultz A Lien L Jaikaran DBreed J Crowhurst K Sansom M Biophys J 1997 73 770(480) Nonner W Chen D Eisenberg B Biophys J 1998 74 2327(481) Roth R J Phys Condens Matter 2010 22 063102(482) Woolf T Roux B Proc Natl Acad Sci USA 1994 9111631(483) Hummer G New J Phys 2005 7 34(484) Paine P L Scherr P Biophys J 1975 15 1087(485) Roux B Biophys J 1999 77 139(486) Corry B Allen T Kuyucak S Chung S Biophys J 200180 195(487) Cooper K Jakobsson E Wolynes P Prog Biophys Mol Biol1985 46 51(488) Mackerell A D J Comput Chem 2004 25 1584(489) MacKerell D A Bashford D Bellott Dunbrack L REvanseck J D Field M J Fischer S Gao J Guo H Ha SJoseph-McCarthy D Kuchnir L Kuczera K Lau F T K MattosC Michnick S Ngo T Nguyen D T Prodhom B Reiher W ERoux B Schlenkrich M Smith J C Stote R Straub J WatanabeM Wiorkiewicz-Kuczera J Yin D Karplus M J Phys Chem B1998 102 3586(490) Weiner P K Kollman P A J Comput Chem 1981 2 287

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAF

(491) Cornell W D Cieplak P Bayly C I Gould I R Merz KM Ferguson D M Spellmeyer D C Fox T Caldwell J WKollman P A J Am Chem Soc 1995 117 5179(492) Jorgensen W L Maxwell D S Tirado-Rives J J Am ChemSoc 1996 118 11225(493) Kaminski G A Friesner R A Tirado-Rives J Jorgensen WL J Phys Chem B 2001 105 6474(494) Hermans J Berendsen H J C Van Gunsteren W FPostma J P M Biopolymers 1984 23 1513(495) Schmid N Eichenberger A P Choutko A Riniker SWinger M Mark A E van Gunsteren W F Eur Biophys J 201140 843(496) Klauda J B Venable R M Freites J A OrsquoConnor J WTobias D J Mondragon-Ramirez C Vorobyov I MacKerell A DPastor R W J Phys Chem B 2010 114 7830(497) Wang J Wolf R M Caldwell J W Kollman P A Case DA J Comput Chem 2004 25 1157(498) Liu Y Chipot C Shao X Cai W Phys Bio 2011 8056005(499) Daura X Mark A E van Gunsteren W F J Comput Chem1998 19 535(500) Berger O Edholm O Jahnig F Biophys J 1997 72 2002(501) Cordomiacute A Caltabiano G Pardo L J Chem TheoryComput 2012 8 948(502) Aksimentiev A Wells D Sotomayor M Membrane ProteinTutorial httpwwwksuiuceduTrainingTutorialssciencemembranemem-tutorialpdfrelax(503) Humphrey W Dalke A Schulten K J Mol Graphics 199614 33(504) Brooks B R Bruccoleri R E Olafson B D States D JSwaminathan S Karplus M J Comput Chem 1983 187(505) Jo S Lim J B Klauda J B Im W Biophys J 2009 97 50(506) Ayton G S Voth G A Curr Opin Struct Biol 2009 19 138(507) Marrink S J de Vries A H Tieleman D P BiochimBiophys Acta 2009 1788 149(508) Nielsen S O Lopez C F Srinivas G Klein M L J PhysCondens Matter 2004 16 R481(509) Yesylevskyy S O Schafer L V Sengupta D Marrink S JPLoS Comput Biol 2010 6 e1000810(510) Wu Z Cui Q Yethiraj A J Phys Chem B 2010 114 10524(511) Sali A Blundell T L J Mol Biol 1993 234 779(512) Capener C E Shrivastava I H Ranatunga K M Forrest LR Smith G R Sansom M S Biophys J 2000 78 2929(513) Roux B Comput Phys Commun 1995 91 275(514) Kollman P Chem Rev 1993 93 2395(515) Pohorille A Jarzynski C Chipot C J Phys Chem B 2010114 10235(516) Torrie G Valleau J J Comput Phys 1977 23 187(517) Kumar S Bouzida D Swendsen R H Kollman P ARosenberg J M J Comput Chem 1992 13 1011(518) Woo H-J Roux B Proc Natl Acad Sci USA 2005 1026825(519) Singh U C Brown F K Bash P A Kollman P A J AmChem Soc 1987 109 1607(520) Grubmuller H Heymann B Tavan P Science 1996 271997(521) Isralewitz B Izrailev S Schulten K Biophys J 1997 732972(522) Izrailev S Stepaniants S Balsera M Oono Y Schulten KBiophys J 1997 72 1568(523) Stepaniants S Izrailev S Schulten K J Mol Mod 1997 3473(524) Marrink S-J Berger O Tieleman P Jahnig F Biophys J1998 74 931(525) Kosztin D Izrailev S Schulten K Biophys J 1999 76 188(526) Hummer G Szabo A Acc Chem Res 2005 38 504(527) Jarzynski C Phys Rev Lett 1997 78 2690(528) Bucher D Guidoni L Rothlisberger U Biophys J 2007 932315

(529) Arkin I T Xu H F Jensen M O Arbely E Bennett E RBowers K J Chow E Dror R O Eastwood M P Flitman-TeneR Gregersen B A Klepeis J L Kolossvary I Shan Y B Shaw DE Science 2007 317 799(530) Warshel A Sussman F King G Biochemistry 1986 25 8368(531) Li L Vorobyov I Mackerell A D Allen T W Biophys J2007 94 L11(532) Li L Vorobyov I Allen T W J Phys Chem B 2008 1129574(533) Yoo J Cui Q Biophys J 2008 94 L61(534) MacCallum J L Bennett W F D Tieleman D P Biophys J2008 94 3393(535) Yoo J Cui Q Biophys J 2010 99 1529(536) Johansson A C V Lindahl E J Phys Chem B 2009 113245(537) Honig B Sharp K Yang A S J Phys Chem 1993 97 1101(538) Lim C Bashford D Karplus M J Phys Chem 1991 955610(539) Warshel A Papazyan A Curr Opin Struct Biol 1998 8 211(540) Ullmann G M Knapp E-W Eur Biophys J 1999 28 533(541) Srinivasan J Trevathan M W Beroza P Case D A TheorChem Acc 1999 101 426(542) Koumanov A Ruterjans H Karshikoff A Proteins StructFunct Genet 2002 46 85(543) Mongan J Case D A McCammon J A J Comput Chem2004 25 2038(544) Mongan J Case D A Curr Opin Struct Biol 2005 15 157(545) Khandogin J Brooks C L Biochemistry 2006 45 9363(546) Gunner G Mao J Song Y Kim J Biochim Biophys ActaBioenerg 2006 1757 942(547) Spassov V Z Yan L Protein Sci 2008 17 1955(548) Karshikoff A Spassov V Cowan S W Ladenstein RSchirmer T J Mol Biol 1994 240 372(549) Tanizaki S Feig M J Chem Phys 2005 122 124706(550) Gordon J C Myers J B Folta T Shoja V Heath L SOnufriev A Nucleic Acids Res 2005 33 W368(551) Olsson M H M Soslashndergaard C R Rostkowski M JensenJ H J Chem Theory Comput 2011 7 525(552) Jo S Vargyas M Vasko-Szedlar J Roux B Im W NucleicAcids Res 2008 36 W270(553) Shaw D E Chao J C Eastwood M P Gagliardo JGrossman J P P Ho C R Lerardi D J Kolossvary I Klepeis JL Layman T McLeavey C Deneroff M M Moraes M AMueller R Priest E C Shan Y Spengler J Theobald M TowlesB Wang S C Dror R O Kuskin J S Larson R H Salmon J KYoung C Batson B Bowers K J Commun ACM 2008 51 91(554) Shaw D E J Comput Chem 2005 26 1318(555) Dror R O Jensen M O Borhani D W Shaw D E J GenPhysiol 2010 135 555(556) Dror R O Dirks R M Grossman J P Xu H Shaw D EAnnu Rev Biochem 2012 41 429(557) Dror R O Pan A C Arlow D H Borhani D WMaragakis P Shan Y Xu H Shaw D E Proc Natl Acad Sci USA2011 108 13118(558) Rosenbaum D M Zhang C Lyons J A Holl R AragaoD Arlow D H Rasmussen S G F Choi H-J J Devree B TSunahara R K Chae P S Gellman S H Dror R O Shaw D EWeis W I Caffrey M Gmeiner P Kobilka B K Nature 2011 469236(559) Kruse A C Hu J Pan A C Arlow D H Rosenbaum DM Rosemond E Green H F Liu T Chae P S Dror R OShaw D E Weis W I Wess J Kobilka B K Nature 2012 482552(560) Jensen M O Dror R O Xu H F Borhani D W Arkin IT Eastwood M P Shaw D E Proc Natl Acad Sci USA 2008105 14430(561) Vorobyov I V Anisimov V M MacKerell A D J PhysChem B 2005 109 18988

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAG

(25) Bingham N C Smith N E C Cross T A Busath D DBiopolymers 2003 71 593(26) Yu C-H Pomes R J Am Chem Soc 2003 125 13890(27) Yu C-H Cukierman S Pomes R Biophys J 2003 84 816(28) Allen T W Andersen O S Roux B J Am Chem Soc 2003125 9868(29) Allen T W Andersen O S Roux B J Gen Physiol 2004124 679(30) Allen T W Andersen O S Roux B Proc Natl Acad SciUSA 2004 101 117(31) Liu Z Xu Y Tang P Biophys J 2005 88 3784(32) Corry B Chung S-H Eur Biophys J 2005 34 208(33) Bastug T Kuyucak S Eur Biophys J 2005 34 377(34) Bastug T Gray-Weale A Patra S M Kuyucak S Biophys J2006 90 2285(35) Allen T W Andersen O S Roux B Biophys Chem 2006124 251(36) Allen T W Andersen O S Roux B Biophys J 2006 903447(37) Mamonov A B Kurnikova M G Coalson R D BiophysChem 2006 124 268(38) Liu Z Xu Y Tang P J Phys Chem B 2006 110 12789(39) Kelkar D A Chattopadhyay A Biochim Biophys ActaBioenerg 2007 1768 2011(40) Bastug T Kuyucak S J Chem Phys 2007 126 105103(41) Bastug T Chen P-C Patra S M Kuyucak S J Chem Phys2008 128 155104(42) De Fabritiis G Coveney P V Villa-Freixa J Proteins StructFunct Bioinf 2008 73 185(43) Forney M Janosi L Kosztin I Phys Rev E 2008 78 1(44) Patel S Davis J E Bauer B A J Am Chem Soc 2009 13113890(45) Dryga A Warshel A J Phys Chem B 2010 114 12720(46) Li Y Andersen O S Roux B J Phys Chem B 2010 11413881(47) Balme S Janot J-m Berardo L Bonhenry D KraszewskiS Picaud F Ramseyer C Gerhardt I C Eug P Nano Lett 201111 712(48) Giorgino T De Fabritiis G J Chem Theory Comput 2011 71943(49) Kim T Lee K Morris P Pastor R Andersen O Im WBiophys J 2012 102 1551(50) Kato M Warshel A J Phys Chem B 2005 109 19516(51) Gordon D Krishnamurthy V Chung S-H J Chem Phys2009 131 134102(52) Mamonov A B Coalson R D Nitzan A Kurnikova M GBiophys J 2003 84 3646(53) Dorman V L Jordan P C Biophys J 2004 86 3529(54) Chen D Wei G-W J Chem Phys 2012 136 134109(55) Im W J Mol Biol 2002 322 851(56) Miedema H Meter-Arkema A Wierenga J Tang JEisenberg B Nonner W Hektor H Gillespie D Meijberg WBiophys J 2004 87 3137(57) Miedema H Vrouenraets M Wierenga J Gillespie DEisenberg B Meijberg W Nonner W Biophys J 2006 91 4392(58) Aguilella-Arzo M Garca-Celma J J Cervera J Alcaraz AAguilella V M Bioelectrochemistry 2007 70 320(59) Aguilella-Arzo M Andrio A Aguilella V M Alcaraz A PhysChem Chem Phys 2009 11 358(60) Garca-Gimenez E Lopez M L Aguilella V M Alcaraz ABiochem Biophys Res Commun 2011 404 330(61) Aguilella V M Queralt-Martn M Aguilella-Arzo M AlcarazA Integr Biol 2011 3 159(62) Im W Seefeld S Roux B Biophys J 2000 79 788(63) Im W Roux B J Chem Phys 2001 115 4850(64) Marreiro D Saraniti M Aboud S J Phys Condens Matter2007 19 215203(65) Tieleman T Berendsen B Biophys J 1998 74 2786

(66) Bond P J Faraldo-Gomez J D Sansom M S P Biophys J2002 83 763(67) Im W Roux B J Mol Biol 2002 319 1177(68) Zachariae U Helms V Engelhardt H Biophys J 2003 85954(69) Danelon C Suenaga A Winterhalter M Yamato I BiophysChem 2003 104 591(70) Varma S Jakobsson E Biophys J 2004 86 690(71) Varma S Chiu S-W W Jakobsson E Biophys J 2006 90112(72) Zachariae U Kluhspies T De S Engelhardt H Zeth K JBiol Chem 2006 281 7413(73) Khalid S Bond P J Deol S S Sansom M S P ProteinsStruct Funct Bioinf 2006 63 6(74) Bond P J Sansom M S P J Am Chem Soc 2006 128 2697(75) van Hijkoop V J Dammers A J Malek K Coppens M-O JChem Phys 2007 127 085101(76) Bond P J Derrick J P Sansom M S P Biophys J 2007 92L23(77) Chen M Khalid S Sansom M S P Bayley H Proc NatlAcad Sci USA 2008 105 6272(78) Chimerel C Movileanu L Pezeshki S Winterhalter MKleinekathofer U Eur Biophys J 2008 38 121(79) Pezeshki S Chimerel C Bessonov A N Winterhalter MKleinekathofer U Biophys J 2009 97 1898(80) Pongprayoon P Beckstein O Wee C L Sansom M S PProc Natl Acad Sci USA 2009 106 21614(81) Biro I Pezeshki S Weingart H Winterhalter MKleinekathofer U Biophys J 2010 98 1830(82) Kumar A Hajjar E Ruggerone P Ceccarelli M J PhysCondens Matter 2010 22 454125(83) Faraudo J Calero C Aguilella-Arzo M Biophys J 2010 992107(84) Vrouenraets M Miedema H Eur Biophys J 2010 39 1563(85) Calero C Faraudo J Aguilella-Arzo M Phys Rev E 2011 831(86) Modi N Singh P R Mahendran K R Schulz RWinterhalter M Kleinekath U J Phys Chem Lett 2011 2 2331(87) Singh P R Ceccarelli M Lovelle M Winterhalter MMahendran K R J Phys Chem B 2012 116 4433(88) Noskov S Y Im W Roux B Biophys J 2004 87 2299(89) Misakian M Kasianowicz J J J Membr Biol 2003 195 137(90) Aksimentiev A Schulten K Biophys J 2005 88 3745(91) Aguilella-Arzo M Aguilella V M Eur Phys J E 2010 31 429(92) Simakov N A Kurnikova M G J Phys Chem B 2010 11415180(93) Bhattacharya S Muzard J Payet L Bockelman UAksimentiev A Viasnoff V J Phys Chem C 2011 115 4255(94) Egwolf B Roux B J Mol Biol 2010 401 831(95) Egwolf B Luo Y Walters D E Roux B J Phys Chem B2010 114 2901(96) Shilov I Y Kurnikova M G J Phys Chem B 2003 107 7189(97) Mathe J Aksimentiev A Nelson D R Schulten K MellerA Proc Natl Acad Sci USA 2005 102 12377(98) Wells D B Abramkina V Aksimentiev A J Chem Phys2007 127 125101(99) Bond P J Guy A T Heron A J Bayley H Khalid SBiochemistry 2011 50 3777(100) OrsquoKeeffe J Cozmuta I Bose D Stolc V Chem Phys 2007342 25(101) Luo Y Egwolf B Walters D E Roux B J Phys Chem B2010 114 952(102) De Biase P M Solano C J F Markosyan S Czapla LNoskov S Y J Chem Theory Comput 2012 8 2540(103) Roux B Berneche S Im W Biochemistry 2000 39 13295(104) Grabe M Lecar H Jan Y N Jan L Y Proc Natl Acad SciUSA 2004 101 17640(105) Jogini V Roux B J Mol Biol 2005 354 272

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAA

(106) Robertson J L Palmer L G Roux B J Gen Physiol 2008132 613(107) Jung Y-W Lu B Mascagni M J Chem Phys 2009 131215101(108) Nekouzadeh A Rudy Y PLoS ONE 2011 6 e20186(109) Gardner C L Jones J R J Theor Biol 2011 291 10(110) Allen T W Chung S H Biochim Biophys Acta 2001 151583(111) Chung S-H Allen T W Kuyucak S Biophys J 2002 82628(112) Burykin A Kato M Warshel A Proteins Struct FunctGenet 2003 52 412(113) Berneche S Roux B Proc Natl Acad Sci USA 2003 1008644(114) Chung S-H Corry B Biophys J 2007 93 44(115) Hoyles M Krishnamurthy V Siksik M Chung S-HBiophys J 2008 94 366(116) Gordon D Chung S-H Biophys J 2011 101 2671(117) Gordon D Chen R Ho J Coote M L Chung S-H JPhys Chem B 2012 116 1933(118) Luzhkov V B Aringqvist J Biochim Biophys Acta 2000 1481360(119) Berneche S Roux B Biophys J 2000 78 2900(120) Aringqvist J Luzhkov V Nature 2000 404 881(121) Shrivastava I H Sansom M S Biophys J 2000 78 557(122) Luzhkov V B Aringqvist J FEBS Lett 2001 495 191(123) Luzhkov V B Aringqvist J Biochim Biophys Acta 2001 1548194(124) Ranatunga K M Shrivastava I H Smith G R Sansom MS Biophys J 2001 80 1210(125) Isralewitz B Baudry J Gullingsrud J Kosztin D SchultenK J Mol Graphics Modell 2001 19 13(126) Berneche S Roux B Nature 2001 414 73(127) Berneche S Roux B Biophys J 2002 82 772(128) Biggin P C Smith G R Shrivastava I Choe S SansomM S Biochim Biophys Acta 2001 1510 1(129) Capener C E Sansom M S P J Phys Chem B 2002 1064543(130) Sansom M S P Shrivastava I H Curr Biol 2002 12 R65(131) Bright J N Shrivastava I H Cordes F S Sansom M S PBiopolymers 2002 64 303(132) Shrivastava I H Peter Tieleman D Biggin P C SansomM S Biophys J 2002 83 633(133) Faraldo-Gomez J D Smith G R Sansom M S P EurBiophys J 2002 31 217(134) Shrivastava I H Sansom M S P Eur Biophys J 2002 31207(135) Sansom M S P Shrivastava I H Bright J N Tate JCapener C E Biggin P C Biochim Biophys Acta 2002 1565 294(136) Eriksson M A L Roux B Biophys J 2002 83 2595(137) Domene C Sansom M S P Biophys J 2003 85 2787(138) Luzhkov V B Osterberg F Aringqvist J FEBS Lett 2003 554159(139) Luzhkov V B Nilsson J Aringrhem P Aringqvist J BiochimBiophys Acta 2003 1652 35(140) Beckstein O Biggin P C Bond P Bright J N DomeneC Grottesi A Holyoake J Sansom M S FEBS Lett 2003 555 85(141) Noskov S Y Berneche S Roux B Nature 2004 431 830(142) Miloshevsky G V Jordan P C Trends Neurosci 2004 27308(143) Domene C Grottesi A Sansom M S P Biophys J 200487 256(144) Tieleman D P Robertson K M Maccallum J LMonticelli L Int J Quantum Chem 2004 100 1071(145) Monticelli L Robertson K M MacCallum J L TielemanD P FEBS Lett 2004 564 325(146) Treptow W Maigret B Chipot C Tarek M Biophys J2004 87 2365(147) Osterberg F Aringqvist J FEBS Lett 2005 579 2939

(148) Roux B Annu Rev Biophys Biomol Struct 2005 34 153(149) Luzhkov V B Aringqvist J Biochim Biophys Acta 2005 1747109(150) Sansom M S P Bond P J Deol S S Grottesi A HaiderS Sands Z A Biochem Soc Trans 2005 33 916(151) Khalili-Araghi F Tajkhorshid E Schulten K Biophys J2006 91 L72(152) Sands Z A Grottesi A Sansom M S P Biophys J 2006 901598(153) Hellgren M Sandberg L Edholm O Biophys Chem 2006120 1(154) Tieleman D P Clin Exp Pharmacol Physiol 2006 33 893(155) Freites J A Tobias D J White S H Biophys J 2006 91L90(156) Treptow W Tarek M Biophys J 2006 91 L81(157) Treptow W Tarek M Biophys J 2006 90 L64(158) Boiteux C Kraszewski S Ramseyer C Girardet C J MolModel 2007 13 699(159) Faraldo-Gomez J D Kutluay E Jogini V Zhao YHeginbotham L Roux B J Mol Biol 2007 365 649(160) Haider S Khalid S Tucker S J Ashcroft F M SansomM S P Biochemistry 2007 46 3643(161) Kona J Minozzi M Torre V Carloni P Theor Chem Acc2007 117 1121(162) Sands Z A Sansom M S P Structure 2007 15 235(163) Bostick D L Brooks C L Proc Natl Acad Sci USA 2007104 9260(164) Gwan J-F Baumgaertner A J Chem Phys 2007 127045103(165) Bond P J Sansom M Proc Natl Acad Sci USA 2007 1042631(166) Kutteh R Vandenberg J I Kuyucak S J Phys Chem B2007 111 1090(167) Pathak M M Yarov-Yarovoy V Agarwal G Roux BBarth P Kohout S Tombola F Isacoff E Y Neuron 2007 56 124(168) Noskov S Y Roux B Biophys Chem 2006 124 279(169) Domene C Cent Eur J Chem 2007 5 635(170) Tayefeh S Kloss T Thiel G Hertel B Moroni A Kast SM Biochemistry 2007 46 4826(171) Lindahl E Sansom M S P Curr Opin Struct Biol 2008 18425(172) Han M Zhang J Z H J Phys Chem B 2008 112 16966(173) Roux B Biophys J 2008 95 4205(174) Fowler P W Tai K Sansom M S P Biophys J 2008 955062(175) Recanatini M Cavalli A Masetti M ChemMedChem 20083 523(176) Piccinini E Ceccarelli M Affinito F Brunetti R BolognaI Fisica D Monserrato C Ca I-M Fisica D Methods 2008 173minus183(177) Sompornpisut P Roux B Perozo E Biophys J 2008 955349(178) Bjelkmar P Niemela P S Vattulainen I Lindahl E PLoSComput Biol 2009 5 e1000289(179) Treptow W Tarek M Klein M L J Am Chem Soc 2009131 2107(180) Domene C Furini S J Mol Biol 2009 389 637(181) Furini S Beckstein O Domene C Proteins Struct FunctBioinf 2009 74 437(182) Furini S Domene C Proc Natl Acad Sci USA 2009 10616074(183) Jensen M O Borhani D W Lindorff-Larsen K MaragakisP Jogini V Eastwood M P Dror R O Shaw D E Proc NatlAcad Sci USA 2010 107 5833(184) Anishkin A Milac A L Guy H R Proteins Struct FunctBioinf 2010 78 932(185) Khalili-Araghi F Jogini V Yarov-Yarovoy V TajkhorshidE Roux B Schulten K Biophys J 2010 98 2189

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAB

(186) Pan A C Cuello L G Perozo E Roux B J Gen Physiol2011 138 571(187) Bastug T Kuyucak S Biophys J 2011 100 629(188) Schiesaro A Ecker G F Prediction of hERG ChannelInhibition Using In Silico Techniques In Ion Channels and TheirInhibitors Gupta S P Ed Springer-Verlag BerlinHeidelberg 2011pp 191minus239(189) Delemotte L Tarek M Klein M L Amaral C TreptowW Proc Natl Acad Sci USA 2011 108 6109(190) Chakrapani S Cordero-Morales J F Jogini V Pan A CCortes D M Roux B Perozo E Nat Struct Mol Biol 2011 18 67(191) Furini S Domene C J Mol Biol 2011 409 867(192) Khalili-Araghi F Tajkhorshid E Roux B Schulten KBiophys J 2012 102 258(193) Knape K Linder T Wolschann P Beyer A Stary-Weinzinger A PLoS ONE 2011 6 e28778(194) Domene C Furini S Biochemistry 2012 51 1559(195) Yang H Gao Z Li P Yu K Yu Y Xu T-L Li M JiangH Biophys J 2012 102 1815(196) Jensen M O Jogini V Borhani D W Leffler A E DrorR O Shaw D E Science 2012 336 229(197) Treptow W Klein M L J Phys Chem Lett 2012 3 1017(198) Garofoli S Jordan P C Biophys J 2003 84 2814(199) Corry B Vora T Chung S-H Biochim Biophys Acta 20051711 72(200) Huetz P Boiteux C Compoint M Ramseyer C GirardetC J Chem Phys 2006 124 044703(201) Bisset D Chung S-H Biochim Biophys Acta 2008 17782273(202) Wee C L Gavaghan D Sansom M S P Biophys J 201098 1558(203) Mafe S Pellicer J Cervera J J Chem Phys 2005 122204712(204) Treptow W Marrink S-J Tarek M J Phys Chem B 2008112 3277(205) Dryga A Chakrabarty S Vicatos S Warshel A Proc NatlAcad Sci USA 2012 109 3335(206) Dryga A Chakrabarty S Vicatos S Warshel A BiochimBiophys Acta 2012 1818 303(207) Guidoni L Carloni P Biochim Biophys Acta 2002 1563 1(208) Bucher D Raugei S Guidoni L Dal Peraro MRothlisberger U Carloni P Klein M L Biophys Chem 2006124 292(209) Kariev A M Znamenskiy V S Green M E BiochimBiophys Acta 2007 1768 1218(210) Bucher D Guidoni L Maurer P Rothlisberger U J ChemTheory Comput 2009 5 2173(211) Bucher D Rothlisberger U J Gen Physiol 2010 135 549(212) Hung A Tai K Sansom M S P Biophys J 2005 88 3321(213) Law R J Henchman R H McCammon J A Proc NatlAcad Sci USA 2005 102 6813(214) Gao M Schulten K Biophys J 2006 90 3267(215) Xu Y Barrantes F J Luo X Chen K Shen J Jiang H JAm Chem Soc 2005 127 1291(216) Xu Y Barrantes F J Shen J Luo X Zhu W Chen KJiang H J Phys Chem B 2006 110 20640(217) Cheng X Wang H Grant B Sine S M McCammon J APLoS Comput Biol 2006 2 e134(218) Law R J Lightstone F C Biophys J 2009 97 1586(219) Brannigan G Lebard D N Henin J Eckenhoff R GKlein M L Proc Natl Acad Sci USA 2010 107 14122(220) Dimitropoulos N Papakyriakou A Dalkas G A ChasapisC T Poulas K Spyroulias G A Proteins Struct Funct Bioinf 201179 142(221) Chen X Cui Q Tang Y Yoo J Yethiraj A Biophys J2008 95 563(222) Tang Y Cao G Chen X Yoo J Yethiraj A Cui QBiophys J 2006 91 1248

(223) Tang Y Yoo J Yethiraj A Cui Q Chen X Biophys J2008 95 581(224) Li S Zhang X Wang W J Phys Chem B 2009 113 14431(225) Song C Corry B PLoS ONE 2011 6 e21204(226) Wiggins P Phillips R Proc Natl Acad Sci USA 2004 1014071(227) Wiggins P Phillips R Biophys J 2005 88 880(228) Ursell T Huang K C Peterson E Phillips R PLoSComput Biol 2007 3 e81(229) Vora T Corry B Chung S-H Biochim Biophys Acta 20061758 730(230) Kong Y Shen Y Warth T E Ma J Proc Natl Acad SciUSA 2002 99 5999(231) Sukharev S Durell S R Guy H R Biophys J 2001 81 917(232) Sukharev S Betanzos M Chiang C-S S Guy H RNature 2001 409 720(233) Betanzos M Chiang C-S S Guy H R Sukharev S NatStruct Biol 2002 9 704(234) Gullingsrud J Kosztin D Schulten K Biophys J 2001 802074(235) Elmore D E Dougherty D A Biophys J 2001 81 1345(236) Bilston L E Mylvaganam K FEBS Lett 2002 512 185(237) Colombo G Marrink S J Mark A E Biophys J 2003 842331(238) Gullingsrud J Schulten K Biophys J 2003 85 2087(239) Gullingsrud J Schulten K Biophys J 2004 86 3496(240) Elmore D E Dougherty D A Biophys J 2003 85 1512(241) Sotomayor M Schulten K Biophys J 2004 87 3050(242) Anishkin A Sukharev S Biophys J 2004 86 2883(243) Spronk S A Elmore D E Dougherty D A Biophys J 200690 3555(244) Sotomayor M Vasquez V Perozo E Schulten K Biophys J2007 92 886(245) Corry B Martinac B Biochim Biophys Acta 2008 17781859(246) Corry B Jayatilaka D Biophys J 2008 95 2711(247) Anishkin A Akitake B Kamaraju K Chiang C-SSukharev S J Phys Condens Matter 2010 22 454120(248) Gamini R Sotomayor M Chipot C Schulten K Biophys J2011 101 80(249) Meyer G R Gullingsrud J Schulten K Martinac BBiophys J 2006 91 1630(250) Debret G Valadie H Stadler A M Etchebest C ProteinsStruct Funct Genet 2008 71 1183(251) Jeon J Voth G A Biophys J 2008 94 3497(252) Monticelli L Kandasamy S Periole X Larson RTieleman D P Marrink S J J Chem Theory Comput 2008 4 819(253) Yefimov S van der Giessen E Onck P Marrink S JBiophys J 2008 94 2994(254) Louhivuori M Risselada H J van der Giessen E MarrinkS J Proc Natl Acad Sci USA 2010 107 19856(255) Corry B Hurst A C Pal P Nomura T Rigby PMartinac B J Gen Physiol 2010 136 483(256) Vasquez V Sotomayor M Cordero-Morales J Schulten KPerozo E Science 2008 321 1210(257) Vasquez V Sotomayor M Cortes D M Roux B SchultenK Perozo E J Mol Biol 2008 378 55(258) Sotomayor M van der Straaten T A Ravaioli U SchultenK Biophys J 2006 90 3496(259) Choudhary O P Ujwal R Kowallis W Coalson RAbramson J Grabe M J Mol Biol 2010 396 580(260) Cohen J Schulten K Biophys J 2004 86 836(261) Suenaga A Yeh J Z Taiji M Toyama A Takeuchi HSon M Takayama K Iwamoto M Sato I Narahashi TKonagaya A Goto K Biophys Chem 2006 120 36(262) Rui H Lee K I Pastor R W Im W Biophys J 2011 100602(263) Krammer E-M Homble F Prevost M PLoS One 2011 6e27994

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAC

(264) Cheng M H Coalson R D Biophys J 2012 102 1363(265) Corry B OrsquoMara M Chung S-H Biophys J 2004 86 846(266) Bisset D Corry B Chung S-H Biophys J 2005 89 179(267) Cheng M H Mamonov A B Dukes J W Coalson R D JPhys Chem B 2007 111 5956(268) Lee K I Rui H Pastor R W Im W Biophys J 2011 100611(269) Burykin A Warshel A Biophys J 2003 85 3696(270) Stroud R M Savage D Miercke L J Lee J K KhademiS Harries W FEBS Lett 2003 555 79(271) Jensen M O Tajkhorshid E Schulten K Biophys J 200385 2884(272) de Groot B L Frigato T Helms V Grubmuller H J MolBiol 2003 333 279(273) Chen H Wu Y Voth G A Biophys J 2006 90 L73(274) Wang Y Tajkhorshid E J Nutr 2007 137 1509S(275) Bostick D L Brooks C L PLoS Comput Biol 2007 3 e22(276) Bostick D L Charles L L B Biophys J 2007 92 L103(277) Wang S Orabi E A Baday S Berneche S Lamoureux GJ Am Chem Soc 2012 134 10419(278) Luzhkov V B Almlof M Nervall M Aringqvist J Biochemistry2006 45 10807(279) Levitt D G Biophys J 1991 59 271(280) Barcilon V Chen D-P Eisenberg R SIAM J App Math1992 52 1405(281) Chen D P Barcilon V Eisenberg R S Biophys J 1992 611372(282) Chen D Eisenberg R Biophys J 1993 64 1405(283) Chen D P Eisenberg R S Biophys J 1993 65 727(284) Chen D Xu L Tripathy a Meissner G Eisenberg BBiophys J 1997 73 1337(285) Chen D Lear J Eisenberg B Biophys J 1997 72 97(286) Syganow A von Kitzing E J Phys Chem 1995 99 12030(287) Moy G Corry B Kuyucak S Chung S-H Biophys J 200078 2349(288) Corry B Kuyucak S Chung S H Biophys J 2000 78 2364(289) Crozier P Rowley R Holladay N Henderson D BusathD Phys Rev Lett 2001 86 2467(290) Gillespie D Nonner W Eisenberg R S J Phys CondensMatter 2002 14 12129(291) Gillespie D Nonner W Eisenberg R Phys Rev E 2003 681(292) Koumanov A Zachariae U Engelhardt H Karshikoff AEur Biophys J 2003 32 689(293) Kuyucak S Bastug T J Biophys 2003 29 429(294) Corry B Kuyucak S Chung S-H Biophys J 2003 84 3594(295) Beckstein O Tai K Sansom M S P J Am Chem Soc 2004126 14694(296) Graf P Kurnikova M G Coalson R D Nitzan A J PhysChem B 2004 108 2006(297) Kessel A Tieleman D P Ben-Tal N Eur Biophys J 200433 16(298) Baumgartner W Comput Biol Chem 2004 28 67(299) Roux B Allen T Bernche S Im W Q Rev Biophys 200437 15(300) Gillespie D Xu L Wang Y Meissner G J Phys Chem B2005 109 15598(301) Aguilella-Arzo M Aguilella V M Eisenberg R S EurBiophys J 2005 34 314(302) Cheng M H Coalson R D J Phys Chem B 2005 109 488(303) Hwang H Schatz G C Ratner M A J Phys Chem B 2006110 6999(304) Kandt C Ash W L Tieleman D P Methods 2007 41 475(305) Singer A Norbury J SIAM J Appl Math 2009 70 949(306) Bolintineanu D S Sayyed-Ahmad A Davis H T KaznessisY N PLoS Comput Biol 2009 5 e1000277(307) Eisenberg B J Phys Chem C 2010 114 20719(308) Eisenberg B Chem Phys Lett 2011 511 1(309) Lu B Zhou Y Biophys J 2011 100 2475

(310) Eisenberg B Adv Chem Phys 2012 77minus223(311) Krishnamurthy V Chung S-H IEEE Trans Nanobiosci 20054 102(312) Vora T Bisset D Chung S-H Biophys J 2008 95 1600(313) Gordon D Krishnamurthy V Chung S-H Mol Phys 2008106 1353(314) Vora T Corry B Chung S-H Eur Biophys J 2008 38 45(315) Song C Corry B Biophys J 2010 98 404(316) Krishnamurthy V Luk K Y IEEEACM Trans Comput BiolBioinf 2011 8 273(317) Lee K I Jo S Rui H Egwolf B Roux B Pastor R WIm W J Comput Chem 2012 33 331(318) Csanyi E Boda D Gillespie D Kristof T Biochim BiophysActa 2012 1818 592(319) Smondyrev A M Voth G A Biophys J 2002 83 1987(320) Domene C Bond P J Sansom M S P Adv Protein Chem2003 66 159(321) Tarek M Maigret B Chipot C Biophys J 2003 85 2287(322) Biggin P C Grottesi A Sansom M S P From Prokaryotesto Eukaryotes Molecular Modeling and Simulation Studies of IonChannels In Bacterial Ion Channels And Their Eukaryotic HomologsKubalski A Martinac B Eds ASM Press Washington DC 2005pp 133minus152(323) Tajkhorshid E Cohen J Aksimentiev A Sotomayor MSchulten K Towards an Understanding of Membrane Channels InBacterial Ion Channels And Their Eukaryotic Homologs Kubalski AMartinac B Eds ASM Press Washington DC 2005 pp 133minus152(324) Gumbart J Wang Y Aksimentiev A Tajkhorshid ESchulten K Curr Opin Struct Biol 2005 15 423(325) Hwang H Schatz G C Ratner M A J Phys Chem B 2006110 26448(326) Carpenter T Bond P J Khalid S Sansom M S P BiophysJ 2008 95 3790(327) Shaikh S A Tajkhorshid E Biophys J 2008 95 5153(328) Pietra F J Phys Org Chem 2008 21 997(329) Delemotte L Dehez F Treptow W Tarek M J PhysChem B 2008 112 5547(330) Maffeo C Aksimentiev A Biophys J 2009 96 4853(331) Patargias G Martay H Fischer W B J Biomol Struct Dyn2009 27 1(332) Mustafa M Henderson D J Busath D D Proteins StructFunct Bioinf 2009 76 794(333) Khalili-Araghi F Gumbart J Wen P-C Sotomayor MTajkhorshid E Schulten K Curr Opin Struct Biol 2009 19 128(334) Khurana E Dal Peraro M DeVane R Vemparala SDeGrado W F Klein M L Proc Natl Acad Sci USA 2009 1061069(335) Pan J Tieleman D P Nagle J F Kucerka N Tristram-Nagle S Biochim Biophys Acta 2009 1788 1387(336) Nury H Poitevin F Van Renterghem C Changeux J-PCorringer P-J Delarue M Baaden M Proc Natl Acad Sci USA2010 107 6275(337) Cheng M H Coalson R D Tang P J Am Chem Soc 2010132 16442(338) Zhu F Hummer G Proc Natl Acad Sci USA 2010 10719814(339) Kutzner C Grubmuller H de Groot B L Zachariae UBiophys J 2011 101 809(340) Wilson M A Wei C Bjelkmar P Wallace B A PohorilleA Biophys J 2011 100 2394(341) Stansfeld P J Sansom M S P Structure 2011 19 1562(342) Chen C-C Kruger J Sramala I Hsu H-J Henklein PChen Y-M A Fischer W B Biochim Biophys Acta 2011 1808 572(343) Raunest M Kandt C Biochemistry 2012 51 1719(344) Furini S Domene C PLoS Comput Biol 2012 8 e1002476(345) Becucci L Cembran A Karim C B Thomas D DGuidelli R Gao J Veglia G Biophys J 2009 96 L60(346) Gumbart J Khalili-Araghi F Sotomayor M Roux BBiochim Biophys Acta 2011 1818 294

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAD

(347) Carnevale V Treptow W Klein M L J Phys Chem Lett2011 2 2504(348) Bhattacharya S Derrington I M Pavlenok M NiederweisM Gundlach J H Aksimentiev A ACS Nano 2012 6 6960(349) Graf P Nitzan A Kurnikova M G Coalson R D J PhysChem B 2000 104 12324(350) Peter C Hummer G Biophys J 2005 89 2222(351) Boda D Valisko M Eisenberg B Nonner W HendersonD Gillespie D Phys Rev Lett 2007 98 1(352) Thoslashgersen L Schioslashtt B Vosegaard T Nielsen N CTajkhorshid E Biophys J 2008 95 4337(353) Plank G Zhou L Greenstein J L Cortassa S Winslow RL OrsquoRourke B Trayanova N A Philos Trans R Soc A 2008 3663381(354) Eisenberg B Hyon Y Liu C J Chem Phys 2010 133104104(355) Hannongbua S Treesuwan W Boonyarat W AdvancedMolecular Modeling Techniques Applied to Ion Channels Blockers InIon Channels and Their Inhibitors Gupta S P Ed Springer-VerlagBerlinHeidelberg 2011 pp 53minus78(356) Zheng W Auerbach A PLoS Comput Biol 2011 7e1001046(357) Boda D Busath D D Eisenberg B Henderson DNonner W Phys Chem Chem Phys 2002 4 5154(358) Boda D Henderson D Busath D D Mol Phys 2002 1002361(359) Cervera J Schiedt B Ramirez P Europhys Lett 2005 7135(360) Vidal J Gracheva M E Leburton J-P Nanoscale Res Lett2006 2 61(361) Gracheva M Leburton J-P Nanotechnology 2007 18145704(362) Vidal J Gracheva M Leburton J-P Nanoscale Res Lett2007 2 61(363) Cervera J Alcaraz A Schiedt B Neumann R Ramirez PJ Phys Chem C 2007 111 12265(364) Vlassiouk I Smirnov S Siwy Z Nano Lett 2008 8 1978(365) Gillespie D Boda D He Y Apel P Siwy Z S Biophys J2008 95 609(366) Kosin ska I D Hanggi P Phys Rev E 2008 77 1(367) Reiner J E Kasianowicz J J Nablo B J Robertson J W FProc Natl Acad Sci USA 2010 107 12080(368) Zhang Y Voth G A J Chem Theory Comput 2011 7 2277(369) Zhang M Yeh L Qian S Hsu J J Phys Chem C 2012116 4793(370) Yeh L-h Zhang M Qian S Hsu J-p Tseng S J PhysChem C 2012 116 8672(371) Carr R Comer J Ginsberg M Aksimentiev A Lab Chip2011 11 3766(372) Peters M H J Chem Phys 2011 134 025105(373) Comer J Aksimentiev A J Phys Chem C 2012 116 3376(374) Timp W Comer J Aksimentiev A Biophys J 2012 102L37(375) Aksimentiev A Heng J B Timp G Schulten K Biophys J2004 87 2086(376) Heng J B Aksimentiev A Ho C Marks P Grinkova YV Sligar S Schulten K Timp G Biophys J 2006 90 1098(377) Lu D Aksimentiev A Shih A Y Cruz-Chu E FreddolinoP L Arkhipov A Schulten K Phys Bio 2006 3 S40(378) Luan B Aksimentiev A Phys Rev E 2008 78 021912(379) Carr R Weinstock I A Sivaprasadarao A Muller AAksimentiev A Nano Lett 2008 8 3916(380) Comer J Dimitrov V Zhao Q Timp G Aksimentiev ABiophys J 2009 96 593(381) Luan B Aksimentiev A J Phys Condens Matter 2010 22454123(382) Gracheva M Xiong A Aksimentiev A Schulten K TimpG Leburton J-P Nanotechnology 2006 17 622

(383) Gracheva M Aksimentiev A Leburton J-P Nanotechnology2006 17 3160(384) Sigalov G Comer J Timp G Aksimentiev A Nano Lett2008 8 56(385) Cruz-Chu E R Aksimentiev A Schulten K J Phys Chem C2009 113 1850(386) Dorvel B Sigalov G Zhao Q Comer J Dimitrov VMirsaidov U Aksimentiev A Timp G Nucleic Acids Res 2009 374170(387) Wang D Timp W Shim J Mirsaidov U Comer JAksimentiev A Timp G Biophys J 2010 98 599a(388) Comer J Aksimentiev A Nanopore Force SpectroscopyInsights from Molecular Dynamics Simulations In Nanopores Sensingand Fundamental Biological Interactions Bashir R Iqbal S EdsSpringer Science and Business Media LLC New York 2011 Chapter14 pp 335minus356(389) Sathe C Zou X Leburton J-P Schulten K ACS Nano2011 5 8842(390) Wanunu M Bhattacharya S Xie Y Tor Y AksimentievA Drndic M ACS Nano 2011 5 9345(391) Kowalczyk S W Wells D B Aksimentiev A Dekker CNano Lett 2012 12 1038(392) Wells D B Belkin M Comer J Aksimentiev A Nano Lett2012 8 4117(393) Edmonds C M Hudiono Y C Ahmadi A G Hesketh PJ Nair S J Chem Phys 2012 136 065105(394) Saha K K Drndic M Nikolic B K Nano Lett 2012 12 50(395) Hille B Ionic channels of excitable membranes 3rd ed SinauerAssociates Sunderland MA 2001(396) Hodgkin A L Huxley A F J Physiol 1952 117 500(397) Hodgkin A L Huxley A F J Physiol 1952 117 500(398) Alberts B Johnson A Lewis J Raff M Roberts K WalterP Molecular Biology of The Cell 5th ed Garland Science New York ampLondon 2007(399) Watanabe H Sugiura S Kafuku H Hisada T Biophys J2004 87 2074(400) Wong J Goktepe S Kuhl E Comput Methods Appl MechEngrg 2011 200 3139(401) Rowat P Neur Comp 2007 19 1215(402) Tuckwell H C Jost J Physica A 2009 388 4115(403) Linaro D Storace M Giugliano M PLoS Comput Biol2011 7 e1001102(404) Che Y-Q Wang J Zhou S-S Deng B Chaos SolitonsFractals 2009 40 1588(405) Beard D A PLoS Comput Biol 2005 1 e36(406) Townsley L E Tucker W A Sham S Hinton J FBiochemistry 2001 40 11676(407) Chang G Spencer R H Lee A T Barclay M T Rees DC Science 1998 282 2220(408) Bass R B Strop P Barclay M Rees D C Science 2002298 1582(409) Conroy M J Durand A Lupo D Li X-D D BulloughP A Winkler F K Merrick M Proc Natl Acad Sci USA 2007104 1213(410) Uysal S Vasquez V Tereshko V Esaki K Fellouse FSidhu S Koide S Perozo E Kossiakoff A Proc Natl Acad SciUSA 2009 106 6644(411) Long S B Tao X Campbell E B MacKinnon R Nature2007 450 376(412) Gonen T Cheng Y Sliz P Hiroaki Y Fujiyoshi YHarrison S C Walz T Nature 2005 438 633(413) Miyazawa A Fujiyoshi Y Unwin N Nature 2003 423 949(414) Unwin N J Mol Biol 2005 346 967(415) Cowan S Schirmer T Rummel G Steiert M Ghosh RPauptit R Jansonius J Rosenbusch J Nature 1992 358 727(416) Dutzler R Campbell E B MacKinnon R Science 2003 300108(417) Song L Hobaugh M R Shustak C Cheley S Bayley HGouaux J E Science 1996 274 1859

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAE

(418) Malasics A Gillespie D Nonner W Henderson DEisenberg B Boda D Biochim Biophys Acta Biomembr 2009 17882471(419) Giri J Fonseca J Boda D Henderson D Eisenberg BPhys Bio 2011 8 026004(420) Mackay D H Berens P H Wilson K R Hagler A TBiophys J 1984 46 229(421) Morais-Cabral J H Zhou Y MacKinnon R Nature 2001414 37(422) Wulff H Calabresi P A Allie R Yun S Pennington MBeeton C Chandy K G J Clin Invest 2003 111 1703(423) Judge S I V Bever C T Pharmacol Ther 2006 111 224(424) Parsegian A Nature 1969 221 844(425) Rashid M H Kuyucak S J Phys Chem B 2012 116 4812(426) Kung C Nature 2005 436 647(427) Kung C Martinac B Sukharev S Annu Rev Microbiol2010 64 313(428) Sukharev S I Blount P Martinac B Blattner F R KungC Nature 1994 368 265(429) Levina N Totemeyer S Stokes N R Louis P Jones MA Booth I R EMBO J 1999 18 1730(430) Wang W Black S S Edwards M D Miller S Morrison EL Bartlett W Dong C Naismith J H Booth I R Science 2008321 1179(431) Liu Z Gandhi C S Rees D C Nature 2009 461 120(432) Martinac B Buechner M Delcour A H Adler J Kung CProc Natl Acad Sci USA 1987 84 2297(433) Weiss M S Schulz G E J Mol Biol 1992 227 493(434) Kreusch A Schulz G J Mol Biol 1994 243 891(435) Cowan S W Garavito R M Jansonius J N Jenkins J AKarlsson R Konig N Pai E F Pauptit R A Rizkallah P JRosenbusch J P Structure 1995 3 1041(436) Schirmer T Keller T A Wang Y F Rosenbusch J PScience 1995 267 512(437) Dutzler R Rummel G Albert S Hernandez-Alles S PhaleP Rosenbusch J Bened V Schirmer T Structure 1999 7 425(438) Moraes T F Bains M Hancock R E W Strynadka N CJ Nat Struct Mol Biol 2007 14 85(439) Biswas S Mohammad M M Movileanu L van der Berg BStructure 2008 16 1027(440) Tamber S Hancock R E W FEMS Microbiol Lett 2006260 23(441) Liu J Eren E Vijayaraghavan J Cheneke B R Indic Mvan den Berg B Movileanu L Biochemistry 2012 51 2319(442) Cheneke B R van der Berg B Movileanu L Biochemistry2011 50 4987(443) Cheneke B R Indic M van den Berg B Movileanu LBiochemistry 2012 51 5348(444) Vila J Mart S Sanchez-Cespedes J J Antimicrob Chemother2007 59 1210(445) Song L Hobaugh M R Shustak C Cheley S Bayley HGouaux J E Science 1996 274 1859(446) Kasianowicz J Robertson J W F Chan E R Reiner J EStanford V M Annu Rev Anal Chem 2008 1 737(447) Kasianowicz J J Brandin E Branton D Deamer D WProc Natl Acad Sci USA 1996 93 13770(448) Faller R Neiderweis M Schulz G E Science 2004 3031189(449) Butler T Pavlenok M Derrington I Niederweis MGundlach J Proc Natl Acad Sci USA 2008 105 20647(450) Derrington I M Collins M D Pavlenok M NiederweisM Gundlach J H Biophys J 2010 98 422a(451) Manrao E Derrington I Pavlenok M Niederweis MGundlach J PLoS One 2011 6 e25723(452) Roos N Benz R Brdiczka D Biochim Biophys Acta 1982686 204(453) Hiller S Garces R G Malia T J Orekhov V YColombini M Wagner G Science 2008 321 1206

(454) Ujwal R Cascio D Colletier J-P Faham S Zhang JToro L Ping P Proc Natl Acad Sci USA 2008 105 2(455) Bayrhuber M Meins T Habeck M Becker S Giller KVillinger S Vonrhein C Griesinger C Zweckstetter M Zeth KProc Natl Acad Sci USA 2008 105 15370(456) Colombini M Trends Biochem Sci 2009 34 382(457) Hiller S Abramson J Mannella C Wagner G Zeth KTrends Biochem Sci 2010 35 514(458) Hiller S Raschle T Yu T-Y Rice A J Walz T WagnerG Biochim Biophys Acta Bioenerg 2010 1797 66(459) Chen T-Y Annu Rev Physiol 2005 67 809(460) Dutzler R Campbell E B Cadene M Chait B TMacKinnon R Nature 2002 415 287(461) Accardi A Miller C Nature 2004 427 803(462) Steinlein O K Bertrand D Biochem Pharmacol 2008 761175(463) Rose J E Biochem Pharmacol 2007 74 1263(464) Marini A M Soussi-Boudekou S Vissers S Andre B MolCell Biol 1997 17 4282(465) Ninnemann O Jauniaux J C Frommer W B EMBO J1994 13 3464(466) Marini A M Vissers S Urrestarazu A Andre B EMBO J1994 13 3456(467) Khademi S OrsquoConnell J Remis J Robles-Colmenares YMiercke L J W Stroud R M Science 2004 305 1587(468) Javelle A Lupo D Ripoche P Fulford T Merrick MWinkler F K Proc Natl Acad Sci USA 2008 105 5040(469) Gruswitz F OrsquoConnell J Stroud R M Proc Natl Acad SciUSA 2007 104 42(470) Javelle A Lupo D Zheng L Li X-D D Winkler F KMerrick M J Biol Chem 2006 281 39492(471) Gao J Truhlar D G Annu Rev Phys Chem 2002 53 467(472) Kamerlin S C L Vicatos S Dryga A Warshel A AnnuRev Phys Chem 2011 62 41(473) Modi N Winterhalter M Kleinekathofer U Nanoscale2012 4 6166(474) Maffeo C Schopflin R Brutzer H Stehr R AksimentievA Wedemann G Seidel R Phys Rev Lett 2010 105 158101(475) Simonson T Carlsson J Case D A J Am Chem Soc 2004126 4167(476) Rocchia W Alxov E Honig B J Phys Chem B 2001 1056507(477) Baker N Sept D Joseph S Hoist M McCammon J ProcNatl Acad Sci USA 2001 98 10037(478) Ramrez P Aguilella-Arzo M Alcaraz A Cervera JAguilella V M Cell Biochem Biophys 2006 44 287(479) Woolley G Biggin P Schultz A Lien L Jaikaran DBreed J Crowhurst K Sansom M Biophys J 1997 73 770(480) Nonner W Chen D Eisenberg B Biophys J 1998 74 2327(481) Roth R J Phys Condens Matter 2010 22 063102(482) Woolf T Roux B Proc Natl Acad Sci USA 1994 9111631(483) Hummer G New J Phys 2005 7 34(484) Paine P L Scherr P Biophys J 1975 15 1087(485) Roux B Biophys J 1999 77 139(486) Corry B Allen T Kuyucak S Chung S Biophys J 200180 195(487) Cooper K Jakobsson E Wolynes P Prog Biophys Mol Biol1985 46 51(488) Mackerell A D J Comput Chem 2004 25 1584(489) MacKerell D A Bashford D Bellott Dunbrack L REvanseck J D Field M J Fischer S Gao J Guo H Ha SJoseph-McCarthy D Kuchnir L Kuczera K Lau F T K MattosC Michnick S Ngo T Nguyen D T Prodhom B Reiher W ERoux B Schlenkrich M Smith J C Stote R Straub J WatanabeM Wiorkiewicz-Kuczera J Yin D Karplus M J Phys Chem B1998 102 3586(490) Weiner P K Kollman P A J Comput Chem 1981 2 287

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAF

(491) Cornell W D Cieplak P Bayly C I Gould I R Merz KM Ferguson D M Spellmeyer D C Fox T Caldwell J WKollman P A J Am Chem Soc 1995 117 5179(492) Jorgensen W L Maxwell D S Tirado-Rives J J Am ChemSoc 1996 118 11225(493) Kaminski G A Friesner R A Tirado-Rives J Jorgensen WL J Phys Chem B 2001 105 6474(494) Hermans J Berendsen H J C Van Gunsteren W FPostma J P M Biopolymers 1984 23 1513(495) Schmid N Eichenberger A P Choutko A Riniker SWinger M Mark A E van Gunsteren W F Eur Biophys J 201140 843(496) Klauda J B Venable R M Freites J A OrsquoConnor J WTobias D J Mondragon-Ramirez C Vorobyov I MacKerell A DPastor R W J Phys Chem B 2010 114 7830(497) Wang J Wolf R M Caldwell J W Kollman P A Case DA J Comput Chem 2004 25 1157(498) Liu Y Chipot C Shao X Cai W Phys Bio 2011 8056005(499) Daura X Mark A E van Gunsteren W F J Comput Chem1998 19 535(500) Berger O Edholm O Jahnig F Biophys J 1997 72 2002(501) Cordomiacute A Caltabiano G Pardo L J Chem TheoryComput 2012 8 948(502) Aksimentiev A Wells D Sotomayor M Membrane ProteinTutorial httpwwwksuiuceduTrainingTutorialssciencemembranemem-tutorialpdfrelax(503) Humphrey W Dalke A Schulten K J Mol Graphics 199614 33(504) Brooks B R Bruccoleri R E Olafson B D States D JSwaminathan S Karplus M J Comput Chem 1983 187(505) Jo S Lim J B Klauda J B Im W Biophys J 2009 97 50(506) Ayton G S Voth G A Curr Opin Struct Biol 2009 19 138(507) Marrink S J de Vries A H Tieleman D P BiochimBiophys Acta 2009 1788 149(508) Nielsen S O Lopez C F Srinivas G Klein M L J PhysCondens Matter 2004 16 R481(509) Yesylevskyy S O Schafer L V Sengupta D Marrink S JPLoS Comput Biol 2010 6 e1000810(510) Wu Z Cui Q Yethiraj A J Phys Chem B 2010 114 10524(511) Sali A Blundell T L J Mol Biol 1993 234 779(512) Capener C E Shrivastava I H Ranatunga K M Forrest LR Smith G R Sansom M S Biophys J 2000 78 2929(513) Roux B Comput Phys Commun 1995 91 275(514) Kollman P Chem Rev 1993 93 2395(515) Pohorille A Jarzynski C Chipot C J Phys Chem B 2010114 10235(516) Torrie G Valleau J J Comput Phys 1977 23 187(517) Kumar S Bouzida D Swendsen R H Kollman P ARosenberg J M J Comput Chem 1992 13 1011(518) Woo H-J Roux B Proc Natl Acad Sci USA 2005 1026825(519) Singh U C Brown F K Bash P A Kollman P A J AmChem Soc 1987 109 1607(520) Grubmuller H Heymann B Tavan P Science 1996 271997(521) Isralewitz B Izrailev S Schulten K Biophys J 1997 732972(522) Izrailev S Stepaniants S Balsera M Oono Y Schulten KBiophys J 1997 72 1568(523) Stepaniants S Izrailev S Schulten K J Mol Mod 1997 3473(524) Marrink S-J Berger O Tieleman P Jahnig F Biophys J1998 74 931(525) Kosztin D Izrailev S Schulten K Biophys J 1999 76 188(526) Hummer G Szabo A Acc Chem Res 2005 38 504(527) Jarzynski C Phys Rev Lett 1997 78 2690(528) Bucher D Guidoni L Rothlisberger U Biophys J 2007 932315

(529) Arkin I T Xu H F Jensen M O Arbely E Bennett E RBowers K J Chow E Dror R O Eastwood M P Flitman-TeneR Gregersen B A Klepeis J L Kolossvary I Shan Y B Shaw DE Science 2007 317 799(530) Warshel A Sussman F King G Biochemistry 1986 25 8368(531) Li L Vorobyov I Mackerell A D Allen T W Biophys J2007 94 L11(532) Li L Vorobyov I Allen T W J Phys Chem B 2008 1129574(533) Yoo J Cui Q Biophys J 2008 94 L61(534) MacCallum J L Bennett W F D Tieleman D P Biophys J2008 94 3393(535) Yoo J Cui Q Biophys J 2010 99 1529(536) Johansson A C V Lindahl E J Phys Chem B 2009 113245(537) Honig B Sharp K Yang A S J Phys Chem 1993 97 1101(538) Lim C Bashford D Karplus M J Phys Chem 1991 955610(539) Warshel A Papazyan A Curr Opin Struct Biol 1998 8 211(540) Ullmann G M Knapp E-W Eur Biophys J 1999 28 533(541) Srinivasan J Trevathan M W Beroza P Case D A TheorChem Acc 1999 101 426(542) Koumanov A Ruterjans H Karshikoff A Proteins StructFunct Genet 2002 46 85(543) Mongan J Case D A McCammon J A J Comput Chem2004 25 2038(544) Mongan J Case D A Curr Opin Struct Biol 2005 15 157(545) Khandogin J Brooks C L Biochemistry 2006 45 9363(546) Gunner G Mao J Song Y Kim J Biochim Biophys ActaBioenerg 2006 1757 942(547) Spassov V Z Yan L Protein Sci 2008 17 1955(548) Karshikoff A Spassov V Cowan S W Ladenstein RSchirmer T J Mol Biol 1994 240 372(549) Tanizaki S Feig M J Chem Phys 2005 122 124706(550) Gordon J C Myers J B Folta T Shoja V Heath L SOnufriev A Nucleic Acids Res 2005 33 W368(551) Olsson M H M Soslashndergaard C R Rostkowski M JensenJ H J Chem Theory Comput 2011 7 525(552) Jo S Vargyas M Vasko-Szedlar J Roux B Im W NucleicAcids Res 2008 36 W270(553) Shaw D E Chao J C Eastwood M P Gagliardo JGrossman J P P Ho C R Lerardi D J Kolossvary I Klepeis JL Layman T McLeavey C Deneroff M M Moraes M AMueller R Priest E C Shan Y Spengler J Theobald M TowlesB Wang S C Dror R O Kuskin J S Larson R H Salmon J KYoung C Batson B Bowers K J Commun ACM 2008 51 91(554) Shaw D E J Comput Chem 2005 26 1318(555) Dror R O Jensen M O Borhani D W Shaw D E J GenPhysiol 2010 135 555(556) Dror R O Dirks R M Grossman J P Xu H Shaw D EAnnu Rev Biochem 2012 41 429(557) Dror R O Pan A C Arlow D H Borhani D WMaragakis P Shan Y Xu H Shaw D E Proc Natl Acad Sci USA2011 108 13118(558) Rosenbaum D M Zhang C Lyons J A Holl R AragaoD Arlow D H Rasmussen S G F Choi H-J J Devree B TSunahara R K Chae P S Gellman S H Dror R O Shaw D EWeis W I Caffrey M Gmeiner P Kobilka B K Nature 2011 469236(559) Kruse A C Hu J Pan A C Arlow D H Rosenbaum DM Rosemond E Green H F Liu T Chae P S Dror R OShaw D E Weis W I Wess J Kobilka B K Nature 2012 482552(560) Jensen M O Dror R O Xu H F Borhani D W Arkin IT Eastwood M P Shaw D E Proc Natl Acad Sci USA 2008105 14430(561) Vorobyov I V Anisimov V M MacKerell A D J PhysChem B 2005 109 18988

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAG

(106) Robertson J L Palmer L G Roux B J Gen Physiol 2008132 613(107) Jung Y-W Lu B Mascagni M J Chem Phys 2009 131215101(108) Nekouzadeh A Rudy Y PLoS ONE 2011 6 e20186(109) Gardner C L Jones J R J Theor Biol 2011 291 10(110) Allen T W Chung S H Biochim Biophys Acta 2001 151583(111) Chung S-H Allen T W Kuyucak S Biophys J 2002 82628(112) Burykin A Kato M Warshel A Proteins Struct FunctGenet 2003 52 412(113) Berneche S Roux B Proc Natl Acad Sci USA 2003 1008644(114) Chung S-H Corry B Biophys J 2007 93 44(115) Hoyles M Krishnamurthy V Siksik M Chung S-HBiophys J 2008 94 366(116) Gordon D Chung S-H Biophys J 2011 101 2671(117) Gordon D Chen R Ho J Coote M L Chung S-H JPhys Chem B 2012 116 1933(118) Luzhkov V B Aringqvist J Biochim Biophys Acta 2000 1481360(119) Berneche S Roux B Biophys J 2000 78 2900(120) Aringqvist J Luzhkov V Nature 2000 404 881(121) Shrivastava I H Sansom M S Biophys J 2000 78 557(122) Luzhkov V B Aringqvist J FEBS Lett 2001 495 191(123) Luzhkov V B Aringqvist J Biochim Biophys Acta 2001 1548194(124) Ranatunga K M Shrivastava I H Smith G R Sansom MS Biophys J 2001 80 1210(125) Isralewitz B Baudry J Gullingsrud J Kosztin D SchultenK J Mol Graphics Modell 2001 19 13(126) Berneche S Roux B Nature 2001 414 73(127) Berneche S Roux B Biophys J 2002 82 772(128) Biggin P C Smith G R Shrivastava I Choe S SansomM S Biochim Biophys Acta 2001 1510 1(129) Capener C E Sansom M S P J Phys Chem B 2002 1064543(130) Sansom M S P Shrivastava I H Curr Biol 2002 12 R65(131) Bright J N Shrivastava I H Cordes F S Sansom M S PBiopolymers 2002 64 303(132) Shrivastava I H Peter Tieleman D Biggin P C SansomM S Biophys J 2002 83 633(133) Faraldo-Gomez J D Smith G R Sansom M S P EurBiophys J 2002 31 217(134) Shrivastava I H Sansom M S P Eur Biophys J 2002 31207(135) Sansom M S P Shrivastava I H Bright J N Tate JCapener C E Biggin P C Biochim Biophys Acta 2002 1565 294(136) Eriksson M A L Roux B Biophys J 2002 83 2595(137) Domene C Sansom M S P Biophys J 2003 85 2787(138) Luzhkov V B Osterberg F Aringqvist J FEBS Lett 2003 554159(139) Luzhkov V B Nilsson J Aringrhem P Aringqvist J BiochimBiophys Acta 2003 1652 35(140) Beckstein O Biggin P C Bond P Bright J N DomeneC Grottesi A Holyoake J Sansom M S FEBS Lett 2003 555 85(141) Noskov S Y Berneche S Roux B Nature 2004 431 830(142) Miloshevsky G V Jordan P C Trends Neurosci 2004 27308(143) Domene C Grottesi A Sansom M S P Biophys J 200487 256(144) Tieleman D P Robertson K M Maccallum J LMonticelli L Int J Quantum Chem 2004 100 1071(145) Monticelli L Robertson K M MacCallum J L TielemanD P FEBS Lett 2004 564 325(146) Treptow W Maigret B Chipot C Tarek M Biophys J2004 87 2365(147) Osterberg F Aringqvist J FEBS Lett 2005 579 2939

(148) Roux B Annu Rev Biophys Biomol Struct 2005 34 153(149) Luzhkov V B Aringqvist J Biochim Biophys Acta 2005 1747109(150) Sansom M S P Bond P J Deol S S Grottesi A HaiderS Sands Z A Biochem Soc Trans 2005 33 916(151) Khalili-Araghi F Tajkhorshid E Schulten K Biophys J2006 91 L72(152) Sands Z A Grottesi A Sansom M S P Biophys J 2006 901598(153) Hellgren M Sandberg L Edholm O Biophys Chem 2006120 1(154) Tieleman D P Clin Exp Pharmacol Physiol 2006 33 893(155) Freites J A Tobias D J White S H Biophys J 2006 91L90(156) Treptow W Tarek M Biophys J 2006 91 L81(157) Treptow W Tarek M Biophys J 2006 90 L64(158) Boiteux C Kraszewski S Ramseyer C Girardet C J MolModel 2007 13 699(159) Faraldo-Gomez J D Kutluay E Jogini V Zhao YHeginbotham L Roux B J Mol Biol 2007 365 649(160) Haider S Khalid S Tucker S J Ashcroft F M SansomM S P Biochemistry 2007 46 3643(161) Kona J Minozzi M Torre V Carloni P Theor Chem Acc2007 117 1121(162) Sands Z A Sansom M S P Structure 2007 15 235(163) Bostick D L Brooks C L Proc Natl Acad Sci USA 2007104 9260(164) Gwan J-F Baumgaertner A J Chem Phys 2007 127045103(165) Bond P J Sansom M Proc Natl Acad Sci USA 2007 1042631(166) Kutteh R Vandenberg J I Kuyucak S J Phys Chem B2007 111 1090(167) Pathak M M Yarov-Yarovoy V Agarwal G Roux BBarth P Kohout S Tombola F Isacoff E Y Neuron 2007 56 124(168) Noskov S Y Roux B Biophys Chem 2006 124 279(169) Domene C Cent Eur J Chem 2007 5 635(170) Tayefeh S Kloss T Thiel G Hertel B Moroni A Kast SM Biochemistry 2007 46 4826(171) Lindahl E Sansom M S P Curr Opin Struct Biol 2008 18425(172) Han M Zhang J Z H J Phys Chem B 2008 112 16966(173) Roux B Biophys J 2008 95 4205(174) Fowler P W Tai K Sansom M S P Biophys J 2008 955062(175) Recanatini M Cavalli A Masetti M ChemMedChem 20083 523(176) Piccinini E Ceccarelli M Affinito F Brunetti R BolognaI Fisica D Monserrato C Ca I-M Fisica D Methods 2008 173minus183(177) Sompornpisut P Roux B Perozo E Biophys J 2008 955349(178) Bjelkmar P Niemela P S Vattulainen I Lindahl E PLoSComput Biol 2009 5 e1000289(179) Treptow W Tarek M Klein M L J Am Chem Soc 2009131 2107(180) Domene C Furini S J Mol Biol 2009 389 637(181) Furini S Beckstein O Domene C Proteins Struct FunctBioinf 2009 74 437(182) Furini S Domene C Proc Natl Acad Sci USA 2009 10616074(183) Jensen M O Borhani D W Lindorff-Larsen K MaragakisP Jogini V Eastwood M P Dror R O Shaw D E Proc NatlAcad Sci USA 2010 107 5833(184) Anishkin A Milac A L Guy H R Proteins Struct FunctBioinf 2010 78 932(185) Khalili-Araghi F Jogini V Yarov-Yarovoy V TajkhorshidE Roux B Schulten K Biophys J 2010 98 2189

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAB

(186) Pan A C Cuello L G Perozo E Roux B J Gen Physiol2011 138 571(187) Bastug T Kuyucak S Biophys J 2011 100 629(188) Schiesaro A Ecker G F Prediction of hERG ChannelInhibition Using In Silico Techniques In Ion Channels and TheirInhibitors Gupta S P Ed Springer-Verlag BerlinHeidelberg 2011pp 191minus239(189) Delemotte L Tarek M Klein M L Amaral C TreptowW Proc Natl Acad Sci USA 2011 108 6109(190) Chakrapani S Cordero-Morales J F Jogini V Pan A CCortes D M Roux B Perozo E Nat Struct Mol Biol 2011 18 67(191) Furini S Domene C J Mol Biol 2011 409 867(192) Khalili-Araghi F Tajkhorshid E Roux B Schulten KBiophys J 2012 102 258(193) Knape K Linder T Wolschann P Beyer A Stary-Weinzinger A PLoS ONE 2011 6 e28778(194) Domene C Furini S Biochemistry 2012 51 1559(195) Yang H Gao Z Li P Yu K Yu Y Xu T-L Li M JiangH Biophys J 2012 102 1815(196) Jensen M O Jogini V Borhani D W Leffler A E DrorR O Shaw D E Science 2012 336 229(197) Treptow W Klein M L J Phys Chem Lett 2012 3 1017(198) Garofoli S Jordan P C Biophys J 2003 84 2814(199) Corry B Vora T Chung S-H Biochim Biophys Acta 20051711 72(200) Huetz P Boiteux C Compoint M Ramseyer C GirardetC J Chem Phys 2006 124 044703(201) Bisset D Chung S-H Biochim Biophys Acta 2008 17782273(202) Wee C L Gavaghan D Sansom M S P Biophys J 201098 1558(203) Mafe S Pellicer J Cervera J J Chem Phys 2005 122204712(204) Treptow W Marrink S-J Tarek M J Phys Chem B 2008112 3277(205) Dryga A Chakrabarty S Vicatos S Warshel A Proc NatlAcad Sci USA 2012 109 3335(206) Dryga A Chakrabarty S Vicatos S Warshel A BiochimBiophys Acta 2012 1818 303(207) Guidoni L Carloni P Biochim Biophys Acta 2002 1563 1(208) Bucher D Raugei S Guidoni L Dal Peraro MRothlisberger U Carloni P Klein M L Biophys Chem 2006124 292(209) Kariev A M Znamenskiy V S Green M E BiochimBiophys Acta 2007 1768 1218(210) Bucher D Guidoni L Maurer P Rothlisberger U J ChemTheory Comput 2009 5 2173(211) Bucher D Rothlisberger U J Gen Physiol 2010 135 549(212) Hung A Tai K Sansom M S P Biophys J 2005 88 3321(213) Law R J Henchman R H McCammon J A Proc NatlAcad Sci USA 2005 102 6813(214) Gao M Schulten K Biophys J 2006 90 3267(215) Xu Y Barrantes F J Luo X Chen K Shen J Jiang H JAm Chem Soc 2005 127 1291(216) Xu Y Barrantes F J Shen J Luo X Zhu W Chen KJiang H J Phys Chem B 2006 110 20640(217) Cheng X Wang H Grant B Sine S M McCammon J APLoS Comput Biol 2006 2 e134(218) Law R J Lightstone F C Biophys J 2009 97 1586(219) Brannigan G Lebard D N Henin J Eckenhoff R GKlein M L Proc Natl Acad Sci USA 2010 107 14122(220) Dimitropoulos N Papakyriakou A Dalkas G A ChasapisC T Poulas K Spyroulias G A Proteins Struct Funct Bioinf 201179 142(221) Chen X Cui Q Tang Y Yoo J Yethiraj A Biophys J2008 95 563(222) Tang Y Cao G Chen X Yoo J Yethiraj A Cui QBiophys J 2006 91 1248

(223) Tang Y Yoo J Yethiraj A Cui Q Chen X Biophys J2008 95 581(224) Li S Zhang X Wang W J Phys Chem B 2009 113 14431(225) Song C Corry B PLoS ONE 2011 6 e21204(226) Wiggins P Phillips R Proc Natl Acad Sci USA 2004 1014071(227) Wiggins P Phillips R Biophys J 2005 88 880(228) Ursell T Huang K C Peterson E Phillips R PLoSComput Biol 2007 3 e81(229) Vora T Corry B Chung S-H Biochim Biophys Acta 20061758 730(230) Kong Y Shen Y Warth T E Ma J Proc Natl Acad SciUSA 2002 99 5999(231) Sukharev S Durell S R Guy H R Biophys J 2001 81 917(232) Sukharev S Betanzos M Chiang C-S S Guy H RNature 2001 409 720(233) Betanzos M Chiang C-S S Guy H R Sukharev S NatStruct Biol 2002 9 704(234) Gullingsrud J Kosztin D Schulten K Biophys J 2001 802074(235) Elmore D E Dougherty D A Biophys J 2001 81 1345(236) Bilston L E Mylvaganam K FEBS Lett 2002 512 185(237) Colombo G Marrink S J Mark A E Biophys J 2003 842331(238) Gullingsrud J Schulten K Biophys J 2003 85 2087(239) Gullingsrud J Schulten K Biophys J 2004 86 3496(240) Elmore D E Dougherty D A Biophys J 2003 85 1512(241) Sotomayor M Schulten K Biophys J 2004 87 3050(242) Anishkin A Sukharev S Biophys J 2004 86 2883(243) Spronk S A Elmore D E Dougherty D A Biophys J 200690 3555(244) Sotomayor M Vasquez V Perozo E Schulten K Biophys J2007 92 886(245) Corry B Martinac B Biochim Biophys Acta 2008 17781859(246) Corry B Jayatilaka D Biophys J 2008 95 2711(247) Anishkin A Akitake B Kamaraju K Chiang C-SSukharev S J Phys Condens Matter 2010 22 454120(248) Gamini R Sotomayor M Chipot C Schulten K Biophys J2011 101 80(249) Meyer G R Gullingsrud J Schulten K Martinac BBiophys J 2006 91 1630(250) Debret G Valadie H Stadler A M Etchebest C ProteinsStruct Funct Genet 2008 71 1183(251) Jeon J Voth G A Biophys J 2008 94 3497(252) Monticelli L Kandasamy S Periole X Larson RTieleman D P Marrink S J J Chem Theory Comput 2008 4 819(253) Yefimov S van der Giessen E Onck P Marrink S JBiophys J 2008 94 2994(254) Louhivuori M Risselada H J van der Giessen E MarrinkS J Proc Natl Acad Sci USA 2010 107 19856(255) Corry B Hurst A C Pal P Nomura T Rigby PMartinac B J Gen Physiol 2010 136 483(256) Vasquez V Sotomayor M Cordero-Morales J Schulten KPerozo E Science 2008 321 1210(257) Vasquez V Sotomayor M Cortes D M Roux B SchultenK Perozo E J Mol Biol 2008 378 55(258) Sotomayor M van der Straaten T A Ravaioli U SchultenK Biophys J 2006 90 3496(259) Choudhary O P Ujwal R Kowallis W Coalson RAbramson J Grabe M J Mol Biol 2010 396 580(260) Cohen J Schulten K Biophys J 2004 86 836(261) Suenaga A Yeh J Z Taiji M Toyama A Takeuchi HSon M Takayama K Iwamoto M Sato I Narahashi TKonagaya A Goto K Biophys Chem 2006 120 36(262) Rui H Lee K I Pastor R W Im W Biophys J 2011 100602(263) Krammer E-M Homble F Prevost M PLoS One 2011 6e27994

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAC

(264) Cheng M H Coalson R D Biophys J 2012 102 1363(265) Corry B OrsquoMara M Chung S-H Biophys J 2004 86 846(266) Bisset D Corry B Chung S-H Biophys J 2005 89 179(267) Cheng M H Mamonov A B Dukes J W Coalson R D JPhys Chem B 2007 111 5956(268) Lee K I Rui H Pastor R W Im W Biophys J 2011 100611(269) Burykin A Warshel A Biophys J 2003 85 3696(270) Stroud R M Savage D Miercke L J Lee J K KhademiS Harries W FEBS Lett 2003 555 79(271) Jensen M O Tajkhorshid E Schulten K Biophys J 200385 2884(272) de Groot B L Frigato T Helms V Grubmuller H J MolBiol 2003 333 279(273) Chen H Wu Y Voth G A Biophys J 2006 90 L73(274) Wang Y Tajkhorshid E J Nutr 2007 137 1509S(275) Bostick D L Brooks C L PLoS Comput Biol 2007 3 e22(276) Bostick D L Charles L L B Biophys J 2007 92 L103(277) Wang S Orabi E A Baday S Berneche S Lamoureux GJ Am Chem Soc 2012 134 10419(278) Luzhkov V B Almlof M Nervall M Aringqvist J Biochemistry2006 45 10807(279) Levitt D G Biophys J 1991 59 271(280) Barcilon V Chen D-P Eisenberg R SIAM J App Math1992 52 1405(281) Chen D P Barcilon V Eisenberg R S Biophys J 1992 611372(282) Chen D Eisenberg R Biophys J 1993 64 1405(283) Chen D P Eisenberg R S Biophys J 1993 65 727(284) Chen D Xu L Tripathy a Meissner G Eisenberg BBiophys J 1997 73 1337(285) Chen D Lear J Eisenberg B Biophys J 1997 72 97(286) Syganow A von Kitzing E J Phys Chem 1995 99 12030(287) Moy G Corry B Kuyucak S Chung S-H Biophys J 200078 2349(288) Corry B Kuyucak S Chung S H Biophys J 2000 78 2364(289) Crozier P Rowley R Holladay N Henderson D BusathD Phys Rev Lett 2001 86 2467(290) Gillespie D Nonner W Eisenberg R S J Phys CondensMatter 2002 14 12129(291) Gillespie D Nonner W Eisenberg R Phys Rev E 2003 681(292) Koumanov A Zachariae U Engelhardt H Karshikoff AEur Biophys J 2003 32 689(293) Kuyucak S Bastug T J Biophys 2003 29 429(294) Corry B Kuyucak S Chung S-H Biophys J 2003 84 3594(295) Beckstein O Tai K Sansom M S P J Am Chem Soc 2004126 14694(296) Graf P Kurnikova M G Coalson R D Nitzan A J PhysChem B 2004 108 2006(297) Kessel A Tieleman D P Ben-Tal N Eur Biophys J 200433 16(298) Baumgartner W Comput Biol Chem 2004 28 67(299) Roux B Allen T Bernche S Im W Q Rev Biophys 200437 15(300) Gillespie D Xu L Wang Y Meissner G J Phys Chem B2005 109 15598(301) Aguilella-Arzo M Aguilella V M Eisenberg R S EurBiophys J 2005 34 314(302) Cheng M H Coalson R D J Phys Chem B 2005 109 488(303) Hwang H Schatz G C Ratner M A J Phys Chem B 2006110 6999(304) Kandt C Ash W L Tieleman D P Methods 2007 41 475(305) Singer A Norbury J SIAM J Appl Math 2009 70 949(306) Bolintineanu D S Sayyed-Ahmad A Davis H T KaznessisY N PLoS Comput Biol 2009 5 e1000277(307) Eisenberg B J Phys Chem C 2010 114 20719(308) Eisenberg B Chem Phys Lett 2011 511 1(309) Lu B Zhou Y Biophys J 2011 100 2475

(310) Eisenberg B Adv Chem Phys 2012 77minus223(311) Krishnamurthy V Chung S-H IEEE Trans Nanobiosci 20054 102(312) Vora T Bisset D Chung S-H Biophys J 2008 95 1600(313) Gordon D Krishnamurthy V Chung S-H Mol Phys 2008106 1353(314) Vora T Corry B Chung S-H Eur Biophys J 2008 38 45(315) Song C Corry B Biophys J 2010 98 404(316) Krishnamurthy V Luk K Y IEEEACM Trans Comput BiolBioinf 2011 8 273(317) Lee K I Jo S Rui H Egwolf B Roux B Pastor R WIm W J Comput Chem 2012 33 331(318) Csanyi E Boda D Gillespie D Kristof T Biochim BiophysActa 2012 1818 592(319) Smondyrev A M Voth G A Biophys J 2002 83 1987(320) Domene C Bond P J Sansom M S P Adv Protein Chem2003 66 159(321) Tarek M Maigret B Chipot C Biophys J 2003 85 2287(322) Biggin P C Grottesi A Sansom M S P From Prokaryotesto Eukaryotes Molecular Modeling and Simulation Studies of IonChannels In Bacterial Ion Channels And Their Eukaryotic HomologsKubalski A Martinac B Eds ASM Press Washington DC 2005pp 133minus152(323) Tajkhorshid E Cohen J Aksimentiev A Sotomayor MSchulten K Towards an Understanding of Membrane Channels InBacterial Ion Channels And Their Eukaryotic Homologs Kubalski AMartinac B Eds ASM Press Washington DC 2005 pp 133minus152(324) Gumbart J Wang Y Aksimentiev A Tajkhorshid ESchulten K Curr Opin Struct Biol 2005 15 423(325) Hwang H Schatz G C Ratner M A J Phys Chem B 2006110 26448(326) Carpenter T Bond P J Khalid S Sansom M S P BiophysJ 2008 95 3790(327) Shaikh S A Tajkhorshid E Biophys J 2008 95 5153(328) Pietra F J Phys Org Chem 2008 21 997(329) Delemotte L Dehez F Treptow W Tarek M J PhysChem B 2008 112 5547(330) Maffeo C Aksimentiev A Biophys J 2009 96 4853(331) Patargias G Martay H Fischer W B J Biomol Struct Dyn2009 27 1(332) Mustafa M Henderson D J Busath D D Proteins StructFunct Bioinf 2009 76 794(333) Khalili-Araghi F Gumbart J Wen P-C Sotomayor MTajkhorshid E Schulten K Curr Opin Struct Biol 2009 19 128(334) Khurana E Dal Peraro M DeVane R Vemparala SDeGrado W F Klein M L Proc Natl Acad Sci USA 2009 1061069(335) Pan J Tieleman D P Nagle J F Kucerka N Tristram-Nagle S Biochim Biophys Acta 2009 1788 1387(336) Nury H Poitevin F Van Renterghem C Changeux J-PCorringer P-J Delarue M Baaden M Proc Natl Acad Sci USA2010 107 6275(337) Cheng M H Coalson R D Tang P J Am Chem Soc 2010132 16442(338) Zhu F Hummer G Proc Natl Acad Sci USA 2010 10719814(339) Kutzner C Grubmuller H de Groot B L Zachariae UBiophys J 2011 101 809(340) Wilson M A Wei C Bjelkmar P Wallace B A PohorilleA Biophys J 2011 100 2394(341) Stansfeld P J Sansom M S P Structure 2011 19 1562(342) Chen C-C Kruger J Sramala I Hsu H-J Henklein PChen Y-M A Fischer W B Biochim Biophys Acta 2011 1808 572(343) Raunest M Kandt C Biochemistry 2012 51 1719(344) Furini S Domene C PLoS Comput Biol 2012 8 e1002476(345) Becucci L Cembran A Karim C B Thomas D DGuidelli R Gao J Veglia G Biophys J 2009 96 L60(346) Gumbart J Khalili-Araghi F Sotomayor M Roux BBiochim Biophys Acta 2011 1818 294

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAD

(347) Carnevale V Treptow W Klein M L J Phys Chem Lett2011 2 2504(348) Bhattacharya S Derrington I M Pavlenok M NiederweisM Gundlach J H Aksimentiev A ACS Nano 2012 6 6960(349) Graf P Nitzan A Kurnikova M G Coalson R D J PhysChem B 2000 104 12324(350) Peter C Hummer G Biophys J 2005 89 2222(351) Boda D Valisko M Eisenberg B Nonner W HendersonD Gillespie D Phys Rev Lett 2007 98 1(352) Thoslashgersen L Schioslashtt B Vosegaard T Nielsen N CTajkhorshid E Biophys J 2008 95 4337(353) Plank G Zhou L Greenstein J L Cortassa S Winslow RL OrsquoRourke B Trayanova N A Philos Trans R Soc A 2008 3663381(354) Eisenberg B Hyon Y Liu C J Chem Phys 2010 133104104(355) Hannongbua S Treesuwan W Boonyarat W AdvancedMolecular Modeling Techniques Applied to Ion Channels Blockers InIon Channels and Their Inhibitors Gupta S P Ed Springer-VerlagBerlinHeidelberg 2011 pp 53minus78(356) Zheng W Auerbach A PLoS Comput Biol 2011 7e1001046(357) Boda D Busath D D Eisenberg B Henderson DNonner W Phys Chem Chem Phys 2002 4 5154(358) Boda D Henderson D Busath D D Mol Phys 2002 1002361(359) Cervera J Schiedt B Ramirez P Europhys Lett 2005 7135(360) Vidal J Gracheva M E Leburton J-P Nanoscale Res Lett2006 2 61(361) Gracheva M Leburton J-P Nanotechnology 2007 18145704(362) Vidal J Gracheva M Leburton J-P Nanoscale Res Lett2007 2 61(363) Cervera J Alcaraz A Schiedt B Neumann R Ramirez PJ Phys Chem C 2007 111 12265(364) Vlassiouk I Smirnov S Siwy Z Nano Lett 2008 8 1978(365) Gillespie D Boda D He Y Apel P Siwy Z S Biophys J2008 95 609(366) Kosin ska I D Hanggi P Phys Rev E 2008 77 1(367) Reiner J E Kasianowicz J J Nablo B J Robertson J W FProc Natl Acad Sci USA 2010 107 12080(368) Zhang Y Voth G A J Chem Theory Comput 2011 7 2277(369) Zhang M Yeh L Qian S Hsu J J Phys Chem C 2012116 4793(370) Yeh L-h Zhang M Qian S Hsu J-p Tseng S J PhysChem C 2012 116 8672(371) Carr R Comer J Ginsberg M Aksimentiev A Lab Chip2011 11 3766(372) Peters M H J Chem Phys 2011 134 025105(373) Comer J Aksimentiev A J Phys Chem C 2012 116 3376(374) Timp W Comer J Aksimentiev A Biophys J 2012 102L37(375) Aksimentiev A Heng J B Timp G Schulten K Biophys J2004 87 2086(376) Heng J B Aksimentiev A Ho C Marks P Grinkova YV Sligar S Schulten K Timp G Biophys J 2006 90 1098(377) Lu D Aksimentiev A Shih A Y Cruz-Chu E FreddolinoP L Arkhipov A Schulten K Phys Bio 2006 3 S40(378) Luan B Aksimentiev A Phys Rev E 2008 78 021912(379) Carr R Weinstock I A Sivaprasadarao A Muller AAksimentiev A Nano Lett 2008 8 3916(380) Comer J Dimitrov V Zhao Q Timp G Aksimentiev ABiophys J 2009 96 593(381) Luan B Aksimentiev A J Phys Condens Matter 2010 22454123(382) Gracheva M Xiong A Aksimentiev A Schulten K TimpG Leburton J-P Nanotechnology 2006 17 622

(383) Gracheva M Aksimentiev A Leburton J-P Nanotechnology2006 17 3160(384) Sigalov G Comer J Timp G Aksimentiev A Nano Lett2008 8 56(385) Cruz-Chu E R Aksimentiev A Schulten K J Phys Chem C2009 113 1850(386) Dorvel B Sigalov G Zhao Q Comer J Dimitrov VMirsaidov U Aksimentiev A Timp G Nucleic Acids Res 2009 374170(387) Wang D Timp W Shim J Mirsaidov U Comer JAksimentiev A Timp G Biophys J 2010 98 599a(388) Comer J Aksimentiev A Nanopore Force SpectroscopyInsights from Molecular Dynamics Simulations In Nanopores Sensingand Fundamental Biological Interactions Bashir R Iqbal S EdsSpringer Science and Business Media LLC New York 2011 Chapter14 pp 335minus356(389) Sathe C Zou X Leburton J-P Schulten K ACS Nano2011 5 8842(390) Wanunu M Bhattacharya S Xie Y Tor Y AksimentievA Drndic M ACS Nano 2011 5 9345(391) Kowalczyk S W Wells D B Aksimentiev A Dekker CNano Lett 2012 12 1038(392) Wells D B Belkin M Comer J Aksimentiev A Nano Lett2012 8 4117(393) Edmonds C M Hudiono Y C Ahmadi A G Hesketh PJ Nair S J Chem Phys 2012 136 065105(394) Saha K K Drndic M Nikolic B K Nano Lett 2012 12 50(395) Hille B Ionic channels of excitable membranes 3rd ed SinauerAssociates Sunderland MA 2001(396) Hodgkin A L Huxley A F J Physiol 1952 117 500(397) Hodgkin A L Huxley A F J Physiol 1952 117 500(398) Alberts B Johnson A Lewis J Raff M Roberts K WalterP Molecular Biology of The Cell 5th ed Garland Science New York ampLondon 2007(399) Watanabe H Sugiura S Kafuku H Hisada T Biophys J2004 87 2074(400) Wong J Goktepe S Kuhl E Comput Methods Appl MechEngrg 2011 200 3139(401) Rowat P Neur Comp 2007 19 1215(402) Tuckwell H C Jost J Physica A 2009 388 4115(403) Linaro D Storace M Giugliano M PLoS Comput Biol2011 7 e1001102(404) Che Y-Q Wang J Zhou S-S Deng B Chaos SolitonsFractals 2009 40 1588(405) Beard D A PLoS Comput Biol 2005 1 e36(406) Townsley L E Tucker W A Sham S Hinton J FBiochemistry 2001 40 11676(407) Chang G Spencer R H Lee A T Barclay M T Rees DC Science 1998 282 2220(408) Bass R B Strop P Barclay M Rees D C Science 2002298 1582(409) Conroy M J Durand A Lupo D Li X-D D BulloughP A Winkler F K Merrick M Proc Natl Acad Sci USA 2007104 1213(410) Uysal S Vasquez V Tereshko V Esaki K Fellouse FSidhu S Koide S Perozo E Kossiakoff A Proc Natl Acad SciUSA 2009 106 6644(411) Long S B Tao X Campbell E B MacKinnon R Nature2007 450 376(412) Gonen T Cheng Y Sliz P Hiroaki Y Fujiyoshi YHarrison S C Walz T Nature 2005 438 633(413) Miyazawa A Fujiyoshi Y Unwin N Nature 2003 423 949(414) Unwin N J Mol Biol 2005 346 967(415) Cowan S Schirmer T Rummel G Steiert M Ghosh RPauptit R Jansonius J Rosenbusch J Nature 1992 358 727(416) Dutzler R Campbell E B MacKinnon R Science 2003 300108(417) Song L Hobaugh M R Shustak C Cheley S Bayley HGouaux J E Science 1996 274 1859

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAE

(418) Malasics A Gillespie D Nonner W Henderson DEisenberg B Boda D Biochim Biophys Acta Biomembr 2009 17882471(419) Giri J Fonseca J Boda D Henderson D Eisenberg BPhys Bio 2011 8 026004(420) Mackay D H Berens P H Wilson K R Hagler A TBiophys J 1984 46 229(421) Morais-Cabral J H Zhou Y MacKinnon R Nature 2001414 37(422) Wulff H Calabresi P A Allie R Yun S Pennington MBeeton C Chandy K G J Clin Invest 2003 111 1703(423) Judge S I V Bever C T Pharmacol Ther 2006 111 224(424) Parsegian A Nature 1969 221 844(425) Rashid M H Kuyucak S J Phys Chem B 2012 116 4812(426) Kung C Nature 2005 436 647(427) Kung C Martinac B Sukharev S Annu Rev Microbiol2010 64 313(428) Sukharev S I Blount P Martinac B Blattner F R KungC Nature 1994 368 265(429) Levina N Totemeyer S Stokes N R Louis P Jones MA Booth I R EMBO J 1999 18 1730(430) Wang W Black S S Edwards M D Miller S Morrison EL Bartlett W Dong C Naismith J H Booth I R Science 2008321 1179(431) Liu Z Gandhi C S Rees D C Nature 2009 461 120(432) Martinac B Buechner M Delcour A H Adler J Kung CProc Natl Acad Sci USA 1987 84 2297(433) Weiss M S Schulz G E J Mol Biol 1992 227 493(434) Kreusch A Schulz G J Mol Biol 1994 243 891(435) Cowan S W Garavito R M Jansonius J N Jenkins J AKarlsson R Konig N Pai E F Pauptit R A Rizkallah P JRosenbusch J P Structure 1995 3 1041(436) Schirmer T Keller T A Wang Y F Rosenbusch J PScience 1995 267 512(437) Dutzler R Rummel G Albert S Hernandez-Alles S PhaleP Rosenbusch J Bened V Schirmer T Structure 1999 7 425(438) Moraes T F Bains M Hancock R E W Strynadka N CJ Nat Struct Mol Biol 2007 14 85(439) Biswas S Mohammad M M Movileanu L van der Berg BStructure 2008 16 1027(440) Tamber S Hancock R E W FEMS Microbiol Lett 2006260 23(441) Liu J Eren E Vijayaraghavan J Cheneke B R Indic Mvan den Berg B Movileanu L Biochemistry 2012 51 2319(442) Cheneke B R van der Berg B Movileanu L Biochemistry2011 50 4987(443) Cheneke B R Indic M van den Berg B Movileanu LBiochemistry 2012 51 5348(444) Vila J Mart S Sanchez-Cespedes J J Antimicrob Chemother2007 59 1210(445) Song L Hobaugh M R Shustak C Cheley S Bayley HGouaux J E Science 1996 274 1859(446) Kasianowicz J Robertson J W F Chan E R Reiner J EStanford V M Annu Rev Anal Chem 2008 1 737(447) Kasianowicz J J Brandin E Branton D Deamer D WProc Natl Acad Sci USA 1996 93 13770(448) Faller R Neiderweis M Schulz G E Science 2004 3031189(449) Butler T Pavlenok M Derrington I Niederweis MGundlach J Proc Natl Acad Sci USA 2008 105 20647(450) Derrington I M Collins M D Pavlenok M NiederweisM Gundlach J H Biophys J 2010 98 422a(451) Manrao E Derrington I Pavlenok M Niederweis MGundlach J PLoS One 2011 6 e25723(452) Roos N Benz R Brdiczka D Biochim Biophys Acta 1982686 204(453) Hiller S Garces R G Malia T J Orekhov V YColombini M Wagner G Science 2008 321 1206

(454) Ujwal R Cascio D Colletier J-P Faham S Zhang JToro L Ping P Proc Natl Acad Sci USA 2008 105 2(455) Bayrhuber M Meins T Habeck M Becker S Giller KVillinger S Vonrhein C Griesinger C Zweckstetter M Zeth KProc Natl Acad Sci USA 2008 105 15370(456) Colombini M Trends Biochem Sci 2009 34 382(457) Hiller S Abramson J Mannella C Wagner G Zeth KTrends Biochem Sci 2010 35 514(458) Hiller S Raschle T Yu T-Y Rice A J Walz T WagnerG Biochim Biophys Acta Bioenerg 2010 1797 66(459) Chen T-Y Annu Rev Physiol 2005 67 809(460) Dutzler R Campbell E B Cadene M Chait B TMacKinnon R Nature 2002 415 287(461) Accardi A Miller C Nature 2004 427 803(462) Steinlein O K Bertrand D Biochem Pharmacol 2008 761175(463) Rose J E Biochem Pharmacol 2007 74 1263(464) Marini A M Soussi-Boudekou S Vissers S Andre B MolCell Biol 1997 17 4282(465) Ninnemann O Jauniaux J C Frommer W B EMBO J1994 13 3464(466) Marini A M Vissers S Urrestarazu A Andre B EMBO J1994 13 3456(467) Khademi S OrsquoConnell J Remis J Robles-Colmenares YMiercke L J W Stroud R M Science 2004 305 1587(468) Javelle A Lupo D Ripoche P Fulford T Merrick MWinkler F K Proc Natl Acad Sci USA 2008 105 5040(469) Gruswitz F OrsquoConnell J Stroud R M Proc Natl Acad SciUSA 2007 104 42(470) Javelle A Lupo D Zheng L Li X-D D Winkler F KMerrick M J Biol Chem 2006 281 39492(471) Gao J Truhlar D G Annu Rev Phys Chem 2002 53 467(472) Kamerlin S C L Vicatos S Dryga A Warshel A AnnuRev Phys Chem 2011 62 41(473) Modi N Winterhalter M Kleinekathofer U Nanoscale2012 4 6166(474) Maffeo C Schopflin R Brutzer H Stehr R AksimentievA Wedemann G Seidel R Phys Rev Lett 2010 105 158101(475) Simonson T Carlsson J Case D A J Am Chem Soc 2004126 4167(476) Rocchia W Alxov E Honig B J Phys Chem B 2001 1056507(477) Baker N Sept D Joseph S Hoist M McCammon J ProcNatl Acad Sci USA 2001 98 10037(478) Ramrez P Aguilella-Arzo M Alcaraz A Cervera JAguilella V M Cell Biochem Biophys 2006 44 287(479) Woolley G Biggin P Schultz A Lien L Jaikaran DBreed J Crowhurst K Sansom M Biophys J 1997 73 770(480) Nonner W Chen D Eisenberg B Biophys J 1998 74 2327(481) Roth R J Phys Condens Matter 2010 22 063102(482) Woolf T Roux B Proc Natl Acad Sci USA 1994 9111631(483) Hummer G New J Phys 2005 7 34(484) Paine P L Scherr P Biophys J 1975 15 1087(485) Roux B Biophys J 1999 77 139(486) Corry B Allen T Kuyucak S Chung S Biophys J 200180 195(487) Cooper K Jakobsson E Wolynes P Prog Biophys Mol Biol1985 46 51(488) Mackerell A D J Comput Chem 2004 25 1584(489) MacKerell D A Bashford D Bellott Dunbrack L REvanseck J D Field M J Fischer S Gao J Guo H Ha SJoseph-McCarthy D Kuchnir L Kuczera K Lau F T K MattosC Michnick S Ngo T Nguyen D T Prodhom B Reiher W ERoux B Schlenkrich M Smith J C Stote R Straub J WatanabeM Wiorkiewicz-Kuczera J Yin D Karplus M J Phys Chem B1998 102 3586(490) Weiner P K Kollman P A J Comput Chem 1981 2 287

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAF

(491) Cornell W D Cieplak P Bayly C I Gould I R Merz KM Ferguson D M Spellmeyer D C Fox T Caldwell J WKollman P A J Am Chem Soc 1995 117 5179(492) Jorgensen W L Maxwell D S Tirado-Rives J J Am ChemSoc 1996 118 11225(493) Kaminski G A Friesner R A Tirado-Rives J Jorgensen WL J Phys Chem B 2001 105 6474(494) Hermans J Berendsen H J C Van Gunsteren W FPostma J P M Biopolymers 1984 23 1513(495) Schmid N Eichenberger A P Choutko A Riniker SWinger M Mark A E van Gunsteren W F Eur Biophys J 201140 843(496) Klauda J B Venable R M Freites J A OrsquoConnor J WTobias D J Mondragon-Ramirez C Vorobyov I MacKerell A DPastor R W J Phys Chem B 2010 114 7830(497) Wang J Wolf R M Caldwell J W Kollman P A Case DA J Comput Chem 2004 25 1157(498) Liu Y Chipot C Shao X Cai W Phys Bio 2011 8056005(499) Daura X Mark A E van Gunsteren W F J Comput Chem1998 19 535(500) Berger O Edholm O Jahnig F Biophys J 1997 72 2002(501) Cordomiacute A Caltabiano G Pardo L J Chem TheoryComput 2012 8 948(502) Aksimentiev A Wells D Sotomayor M Membrane ProteinTutorial httpwwwksuiuceduTrainingTutorialssciencemembranemem-tutorialpdfrelax(503) Humphrey W Dalke A Schulten K J Mol Graphics 199614 33(504) Brooks B R Bruccoleri R E Olafson B D States D JSwaminathan S Karplus M J Comput Chem 1983 187(505) Jo S Lim J B Klauda J B Im W Biophys J 2009 97 50(506) Ayton G S Voth G A Curr Opin Struct Biol 2009 19 138(507) Marrink S J de Vries A H Tieleman D P BiochimBiophys Acta 2009 1788 149(508) Nielsen S O Lopez C F Srinivas G Klein M L J PhysCondens Matter 2004 16 R481(509) Yesylevskyy S O Schafer L V Sengupta D Marrink S JPLoS Comput Biol 2010 6 e1000810(510) Wu Z Cui Q Yethiraj A J Phys Chem B 2010 114 10524(511) Sali A Blundell T L J Mol Biol 1993 234 779(512) Capener C E Shrivastava I H Ranatunga K M Forrest LR Smith G R Sansom M S Biophys J 2000 78 2929(513) Roux B Comput Phys Commun 1995 91 275(514) Kollman P Chem Rev 1993 93 2395(515) Pohorille A Jarzynski C Chipot C J Phys Chem B 2010114 10235(516) Torrie G Valleau J J Comput Phys 1977 23 187(517) Kumar S Bouzida D Swendsen R H Kollman P ARosenberg J M J Comput Chem 1992 13 1011(518) Woo H-J Roux B Proc Natl Acad Sci USA 2005 1026825(519) Singh U C Brown F K Bash P A Kollman P A J AmChem Soc 1987 109 1607(520) Grubmuller H Heymann B Tavan P Science 1996 271997(521) Isralewitz B Izrailev S Schulten K Biophys J 1997 732972(522) Izrailev S Stepaniants S Balsera M Oono Y Schulten KBiophys J 1997 72 1568(523) Stepaniants S Izrailev S Schulten K J Mol Mod 1997 3473(524) Marrink S-J Berger O Tieleman P Jahnig F Biophys J1998 74 931(525) Kosztin D Izrailev S Schulten K Biophys J 1999 76 188(526) Hummer G Szabo A Acc Chem Res 2005 38 504(527) Jarzynski C Phys Rev Lett 1997 78 2690(528) Bucher D Guidoni L Rothlisberger U Biophys J 2007 932315

(529) Arkin I T Xu H F Jensen M O Arbely E Bennett E RBowers K J Chow E Dror R O Eastwood M P Flitman-TeneR Gregersen B A Klepeis J L Kolossvary I Shan Y B Shaw DE Science 2007 317 799(530) Warshel A Sussman F King G Biochemistry 1986 25 8368(531) Li L Vorobyov I Mackerell A D Allen T W Biophys J2007 94 L11(532) Li L Vorobyov I Allen T W J Phys Chem B 2008 1129574(533) Yoo J Cui Q Biophys J 2008 94 L61(534) MacCallum J L Bennett W F D Tieleman D P Biophys J2008 94 3393(535) Yoo J Cui Q Biophys J 2010 99 1529(536) Johansson A C V Lindahl E J Phys Chem B 2009 113245(537) Honig B Sharp K Yang A S J Phys Chem 1993 97 1101(538) Lim C Bashford D Karplus M J Phys Chem 1991 955610(539) Warshel A Papazyan A Curr Opin Struct Biol 1998 8 211(540) Ullmann G M Knapp E-W Eur Biophys J 1999 28 533(541) Srinivasan J Trevathan M W Beroza P Case D A TheorChem Acc 1999 101 426(542) Koumanov A Ruterjans H Karshikoff A Proteins StructFunct Genet 2002 46 85(543) Mongan J Case D A McCammon J A J Comput Chem2004 25 2038(544) Mongan J Case D A Curr Opin Struct Biol 2005 15 157(545) Khandogin J Brooks C L Biochemistry 2006 45 9363(546) Gunner G Mao J Song Y Kim J Biochim Biophys ActaBioenerg 2006 1757 942(547) Spassov V Z Yan L Protein Sci 2008 17 1955(548) Karshikoff A Spassov V Cowan S W Ladenstein RSchirmer T J Mol Biol 1994 240 372(549) Tanizaki S Feig M J Chem Phys 2005 122 124706(550) Gordon J C Myers J B Folta T Shoja V Heath L SOnufriev A Nucleic Acids Res 2005 33 W368(551) Olsson M H M Soslashndergaard C R Rostkowski M JensenJ H J Chem Theory Comput 2011 7 525(552) Jo S Vargyas M Vasko-Szedlar J Roux B Im W NucleicAcids Res 2008 36 W270(553) Shaw D E Chao J C Eastwood M P Gagliardo JGrossman J P P Ho C R Lerardi D J Kolossvary I Klepeis JL Layman T McLeavey C Deneroff M M Moraes M AMueller R Priest E C Shan Y Spengler J Theobald M TowlesB Wang S C Dror R O Kuskin J S Larson R H Salmon J KYoung C Batson B Bowers K J Commun ACM 2008 51 91(554) Shaw D E J Comput Chem 2005 26 1318(555) Dror R O Jensen M O Borhani D W Shaw D E J GenPhysiol 2010 135 555(556) Dror R O Dirks R M Grossman J P Xu H Shaw D EAnnu Rev Biochem 2012 41 429(557) Dror R O Pan A C Arlow D H Borhani D WMaragakis P Shan Y Xu H Shaw D E Proc Natl Acad Sci USA2011 108 13118(558) Rosenbaum D M Zhang C Lyons J A Holl R AragaoD Arlow D H Rasmussen S G F Choi H-J J Devree B TSunahara R K Chae P S Gellman S H Dror R O Shaw D EWeis W I Caffrey M Gmeiner P Kobilka B K Nature 2011 469236(559) Kruse A C Hu J Pan A C Arlow D H Rosenbaum DM Rosemond E Green H F Liu T Chae P S Dror R OShaw D E Weis W I Wess J Kobilka B K Nature 2012 482552(560) Jensen M O Dror R O Xu H F Borhani D W Arkin IT Eastwood M P Shaw D E Proc Natl Acad Sci USA 2008105 14430(561) Vorobyov I V Anisimov V M MacKerell A D J PhysChem B 2005 109 18988

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAG

(186) Pan A C Cuello L G Perozo E Roux B J Gen Physiol2011 138 571(187) Bastug T Kuyucak S Biophys J 2011 100 629(188) Schiesaro A Ecker G F Prediction of hERG ChannelInhibition Using In Silico Techniques In Ion Channels and TheirInhibitors Gupta S P Ed Springer-Verlag BerlinHeidelberg 2011pp 191minus239(189) Delemotte L Tarek M Klein M L Amaral C TreptowW Proc Natl Acad Sci USA 2011 108 6109(190) Chakrapani S Cordero-Morales J F Jogini V Pan A CCortes D M Roux B Perozo E Nat Struct Mol Biol 2011 18 67(191) Furini S Domene C J Mol Biol 2011 409 867(192) Khalili-Araghi F Tajkhorshid E Roux B Schulten KBiophys J 2012 102 258(193) Knape K Linder T Wolschann P Beyer A Stary-Weinzinger A PLoS ONE 2011 6 e28778(194) Domene C Furini S Biochemistry 2012 51 1559(195) Yang H Gao Z Li P Yu K Yu Y Xu T-L Li M JiangH Biophys J 2012 102 1815(196) Jensen M O Jogini V Borhani D W Leffler A E DrorR O Shaw D E Science 2012 336 229(197) Treptow W Klein M L J Phys Chem Lett 2012 3 1017(198) Garofoli S Jordan P C Biophys J 2003 84 2814(199) Corry B Vora T Chung S-H Biochim Biophys Acta 20051711 72(200) Huetz P Boiteux C Compoint M Ramseyer C GirardetC J Chem Phys 2006 124 044703(201) Bisset D Chung S-H Biochim Biophys Acta 2008 17782273(202) Wee C L Gavaghan D Sansom M S P Biophys J 201098 1558(203) Mafe S Pellicer J Cervera J J Chem Phys 2005 122204712(204) Treptow W Marrink S-J Tarek M J Phys Chem B 2008112 3277(205) Dryga A Chakrabarty S Vicatos S Warshel A Proc NatlAcad Sci USA 2012 109 3335(206) Dryga A Chakrabarty S Vicatos S Warshel A BiochimBiophys Acta 2012 1818 303(207) Guidoni L Carloni P Biochim Biophys Acta 2002 1563 1(208) Bucher D Raugei S Guidoni L Dal Peraro MRothlisberger U Carloni P Klein M L Biophys Chem 2006124 292(209) Kariev A M Znamenskiy V S Green M E BiochimBiophys Acta 2007 1768 1218(210) Bucher D Guidoni L Maurer P Rothlisberger U J ChemTheory Comput 2009 5 2173(211) Bucher D Rothlisberger U J Gen Physiol 2010 135 549(212) Hung A Tai K Sansom M S P Biophys J 2005 88 3321(213) Law R J Henchman R H McCammon J A Proc NatlAcad Sci USA 2005 102 6813(214) Gao M Schulten K Biophys J 2006 90 3267(215) Xu Y Barrantes F J Luo X Chen K Shen J Jiang H JAm Chem Soc 2005 127 1291(216) Xu Y Barrantes F J Shen J Luo X Zhu W Chen KJiang H J Phys Chem B 2006 110 20640(217) Cheng X Wang H Grant B Sine S M McCammon J APLoS Comput Biol 2006 2 e134(218) Law R J Lightstone F C Biophys J 2009 97 1586(219) Brannigan G Lebard D N Henin J Eckenhoff R GKlein M L Proc Natl Acad Sci USA 2010 107 14122(220) Dimitropoulos N Papakyriakou A Dalkas G A ChasapisC T Poulas K Spyroulias G A Proteins Struct Funct Bioinf 201179 142(221) Chen X Cui Q Tang Y Yoo J Yethiraj A Biophys J2008 95 563(222) Tang Y Cao G Chen X Yoo J Yethiraj A Cui QBiophys J 2006 91 1248

(223) Tang Y Yoo J Yethiraj A Cui Q Chen X Biophys J2008 95 581(224) Li S Zhang X Wang W J Phys Chem B 2009 113 14431(225) Song C Corry B PLoS ONE 2011 6 e21204(226) Wiggins P Phillips R Proc Natl Acad Sci USA 2004 1014071(227) Wiggins P Phillips R Biophys J 2005 88 880(228) Ursell T Huang K C Peterson E Phillips R PLoSComput Biol 2007 3 e81(229) Vora T Corry B Chung S-H Biochim Biophys Acta 20061758 730(230) Kong Y Shen Y Warth T E Ma J Proc Natl Acad SciUSA 2002 99 5999(231) Sukharev S Durell S R Guy H R Biophys J 2001 81 917(232) Sukharev S Betanzos M Chiang C-S S Guy H RNature 2001 409 720(233) Betanzos M Chiang C-S S Guy H R Sukharev S NatStruct Biol 2002 9 704(234) Gullingsrud J Kosztin D Schulten K Biophys J 2001 802074(235) Elmore D E Dougherty D A Biophys J 2001 81 1345(236) Bilston L E Mylvaganam K FEBS Lett 2002 512 185(237) Colombo G Marrink S J Mark A E Biophys J 2003 842331(238) Gullingsrud J Schulten K Biophys J 2003 85 2087(239) Gullingsrud J Schulten K Biophys J 2004 86 3496(240) Elmore D E Dougherty D A Biophys J 2003 85 1512(241) Sotomayor M Schulten K Biophys J 2004 87 3050(242) Anishkin A Sukharev S Biophys J 2004 86 2883(243) Spronk S A Elmore D E Dougherty D A Biophys J 200690 3555(244) Sotomayor M Vasquez V Perozo E Schulten K Biophys J2007 92 886(245) Corry B Martinac B Biochim Biophys Acta 2008 17781859(246) Corry B Jayatilaka D Biophys J 2008 95 2711(247) Anishkin A Akitake B Kamaraju K Chiang C-SSukharev S J Phys Condens Matter 2010 22 454120(248) Gamini R Sotomayor M Chipot C Schulten K Biophys J2011 101 80(249) Meyer G R Gullingsrud J Schulten K Martinac BBiophys J 2006 91 1630(250) Debret G Valadie H Stadler A M Etchebest C ProteinsStruct Funct Genet 2008 71 1183(251) Jeon J Voth G A Biophys J 2008 94 3497(252) Monticelli L Kandasamy S Periole X Larson RTieleman D P Marrink S J J Chem Theory Comput 2008 4 819(253) Yefimov S van der Giessen E Onck P Marrink S JBiophys J 2008 94 2994(254) Louhivuori M Risselada H J van der Giessen E MarrinkS J Proc Natl Acad Sci USA 2010 107 19856(255) Corry B Hurst A C Pal P Nomura T Rigby PMartinac B J Gen Physiol 2010 136 483(256) Vasquez V Sotomayor M Cordero-Morales J Schulten KPerozo E Science 2008 321 1210(257) Vasquez V Sotomayor M Cortes D M Roux B SchultenK Perozo E J Mol Biol 2008 378 55(258) Sotomayor M van der Straaten T A Ravaioli U SchultenK Biophys J 2006 90 3496(259) Choudhary O P Ujwal R Kowallis W Coalson RAbramson J Grabe M J Mol Biol 2010 396 580(260) Cohen J Schulten K Biophys J 2004 86 836(261) Suenaga A Yeh J Z Taiji M Toyama A Takeuchi HSon M Takayama K Iwamoto M Sato I Narahashi TKonagaya A Goto K Biophys Chem 2006 120 36(262) Rui H Lee K I Pastor R W Im W Biophys J 2011 100602(263) Krammer E-M Homble F Prevost M PLoS One 2011 6e27994

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAC

(264) Cheng M H Coalson R D Biophys J 2012 102 1363(265) Corry B OrsquoMara M Chung S-H Biophys J 2004 86 846(266) Bisset D Corry B Chung S-H Biophys J 2005 89 179(267) Cheng M H Mamonov A B Dukes J W Coalson R D JPhys Chem B 2007 111 5956(268) Lee K I Rui H Pastor R W Im W Biophys J 2011 100611(269) Burykin A Warshel A Biophys J 2003 85 3696(270) Stroud R M Savage D Miercke L J Lee J K KhademiS Harries W FEBS Lett 2003 555 79(271) Jensen M O Tajkhorshid E Schulten K Biophys J 200385 2884(272) de Groot B L Frigato T Helms V Grubmuller H J MolBiol 2003 333 279(273) Chen H Wu Y Voth G A Biophys J 2006 90 L73(274) Wang Y Tajkhorshid E J Nutr 2007 137 1509S(275) Bostick D L Brooks C L PLoS Comput Biol 2007 3 e22(276) Bostick D L Charles L L B Biophys J 2007 92 L103(277) Wang S Orabi E A Baday S Berneche S Lamoureux GJ Am Chem Soc 2012 134 10419(278) Luzhkov V B Almlof M Nervall M Aringqvist J Biochemistry2006 45 10807(279) Levitt D G Biophys J 1991 59 271(280) Barcilon V Chen D-P Eisenberg R SIAM J App Math1992 52 1405(281) Chen D P Barcilon V Eisenberg R S Biophys J 1992 611372(282) Chen D Eisenberg R Biophys J 1993 64 1405(283) Chen D P Eisenberg R S Biophys J 1993 65 727(284) Chen D Xu L Tripathy a Meissner G Eisenberg BBiophys J 1997 73 1337(285) Chen D Lear J Eisenberg B Biophys J 1997 72 97(286) Syganow A von Kitzing E J Phys Chem 1995 99 12030(287) Moy G Corry B Kuyucak S Chung S-H Biophys J 200078 2349(288) Corry B Kuyucak S Chung S H Biophys J 2000 78 2364(289) Crozier P Rowley R Holladay N Henderson D BusathD Phys Rev Lett 2001 86 2467(290) Gillespie D Nonner W Eisenberg R S J Phys CondensMatter 2002 14 12129(291) Gillespie D Nonner W Eisenberg R Phys Rev E 2003 681(292) Koumanov A Zachariae U Engelhardt H Karshikoff AEur Biophys J 2003 32 689(293) Kuyucak S Bastug T J Biophys 2003 29 429(294) Corry B Kuyucak S Chung S-H Biophys J 2003 84 3594(295) Beckstein O Tai K Sansom M S P J Am Chem Soc 2004126 14694(296) Graf P Kurnikova M G Coalson R D Nitzan A J PhysChem B 2004 108 2006(297) Kessel A Tieleman D P Ben-Tal N Eur Biophys J 200433 16(298) Baumgartner W Comput Biol Chem 2004 28 67(299) Roux B Allen T Bernche S Im W Q Rev Biophys 200437 15(300) Gillespie D Xu L Wang Y Meissner G J Phys Chem B2005 109 15598(301) Aguilella-Arzo M Aguilella V M Eisenberg R S EurBiophys J 2005 34 314(302) Cheng M H Coalson R D J Phys Chem B 2005 109 488(303) Hwang H Schatz G C Ratner M A J Phys Chem B 2006110 6999(304) Kandt C Ash W L Tieleman D P Methods 2007 41 475(305) Singer A Norbury J SIAM J Appl Math 2009 70 949(306) Bolintineanu D S Sayyed-Ahmad A Davis H T KaznessisY N PLoS Comput Biol 2009 5 e1000277(307) Eisenberg B J Phys Chem C 2010 114 20719(308) Eisenberg B Chem Phys Lett 2011 511 1(309) Lu B Zhou Y Biophys J 2011 100 2475

(310) Eisenberg B Adv Chem Phys 2012 77minus223(311) Krishnamurthy V Chung S-H IEEE Trans Nanobiosci 20054 102(312) Vora T Bisset D Chung S-H Biophys J 2008 95 1600(313) Gordon D Krishnamurthy V Chung S-H Mol Phys 2008106 1353(314) Vora T Corry B Chung S-H Eur Biophys J 2008 38 45(315) Song C Corry B Biophys J 2010 98 404(316) Krishnamurthy V Luk K Y IEEEACM Trans Comput BiolBioinf 2011 8 273(317) Lee K I Jo S Rui H Egwolf B Roux B Pastor R WIm W J Comput Chem 2012 33 331(318) Csanyi E Boda D Gillespie D Kristof T Biochim BiophysActa 2012 1818 592(319) Smondyrev A M Voth G A Biophys J 2002 83 1987(320) Domene C Bond P J Sansom M S P Adv Protein Chem2003 66 159(321) Tarek M Maigret B Chipot C Biophys J 2003 85 2287(322) Biggin P C Grottesi A Sansom M S P From Prokaryotesto Eukaryotes Molecular Modeling and Simulation Studies of IonChannels In Bacterial Ion Channels And Their Eukaryotic HomologsKubalski A Martinac B Eds ASM Press Washington DC 2005pp 133minus152(323) Tajkhorshid E Cohen J Aksimentiev A Sotomayor MSchulten K Towards an Understanding of Membrane Channels InBacterial Ion Channels And Their Eukaryotic Homologs Kubalski AMartinac B Eds ASM Press Washington DC 2005 pp 133minus152(324) Gumbart J Wang Y Aksimentiev A Tajkhorshid ESchulten K Curr Opin Struct Biol 2005 15 423(325) Hwang H Schatz G C Ratner M A J Phys Chem B 2006110 26448(326) Carpenter T Bond P J Khalid S Sansom M S P BiophysJ 2008 95 3790(327) Shaikh S A Tajkhorshid E Biophys J 2008 95 5153(328) Pietra F J Phys Org Chem 2008 21 997(329) Delemotte L Dehez F Treptow W Tarek M J PhysChem B 2008 112 5547(330) Maffeo C Aksimentiev A Biophys J 2009 96 4853(331) Patargias G Martay H Fischer W B J Biomol Struct Dyn2009 27 1(332) Mustafa M Henderson D J Busath D D Proteins StructFunct Bioinf 2009 76 794(333) Khalili-Araghi F Gumbart J Wen P-C Sotomayor MTajkhorshid E Schulten K Curr Opin Struct Biol 2009 19 128(334) Khurana E Dal Peraro M DeVane R Vemparala SDeGrado W F Klein M L Proc Natl Acad Sci USA 2009 1061069(335) Pan J Tieleman D P Nagle J F Kucerka N Tristram-Nagle S Biochim Biophys Acta 2009 1788 1387(336) Nury H Poitevin F Van Renterghem C Changeux J-PCorringer P-J Delarue M Baaden M Proc Natl Acad Sci USA2010 107 6275(337) Cheng M H Coalson R D Tang P J Am Chem Soc 2010132 16442(338) Zhu F Hummer G Proc Natl Acad Sci USA 2010 10719814(339) Kutzner C Grubmuller H de Groot B L Zachariae UBiophys J 2011 101 809(340) Wilson M A Wei C Bjelkmar P Wallace B A PohorilleA Biophys J 2011 100 2394(341) Stansfeld P J Sansom M S P Structure 2011 19 1562(342) Chen C-C Kruger J Sramala I Hsu H-J Henklein PChen Y-M A Fischer W B Biochim Biophys Acta 2011 1808 572(343) Raunest M Kandt C Biochemistry 2012 51 1719(344) Furini S Domene C PLoS Comput Biol 2012 8 e1002476(345) Becucci L Cembran A Karim C B Thomas D DGuidelli R Gao J Veglia G Biophys J 2009 96 L60(346) Gumbart J Khalili-Araghi F Sotomayor M Roux BBiochim Biophys Acta 2011 1818 294

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAD

(347) Carnevale V Treptow W Klein M L J Phys Chem Lett2011 2 2504(348) Bhattacharya S Derrington I M Pavlenok M NiederweisM Gundlach J H Aksimentiev A ACS Nano 2012 6 6960(349) Graf P Nitzan A Kurnikova M G Coalson R D J PhysChem B 2000 104 12324(350) Peter C Hummer G Biophys J 2005 89 2222(351) Boda D Valisko M Eisenberg B Nonner W HendersonD Gillespie D Phys Rev Lett 2007 98 1(352) Thoslashgersen L Schioslashtt B Vosegaard T Nielsen N CTajkhorshid E Biophys J 2008 95 4337(353) Plank G Zhou L Greenstein J L Cortassa S Winslow RL OrsquoRourke B Trayanova N A Philos Trans R Soc A 2008 3663381(354) Eisenberg B Hyon Y Liu C J Chem Phys 2010 133104104(355) Hannongbua S Treesuwan W Boonyarat W AdvancedMolecular Modeling Techniques Applied to Ion Channels Blockers InIon Channels and Their Inhibitors Gupta S P Ed Springer-VerlagBerlinHeidelberg 2011 pp 53minus78(356) Zheng W Auerbach A PLoS Comput Biol 2011 7e1001046(357) Boda D Busath D D Eisenberg B Henderson DNonner W Phys Chem Chem Phys 2002 4 5154(358) Boda D Henderson D Busath D D Mol Phys 2002 1002361(359) Cervera J Schiedt B Ramirez P Europhys Lett 2005 7135(360) Vidal J Gracheva M E Leburton J-P Nanoscale Res Lett2006 2 61(361) Gracheva M Leburton J-P Nanotechnology 2007 18145704(362) Vidal J Gracheva M Leburton J-P Nanoscale Res Lett2007 2 61(363) Cervera J Alcaraz A Schiedt B Neumann R Ramirez PJ Phys Chem C 2007 111 12265(364) Vlassiouk I Smirnov S Siwy Z Nano Lett 2008 8 1978(365) Gillespie D Boda D He Y Apel P Siwy Z S Biophys J2008 95 609(366) Kosin ska I D Hanggi P Phys Rev E 2008 77 1(367) Reiner J E Kasianowicz J J Nablo B J Robertson J W FProc Natl Acad Sci USA 2010 107 12080(368) Zhang Y Voth G A J Chem Theory Comput 2011 7 2277(369) Zhang M Yeh L Qian S Hsu J J Phys Chem C 2012116 4793(370) Yeh L-h Zhang M Qian S Hsu J-p Tseng S J PhysChem C 2012 116 8672(371) Carr R Comer J Ginsberg M Aksimentiev A Lab Chip2011 11 3766(372) Peters M H J Chem Phys 2011 134 025105(373) Comer J Aksimentiev A J Phys Chem C 2012 116 3376(374) Timp W Comer J Aksimentiev A Biophys J 2012 102L37(375) Aksimentiev A Heng J B Timp G Schulten K Biophys J2004 87 2086(376) Heng J B Aksimentiev A Ho C Marks P Grinkova YV Sligar S Schulten K Timp G Biophys J 2006 90 1098(377) Lu D Aksimentiev A Shih A Y Cruz-Chu E FreddolinoP L Arkhipov A Schulten K Phys Bio 2006 3 S40(378) Luan B Aksimentiev A Phys Rev E 2008 78 021912(379) Carr R Weinstock I A Sivaprasadarao A Muller AAksimentiev A Nano Lett 2008 8 3916(380) Comer J Dimitrov V Zhao Q Timp G Aksimentiev ABiophys J 2009 96 593(381) Luan B Aksimentiev A J Phys Condens Matter 2010 22454123(382) Gracheva M Xiong A Aksimentiev A Schulten K TimpG Leburton J-P Nanotechnology 2006 17 622

(383) Gracheva M Aksimentiev A Leburton J-P Nanotechnology2006 17 3160(384) Sigalov G Comer J Timp G Aksimentiev A Nano Lett2008 8 56(385) Cruz-Chu E R Aksimentiev A Schulten K J Phys Chem C2009 113 1850(386) Dorvel B Sigalov G Zhao Q Comer J Dimitrov VMirsaidov U Aksimentiev A Timp G Nucleic Acids Res 2009 374170(387) Wang D Timp W Shim J Mirsaidov U Comer JAksimentiev A Timp G Biophys J 2010 98 599a(388) Comer J Aksimentiev A Nanopore Force SpectroscopyInsights from Molecular Dynamics Simulations In Nanopores Sensingand Fundamental Biological Interactions Bashir R Iqbal S EdsSpringer Science and Business Media LLC New York 2011 Chapter14 pp 335minus356(389) Sathe C Zou X Leburton J-P Schulten K ACS Nano2011 5 8842(390) Wanunu M Bhattacharya S Xie Y Tor Y AksimentievA Drndic M ACS Nano 2011 5 9345(391) Kowalczyk S W Wells D B Aksimentiev A Dekker CNano Lett 2012 12 1038(392) Wells D B Belkin M Comer J Aksimentiev A Nano Lett2012 8 4117(393) Edmonds C M Hudiono Y C Ahmadi A G Hesketh PJ Nair S J Chem Phys 2012 136 065105(394) Saha K K Drndic M Nikolic B K Nano Lett 2012 12 50(395) Hille B Ionic channels of excitable membranes 3rd ed SinauerAssociates Sunderland MA 2001(396) Hodgkin A L Huxley A F J Physiol 1952 117 500(397) Hodgkin A L Huxley A F J Physiol 1952 117 500(398) Alberts B Johnson A Lewis J Raff M Roberts K WalterP Molecular Biology of The Cell 5th ed Garland Science New York ampLondon 2007(399) Watanabe H Sugiura S Kafuku H Hisada T Biophys J2004 87 2074(400) Wong J Goktepe S Kuhl E Comput Methods Appl MechEngrg 2011 200 3139(401) Rowat P Neur Comp 2007 19 1215(402) Tuckwell H C Jost J Physica A 2009 388 4115(403) Linaro D Storace M Giugliano M PLoS Comput Biol2011 7 e1001102(404) Che Y-Q Wang J Zhou S-S Deng B Chaos SolitonsFractals 2009 40 1588(405) Beard D A PLoS Comput Biol 2005 1 e36(406) Townsley L E Tucker W A Sham S Hinton J FBiochemistry 2001 40 11676(407) Chang G Spencer R H Lee A T Barclay M T Rees DC Science 1998 282 2220(408) Bass R B Strop P Barclay M Rees D C Science 2002298 1582(409) Conroy M J Durand A Lupo D Li X-D D BulloughP A Winkler F K Merrick M Proc Natl Acad Sci USA 2007104 1213(410) Uysal S Vasquez V Tereshko V Esaki K Fellouse FSidhu S Koide S Perozo E Kossiakoff A Proc Natl Acad SciUSA 2009 106 6644(411) Long S B Tao X Campbell E B MacKinnon R Nature2007 450 376(412) Gonen T Cheng Y Sliz P Hiroaki Y Fujiyoshi YHarrison S C Walz T Nature 2005 438 633(413) Miyazawa A Fujiyoshi Y Unwin N Nature 2003 423 949(414) Unwin N J Mol Biol 2005 346 967(415) Cowan S Schirmer T Rummel G Steiert M Ghosh RPauptit R Jansonius J Rosenbusch J Nature 1992 358 727(416) Dutzler R Campbell E B MacKinnon R Science 2003 300108(417) Song L Hobaugh M R Shustak C Cheley S Bayley HGouaux J E Science 1996 274 1859

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAE

(418) Malasics A Gillespie D Nonner W Henderson DEisenberg B Boda D Biochim Biophys Acta Biomembr 2009 17882471(419) Giri J Fonseca J Boda D Henderson D Eisenberg BPhys Bio 2011 8 026004(420) Mackay D H Berens P H Wilson K R Hagler A TBiophys J 1984 46 229(421) Morais-Cabral J H Zhou Y MacKinnon R Nature 2001414 37(422) Wulff H Calabresi P A Allie R Yun S Pennington MBeeton C Chandy K G J Clin Invest 2003 111 1703(423) Judge S I V Bever C T Pharmacol Ther 2006 111 224(424) Parsegian A Nature 1969 221 844(425) Rashid M H Kuyucak S J Phys Chem B 2012 116 4812(426) Kung C Nature 2005 436 647(427) Kung C Martinac B Sukharev S Annu Rev Microbiol2010 64 313(428) Sukharev S I Blount P Martinac B Blattner F R KungC Nature 1994 368 265(429) Levina N Totemeyer S Stokes N R Louis P Jones MA Booth I R EMBO J 1999 18 1730(430) Wang W Black S S Edwards M D Miller S Morrison EL Bartlett W Dong C Naismith J H Booth I R Science 2008321 1179(431) Liu Z Gandhi C S Rees D C Nature 2009 461 120(432) Martinac B Buechner M Delcour A H Adler J Kung CProc Natl Acad Sci USA 1987 84 2297(433) Weiss M S Schulz G E J Mol Biol 1992 227 493(434) Kreusch A Schulz G J Mol Biol 1994 243 891(435) Cowan S W Garavito R M Jansonius J N Jenkins J AKarlsson R Konig N Pai E F Pauptit R A Rizkallah P JRosenbusch J P Structure 1995 3 1041(436) Schirmer T Keller T A Wang Y F Rosenbusch J PScience 1995 267 512(437) Dutzler R Rummel G Albert S Hernandez-Alles S PhaleP Rosenbusch J Bened V Schirmer T Structure 1999 7 425(438) Moraes T F Bains M Hancock R E W Strynadka N CJ Nat Struct Mol Biol 2007 14 85(439) Biswas S Mohammad M M Movileanu L van der Berg BStructure 2008 16 1027(440) Tamber S Hancock R E W FEMS Microbiol Lett 2006260 23(441) Liu J Eren E Vijayaraghavan J Cheneke B R Indic Mvan den Berg B Movileanu L Biochemistry 2012 51 2319(442) Cheneke B R van der Berg B Movileanu L Biochemistry2011 50 4987(443) Cheneke B R Indic M van den Berg B Movileanu LBiochemistry 2012 51 5348(444) Vila J Mart S Sanchez-Cespedes J J Antimicrob Chemother2007 59 1210(445) Song L Hobaugh M R Shustak C Cheley S Bayley HGouaux J E Science 1996 274 1859(446) Kasianowicz J Robertson J W F Chan E R Reiner J EStanford V M Annu Rev Anal Chem 2008 1 737(447) Kasianowicz J J Brandin E Branton D Deamer D WProc Natl Acad Sci USA 1996 93 13770(448) Faller R Neiderweis M Schulz G E Science 2004 3031189(449) Butler T Pavlenok M Derrington I Niederweis MGundlach J Proc Natl Acad Sci USA 2008 105 20647(450) Derrington I M Collins M D Pavlenok M NiederweisM Gundlach J H Biophys J 2010 98 422a(451) Manrao E Derrington I Pavlenok M Niederweis MGundlach J PLoS One 2011 6 e25723(452) Roos N Benz R Brdiczka D Biochim Biophys Acta 1982686 204(453) Hiller S Garces R G Malia T J Orekhov V YColombini M Wagner G Science 2008 321 1206

(454) Ujwal R Cascio D Colletier J-P Faham S Zhang JToro L Ping P Proc Natl Acad Sci USA 2008 105 2(455) Bayrhuber M Meins T Habeck M Becker S Giller KVillinger S Vonrhein C Griesinger C Zweckstetter M Zeth KProc Natl Acad Sci USA 2008 105 15370(456) Colombini M Trends Biochem Sci 2009 34 382(457) Hiller S Abramson J Mannella C Wagner G Zeth KTrends Biochem Sci 2010 35 514(458) Hiller S Raschle T Yu T-Y Rice A J Walz T WagnerG Biochim Biophys Acta Bioenerg 2010 1797 66(459) Chen T-Y Annu Rev Physiol 2005 67 809(460) Dutzler R Campbell E B Cadene M Chait B TMacKinnon R Nature 2002 415 287(461) Accardi A Miller C Nature 2004 427 803(462) Steinlein O K Bertrand D Biochem Pharmacol 2008 761175(463) Rose J E Biochem Pharmacol 2007 74 1263(464) Marini A M Soussi-Boudekou S Vissers S Andre B MolCell Biol 1997 17 4282(465) Ninnemann O Jauniaux J C Frommer W B EMBO J1994 13 3464(466) Marini A M Vissers S Urrestarazu A Andre B EMBO J1994 13 3456(467) Khademi S OrsquoConnell J Remis J Robles-Colmenares YMiercke L J W Stroud R M Science 2004 305 1587(468) Javelle A Lupo D Ripoche P Fulford T Merrick MWinkler F K Proc Natl Acad Sci USA 2008 105 5040(469) Gruswitz F OrsquoConnell J Stroud R M Proc Natl Acad SciUSA 2007 104 42(470) Javelle A Lupo D Zheng L Li X-D D Winkler F KMerrick M J Biol Chem 2006 281 39492(471) Gao J Truhlar D G Annu Rev Phys Chem 2002 53 467(472) Kamerlin S C L Vicatos S Dryga A Warshel A AnnuRev Phys Chem 2011 62 41(473) Modi N Winterhalter M Kleinekathofer U Nanoscale2012 4 6166(474) Maffeo C Schopflin R Brutzer H Stehr R AksimentievA Wedemann G Seidel R Phys Rev Lett 2010 105 158101(475) Simonson T Carlsson J Case D A J Am Chem Soc 2004126 4167(476) Rocchia W Alxov E Honig B J Phys Chem B 2001 1056507(477) Baker N Sept D Joseph S Hoist M McCammon J ProcNatl Acad Sci USA 2001 98 10037(478) Ramrez P Aguilella-Arzo M Alcaraz A Cervera JAguilella V M Cell Biochem Biophys 2006 44 287(479) Woolley G Biggin P Schultz A Lien L Jaikaran DBreed J Crowhurst K Sansom M Biophys J 1997 73 770(480) Nonner W Chen D Eisenberg B Biophys J 1998 74 2327(481) Roth R J Phys Condens Matter 2010 22 063102(482) Woolf T Roux B Proc Natl Acad Sci USA 1994 9111631(483) Hummer G New J Phys 2005 7 34(484) Paine P L Scherr P Biophys J 1975 15 1087(485) Roux B Biophys J 1999 77 139(486) Corry B Allen T Kuyucak S Chung S Biophys J 200180 195(487) Cooper K Jakobsson E Wolynes P Prog Biophys Mol Biol1985 46 51(488) Mackerell A D J Comput Chem 2004 25 1584(489) MacKerell D A Bashford D Bellott Dunbrack L REvanseck J D Field M J Fischer S Gao J Guo H Ha SJoseph-McCarthy D Kuchnir L Kuczera K Lau F T K MattosC Michnick S Ngo T Nguyen D T Prodhom B Reiher W ERoux B Schlenkrich M Smith J C Stote R Straub J WatanabeM Wiorkiewicz-Kuczera J Yin D Karplus M J Phys Chem B1998 102 3586(490) Weiner P K Kollman P A J Comput Chem 1981 2 287

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAF

(491) Cornell W D Cieplak P Bayly C I Gould I R Merz KM Ferguson D M Spellmeyer D C Fox T Caldwell J WKollman P A J Am Chem Soc 1995 117 5179(492) Jorgensen W L Maxwell D S Tirado-Rives J J Am ChemSoc 1996 118 11225(493) Kaminski G A Friesner R A Tirado-Rives J Jorgensen WL J Phys Chem B 2001 105 6474(494) Hermans J Berendsen H J C Van Gunsteren W FPostma J P M Biopolymers 1984 23 1513(495) Schmid N Eichenberger A P Choutko A Riniker SWinger M Mark A E van Gunsteren W F Eur Biophys J 201140 843(496) Klauda J B Venable R M Freites J A OrsquoConnor J WTobias D J Mondragon-Ramirez C Vorobyov I MacKerell A DPastor R W J Phys Chem B 2010 114 7830(497) Wang J Wolf R M Caldwell J W Kollman P A Case DA J Comput Chem 2004 25 1157(498) Liu Y Chipot C Shao X Cai W Phys Bio 2011 8056005(499) Daura X Mark A E van Gunsteren W F J Comput Chem1998 19 535(500) Berger O Edholm O Jahnig F Biophys J 1997 72 2002(501) Cordomiacute A Caltabiano G Pardo L J Chem TheoryComput 2012 8 948(502) Aksimentiev A Wells D Sotomayor M Membrane ProteinTutorial httpwwwksuiuceduTrainingTutorialssciencemembranemem-tutorialpdfrelax(503) Humphrey W Dalke A Schulten K J Mol Graphics 199614 33(504) Brooks B R Bruccoleri R E Olafson B D States D JSwaminathan S Karplus M J Comput Chem 1983 187(505) Jo S Lim J B Klauda J B Im W Biophys J 2009 97 50(506) Ayton G S Voth G A Curr Opin Struct Biol 2009 19 138(507) Marrink S J de Vries A H Tieleman D P BiochimBiophys Acta 2009 1788 149(508) Nielsen S O Lopez C F Srinivas G Klein M L J PhysCondens Matter 2004 16 R481(509) Yesylevskyy S O Schafer L V Sengupta D Marrink S JPLoS Comput Biol 2010 6 e1000810(510) Wu Z Cui Q Yethiraj A J Phys Chem B 2010 114 10524(511) Sali A Blundell T L J Mol Biol 1993 234 779(512) Capener C E Shrivastava I H Ranatunga K M Forrest LR Smith G R Sansom M S Biophys J 2000 78 2929(513) Roux B Comput Phys Commun 1995 91 275(514) Kollman P Chem Rev 1993 93 2395(515) Pohorille A Jarzynski C Chipot C J Phys Chem B 2010114 10235(516) Torrie G Valleau J J Comput Phys 1977 23 187(517) Kumar S Bouzida D Swendsen R H Kollman P ARosenberg J M J Comput Chem 1992 13 1011(518) Woo H-J Roux B Proc Natl Acad Sci USA 2005 1026825(519) Singh U C Brown F K Bash P A Kollman P A J AmChem Soc 1987 109 1607(520) Grubmuller H Heymann B Tavan P Science 1996 271997(521) Isralewitz B Izrailev S Schulten K Biophys J 1997 732972(522) Izrailev S Stepaniants S Balsera M Oono Y Schulten KBiophys J 1997 72 1568(523) Stepaniants S Izrailev S Schulten K J Mol Mod 1997 3473(524) Marrink S-J Berger O Tieleman P Jahnig F Biophys J1998 74 931(525) Kosztin D Izrailev S Schulten K Biophys J 1999 76 188(526) Hummer G Szabo A Acc Chem Res 2005 38 504(527) Jarzynski C Phys Rev Lett 1997 78 2690(528) Bucher D Guidoni L Rothlisberger U Biophys J 2007 932315

(529) Arkin I T Xu H F Jensen M O Arbely E Bennett E RBowers K J Chow E Dror R O Eastwood M P Flitman-TeneR Gregersen B A Klepeis J L Kolossvary I Shan Y B Shaw DE Science 2007 317 799(530) Warshel A Sussman F King G Biochemistry 1986 25 8368(531) Li L Vorobyov I Mackerell A D Allen T W Biophys J2007 94 L11(532) Li L Vorobyov I Allen T W J Phys Chem B 2008 1129574(533) Yoo J Cui Q Biophys J 2008 94 L61(534) MacCallum J L Bennett W F D Tieleman D P Biophys J2008 94 3393(535) Yoo J Cui Q Biophys J 2010 99 1529(536) Johansson A C V Lindahl E J Phys Chem B 2009 113245(537) Honig B Sharp K Yang A S J Phys Chem 1993 97 1101(538) Lim C Bashford D Karplus M J Phys Chem 1991 955610(539) Warshel A Papazyan A Curr Opin Struct Biol 1998 8 211(540) Ullmann G M Knapp E-W Eur Biophys J 1999 28 533(541) Srinivasan J Trevathan M W Beroza P Case D A TheorChem Acc 1999 101 426(542) Koumanov A Ruterjans H Karshikoff A Proteins StructFunct Genet 2002 46 85(543) Mongan J Case D A McCammon J A J Comput Chem2004 25 2038(544) Mongan J Case D A Curr Opin Struct Biol 2005 15 157(545) Khandogin J Brooks C L Biochemistry 2006 45 9363(546) Gunner G Mao J Song Y Kim J Biochim Biophys ActaBioenerg 2006 1757 942(547) Spassov V Z Yan L Protein Sci 2008 17 1955(548) Karshikoff A Spassov V Cowan S W Ladenstein RSchirmer T J Mol Biol 1994 240 372(549) Tanizaki S Feig M J Chem Phys 2005 122 124706(550) Gordon J C Myers J B Folta T Shoja V Heath L SOnufriev A Nucleic Acids Res 2005 33 W368(551) Olsson M H M Soslashndergaard C R Rostkowski M JensenJ H J Chem Theory Comput 2011 7 525(552) Jo S Vargyas M Vasko-Szedlar J Roux B Im W NucleicAcids Res 2008 36 W270(553) Shaw D E Chao J C Eastwood M P Gagliardo JGrossman J P P Ho C R Lerardi D J Kolossvary I Klepeis JL Layman T McLeavey C Deneroff M M Moraes M AMueller R Priest E C Shan Y Spengler J Theobald M TowlesB Wang S C Dror R O Kuskin J S Larson R H Salmon J KYoung C Batson B Bowers K J Commun ACM 2008 51 91(554) Shaw D E J Comput Chem 2005 26 1318(555) Dror R O Jensen M O Borhani D W Shaw D E J GenPhysiol 2010 135 555(556) Dror R O Dirks R M Grossman J P Xu H Shaw D EAnnu Rev Biochem 2012 41 429(557) Dror R O Pan A C Arlow D H Borhani D WMaragakis P Shan Y Xu H Shaw D E Proc Natl Acad Sci USA2011 108 13118(558) Rosenbaum D M Zhang C Lyons J A Holl R AragaoD Arlow D H Rasmussen S G F Choi H-J J Devree B TSunahara R K Chae P S Gellman S H Dror R O Shaw D EWeis W I Caffrey M Gmeiner P Kobilka B K Nature 2011 469236(559) Kruse A C Hu J Pan A C Arlow D H Rosenbaum DM Rosemond E Green H F Liu T Chae P S Dror R OShaw D E Weis W I Wess J Kobilka B K Nature 2012 482552(560) Jensen M O Dror R O Xu H F Borhani D W Arkin IT Eastwood M P Shaw D E Proc Natl Acad Sci USA 2008105 14430(561) Vorobyov I V Anisimov V M MacKerell A D J PhysChem B 2005 109 18988

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAG

(264) Cheng M H Coalson R D Biophys J 2012 102 1363(265) Corry B OrsquoMara M Chung S-H Biophys J 2004 86 846(266) Bisset D Corry B Chung S-H Biophys J 2005 89 179(267) Cheng M H Mamonov A B Dukes J W Coalson R D JPhys Chem B 2007 111 5956(268) Lee K I Rui H Pastor R W Im W Biophys J 2011 100611(269) Burykin A Warshel A Biophys J 2003 85 3696(270) Stroud R M Savage D Miercke L J Lee J K KhademiS Harries W FEBS Lett 2003 555 79(271) Jensen M O Tajkhorshid E Schulten K Biophys J 200385 2884(272) de Groot B L Frigato T Helms V Grubmuller H J MolBiol 2003 333 279(273) Chen H Wu Y Voth G A Biophys J 2006 90 L73(274) Wang Y Tajkhorshid E J Nutr 2007 137 1509S(275) Bostick D L Brooks C L PLoS Comput Biol 2007 3 e22(276) Bostick D L Charles L L B Biophys J 2007 92 L103(277) Wang S Orabi E A Baday S Berneche S Lamoureux GJ Am Chem Soc 2012 134 10419(278) Luzhkov V B Almlof M Nervall M Aringqvist J Biochemistry2006 45 10807(279) Levitt D G Biophys J 1991 59 271(280) Barcilon V Chen D-P Eisenberg R SIAM J App Math1992 52 1405(281) Chen D P Barcilon V Eisenberg R S Biophys J 1992 611372(282) Chen D Eisenberg R Biophys J 1993 64 1405(283) Chen D P Eisenberg R S Biophys J 1993 65 727(284) Chen D Xu L Tripathy a Meissner G Eisenberg BBiophys J 1997 73 1337(285) Chen D Lear J Eisenberg B Biophys J 1997 72 97(286) Syganow A von Kitzing E J Phys Chem 1995 99 12030(287) Moy G Corry B Kuyucak S Chung S-H Biophys J 200078 2349(288) Corry B Kuyucak S Chung S H Biophys J 2000 78 2364(289) Crozier P Rowley R Holladay N Henderson D BusathD Phys Rev Lett 2001 86 2467(290) Gillespie D Nonner W Eisenberg R S J Phys CondensMatter 2002 14 12129(291) Gillespie D Nonner W Eisenberg R Phys Rev E 2003 681(292) Koumanov A Zachariae U Engelhardt H Karshikoff AEur Biophys J 2003 32 689(293) Kuyucak S Bastug T J Biophys 2003 29 429(294) Corry B Kuyucak S Chung S-H Biophys J 2003 84 3594(295) Beckstein O Tai K Sansom M S P J Am Chem Soc 2004126 14694(296) Graf P Kurnikova M G Coalson R D Nitzan A J PhysChem B 2004 108 2006(297) Kessel A Tieleman D P Ben-Tal N Eur Biophys J 200433 16(298) Baumgartner W Comput Biol Chem 2004 28 67(299) Roux B Allen T Bernche S Im W Q Rev Biophys 200437 15(300) Gillespie D Xu L Wang Y Meissner G J Phys Chem B2005 109 15598(301) Aguilella-Arzo M Aguilella V M Eisenberg R S EurBiophys J 2005 34 314(302) Cheng M H Coalson R D J Phys Chem B 2005 109 488(303) Hwang H Schatz G C Ratner M A J Phys Chem B 2006110 6999(304) Kandt C Ash W L Tieleman D P Methods 2007 41 475(305) Singer A Norbury J SIAM J Appl Math 2009 70 949(306) Bolintineanu D S Sayyed-Ahmad A Davis H T KaznessisY N PLoS Comput Biol 2009 5 e1000277(307) Eisenberg B J Phys Chem C 2010 114 20719(308) Eisenberg B Chem Phys Lett 2011 511 1(309) Lu B Zhou Y Biophys J 2011 100 2475

(310) Eisenberg B Adv Chem Phys 2012 77minus223(311) Krishnamurthy V Chung S-H IEEE Trans Nanobiosci 20054 102(312) Vora T Bisset D Chung S-H Biophys J 2008 95 1600(313) Gordon D Krishnamurthy V Chung S-H Mol Phys 2008106 1353(314) Vora T Corry B Chung S-H Eur Biophys J 2008 38 45(315) Song C Corry B Biophys J 2010 98 404(316) Krishnamurthy V Luk K Y IEEEACM Trans Comput BiolBioinf 2011 8 273(317) Lee K I Jo S Rui H Egwolf B Roux B Pastor R WIm W J Comput Chem 2012 33 331(318) Csanyi E Boda D Gillespie D Kristof T Biochim BiophysActa 2012 1818 592(319) Smondyrev A M Voth G A Biophys J 2002 83 1987(320) Domene C Bond P J Sansom M S P Adv Protein Chem2003 66 159(321) Tarek M Maigret B Chipot C Biophys J 2003 85 2287(322) Biggin P C Grottesi A Sansom M S P From Prokaryotesto Eukaryotes Molecular Modeling and Simulation Studies of IonChannels In Bacterial Ion Channels And Their Eukaryotic HomologsKubalski A Martinac B Eds ASM Press Washington DC 2005pp 133minus152(323) Tajkhorshid E Cohen J Aksimentiev A Sotomayor MSchulten K Towards an Understanding of Membrane Channels InBacterial Ion Channels And Their Eukaryotic Homologs Kubalski AMartinac B Eds ASM Press Washington DC 2005 pp 133minus152(324) Gumbart J Wang Y Aksimentiev A Tajkhorshid ESchulten K Curr Opin Struct Biol 2005 15 423(325) Hwang H Schatz G C Ratner M A J Phys Chem B 2006110 26448(326) Carpenter T Bond P J Khalid S Sansom M S P BiophysJ 2008 95 3790(327) Shaikh S A Tajkhorshid E Biophys J 2008 95 5153(328) Pietra F J Phys Org Chem 2008 21 997(329) Delemotte L Dehez F Treptow W Tarek M J PhysChem B 2008 112 5547(330) Maffeo C Aksimentiev A Biophys J 2009 96 4853(331) Patargias G Martay H Fischer W B J Biomol Struct Dyn2009 27 1(332) Mustafa M Henderson D J Busath D D Proteins StructFunct Bioinf 2009 76 794(333) Khalili-Araghi F Gumbart J Wen P-C Sotomayor MTajkhorshid E Schulten K Curr Opin Struct Biol 2009 19 128(334) Khurana E Dal Peraro M DeVane R Vemparala SDeGrado W F Klein M L Proc Natl Acad Sci USA 2009 1061069(335) Pan J Tieleman D P Nagle J F Kucerka N Tristram-Nagle S Biochim Biophys Acta 2009 1788 1387(336) Nury H Poitevin F Van Renterghem C Changeux J-PCorringer P-J Delarue M Baaden M Proc Natl Acad Sci USA2010 107 6275(337) Cheng M H Coalson R D Tang P J Am Chem Soc 2010132 16442(338) Zhu F Hummer G Proc Natl Acad Sci USA 2010 10719814(339) Kutzner C Grubmuller H de Groot B L Zachariae UBiophys J 2011 101 809(340) Wilson M A Wei C Bjelkmar P Wallace B A PohorilleA Biophys J 2011 100 2394(341) Stansfeld P J Sansom M S P Structure 2011 19 1562(342) Chen C-C Kruger J Sramala I Hsu H-J Henklein PChen Y-M A Fischer W B Biochim Biophys Acta 2011 1808 572(343) Raunest M Kandt C Biochemistry 2012 51 1719(344) Furini S Domene C PLoS Comput Biol 2012 8 e1002476(345) Becucci L Cembran A Karim C B Thomas D DGuidelli R Gao J Veglia G Biophys J 2009 96 L60(346) Gumbart J Khalili-Araghi F Sotomayor M Roux BBiochim Biophys Acta 2011 1818 294

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAD

(347) Carnevale V Treptow W Klein M L J Phys Chem Lett2011 2 2504(348) Bhattacharya S Derrington I M Pavlenok M NiederweisM Gundlach J H Aksimentiev A ACS Nano 2012 6 6960(349) Graf P Nitzan A Kurnikova M G Coalson R D J PhysChem B 2000 104 12324(350) Peter C Hummer G Biophys J 2005 89 2222(351) Boda D Valisko M Eisenberg B Nonner W HendersonD Gillespie D Phys Rev Lett 2007 98 1(352) Thoslashgersen L Schioslashtt B Vosegaard T Nielsen N CTajkhorshid E Biophys J 2008 95 4337(353) Plank G Zhou L Greenstein J L Cortassa S Winslow RL OrsquoRourke B Trayanova N A Philos Trans R Soc A 2008 3663381(354) Eisenberg B Hyon Y Liu C J Chem Phys 2010 133104104(355) Hannongbua S Treesuwan W Boonyarat W AdvancedMolecular Modeling Techniques Applied to Ion Channels Blockers InIon Channels and Their Inhibitors Gupta S P Ed Springer-VerlagBerlinHeidelberg 2011 pp 53minus78(356) Zheng W Auerbach A PLoS Comput Biol 2011 7e1001046(357) Boda D Busath D D Eisenberg B Henderson DNonner W Phys Chem Chem Phys 2002 4 5154(358) Boda D Henderson D Busath D D Mol Phys 2002 1002361(359) Cervera J Schiedt B Ramirez P Europhys Lett 2005 7135(360) Vidal J Gracheva M E Leburton J-P Nanoscale Res Lett2006 2 61(361) Gracheva M Leburton J-P Nanotechnology 2007 18145704(362) Vidal J Gracheva M Leburton J-P Nanoscale Res Lett2007 2 61(363) Cervera J Alcaraz A Schiedt B Neumann R Ramirez PJ Phys Chem C 2007 111 12265(364) Vlassiouk I Smirnov S Siwy Z Nano Lett 2008 8 1978(365) Gillespie D Boda D He Y Apel P Siwy Z S Biophys J2008 95 609(366) Kosin ska I D Hanggi P Phys Rev E 2008 77 1(367) Reiner J E Kasianowicz J J Nablo B J Robertson J W FProc Natl Acad Sci USA 2010 107 12080(368) Zhang Y Voth G A J Chem Theory Comput 2011 7 2277(369) Zhang M Yeh L Qian S Hsu J J Phys Chem C 2012116 4793(370) Yeh L-h Zhang M Qian S Hsu J-p Tseng S J PhysChem C 2012 116 8672(371) Carr R Comer J Ginsberg M Aksimentiev A Lab Chip2011 11 3766(372) Peters M H J Chem Phys 2011 134 025105(373) Comer J Aksimentiev A J Phys Chem C 2012 116 3376(374) Timp W Comer J Aksimentiev A Biophys J 2012 102L37(375) Aksimentiev A Heng J B Timp G Schulten K Biophys J2004 87 2086(376) Heng J B Aksimentiev A Ho C Marks P Grinkova YV Sligar S Schulten K Timp G Biophys J 2006 90 1098(377) Lu D Aksimentiev A Shih A Y Cruz-Chu E FreddolinoP L Arkhipov A Schulten K Phys Bio 2006 3 S40(378) Luan B Aksimentiev A Phys Rev E 2008 78 021912(379) Carr R Weinstock I A Sivaprasadarao A Muller AAksimentiev A Nano Lett 2008 8 3916(380) Comer J Dimitrov V Zhao Q Timp G Aksimentiev ABiophys J 2009 96 593(381) Luan B Aksimentiev A J Phys Condens Matter 2010 22454123(382) Gracheva M Xiong A Aksimentiev A Schulten K TimpG Leburton J-P Nanotechnology 2006 17 622

(383) Gracheva M Aksimentiev A Leburton J-P Nanotechnology2006 17 3160(384) Sigalov G Comer J Timp G Aksimentiev A Nano Lett2008 8 56(385) Cruz-Chu E R Aksimentiev A Schulten K J Phys Chem C2009 113 1850(386) Dorvel B Sigalov G Zhao Q Comer J Dimitrov VMirsaidov U Aksimentiev A Timp G Nucleic Acids Res 2009 374170(387) Wang D Timp W Shim J Mirsaidov U Comer JAksimentiev A Timp G Biophys J 2010 98 599a(388) Comer J Aksimentiev A Nanopore Force SpectroscopyInsights from Molecular Dynamics Simulations In Nanopores Sensingand Fundamental Biological Interactions Bashir R Iqbal S EdsSpringer Science and Business Media LLC New York 2011 Chapter14 pp 335minus356(389) Sathe C Zou X Leburton J-P Schulten K ACS Nano2011 5 8842(390) Wanunu M Bhattacharya S Xie Y Tor Y AksimentievA Drndic M ACS Nano 2011 5 9345(391) Kowalczyk S W Wells D B Aksimentiev A Dekker CNano Lett 2012 12 1038(392) Wells D B Belkin M Comer J Aksimentiev A Nano Lett2012 8 4117(393) Edmonds C M Hudiono Y C Ahmadi A G Hesketh PJ Nair S J Chem Phys 2012 136 065105(394) Saha K K Drndic M Nikolic B K Nano Lett 2012 12 50(395) Hille B Ionic channels of excitable membranes 3rd ed SinauerAssociates Sunderland MA 2001(396) Hodgkin A L Huxley A F J Physiol 1952 117 500(397) Hodgkin A L Huxley A F J Physiol 1952 117 500(398) Alberts B Johnson A Lewis J Raff M Roberts K WalterP Molecular Biology of The Cell 5th ed Garland Science New York ampLondon 2007(399) Watanabe H Sugiura S Kafuku H Hisada T Biophys J2004 87 2074(400) Wong J Goktepe S Kuhl E Comput Methods Appl MechEngrg 2011 200 3139(401) Rowat P Neur Comp 2007 19 1215(402) Tuckwell H C Jost J Physica A 2009 388 4115(403) Linaro D Storace M Giugliano M PLoS Comput Biol2011 7 e1001102(404) Che Y-Q Wang J Zhou S-S Deng B Chaos SolitonsFractals 2009 40 1588(405) Beard D A PLoS Comput Biol 2005 1 e36(406) Townsley L E Tucker W A Sham S Hinton J FBiochemistry 2001 40 11676(407) Chang G Spencer R H Lee A T Barclay M T Rees DC Science 1998 282 2220(408) Bass R B Strop P Barclay M Rees D C Science 2002298 1582(409) Conroy M J Durand A Lupo D Li X-D D BulloughP A Winkler F K Merrick M Proc Natl Acad Sci USA 2007104 1213(410) Uysal S Vasquez V Tereshko V Esaki K Fellouse FSidhu S Koide S Perozo E Kossiakoff A Proc Natl Acad SciUSA 2009 106 6644(411) Long S B Tao X Campbell E B MacKinnon R Nature2007 450 376(412) Gonen T Cheng Y Sliz P Hiroaki Y Fujiyoshi YHarrison S C Walz T Nature 2005 438 633(413) Miyazawa A Fujiyoshi Y Unwin N Nature 2003 423 949(414) Unwin N J Mol Biol 2005 346 967(415) Cowan S Schirmer T Rummel G Steiert M Ghosh RPauptit R Jansonius J Rosenbusch J Nature 1992 358 727(416) Dutzler R Campbell E B MacKinnon R Science 2003 300108(417) Song L Hobaugh M R Shustak C Cheley S Bayley HGouaux J E Science 1996 274 1859

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAE

(418) Malasics A Gillespie D Nonner W Henderson DEisenberg B Boda D Biochim Biophys Acta Biomembr 2009 17882471(419) Giri J Fonseca J Boda D Henderson D Eisenberg BPhys Bio 2011 8 026004(420) Mackay D H Berens P H Wilson K R Hagler A TBiophys J 1984 46 229(421) Morais-Cabral J H Zhou Y MacKinnon R Nature 2001414 37(422) Wulff H Calabresi P A Allie R Yun S Pennington MBeeton C Chandy K G J Clin Invest 2003 111 1703(423) Judge S I V Bever C T Pharmacol Ther 2006 111 224(424) Parsegian A Nature 1969 221 844(425) Rashid M H Kuyucak S J Phys Chem B 2012 116 4812(426) Kung C Nature 2005 436 647(427) Kung C Martinac B Sukharev S Annu Rev Microbiol2010 64 313(428) Sukharev S I Blount P Martinac B Blattner F R KungC Nature 1994 368 265(429) Levina N Totemeyer S Stokes N R Louis P Jones MA Booth I R EMBO J 1999 18 1730(430) Wang W Black S S Edwards M D Miller S Morrison EL Bartlett W Dong C Naismith J H Booth I R Science 2008321 1179(431) Liu Z Gandhi C S Rees D C Nature 2009 461 120(432) Martinac B Buechner M Delcour A H Adler J Kung CProc Natl Acad Sci USA 1987 84 2297(433) Weiss M S Schulz G E J Mol Biol 1992 227 493(434) Kreusch A Schulz G J Mol Biol 1994 243 891(435) Cowan S W Garavito R M Jansonius J N Jenkins J AKarlsson R Konig N Pai E F Pauptit R A Rizkallah P JRosenbusch J P Structure 1995 3 1041(436) Schirmer T Keller T A Wang Y F Rosenbusch J PScience 1995 267 512(437) Dutzler R Rummel G Albert S Hernandez-Alles S PhaleP Rosenbusch J Bened V Schirmer T Structure 1999 7 425(438) Moraes T F Bains M Hancock R E W Strynadka N CJ Nat Struct Mol Biol 2007 14 85(439) Biswas S Mohammad M M Movileanu L van der Berg BStructure 2008 16 1027(440) Tamber S Hancock R E W FEMS Microbiol Lett 2006260 23(441) Liu J Eren E Vijayaraghavan J Cheneke B R Indic Mvan den Berg B Movileanu L Biochemistry 2012 51 2319(442) Cheneke B R van der Berg B Movileanu L Biochemistry2011 50 4987(443) Cheneke B R Indic M van den Berg B Movileanu LBiochemistry 2012 51 5348(444) Vila J Mart S Sanchez-Cespedes J J Antimicrob Chemother2007 59 1210(445) Song L Hobaugh M R Shustak C Cheley S Bayley HGouaux J E Science 1996 274 1859(446) Kasianowicz J Robertson J W F Chan E R Reiner J EStanford V M Annu Rev Anal Chem 2008 1 737(447) Kasianowicz J J Brandin E Branton D Deamer D WProc Natl Acad Sci USA 1996 93 13770(448) Faller R Neiderweis M Schulz G E Science 2004 3031189(449) Butler T Pavlenok M Derrington I Niederweis MGundlach J Proc Natl Acad Sci USA 2008 105 20647(450) Derrington I M Collins M D Pavlenok M NiederweisM Gundlach J H Biophys J 2010 98 422a(451) Manrao E Derrington I Pavlenok M Niederweis MGundlach J PLoS One 2011 6 e25723(452) Roos N Benz R Brdiczka D Biochim Biophys Acta 1982686 204(453) Hiller S Garces R G Malia T J Orekhov V YColombini M Wagner G Science 2008 321 1206

(454) Ujwal R Cascio D Colletier J-P Faham S Zhang JToro L Ping P Proc Natl Acad Sci USA 2008 105 2(455) Bayrhuber M Meins T Habeck M Becker S Giller KVillinger S Vonrhein C Griesinger C Zweckstetter M Zeth KProc Natl Acad Sci USA 2008 105 15370(456) Colombini M Trends Biochem Sci 2009 34 382(457) Hiller S Abramson J Mannella C Wagner G Zeth KTrends Biochem Sci 2010 35 514(458) Hiller S Raschle T Yu T-Y Rice A J Walz T WagnerG Biochim Biophys Acta Bioenerg 2010 1797 66(459) Chen T-Y Annu Rev Physiol 2005 67 809(460) Dutzler R Campbell E B Cadene M Chait B TMacKinnon R Nature 2002 415 287(461) Accardi A Miller C Nature 2004 427 803(462) Steinlein O K Bertrand D Biochem Pharmacol 2008 761175(463) Rose J E Biochem Pharmacol 2007 74 1263(464) Marini A M Soussi-Boudekou S Vissers S Andre B MolCell Biol 1997 17 4282(465) Ninnemann O Jauniaux J C Frommer W B EMBO J1994 13 3464(466) Marini A M Vissers S Urrestarazu A Andre B EMBO J1994 13 3456(467) Khademi S OrsquoConnell J Remis J Robles-Colmenares YMiercke L J W Stroud R M Science 2004 305 1587(468) Javelle A Lupo D Ripoche P Fulford T Merrick MWinkler F K Proc Natl Acad Sci USA 2008 105 5040(469) Gruswitz F OrsquoConnell J Stroud R M Proc Natl Acad SciUSA 2007 104 42(470) Javelle A Lupo D Zheng L Li X-D D Winkler F KMerrick M J Biol Chem 2006 281 39492(471) Gao J Truhlar D G Annu Rev Phys Chem 2002 53 467(472) Kamerlin S C L Vicatos S Dryga A Warshel A AnnuRev Phys Chem 2011 62 41(473) Modi N Winterhalter M Kleinekathofer U Nanoscale2012 4 6166(474) Maffeo C Schopflin R Brutzer H Stehr R AksimentievA Wedemann G Seidel R Phys Rev Lett 2010 105 158101(475) Simonson T Carlsson J Case D A J Am Chem Soc 2004126 4167(476) Rocchia W Alxov E Honig B J Phys Chem B 2001 1056507(477) Baker N Sept D Joseph S Hoist M McCammon J ProcNatl Acad Sci USA 2001 98 10037(478) Ramrez P Aguilella-Arzo M Alcaraz A Cervera JAguilella V M Cell Biochem Biophys 2006 44 287(479) Woolley G Biggin P Schultz A Lien L Jaikaran DBreed J Crowhurst K Sansom M Biophys J 1997 73 770(480) Nonner W Chen D Eisenberg B Biophys J 1998 74 2327(481) Roth R J Phys Condens Matter 2010 22 063102(482) Woolf T Roux B Proc Natl Acad Sci USA 1994 9111631(483) Hummer G New J Phys 2005 7 34(484) Paine P L Scherr P Biophys J 1975 15 1087(485) Roux B Biophys J 1999 77 139(486) Corry B Allen T Kuyucak S Chung S Biophys J 200180 195(487) Cooper K Jakobsson E Wolynes P Prog Biophys Mol Biol1985 46 51(488) Mackerell A D J Comput Chem 2004 25 1584(489) MacKerell D A Bashford D Bellott Dunbrack L REvanseck J D Field M J Fischer S Gao J Guo H Ha SJoseph-McCarthy D Kuchnir L Kuczera K Lau F T K MattosC Michnick S Ngo T Nguyen D T Prodhom B Reiher W ERoux B Schlenkrich M Smith J C Stote R Straub J WatanabeM Wiorkiewicz-Kuczera J Yin D Karplus M J Phys Chem B1998 102 3586(490) Weiner P K Kollman P A J Comput Chem 1981 2 287

Chemical Reviews Review

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(491) Cornell W D Cieplak P Bayly C I Gould I R Merz KM Ferguson D M Spellmeyer D C Fox T Caldwell J WKollman P A J Am Chem Soc 1995 117 5179(492) Jorgensen W L Maxwell D S Tirado-Rives J J Am ChemSoc 1996 118 11225(493) Kaminski G A Friesner R A Tirado-Rives J Jorgensen WL J Phys Chem B 2001 105 6474(494) Hermans J Berendsen H J C Van Gunsteren W FPostma J P M Biopolymers 1984 23 1513(495) Schmid N Eichenberger A P Choutko A Riniker SWinger M Mark A E van Gunsteren W F Eur Biophys J 201140 843(496) Klauda J B Venable R M Freites J A OrsquoConnor J WTobias D J Mondragon-Ramirez C Vorobyov I MacKerell A DPastor R W J Phys Chem B 2010 114 7830(497) Wang J Wolf R M Caldwell J W Kollman P A Case DA J Comput Chem 2004 25 1157(498) Liu Y Chipot C Shao X Cai W Phys Bio 2011 8056005(499) Daura X Mark A E van Gunsteren W F J Comput Chem1998 19 535(500) Berger O Edholm O Jahnig F Biophys J 1997 72 2002(501) Cordomiacute A Caltabiano G Pardo L J Chem TheoryComput 2012 8 948(502) Aksimentiev A Wells D Sotomayor M Membrane ProteinTutorial httpwwwksuiuceduTrainingTutorialssciencemembranemem-tutorialpdfrelax(503) Humphrey W Dalke A Schulten K J Mol Graphics 199614 33(504) Brooks B R Bruccoleri R E Olafson B D States D JSwaminathan S Karplus M J Comput Chem 1983 187(505) Jo S Lim J B Klauda J B Im W Biophys J 2009 97 50(506) Ayton G S Voth G A Curr Opin Struct Biol 2009 19 138(507) Marrink S J de Vries A H Tieleman D P BiochimBiophys Acta 2009 1788 149(508) Nielsen S O Lopez C F Srinivas G Klein M L J PhysCondens Matter 2004 16 R481(509) Yesylevskyy S O Schafer L V Sengupta D Marrink S JPLoS Comput Biol 2010 6 e1000810(510) Wu Z Cui Q Yethiraj A J Phys Chem B 2010 114 10524(511) Sali A Blundell T L J Mol Biol 1993 234 779(512) Capener C E Shrivastava I H Ranatunga K M Forrest LR Smith G R Sansom M S Biophys J 2000 78 2929(513) Roux B Comput Phys Commun 1995 91 275(514) Kollman P Chem Rev 1993 93 2395(515) Pohorille A Jarzynski C Chipot C J Phys Chem B 2010114 10235(516) Torrie G Valleau J J Comput Phys 1977 23 187(517) Kumar S Bouzida D Swendsen R H Kollman P ARosenberg J M J Comput Chem 1992 13 1011(518) Woo H-J Roux B Proc Natl Acad Sci USA 2005 1026825(519) Singh U C Brown F K Bash P A Kollman P A J AmChem Soc 1987 109 1607(520) Grubmuller H Heymann B Tavan P Science 1996 271997(521) Isralewitz B Izrailev S Schulten K Biophys J 1997 732972(522) Izrailev S Stepaniants S Balsera M Oono Y Schulten KBiophys J 1997 72 1568(523) Stepaniants S Izrailev S Schulten K J Mol Mod 1997 3473(524) Marrink S-J Berger O Tieleman P Jahnig F Biophys J1998 74 931(525) Kosztin D Izrailev S Schulten K Biophys J 1999 76 188(526) Hummer G Szabo A Acc Chem Res 2005 38 504(527) Jarzynski C Phys Rev Lett 1997 78 2690(528) Bucher D Guidoni L Rothlisberger U Biophys J 2007 932315

(529) Arkin I T Xu H F Jensen M O Arbely E Bennett E RBowers K J Chow E Dror R O Eastwood M P Flitman-TeneR Gregersen B A Klepeis J L Kolossvary I Shan Y B Shaw DE Science 2007 317 799(530) Warshel A Sussman F King G Biochemistry 1986 25 8368(531) Li L Vorobyov I Mackerell A D Allen T W Biophys J2007 94 L11(532) Li L Vorobyov I Allen T W J Phys Chem B 2008 1129574(533) Yoo J Cui Q Biophys J 2008 94 L61(534) MacCallum J L Bennett W F D Tieleman D P Biophys J2008 94 3393(535) Yoo J Cui Q Biophys J 2010 99 1529(536) Johansson A C V Lindahl E J Phys Chem B 2009 113245(537) Honig B Sharp K Yang A S J Phys Chem 1993 97 1101(538) Lim C Bashford D Karplus M J Phys Chem 1991 955610(539) Warshel A Papazyan A Curr Opin Struct Biol 1998 8 211(540) Ullmann G M Knapp E-W Eur Biophys J 1999 28 533(541) Srinivasan J Trevathan M W Beroza P Case D A TheorChem Acc 1999 101 426(542) Koumanov A Ruterjans H Karshikoff A Proteins StructFunct Genet 2002 46 85(543) Mongan J Case D A McCammon J A J Comput Chem2004 25 2038(544) Mongan J Case D A Curr Opin Struct Biol 2005 15 157(545) Khandogin J Brooks C L Biochemistry 2006 45 9363(546) Gunner G Mao J Song Y Kim J Biochim Biophys ActaBioenerg 2006 1757 942(547) Spassov V Z Yan L Protein Sci 2008 17 1955(548) Karshikoff A Spassov V Cowan S W Ladenstein RSchirmer T J Mol Biol 1994 240 372(549) Tanizaki S Feig M J Chem Phys 2005 122 124706(550) Gordon J C Myers J B Folta T Shoja V Heath L SOnufriev A Nucleic Acids Res 2005 33 W368(551) Olsson M H M Soslashndergaard C R Rostkowski M JensenJ H J Chem Theory Comput 2011 7 525(552) Jo S Vargyas M Vasko-Szedlar J Roux B Im W NucleicAcids Res 2008 36 W270(553) Shaw D E Chao J C Eastwood M P Gagliardo JGrossman J P P Ho C R Lerardi D J Kolossvary I Klepeis JL Layman T McLeavey C Deneroff M M Moraes M AMueller R Priest E C Shan Y Spengler J Theobald M TowlesB Wang S C Dror R O Kuskin J S Larson R H Salmon J KYoung C Batson B Bowers K J Commun ACM 2008 51 91(554) Shaw D E J Comput Chem 2005 26 1318(555) Dror R O Jensen M O Borhani D W Shaw D E J GenPhysiol 2010 135 555(556) Dror R O Dirks R M Grossman J P Xu H Shaw D EAnnu Rev Biochem 2012 41 429(557) Dror R O Pan A C Arlow D H Borhani D WMaragakis P Shan Y Xu H Shaw D E Proc Natl Acad Sci USA2011 108 13118(558) Rosenbaum D M Zhang C Lyons J A Holl R AragaoD Arlow D H Rasmussen S G F Choi H-J J Devree B TSunahara R K Chae P S Gellman S H Dror R O Shaw D EWeis W I Caffrey M Gmeiner P Kobilka B K Nature 2011 469236(559) Kruse A C Hu J Pan A C Arlow D H Rosenbaum DM Rosemond E Green H F Liu T Chae P S Dror R OShaw D E Weis W I Wess J Kobilka B K Nature 2012 482552(560) Jensen M O Dror R O Xu H F Borhani D W Arkin IT Eastwood M P Shaw D E Proc Natl Acad Sci USA 2008105 14430(561) Vorobyov I V Anisimov V M MacKerell A D J PhysChem B 2005 109 18988

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAG

(347) Carnevale V Treptow W Klein M L J Phys Chem Lett2011 2 2504(348) Bhattacharya S Derrington I M Pavlenok M NiederweisM Gundlach J H Aksimentiev A ACS Nano 2012 6 6960(349) Graf P Nitzan A Kurnikova M G Coalson R D J PhysChem B 2000 104 12324(350) Peter C Hummer G Biophys J 2005 89 2222(351) Boda D Valisko M Eisenberg B Nonner W HendersonD Gillespie D Phys Rev Lett 2007 98 1(352) Thoslashgersen L Schioslashtt B Vosegaard T Nielsen N CTajkhorshid E Biophys J 2008 95 4337(353) Plank G Zhou L Greenstein J L Cortassa S Winslow RL OrsquoRourke B Trayanova N A Philos Trans R Soc A 2008 3663381(354) Eisenberg B Hyon Y Liu C J Chem Phys 2010 133104104(355) Hannongbua S Treesuwan W Boonyarat W AdvancedMolecular Modeling Techniques Applied to Ion Channels Blockers InIon Channels and Their Inhibitors Gupta S P Ed Springer-VerlagBerlinHeidelberg 2011 pp 53minus78(356) Zheng W Auerbach A PLoS Comput Biol 2011 7e1001046(357) Boda D Busath D D Eisenberg B Henderson DNonner W Phys Chem Chem Phys 2002 4 5154(358) Boda D Henderson D Busath D D Mol Phys 2002 1002361(359) Cervera J Schiedt B Ramirez P Europhys Lett 2005 7135(360) Vidal J Gracheva M E Leburton J-P Nanoscale Res Lett2006 2 61(361) Gracheva M Leburton J-P Nanotechnology 2007 18145704(362) Vidal J Gracheva M Leburton J-P Nanoscale Res Lett2007 2 61(363) Cervera J Alcaraz A Schiedt B Neumann R Ramirez PJ Phys Chem C 2007 111 12265(364) Vlassiouk I Smirnov S Siwy Z Nano Lett 2008 8 1978(365) Gillespie D Boda D He Y Apel P Siwy Z S Biophys J2008 95 609(366) Kosin ska I D Hanggi P Phys Rev E 2008 77 1(367) Reiner J E Kasianowicz J J Nablo B J Robertson J W FProc Natl Acad Sci USA 2010 107 12080(368) Zhang Y Voth G A J Chem Theory Comput 2011 7 2277(369) Zhang M Yeh L Qian S Hsu J J Phys Chem C 2012116 4793(370) Yeh L-h Zhang M Qian S Hsu J-p Tseng S J PhysChem C 2012 116 8672(371) Carr R Comer J Ginsberg M Aksimentiev A Lab Chip2011 11 3766(372) Peters M H J Chem Phys 2011 134 025105(373) Comer J Aksimentiev A J Phys Chem C 2012 116 3376(374) Timp W Comer J Aksimentiev A Biophys J 2012 102L37(375) Aksimentiev A Heng J B Timp G Schulten K Biophys J2004 87 2086(376) Heng J B Aksimentiev A Ho C Marks P Grinkova YV Sligar S Schulten K Timp G Biophys J 2006 90 1098(377) Lu D Aksimentiev A Shih A Y Cruz-Chu E FreddolinoP L Arkhipov A Schulten K Phys Bio 2006 3 S40(378) Luan B Aksimentiev A Phys Rev E 2008 78 021912(379) Carr R Weinstock I A Sivaprasadarao A Muller AAksimentiev A Nano Lett 2008 8 3916(380) Comer J Dimitrov V Zhao Q Timp G Aksimentiev ABiophys J 2009 96 593(381) Luan B Aksimentiev A J Phys Condens Matter 2010 22454123(382) Gracheva M Xiong A Aksimentiev A Schulten K TimpG Leburton J-P Nanotechnology 2006 17 622

(383) Gracheva M Aksimentiev A Leburton J-P Nanotechnology2006 17 3160(384) Sigalov G Comer J Timp G Aksimentiev A Nano Lett2008 8 56(385) Cruz-Chu E R Aksimentiev A Schulten K J Phys Chem C2009 113 1850(386) Dorvel B Sigalov G Zhao Q Comer J Dimitrov VMirsaidov U Aksimentiev A Timp G Nucleic Acids Res 2009 374170(387) Wang D Timp W Shim J Mirsaidov U Comer JAksimentiev A Timp G Biophys J 2010 98 599a(388) Comer J Aksimentiev A Nanopore Force SpectroscopyInsights from Molecular Dynamics Simulations In Nanopores Sensingand Fundamental Biological Interactions Bashir R Iqbal S EdsSpringer Science and Business Media LLC New York 2011 Chapter14 pp 335minus356(389) Sathe C Zou X Leburton J-P Schulten K ACS Nano2011 5 8842(390) Wanunu M Bhattacharya S Xie Y Tor Y AksimentievA Drndic M ACS Nano 2011 5 9345(391) Kowalczyk S W Wells D B Aksimentiev A Dekker CNano Lett 2012 12 1038(392) Wells D B Belkin M Comer J Aksimentiev A Nano Lett2012 8 4117(393) Edmonds C M Hudiono Y C Ahmadi A G Hesketh PJ Nair S J Chem Phys 2012 136 065105(394) Saha K K Drndic M Nikolic B K Nano Lett 2012 12 50(395) Hille B Ionic channels of excitable membranes 3rd ed SinauerAssociates Sunderland MA 2001(396) Hodgkin A L Huxley A F J Physiol 1952 117 500(397) Hodgkin A L Huxley A F J Physiol 1952 117 500(398) Alberts B Johnson A Lewis J Raff M Roberts K WalterP Molecular Biology of The Cell 5th ed Garland Science New York ampLondon 2007(399) Watanabe H Sugiura S Kafuku H Hisada T Biophys J2004 87 2074(400) Wong J Goktepe S Kuhl E Comput Methods Appl MechEngrg 2011 200 3139(401) Rowat P Neur Comp 2007 19 1215(402) Tuckwell H C Jost J Physica A 2009 388 4115(403) Linaro D Storace M Giugliano M PLoS Comput Biol2011 7 e1001102(404) Che Y-Q Wang J Zhou S-S Deng B Chaos SolitonsFractals 2009 40 1588(405) Beard D A PLoS Comput Biol 2005 1 e36(406) Townsley L E Tucker W A Sham S Hinton J FBiochemistry 2001 40 11676(407) Chang G Spencer R H Lee A T Barclay M T Rees DC Science 1998 282 2220(408) Bass R B Strop P Barclay M Rees D C Science 2002298 1582(409) Conroy M J Durand A Lupo D Li X-D D BulloughP A Winkler F K Merrick M Proc Natl Acad Sci USA 2007104 1213(410) Uysal S Vasquez V Tereshko V Esaki K Fellouse FSidhu S Koide S Perozo E Kossiakoff A Proc Natl Acad SciUSA 2009 106 6644(411) Long S B Tao X Campbell E B MacKinnon R Nature2007 450 376(412) Gonen T Cheng Y Sliz P Hiroaki Y Fujiyoshi YHarrison S C Walz T Nature 2005 438 633(413) Miyazawa A Fujiyoshi Y Unwin N Nature 2003 423 949(414) Unwin N J Mol Biol 2005 346 967(415) Cowan S Schirmer T Rummel G Steiert M Ghosh RPauptit R Jansonius J Rosenbusch J Nature 1992 358 727(416) Dutzler R Campbell E B MacKinnon R Science 2003 300108(417) Song L Hobaugh M R Shustak C Cheley S Bayley HGouaux J E Science 1996 274 1859

Chemical Reviews Review

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(418) Malasics A Gillespie D Nonner W Henderson DEisenberg B Boda D Biochim Biophys Acta Biomembr 2009 17882471(419) Giri J Fonseca J Boda D Henderson D Eisenberg BPhys Bio 2011 8 026004(420) Mackay D H Berens P H Wilson K R Hagler A TBiophys J 1984 46 229(421) Morais-Cabral J H Zhou Y MacKinnon R Nature 2001414 37(422) Wulff H Calabresi P A Allie R Yun S Pennington MBeeton C Chandy K G J Clin Invest 2003 111 1703(423) Judge S I V Bever C T Pharmacol Ther 2006 111 224(424) Parsegian A Nature 1969 221 844(425) Rashid M H Kuyucak S J Phys Chem B 2012 116 4812(426) Kung C Nature 2005 436 647(427) Kung C Martinac B Sukharev S Annu Rev Microbiol2010 64 313(428) Sukharev S I Blount P Martinac B Blattner F R KungC Nature 1994 368 265(429) Levina N Totemeyer S Stokes N R Louis P Jones MA Booth I R EMBO J 1999 18 1730(430) Wang W Black S S Edwards M D Miller S Morrison EL Bartlett W Dong C Naismith J H Booth I R Science 2008321 1179(431) Liu Z Gandhi C S Rees D C Nature 2009 461 120(432) Martinac B Buechner M Delcour A H Adler J Kung CProc Natl Acad Sci USA 1987 84 2297(433) Weiss M S Schulz G E J Mol Biol 1992 227 493(434) Kreusch A Schulz G J Mol Biol 1994 243 891(435) Cowan S W Garavito R M Jansonius J N Jenkins J AKarlsson R Konig N Pai E F Pauptit R A Rizkallah P JRosenbusch J P Structure 1995 3 1041(436) Schirmer T Keller T A Wang Y F Rosenbusch J PScience 1995 267 512(437) Dutzler R Rummel G Albert S Hernandez-Alles S PhaleP Rosenbusch J Bened V Schirmer T Structure 1999 7 425(438) Moraes T F Bains M Hancock R E W Strynadka N CJ Nat Struct Mol Biol 2007 14 85(439) Biswas S Mohammad M M Movileanu L van der Berg BStructure 2008 16 1027(440) Tamber S Hancock R E W FEMS Microbiol Lett 2006260 23(441) Liu J Eren E Vijayaraghavan J Cheneke B R Indic Mvan den Berg B Movileanu L Biochemistry 2012 51 2319(442) Cheneke B R van der Berg B Movileanu L Biochemistry2011 50 4987(443) Cheneke B R Indic M van den Berg B Movileanu LBiochemistry 2012 51 5348(444) Vila J Mart S Sanchez-Cespedes J J Antimicrob Chemother2007 59 1210(445) Song L Hobaugh M R Shustak C Cheley S Bayley HGouaux J E Science 1996 274 1859(446) Kasianowicz J Robertson J W F Chan E R Reiner J EStanford V M Annu Rev Anal Chem 2008 1 737(447) Kasianowicz J J Brandin E Branton D Deamer D WProc Natl Acad Sci USA 1996 93 13770(448) Faller R Neiderweis M Schulz G E Science 2004 3031189(449) Butler T Pavlenok M Derrington I Niederweis MGundlach J Proc Natl Acad Sci USA 2008 105 20647(450) Derrington I M Collins M D Pavlenok M NiederweisM Gundlach J H Biophys J 2010 98 422a(451) Manrao E Derrington I Pavlenok M Niederweis MGundlach J PLoS One 2011 6 e25723(452) Roos N Benz R Brdiczka D Biochim Biophys Acta 1982686 204(453) Hiller S Garces R G Malia T J Orekhov V YColombini M Wagner G Science 2008 321 1206

(454) Ujwal R Cascio D Colletier J-P Faham S Zhang JToro L Ping P Proc Natl Acad Sci USA 2008 105 2(455) Bayrhuber M Meins T Habeck M Becker S Giller KVillinger S Vonrhein C Griesinger C Zweckstetter M Zeth KProc Natl Acad Sci USA 2008 105 15370(456) Colombini M Trends Biochem Sci 2009 34 382(457) Hiller S Abramson J Mannella C Wagner G Zeth KTrends Biochem Sci 2010 35 514(458) Hiller S Raschle T Yu T-Y Rice A J Walz T WagnerG Biochim Biophys Acta Bioenerg 2010 1797 66(459) Chen T-Y Annu Rev Physiol 2005 67 809(460) Dutzler R Campbell E B Cadene M Chait B TMacKinnon R Nature 2002 415 287(461) Accardi A Miller C Nature 2004 427 803(462) Steinlein O K Bertrand D Biochem Pharmacol 2008 761175(463) Rose J E Biochem Pharmacol 2007 74 1263(464) Marini A M Soussi-Boudekou S Vissers S Andre B MolCell Biol 1997 17 4282(465) Ninnemann O Jauniaux J C Frommer W B EMBO J1994 13 3464(466) Marini A M Vissers S Urrestarazu A Andre B EMBO J1994 13 3456(467) Khademi S OrsquoConnell J Remis J Robles-Colmenares YMiercke L J W Stroud R M Science 2004 305 1587(468) Javelle A Lupo D Ripoche P Fulford T Merrick MWinkler F K Proc Natl Acad Sci USA 2008 105 5040(469) Gruswitz F OrsquoConnell J Stroud R M Proc Natl Acad SciUSA 2007 104 42(470) Javelle A Lupo D Zheng L Li X-D D Winkler F KMerrick M J Biol Chem 2006 281 39492(471) Gao J Truhlar D G Annu Rev Phys Chem 2002 53 467(472) Kamerlin S C L Vicatos S Dryga A Warshel A AnnuRev Phys Chem 2011 62 41(473) Modi N Winterhalter M Kleinekathofer U Nanoscale2012 4 6166(474) Maffeo C Schopflin R Brutzer H Stehr R AksimentievA Wedemann G Seidel R Phys Rev Lett 2010 105 158101(475) Simonson T Carlsson J Case D A J Am Chem Soc 2004126 4167(476) Rocchia W Alxov E Honig B J Phys Chem B 2001 1056507(477) Baker N Sept D Joseph S Hoist M McCammon J ProcNatl Acad Sci USA 2001 98 10037(478) Ramrez P Aguilella-Arzo M Alcaraz A Cervera JAguilella V M Cell Biochem Biophys 2006 44 287(479) Woolley G Biggin P Schultz A Lien L Jaikaran DBreed J Crowhurst K Sansom M Biophys J 1997 73 770(480) Nonner W Chen D Eisenberg B Biophys J 1998 74 2327(481) Roth R J Phys Condens Matter 2010 22 063102(482) Woolf T Roux B Proc Natl Acad Sci USA 1994 9111631(483) Hummer G New J Phys 2005 7 34(484) Paine P L Scherr P Biophys J 1975 15 1087(485) Roux B Biophys J 1999 77 139(486) Corry B Allen T Kuyucak S Chung S Biophys J 200180 195(487) Cooper K Jakobsson E Wolynes P Prog Biophys Mol Biol1985 46 51(488) Mackerell A D J Comput Chem 2004 25 1584(489) MacKerell D A Bashford D Bellott Dunbrack L REvanseck J D Field M J Fischer S Gao J Guo H Ha SJoseph-McCarthy D Kuchnir L Kuczera K Lau F T K MattosC Michnick S Ngo T Nguyen D T Prodhom B Reiher W ERoux B Schlenkrich M Smith J C Stote R Straub J WatanabeM Wiorkiewicz-Kuczera J Yin D Karplus M J Phys Chem B1998 102 3586(490) Weiner P K Kollman P A J Comput Chem 1981 2 287

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dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAF

(491) Cornell W D Cieplak P Bayly C I Gould I R Merz KM Ferguson D M Spellmeyer D C Fox T Caldwell J WKollman P A J Am Chem Soc 1995 117 5179(492) Jorgensen W L Maxwell D S Tirado-Rives J J Am ChemSoc 1996 118 11225(493) Kaminski G A Friesner R A Tirado-Rives J Jorgensen WL J Phys Chem B 2001 105 6474(494) Hermans J Berendsen H J C Van Gunsteren W FPostma J P M Biopolymers 1984 23 1513(495) Schmid N Eichenberger A P Choutko A Riniker SWinger M Mark A E van Gunsteren W F Eur Biophys J 201140 843(496) Klauda J B Venable R M Freites J A OrsquoConnor J WTobias D J Mondragon-Ramirez C Vorobyov I MacKerell A DPastor R W J Phys Chem B 2010 114 7830(497) Wang J Wolf R M Caldwell J W Kollman P A Case DA J Comput Chem 2004 25 1157(498) Liu Y Chipot C Shao X Cai W Phys Bio 2011 8056005(499) Daura X Mark A E van Gunsteren W F J Comput Chem1998 19 535(500) Berger O Edholm O Jahnig F Biophys J 1997 72 2002(501) Cordomiacute A Caltabiano G Pardo L J Chem TheoryComput 2012 8 948(502) Aksimentiev A Wells D Sotomayor M Membrane ProteinTutorial httpwwwksuiuceduTrainingTutorialssciencemembranemem-tutorialpdfrelax(503) Humphrey W Dalke A Schulten K J Mol Graphics 199614 33(504) Brooks B R Bruccoleri R E Olafson B D States D JSwaminathan S Karplus M J Comput Chem 1983 187(505) Jo S Lim J B Klauda J B Im W Biophys J 2009 97 50(506) Ayton G S Voth G A Curr Opin Struct Biol 2009 19 138(507) Marrink S J de Vries A H Tieleman D P BiochimBiophys Acta 2009 1788 149(508) Nielsen S O Lopez C F Srinivas G Klein M L J PhysCondens Matter 2004 16 R481(509) Yesylevskyy S O Schafer L V Sengupta D Marrink S JPLoS Comput Biol 2010 6 e1000810(510) Wu Z Cui Q Yethiraj A J Phys Chem B 2010 114 10524(511) Sali A Blundell T L J Mol Biol 1993 234 779(512) Capener C E Shrivastava I H Ranatunga K M Forrest LR Smith G R Sansom M S Biophys J 2000 78 2929(513) Roux B Comput Phys Commun 1995 91 275(514) Kollman P Chem Rev 1993 93 2395(515) Pohorille A Jarzynski C Chipot C J Phys Chem B 2010114 10235(516) Torrie G Valleau J J Comput Phys 1977 23 187(517) Kumar S Bouzida D Swendsen R H Kollman P ARosenberg J M J Comput Chem 1992 13 1011(518) Woo H-J Roux B Proc Natl Acad Sci USA 2005 1026825(519) Singh U C Brown F K Bash P A Kollman P A J AmChem Soc 1987 109 1607(520) Grubmuller H Heymann B Tavan P Science 1996 271997(521) Isralewitz B Izrailev S Schulten K Biophys J 1997 732972(522) Izrailev S Stepaniants S Balsera M Oono Y Schulten KBiophys J 1997 72 1568(523) Stepaniants S Izrailev S Schulten K J Mol Mod 1997 3473(524) Marrink S-J Berger O Tieleman P Jahnig F Biophys J1998 74 931(525) Kosztin D Izrailev S Schulten K Biophys J 1999 76 188(526) Hummer G Szabo A Acc Chem Res 2005 38 504(527) Jarzynski C Phys Rev Lett 1997 78 2690(528) Bucher D Guidoni L Rothlisberger U Biophys J 2007 932315

(529) Arkin I T Xu H F Jensen M O Arbely E Bennett E RBowers K J Chow E Dror R O Eastwood M P Flitman-TeneR Gregersen B A Klepeis J L Kolossvary I Shan Y B Shaw DE Science 2007 317 799(530) Warshel A Sussman F King G Biochemistry 1986 25 8368(531) Li L Vorobyov I Mackerell A D Allen T W Biophys J2007 94 L11(532) Li L Vorobyov I Allen T W J Phys Chem B 2008 1129574(533) Yoo J Cui Q Biophys J 2008 94 L61(534) MacCallum J L Bennett W F D Tieleman D P Biophys J2008 94 3393(535) Yoo J Cui Q Biophys J 2010 99 1529(536) Johansson A C V Lindahl E J Phys Chem B 2009 113245(537) Honig B Sharp K Yang A S J Phys Chem 1993 97 1101(538) Lim C Bashford D Karplus M J Phys Chem 1991 955610(539) Warshel A Papazyan A Curr Opin Struct Biol 1998 8 211(540) Ullmann G M Knapp E-W Eur Biophys J 1999 28 533(541) Srinivasan J Trevathan M W Beroza P Case D A TheorChem Acc 1999 101 426(542) Koumanov A Ruterjans H Karshikoff A Proteins StructFunct Genet 2002 46 85(543) Mongan J Case D A McCammon J A J Comput Chem2004 25 2038(544) Mongan J Case D A Curr Opin Struct Biol 2005 15 157(545) Khandogin J Brooks C L Biochemistry 2006 45 9363(546) Gunner G Mao J Song Y Kim J Biochim Biophys ActaBioenerg 2006 1757 942(547) Spassov V Z Yan L Protein Sci 2008 17 1955(548) Karshikoff A Spassov V Cowan S W Ladenstein RSchirmer T J Mol Biol 1994 240 372(549) Tanizaki S Feig M J Chem Phys 2005 122 124706(550) Gordon J C Myers J B Folta T Shoja V Heath L SOnufriev A Nucleic Acids Res 2005 33 W368(551) Olsson M H M Soslashndergaard C R Rostkowski M JensenJ H J Chem Theory Comput 2011 7 525(552) Jo S Vargyas M Vasko-Szedlar J Roux B Im W NucleicAcids Res 2008 36 W270(553) Shaw D E Chao J C Eastwood M P Gagliardo JGrossman J P P Ho C R Lerardi D J Kolossvary I Klepeis JL Layman T McLeavey C Deneroff M M Moraes M AMueller R Priest E C Shan Y Spengler J Theobald M TowlesB Wang S C Dror R O Kuskin J S Larson R H Salmon J KYoung C Batson B Bowers K J Commun ACM 2008 51 91(554) Shaw D E J Comput Chem 2005 26 1318(555) Dror R O Jensen M O Borhani D W Shaw D E J GenPhysiol 2010 135 555(556) Dror R O Dirks R M Grossman J P Xu H Shaw D EAnnu Rev Biochem 2012 41 429(557) Dror R O Pan A C Arlow D H Borhani D WMaragakis P Shan Y Xu H Shaw D E Proc Natl Acad Sci USA2011 108 13118(558) Rosenbaum D M Zhang C Lyons J A Holl R AragaoD Arlow D H Rasmussen S G F Choi H-J J Devree B TSunahara R K Chae P S Gellman S H Dror R O Shaw D EWeis W I Caffrey M Gmeiner P Kobilka B K Nature 2011 469236(559) Kruse A C Hu J Pan A C Arlow D H Rosenbaum DM Rosemond E Green H F Liu T Chae P S Dror R OShaw D E Weis W I Wess J Kobilka B K Nature 2012 482552(560) Jensen M O Dror R O Xu H F Borhani D W Arkin IT Eastwood M P Shaw D E Proc Natl Acad Sci USA 2008105 14430(561) Vorobyov I V Anisimov V M MacKerell A D J PhysChem B 2005 109 18988

Chemical Reviews Review

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(418) Malasics A Gillespie D Nonner W Henderson DEisenberg B Boda D Biochim Biophys Acta Biomembr 2009 17882471(419) Giri J Fonseca J Boda D Henderson D Eisenberg BPhys Bio 2011 8 026004(420) Mackay D H Berens P H Wilson K R Hagler A TBiophys J 1984 46 229(421) Morais-Cabral J H Zhou Y MacKinnon R Nature 2001414 37(422) Wulff H Calabresi P A Allie R Yun S Pennington MBeeton C Chandy K G J Clin Invest 2003 111 1703(423) Judge S I V Bever C T Pharmacol Ther 2006 111 224(424) Parsegian A Nature 1969 221 844(425) Rashid M H Kuyucak S J Phys Chem B 2012 116 4812(426) Kung C Nature 2005 436 647(427) Kung C Martinac B Sukharev S Annu Rev Microbiol2010 64 313(428) Sukharev S I Blount P Martinac B Blattner F R KungC Nature 1994 368 265(429) Levina N Totemeyer S Stokes N R Louis P Jones MA Booth I R EMBO J 1999 18 1730(430) Wang W Black S S Edwards M D Miller S Morrison EL Bartlett W Dong C Naismith J H Booth I R Science 2008321 1179(431) Liu Z Gandhi C S Rees D C Nature 2009 461 120(432) Martinac B Buechner M Delcour A H Adler J Kung CProc Natl Acad Sci USA 1987 84 2297(433) Weiss M S Schulz G E J Mol Biol 1992 227 493(434) Kreusch A Schulz G J Mol Biol 1994 243 891(435) Cowan S W Garavito R M Jansonius J N Jenkins J AKarlsson R Konig N Pai E F Pauptit R A Rizkallah P JRosenbusch J P Structure 1995 3 1041(436) Schirmer T Keller T A Wang Y F Rosenbusch J PScience 1995 267 512(437) Dutzler R Rummel G Albert S Hernandez-Alles S PhaleP Rosenbusch J Bened V Schirmer T Structure 1999 7 425(438) Moraes T F Bains M Hancock R E W Strynadka N CJ Nat Struct Mol Biol 2007 14 85(439) Biswas S Mohammad M M Movileanu L van der Berg BStructure 2008 16 1027(440) Tamber S Hancock R E W FEMS Microbiol Lett 2006260 23(441) Liu J Eren E Vijayaraghavan J Cheneke B R Indic Mvan den Berg B Movileanu L Biochemistry 2012 51 2319(442) Cheneke B R van der Berg B Movileanu L Biochemistry2011 50 4987(443) Cheneke B R Indic M van den Berg B Movileanu LBiochemistry 2012 51 5348(444) Vila J Mart S Sanchez-Cespedes J J Antimicrob Chemother2007 59 1210(445) Song L Hobaugh M R Shustak C Cheley S Bayley HGouaux J E Science 1996 274 1859(446) Kasianowicz J Robertson J W F Chan E R Reiner J EStanford V M Annu Rev Anal Chem 2008 1 737(447) Kasianowicz J J Brandin E Branton D Deamer D WProc Natl Acad Sci USA 1996 93 13770(448) Faller R Neiderweis M Schulz G E Science 2004 3031189(449) Butler T Pavlenok M Derrington I Niederweis MGundlach J Proc Natl Acad Sci USA 2008 105 20647(450) Derrington I M Collins M D Pavlenok M NiederweisM Gundlach J H Biophys J 2010 98 422a(451) Manrao E Derrington I Pavlenok M Niederweis MGundlach J PLoS One 2011 6 e25723(452) Roos N Benz R Brdiczka D Biochim Biophys Acta 1982686 204(453) Hiller S Garces R G Malia T J Orekhov V YColombini M Wagner G Science 2008 321 1206

(454) Ujwal R Cascio D Colletier J-P Faham S Zhang JToro L Ping P Proc Natl Acad Sci USA 2008 105 2(455) Bayrhuber M Meins T Habeck M Becker S Giller KVillinger S Vonrhein C Griesinger C Zweckstetter M Zeth KProc Natl Acad Sci USA 2008 105 15370(456) Colombini M Trends Biochem Sci 2009 34 382(457) Hiller S Abramson J Mannella C Wagner G Zeth KTrends Biochem Sci 2010 35 514(458) Hiller S Raschle T Yu T-Y Rice A J Walz T WagnerG Biochim Biophys Acta Bioenerg 2010 1797 66(459) Chen T-Y Annu Rev Physiol 2005 67 809(460) Dutzler R Campbell E B Cadene M Chait B TMacKinnon R Nature 2002 415 287(461) Accardi A Miller C Nature 2004 427 803(462) Steinlein O K Bertrand D Biochem Pharmacol 2008 761175(463) Rose J E Biochem Pharmacol 2007 74 1263(464) Marini A M Soussi-Boudekou S Vissers S Andre B MolCell Biol 1997 17 4282(465) Ninnemann O Jauniaux J C Frommer W B EMBO J1994 13 3464(466) Marini A M Vissers S Urrestarazu A Andre B EMBO J1994 13 3456(467) Khademi S OrsquoConnell J Remis J Robles-Colmenares YMiercke L J W Stroud R M Science 2004 305 1587(468) Javelle A Lupo D Ripoche P Fulford T Merrick MWinkler F K Proc Natl Acad Sci USA 2008 105 5040(469) Gruswitz F OrsquoConnell J Stroud R M Proc Natl Acad SciUSA 2007 104 42(470) Javelle A Lupo D Zheng L Li X-D D Winkler F KMerrick M J Biol Chem 2006 281 39492(471) Gao J Truhlar D G Annu Rev Phys Chem 2002 53 467(472) Kamerlin S C L Vicatos S Dryga A Warshel A AnnuRev Phys Chem 2011 62 41(473) Modi N Winterhalter M Kleinekathofer U Nanoscale2012 4 6166(474) Maffeo C Schopflin R Brutzer H Stehr R AksimentievA Wedemann G Seidel R Phys Rev Lett 2010 105 158101(475) Simonson T Carlsson J Case D A J Am Chem Soc 2004126 4167(476) Rocchia W Alxov E Honig B J Phys Chem B 2001 1056507(477) Baker N Sept D Joseph S Hoist M McCammon J ProcNatl Acad Sci USA 2001 98 10037(478) Ramrez P Aguilella-Arzo M Alcaraz A Cervera JAguilella V M Cell Biochem Biophys 2006 44 287(479) Woolley G Biggin P Schultz A Lien L Jaikaran DBreed J Crowhurst K Sansom M Biophys J 1997 73 770(480) Nonner W Chen D Eisenberg B Biophys J 1998 74 2327(481) Roth R J Phys Condens Matter 2010 22 063102(482) Woolf T Roux B Proc Natl Acad Sci USA 1994 9111631(483) Hummer G New J Phys 2005 7 34(484) Paine P L Scherr P Biophys J 1975 15 1087(485) Roux B Biophys J 1999 77 139(486) Corry B Allen T Kuyucak S Chung S Biophys J 200180 195(487) Cooper K Jakobsson E Wolynes P Prog Biophys Mol Biol1985 46 51(488) Mackerell A D J Comput Chem 2004 25 1584(489) MacKerell D A Bashford D Bellott Dunbrack L REvanseck J D Field M J Fischer S Gao J Guo H Ha SJoseph-McCarthy D Kuchnir L Kuczera K Lau F T K MattosC Michnick S Ngo T Nguyen D T Prodhom B Reiher W ERoux B Schlenkrich M Smith J C Stote R Straub J WatanabeM Wiorkiewicz-Kuczera J Yin D Karplus M J Phys Chem B1998 102 3586(490) Weiner P K Kollman P A J Comput Chem 1981 2 287

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAF

(491) Cornell W D Cieplak P Bayly C I Gould I R Merz KM Ferguson D M Spellmeyer D C Fox T Caldwell J WKollman P A J Am Chem Soc 1995 117 5179(492) Jorgensen W L Maxwell D S Tirado-Rives J J Am ChemSoc 1996 118 11225(493) Kaminski G A Friesner R A Tirado-Rives J Jorgensen WL J Phys Chem B 2001 105 6474(494) Hermans J Berendsen H J C Van Gunsteren W FPostma J P M Biopolymers 1984 23 1513(495) Schmid N Eichenberger A P Choutko A Riniker SWinger M Mark A E van Gunsteren W F Eur Biophys J 201140 843(496) Klauda J B Venable R M Freites J A OrsquoConnor J WTobias D J Mondragon-Ramirez C Vorobyov I MacKerell A DPastor R W J Phys Chem B 2010 114 7830(497) Wang J Wolf R M Caldwell J W Kollman P A Case DA J Comput Chem 2004 25 1157(498) Liu Y Chipot C Shao X Cai W Phys Bio 2011 8056005(499) Daura X Mark A E van Gunsteren W F J Comput Chem1998 19 535(500) Berger O Edholm O Jahnig F Biophys J 1997 72 2002(501) Cordomiacute A Caltabiano G Pardo L J Chem TheoryComput 2012 8 948(502) Aksimentiev A Wells D Sotomayor M Membrane ProteinTutorial httpwwwksuiuceduTrainingTutorialssciencemembranemem-tutorialpdfrelax(503) Humphrey W Dalke A Schulten K J Mol Graphics 199614 33(504) Brooks B R Bruccoleri R E Olafson B D States D JSwaminathan S Karplus M J Comput Chem 1983 187(505) Jo S Lim J B Klauda J B Im W Biophys J 2009 97 50(506) Ayton G S Voth G A Curr Opin Struct Biol 2009 19 138(507) Marrink S J de Vries A H Tieleman D P BiochimBiophys Acta 2009 1788 149(508) Nielsen S O Lopez C F Srinivas G Klein M L J PhysCondens Matter 2004 16 R481(509) Yesylevskyy S O Schafer L V Sengupta D Marrink S JPLoS Comput Biol 2010 6 e1000810(510) Wu Z Cui Q Yethiraj A J Phys Chem B 2010 114 10524(511) Sali A Blundell T L J Mol Biol 1993 234 779(512) Capener C E Shrivastava I H Ranatunga K M Forrest LR Smith G R Sansom M S Biophys J 2000 78 2929(513) Roux B Comput Phys Commun 1995 91 275(514) Kollman P Chem Rev 1993 93 2395(515) Pohorille A Jarzynski C Chipot C J Phys Chem B 2010114 10235(516) Torrie G Valleau J J Comput Phys 1977 23 187(517) Kumar S Bouzida D Swendsen R H Kollman P ARosenberg J M J Comput Chem 1992 13 1011(518) Woo H-J Roux B Proc Natl Acad Sci USA 2005 1026825(519) Singh U C Brown F K Bash P A Kollman P A J AmChem Soc 1987 109 1607(520) Grubmuller H Heymann B Tavan P Science 1996 271997(521) Isralewitz B Izrailev S Schulten K Biophys J 1997 732972(522) Izrailev S Stepaniants S Balsera M Oono Y Schulten KBiophys J 1997 72 1568(523) Stepaniants S Izrailev S Schulten K J Mol Mod 1997 3473(524) Marrink S-J Berger O Tieleman P Jahnig F Biophys J1998 74 931(525) Kosztin D Izrailev S Schulten K Biophys J 1999 76 188(526) Hummer G Szabo A Acc Chem Res 2005 38 504(527) Jarzynski C Phys Rev Lett 1997 78 2690(528) Bucher D Guidoni L Rothlisberger U Biophys J 2007 932315

(529) Arkin I T Xu H F Jensen M O Arbely E Bennett E RBowers K J Chow E Dror R O Eastwood M P Flitman-TeneR Gregersen B A Klepeis J L Kolossvary I Shan Y B Shaw DE Science 2007 317 799(530) Warshel A Sussman F King G Biochemistry 1986 25 8368(531) Li L Vorobyov I Mackerell A D Allen T W Biophys J2007 94 L11(532) Li L Vorobyov I Allen T W J Phys Chem B 2008 1129574(533) Yoo J Cui Q Biophys J 2008 94 L61(534) MacCallum J L Bennett W F D Tieleman D P Biophys J2008 94 3393(535) Yoo J Cui Q Biophys J 2010 99 1529(536) Johansson A C V Lindahl E J Phys Chem B 2009 113245(537) Honig B Sharp K Yang A S J Phys Chem 1993 97 1101(538) Lim C Bashford D Karplus M J Phys Chem 1991 955610(539) Warshel A Papazyan A Curr Opin Struct Biol 1998 8 211(540) Ullmann G M Knapp E-W Eur Biophys J 1999 28 533(541) Srinivasan J Trevathan M W Beroza P Case D A TheorChem Acc 1999 101 426(542) Koumanov A Ruterjans H Karshikoff A Proteins StructFunct Genet 2002 46 85(543) Mongan J Case D A McCammon J A J Comput Chem2004 25 2038(544) Mongan J Case D A Curr Opin Struct Biol 2005 15 157(545) Khandogin J Brooks C L Biochemistry 2006 45 9363(546) Gunner G Mao J Song Y Kim J Biochim Biophys ActaBioenerg 2006 1757 942(547) Spassov V Z Yan L Protein Sci 2008 17 1955(548) Karshikoff A Spassov V Cowan S W Ladenstein RSchirmer T J Mol Biol 1994 240 372(549) Tanizaki S Feig M J Chem Phys 2005 122 124706(550) Gordon J C Myers J B Folta T Shoja V Heath L SOnufriev A Nucleic Acids Res 2005 33 W368(551) Olsson M H M Soslashndergaard C R Rostkowski M JensenJ H J Chem Theory Comput 2011 7 525(552) Jo S Vargyas M Vasko-Szedlar J Roux B Im W NucleicAcids Res 2008 36 W270(553) Shaw D E Chao J C Eastwood M P Gagliardo JGrossman J P P Ho C R Lerardi D J Kolossvary I Klepeis JL Layman T McLeavey C Deneroff M M Moraes M AMueller R Priest E C Shan Y Spengler J Theobald M TowlesB Wang S C Dror R O Kuskin J S Larson R H Salmon J KYoung C Batson B Bowers K J Commun ACM 2008 51 91(554) Shaw D E J Comput Chem 2005 26 1318(555) Dror R O Jensen M O Borhani D W Shaw D E J GenPhysiol 2010 135 555(556) Dror R O Dirks R M Grossman J P Xu H Shaw D EAnnu Rev Biochem 2012 41 429(557) Dror R O Pan A C Arlow D H Borhani D WMaragakis P Shan Y Xu H Shaw D E Proc Natl Acad Sci USA2011 108 13118(558) Rosenbaum D M Zhang C Lyons J A Holl R AragaoD Arlow D H Rasmussen S G F Choi H-J J Devree B TSunahara R K Chae P S Gellman S H Dror R O Shaw D EWeis W I Caffrey M Gmeiner P Kobilka B K Nature 2011 469236(559) Kruse A C Hu J Pan A C Arlow D H Rosenbaum DM Rosemond E Green H F Liu T Chae P S Dror R OShaw D E Weis W I Wess J Kobilka B K Nature 2012 482552(560) Jensen M O Dror R O Xu H F Borhani D W Arkin IT Eastwood M P Shaw D E Proc Natl Acad Sci USA 2008105 14430(561) Vorobyov I V Anisimov V M MacKerell A D J PhysChem B 2005 109 18988

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAG

(491) Cornell W D Cieplak P Bayly C I Gould I R Merz KM Ferguson D M Spellmeyer D C Fox T Caldwell J WKollman P A J Am Chem Soc 1995 117 5179(492) Jorgensen W L Maxwell D S Tirado-Rives J J Am ChemSoc 1996 118 11225(493) Kaminski G A Friesner R A Tirado-Rives J Jorgensen WL J Phys Chem B 2001 105 6474(494) Hermans J Berendsen H J C Van Gunsteren W FPostma J P M Biopolymers 1984 23 1513(495) Schmid N Eichenberger A P Choutko A Riniker SWinger M Mark A E van Gunsteren W F Eur Biophys J 201140 843(496) Klauda J B Venable R M Freites J A OrsquoConnor J WTobias D J Mondragon-Ramirez C Vorobyov I MacKerell A DPastor R W J Phys Chem B 2010 114 7830(497) Wang J Wolf R M Caldwell J W Kollman P A Case DA J Comput Chem 2004 25 1157(498) Liu Y Chipot C Shao X Cai W Phys Bio 2011 8056005(499) Daura X Mark A E van Gunsteren W F J Comput Chem1998 19 535(500) Berger O Edholm O Jahnig F Biophys J 1997 72 2002(501) Cordomiacute A Caltabiano G Pardo L J Chem TheoryComput 2012 8 948(502) Aksimentiev A Wells D Sotomayor M Membrane ProteinTutorial httpwwwksuiuceduTrainingTutorialssciencemembranemem-tutorialpdfrelax(503) Humphrey W Dalke A Schulten K J Mol Graphics 199614 33(504) Brooks B R Bruccoleri R E Olafson B D States D JSwaminathan S Karplus M J Comput Chem 1983 187(505) Jo S Lim J B Klauda J B Im W Biophys J 2009 97 50(506) Ayton G S Voth G A Curr Opin Struct Biol 2009 19 138(507) Marrink S J de Vries A H Tieleman D P BiochimBiophys Acta 2009 1788 149(508) Nielsen S O Lopez C F Srinivas G Klein M L J PhysCondens Matter 2004 16 R481(509) Yesylevskyy S O Schafer L V Sengupta D Marrink S JPLoS Comput Biol 2010 6 e1000810(510) Wu Z Cui Q Yethiraj A J Phys Chem B 2010 114 10524(511) Sali A Blundell T L J Mol Biol 1993 234 779(512) Capener C E Shrivastava I H Ranatunga K M Forrest LR Smith G R Sansom M S Biophys J 2000 78 2929(513) Roux B Comput Phys Commun 1995 91 275(514) Kollman P Chem Rev 1993 93 2395(515) Pohorille A Jarzynski C Chipot C J Phys Chem B 2010114 10235(516) Torrie G Valleau J J Comput Phys 1977 23 187(517) Kumar S Bouzida D Swendsen R H Kollman P ARosenberg J M J Comput Chem 1992 13 1011(518) Woo H-J Roux B Proc Natl Acad Sci USA 2005 1026825(519) Singh U C Brown F K Bash P A Kollman P A J AmChem Soc 1987 109 1607(520) Grubmuller H Heymann B Tavan P Science 1996 271997(521) Isralewitz B Izrailev S Schulten K Biophys J 1997 732972(522) Izrailev S Stepaniants S Balsera M Oono Y Schulten KBiophys J 1997 72 1568(523) Stepaniants S Izrailev S Schulten K J Mol Mod 1997 3473(524) Marrink S-J Berger O Tieleman P Jahnig F Biophys J1998 74 931(525) Kosztin D Izrailev S Schulten K Biophys J 1999 76 188(526) Hummer G Szabo A Acc Chem Res 2005 38 504(527) Jarzynski C Phys Rev Lett 1997 78 2690(528) Bucher D Guidoni L Rothlisberger U Biophys J 2007 932315

(529) Arkin I T Xu H F Jensen M O Arbely E Bennett E RBowers K J Chow E Dror R O Eastwood M P Flitman-TeneR Gregersen B A Klepeis J L Kolossvary I Shan Y B Shaw DE Science 2007 317 799(530) Warshel A Sussman F King G Biochemistry 1986 25 8368(531) Li L Vorobyov I Mackerell A D Allen T W Biophys J2007 94 L11(532) Li L Vorobyov I Allen T W J Phys Chem B 2008 1129574(533) Yoo J Cui Q Biophys J 2008 94 L61(534) MacCallum J L Bennett W F D Tieleman D P Biophys J2008 94 3393(535) Yoo J Cui Q Biophys J 2010 99 1529(536) Johansson A C V Lindahl E J Phys Chem B 2009 113245(537) Honig B Sharp K Yang A S J Phys Chem 1993 97 1101(538) Lim C Bashford D Karplus M J Phys Chem 1991 955610(539) Warshel A Papazyan A Curr Opin Struct Biol 1998 8 211(540) Ullmann G M Knapp E-W Eur Biophys J 1999 28 533(541) Srinivasan J Trevathan M W Beroza P Case D A TheorChem Acc 1999 101 426(542) Koumanov A Ruterjans H Karshikoff A Proteins StructFunct Genet 2002 46 85(543) Mongan J Case D A McCammon J A J Comput Chem2004 25 2038(544) Mongan J Case D A Curr Opin Struct Biol 2005 15 157(545) Khandogin J Brooks C L Biochemistry 2006 45 9363(546) Gunner G Mao J Song Y Kim J Biochim Biophys ActaBioenerg 2006 1757 942(547) Spassov V Z Yan L Protein Sci 2008 17 1955(548) Karshikoff A Spassov V Cowan S W Ladenstein RSchirmer T J Mol Biol 1994 240 372(549) Tanizaki S Feig M J Chem Phys 2005 122 124706(550) Gordon J C Myers J B Folta T Shoja V Heath L SOnufriev A Nucleic Acids Res 2005 33 W368(551) Olsson M H M Soslashndergaard C R Rostkowski M JensenJ H J Chem Theory Comput 2011 7 525(552) Jo S Vargyas M Vasko-Szedlar J Roux B Im W NucleicAcids Res 2008 36 W270(553) Shaw D E Chao J C Eastwood M P Gagliardo JGrossman J P P Ho C R Lerardi D J Kolossvary I Klepeis JL Layman T McLeavey C Deneroff M M Moraes M AMueller R Priest E C Shan Y Spengler J Theobald M TowlesB Wang S C Dror R O Kuskin J S Larson R H Salmon J KYoung C Batson B Bowers K J Commun ACM 2008 51 91(554) Shaw D E J Comput Chem 2005 26 1318(555) Dror R O Jensen M O Borhani D W Shaw D E J GenPhysiol 2010 135 555(556) Dror R O Dirks R M Grossman J P Xu H Shaw D EAnnu Rev Biochem 2012 41 429(557) Dror R O Pan A C Arlow D H Borhani D WMaragakis P Shan Y Xu H Shaw D E Proc Natl Acad Sci USA2011 108 13118(558) Rosenbaum D M Zhang C Lyons J A Holl R AragaoD Arlow D H Rasmussen S G F Choi H-J J Devree B TSunahara R K Chae P S Gellman S H Dror R O Shaw D EWeis W I Caffrey M Gmeiner P Kobilka B K Nature 2011 469236(559) Kruse A C Hu J Pan A C Arlow D H Rosenbaum DM Rosemond E Green H F Liu T Chae P S Dror R OShaw D E Weis W I Wess J Kobilka B K Nature 2012 482552(560) Jensen M O Dror R O Xu H F Borhani D W Arkin IT Eastwood M P Shaw D E Proc Natl Acad Sci USA 2008105 14430(561) Vorobyov I V Anisimov V M MacKerell A D J PhysChem B 2005 109 18988

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAG

(562) Jiao D King C Grossfield A Darden T A Ren P J PhysChem B 2006 110 18553(563) Yu H Whitfield T W Harder E Lamoureux GVorobyov I Anisimov V M Mackerell A D Roux B J ChemTheory Comput 2010 6 774(564) Siu S W I Vacha R Jungwirth P Bockmann R A J ChemPhys 2008 128 125103(565) Harder E MacKerell A D Roux B J Am Chem Soc 2009131 2760(566) Lopes P E M Roux B MacKerell A D Theor Chem Acc2009 124 11(567) Ren P Ponder J W J Comput Chem 2002 23 1497(568) Grossfield A Ren P Ponder J W J Am Chem Soc 2003125 15671(569) Ponder J W Wu C Ren P Pande V S Chodera J DSchnieders M J Haque I Mobley D L Lambrecht D S DiStasioR A Head-Gordon M Clark G N I Johnson M E Head-Gordon T J Phys Chem B 2010 114 2549(570) Lamoureux G Alexander D MacKerell J Roux B J ChemPhys 2003 119 5185(571) Baker C M Lopes P E M Zhu X Roux B MacKerell AD J Chem Theory Comput 2010 6 1181(572) Vorobyov I Li L Allen T W J Phys Chem B 2008 1129588(573) Luan B Carr R Caffrey M Aksimentiev A Proteins StructFunct Bioinf 2010 78 21153(574) Cherezov V Wei L Jeremy D Luan B Aksimentiev AKatritch V Caffrey M Proteins Struct Funct Bioinf 2008 71 24(575) Luan B Caffrey M Aksimentiev A Biophys J 2007 933058(576) Hodgkin A Keynes R J Physiol 1955 128 61(577) Iannuzzi M Laio A Parrinello M Phys Rev Lett 2003 90238302(578) Bussi G Laio A Parrinello M Phys Rev Lett 2006 96090601(579) Ensing B De Vivo M Liu Z Moore P Klein M AccChem Res 2006 39 73(580) Decrouy A Juteau M Proteau S Teijiera J Rousseau E JMol Cell Cardiol 1996 28 767(581) Kovacs R J Nelson M T Simmerman H K Jones L R JBiol Chem 1988 263 18364(582) Becucci L Papini M Verardi R Veglia G Guidelli R SoftMatter 2012 8 3881(583) Feng L Campbell E B Hsiung Y MacKinnon R Science2010 330 635(584) Sachs J N Crozier P S Woolf T B J Chem Phys 2004121 10847(585) Aksimentiev A Nanoscale 2010 2 468(586) Yang Z van der Straaten T A Ravaioli U Liu Y J ComputElectron 2005 4 167(587) Paine P L Scherr P Biophys J 1975 15 1087(588) Menestrina G J Membr Biol 1986 90 177(589) Gu L Q Bayley H Biophys J 2000 79 1967(590) Mohammad M M Movileanu L J Phys Chem B 2010 1148750(591) Frankenhaeuser B Y B J Physiol 1960 152 159(592) Bezanilla F Armstrong C M J Gen Physiol 1972 60 588(593) Neyton J Miller C J Gen Physiol 1988 92 569(594) Allen T W Hoyles M Chem Phys Lett 1999 313 358(595) Thompson A N Kim I Panosian T D Iverson T MAllen T W Nimigean C M Nat Struct Mol Biol 2009 16 1317(596) Kim I Allen T W Proc Natl Acad Sci USA 2011 10817963(597) Benz R Egli C Hancock R Biochim Biophys Acta 19931149 224(598) Perozo E Cortes D M Sompornpisut P Kloda AMartinac B Nature 2002 418 942(599) Perozo E Kloda A Cortes D M Martinac B Nat StructBiol 2002 9 696

(600) Lee S-Y Lee A Chen J MacKinnon R Proc Natl AcadSci USA 2005 102 15441(601) Long S B Campbell E B MacKinnon R Science 2005 309897(602) Zuniga L Marquez V Gonzalez-Nilo F D Chipot C CidL P Sepulveda F V Niemeyer M I PLoS One 2011 6 e16141(603) Chen P-C Kuyucak S Biophys J 2009 96 2577(604) Chen P-C Kuyucak S Biophys J 2011 100 2466(605) Bezrukov S M Vodyanoy I Parsegian V A Nature 1994370 279(606) Akeson M Branton D Kasianowicz J J Brandin EDeamer D W Biophys J 1999 77 3227(607) Meller A Nivon L Brandin E Golovchenko J BrantonD Proc Natl Acad Sci USA 2000 97 1079(608) Vercoutere W Winters-Hilt S Olsen H Deamer DHaussler D Akeson M Nat Biotechnol 2001 19 248(609) Kasianowicz J J Bezrukov S M Biophys J 1995 69 94(610) Li J Stein D McMullan C Branton D Aziz M JGolovchenko J A Nature 2001 412 166(611) Heng J B Ho C Kim T Timp R Aksimentiev AGrinkova Y V Sligar S Schulten K Timp G Biophys J 2004 872905(612) Storm A J Chen J H Ling X S Zandergen H WDekker C Nat Mater 2003 2 537(613) Garaj S Hubbard W Reina A Kong J Branton DGolovchenko J A Nature 2010 467 190(614) Merchant C A Healy K Wanunu M Ray V PetermanN Bartel J Fischbein M D Venta K Luo Z Johnson A T CDrndic M Nano Lett 2010 10 2915(615) Schneider G F Kowalczyk S W Calado V E PandraudG Zandbergen H W Vandersypen L M K Dekker C Nano Lett2010 10 3163(616) Gu Q Braha O Conlan S Cheley S Bayley H Nature1999 398 686(617) Gu L Q Serra M D Vincent B Vigh G Cheley SBraha O Bayley H Proc Natl Acad Sci USA 2000 97 3959(618) Kang X-f Cheley S Rice-Ficht A Bayley H J Am ChemSoc 2007 129 4701(619) Liu A Zhao Q Guan X Anal Chim Acta 2010 675 106(620) Nakane J Wiggin M Marziali A Biophys J 2004 87 615(621) Zhao Q Sigalov G Dimitrov V Dorvel B Mirsaidov USligar S Aksimentiev A Timp G Nano Lett 2007 7 1680(622) Hornblower B Coombs A Whitaker R D Kolomeisky APicone S J Meller A Akeson M Nat Mater 2007 4 315(623) Dekker C Nat Nanotechnol 2007 2 209(624) Howorka S Siwy Z Chem Soc Rev 2009 38 2360(625) Venkatesan B M Polans J Comer J Sridhar S WendellD Aksimentiev A Bashir R Biomed Microdevices 2011 13 671(626) Timp W Mirsaidov U Wang D Comer J AksimentievA Timp G IEEE Trans Nanotechnol 2010 9 281(627) Wanunu M Phys Life Rev 2012 1 1(628) Muthukumar M J Chem Phys 1999 111 10371(629) Slonkina E Kolomeisky A B J Chem Phys 2003 118 7112(630) Muthukumar M J Chem Phys 2003 118 5174(631) Howorka S Movileanu L Lu X Magnon M Cheley SBraha O Bayley H J Am Chem Soc 2000 122 2411(632) Howorka S Bayley H Biophys J 2002 83 3202(633) Bezrukov S M Kasianowicz J J Phys Rev Lett 1993 702352(634) Muthukumar M Kong C Y Proc Natl Acad Sci USA2006 103 5273(635) Robertson J W F Rodrigues C G Stanford V MRubinson K A Krasilnikov O V Kasianowicz J J Proc Natl AcadSci USA 2007 104 8207(636) Derrington I Butler T Collins M Manrao E PavlenokM Niederweis M Gundlach J Proc Natl Acad Sci USA 2010107 16060

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dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAH

(637) Manrao E A Derrington I M Laszlo A H Langford KW Hopper M K Gillgren N Pavlenok M Niederweis MGundlach J H Nat Biotechnol 2012 30 349(638) Rincon-Restrepo M Mikhailova E Bayley H Maglia GNano Lett 2011 11 746(639) Comer J Wells D B Aksimentiev A Modeling nanoporesfor sequencing DNA In DNA Nanotechnology Methods and ProtocolsZuccheri G Samori B Eds Humana Press New York 2011 Vol749 Chapter 22 pp 317minus358(640) Wells D B Bhattacharya S Carr R Maffeo C Ho AComer J Aksimentiev A Optimization of the molecular dynamicsmethod for simulations of DNA and ion transport through biologicalnanopores In Nanopore-Based Technology Single Molecule Character-ization and DNA Sequencing Gracheva M E Ed Humana PressNew York 2012 Vol 870 Chapter 10 pp 165minus186(641) Yarov-Yarovoy V DeCaen P G Westenbroek R E PanaC-Y Scheuer T Baker D Catterall W A Proc Natl Acad SciUSA 2012 109 E93

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAI

(637) Manrao E A Derrington I M Laszlo A H Langford KW Hopper M K Gillgren N Pavlenok M Niederweis MGundlach J H Nat Biotechnol 2012 30 349(638) Rincon-Restrepo M Mikhailova E Bayley H Maglia GNano Lett 2011 11 746(639) Comer J Wells D B Aksimentiev A Modeling nanoporesfor sequencing DNA In DNA Nanotechnology Methods and ProtocolsZuccheri G Samori B Eds Humana Press New York 2011 Vol749 Chapter 22 pp 317minus358(640) Wells D B Bhattacharya S Carr R Maffeo C Ho AComer J Aksimentiev A Optimization of the molecular dynamicsmethod for simulations of DNA and ion transport through biologicalnanopores In Nanopore-Based Technology Single Molecule Character-ization and DNA Sequencing Gracheva M E Ed Humana PressNew York 2012 Vol 870 Chapter 10 pp 165minus186(641) Yarov-Yarovoy V DeCaen P G Westenbroek R E PanaC-Y Scheuer T Baker D Catterall W A Proc Natl Acad SciUSA 2012 109 E93

Chemical Reviews Review

dxdoiorg101021cr3002609 | Chem Rev XXXX XXX XXXminusXXXAI