Investigating a Back Door Mechanism of Actin PhosphateRelease by Steered Molecular DynamicsWilly Wriggers* and Klaus SchultenDepartment of Physics and Beckman Institute, University of Illinois at Urbana-Champaign, Urbana, Illinois

ABSTRACT In actin-based cell motility, phos-phate (Pi) release after ATP hydrolysis is an essen-tial biochemical process, but the actual pathway ofPi separation from actin is not well understood. Wereport a series of molecular dynamics simulationsthat induce the dissociation of Pi from actin. Aftercleavage from ATP, the singly protonated phosphate(HPO4

22) rotates about the ADP-associated Ca21 ion,turning away from the negatively charged ADPtowards the putative exit near His73. To reveal themicroscopic processes underlying the release of Pi,adhesion forces were measured when pulling thesubstrate out of its binding pocket. The resultssuggest that the separation from the divalent cationis the rate-limiting step in Pi release. Protonation ofHPO4

22 to H2PO42 lowers the electrostatic barrierduring Pi liberation from the ion. The simulationsrevealed a propensity of charged His731 to form asalt bridge with HPO4

22, but not with H2PO42. His73

stabilizes HPO422 and, thereby, inhibits rapid Pi

release from actin. Arg177 remains attached to Pi

along the putative back door pathway, suggesting ashuttle function that facilitates the transport of Pi

to a binding site on the protein surface. Proteins1999;35:262–273. r 1999 Wiley-Liss, Inc.

Key words: actin function; ATP hydrolysis; divalentcation; phosphate titration; non-equilib-rium molecular dynamics

INTRODUCTION

Actin filaments are dynamic polymers, whose time-dependent self-assembly in the cell cytoplasm plays animportant role in processes involving cell motility.1–3 ATPhydrolysis occurs on the actin subunits following theirendwise addition to the elongating aggregate. The hydroly-sis reaction4 proceeds in two consecutive steps: (1) cleav-age of the b-g phosphoester bond of ATP (rate at 20°C:0.035 s21)5; (2) slow (0.0026 s21)5 liberation of the inor-ganic phosphate (Pi) from the protein. ATP is not requiredfor actin polymerization, although ADP-bound filamentsare less rigid and less stable than ATP-bound filaments.6–8

Kinetic studies suggest that actin’s ATPase activity servesas a destabilizing reaction that promotes depolymerizationof the resulting ADP-bound filament.7 It has been shownthat Pi release, rather than phosphoester bond cleavage, isthe crucial modifier of actin filament dynamics.9

Our work is concerned with the release of Pi into themedium after cleavage of the b-g phosphoester bond. The

coupling between ATP hydrolysis and filament elongationhas been the subject of intense research (reviewed inCarlier6), but the basic structural mechanism of the chemi-cal reaction still remains unknown. Crystal structures ofmonomeric actin in the ADP- and ATP-bound states10 donot reveal any significant nucleotide-specific structuraldifferences or residues that could enhance or regulatecatalysis of the hydrolysis reaction.11 The b- and g-phos-phates of ATP coordinate a Ca21 ion in the gelsolin-actincrystal structure,12 which is probably replaced by Mg21 inthe cell. As observed in other metalloenzymes such as DNApolymerase I,13 the ion may play a crucial role in phos-phoester bond hydrolysis.14

Earlier studies15 have identified two pathways of diffus-ing water molecules that connect actin’s enzymatic sitewith the solvent. The first diffusion pathway extends fromthe phosphate tail of the bound nucleotide to the promi-nent opening of the nucleotide binding pocket on the frontface of the protein (Fig. 1a,b), where the adenine is exposedto the solvent. The second water diffusion pathway isoriented in the opposite direction and forms a distinct,alternative entrance for water molecules from the sur-rounding medium to access the enzymatic site. Figure 1cshows the corresponding small opening at His73 in theactin structure on the back face of the protein, throughwhich Pi is visible. It was argued that the ‘‘front door’’diffusion pathway facilitates the exchange of the nucleo-tide, whereas the distinct ‘‘back door’’ pathway (Fig. 1c)facilitates the release of Pi into the medium.15

Conventional molecular dynamics (MD) is considered toestablish thermodynamic equilibrium in a simulated sys-tem.16 Here, MD was used to investigate the fast relax-ation of Pi after the ATP phosphoester bond cleavage (aperturbation of the system from equilibrium). To investi-gate the stability of the Pi binding pocket and to reveal themicroscopic processes underlying the dissociation of Pi, weemployed steered molecular dynamics (SMD) simulations

A video animation of the simulations in VHS format is availablefrom Dr. Wriggers by request. Animations in Quicktime format can beaccessed through the online version of this manuscript (URLhttp://www.interscience.wiley.com/jpages/0887-3585/suppmat/index.html).

Grant sponsor: National Institutes of Health; Grant number: PHS 5P41 RR05969-04; Grant sponsor: NSF; Grant numbers: BIR-9318159and BIR-9423827-EQ; Grant sponsor: Roy J. Carver Charitable Trust;Grant sponsor: Pittsburgh Supercomputing Center; Grant number:MCA935028P.

*Correspondence to: Willy Wriggers, Ph.D., Department of Chemis-try and Biochemistry, University of California, San Diego, 9500Gilman Drive, La Jolla, CA 92093-0365. E-mail: wriggers@ucsd.edu

Received 10 August 1998; Accepted 4 December 1998

PROTEINS: Structure, Function, and Genetics 35:262–273 (1999)

r 1999 WILEY-LISS, INC.

that dissociate Pi from actin through the back door path-way. In SMD,17,18 time-dependent external forces are ap-plied to a ligand to induce its separation from a protein.SMD has proven to be successful in studies of the dissocia-tion of the avidin-biotin complex17,18 and the separation ofretinal from bacteriorhodopsin.19 The analysis of the inter-actions of the dissociating ligand with the binding pocket,as well as the recording of applied forces and of the ligandposition, yield important structural information aboutligand binding and unbinding.20

Simulations were carried out with either singly ordoubly protonated Pi. In solution at neutral pH, bothprotonation states, HPO4

22 and H2PO42 (pKa 5 7.21),

exist. In the enzyme, after cleavage of the b-g phos-phoester bond by an in-line attack of a nucleophilic watermolecule, Pi is at first singly protonated.21,22 Kinetic experi-ments suggest that subsequent titration of Pi is required toallow release from actin.9,23 In the living cell, the regula-tion of Pi release by its protonation state is believed to actas a clock, altering in a time-dependent manner thestability and mechanical properties of the filament.23

Earlier studies singled out actin’s methylated His73 as aputative modifier of Pi release.15 In the F-actin filamentstructure,24 the toxin phalloidin binds to His73 near theentrance of the back door pathway (Fig. 1c) and, thereby,would delay Pi release, as observed experimentally.25 Thehistidine is methylated in all actin species except inNaegleria gruberi.26 This remarkable methylation haspuzzled researchers for 30 years (reviewed in Solomon andRubenstein27), and the function of the methylation is stillunknown. The model of Pi release proposed in this worksheds new light on the role of the methylation of His73.One effect of the methylation of histidine is to shift the pKa

of the imidazole on histidine. The pKa of histidine is 6.04and that of 3-methylhistidine is 6.56.28 Thus, at pH 7.0,methylhistidine will be considerably more charged thanwill be histidine. We investigated the effect of the Pi

protonation state on the behavior of charged His73 duringthe simulated release of the phosphate.

METHODS

Molecular dynamics simulations of actin were carriedout using the program X-PLOR29 with the CHARMM22all-hydrogen force field.30 The structure of ATP-actin takenas the initial model was from the actin-gelsolin segment-1complex.12 Residues 40–50, missing in the crystal struc-ture, were added based on coordinates from an earliersimulated structure of the protein (500 ps snapshot oftrajectory CTC, described in Wriggers and Schulten15).

We obtained coordinates for 30 water molecules in theactin crystal structure12 from Paul McLaughlin. Watermolecules were placed when a peak in the crystallographicelectron density had at least two hydrogen bonding part-ners within 2.8–3.5 Å distance (Paul McLaughlin, personalcommunication). This conservative restriction was neces-sary to confidently assign water binding sites at 2.5 Åresolution. We searched for additional buried water bind-ing sites in actin with the program Dowser.31 Only twoadditional water binding sites were found,32 indicatingthat the crystal water molecules fill most of the buriedcavities in the protein. Twelve of the crystal water mol-ecules coordinate the charged phosphates and the Ca21 ionin the enzymatic pocket,32 consistent with earlier sugges-tions.15 To account for the effect of surface water, thesystem was immersed in a water shell of 5.6 Å thickness,which corresponds to approximately two layers of water

Fig. 1. Putative pathway of Pi release in actin. a: Front view; b: sideview; c: back view. The protein in c is rotated relative to a by 180° aboutthe horizontal axis and by 45° about the vertical axis, rotating subdomains2 and 4 into the page. ADP (yellow), Ca21 ion (orange), and Pi (red) areshown in van-der-Waals representation. The protein (all residues exceptHis73: blue) from the crystal structure of the actin:gelsolin segment-1

complex12 is represented as a tube (a,b) and in van-der-Waals represen-tation (c). Missing residues in the crystal structure were added asdescribed in Methods. His73 (green) is shown in licorice style (a,b) and invan-der-Waals representation (c). The numbers identify actin’s fourstructural subdomains.10 The figure was generated using the moleculargraphics program VMD.47

263ACTIN Pi RELEASE

molecules. The TIP3P water model33 was used, although itwas modified by omitting internal geometry constraints toprovide water flexibility, as described elsewhere.34 Aftersolvation, the system included 1,159 water molecules andits size was 9,360 atoms.

The system was then prepared for Pi separation bycleavage of the Ob-Pg bond of ATP: the three unprotonatedoxygen atoms of Pi in the protonation state HPO4

22 weresuperimposed with the three g-oxygen atoms of ATP sothat Pi was oriented with the hydroxyl facing the sideopposed to the cleaved Ob-Pg bond. After the placement ofPi, the g-phosphate of ATP was deleted. This procedureapproximated the structure immediately after attack of anucleophilic water molecule with inversion of symmetry atthe phosphate.21,22

Partial charges for ADP, HPO422, and H2PO4

2 atomswere calculated by means of the program Gaussian,35

version 94, as described elsewhere.32 The distances be-tween the four phosphate oxygens of Pi were constrained32

by an additional Hookean potential to 2.46 Å (distancederived from the geometry of ADP b-phosphate). The forceconstant used to preserve the tetrahedral geometry of Pi

was 20 kcal mol21 Å22.The MD simulations were carried out on a cluster of

Hewlett-Packard (Palo Alto, CA) 735/125 work-stations,using a 12 Å-cutoff, all-hydrogen force field, 1 fs integra-tion step, and a dielectric constant e 5 1. The ADP · Pi-actin model was refined by minimization of the totalenergy. The system was assigned initial velocities accord-ing to a Maxwell distribution, heated up to 310 K in stepsof 30 K in a 5-ps time period, and equilibrated at 310 K for5 ps.

For the simulation, the protonation degrees of thehistidine residues of actin were estimated based on theirstability15; the side chain of His73 was simulated in theprotonated (charged) state because of the stabilization ofthis state by the methyl group. Standard partial chargesfor the unmethylated histidines were provided by theCHARMM22 force field.30 Charges for charged 3-methyl-histidine were combined from standard charges of anN-methylamide C-terminus and from charges of doublyprotonated histidine in the standard force field, as de-scribed elsewhere.32

The extraction of Pi from actin was performed by applica-tion of external forces to the Pi phosphorus atom. Theseforces were implemented by restraining the phosphorusharmonically to a restraint point and by moving therestraint point with a constant velocity n in the desireddirection. The most probable separation pathway wasdetermined by inspection of the back face of the protein(Fig. 1c). The pull direction corresponds to the vector(0.250, 0.534, 0.807) in the coordinate system of PDB entry1ATN.10 † The force exerted on Pi is then

F 5 kd, (1)

where k is the force constant, and d is the distance betweenthe phosphorus atom and the restraint point. We chose k 510kBT/Å,2 where kB is Boltzmann’s constant and T is thetemperature, and velocities n ranging from 0.0625 Å/ps to1 Å/ps. These values of the force constant and the velocitiescorrespond to a stiff spring in the drift regime36,18 andallow spatial fluctuations of the phosphate of magnitudedx 5 ÎkBT/k 5 0.32 Å. To realize a movement of therestraint point with nearly constant velocity, the positionof the restraint point was changed every 100 fs by adistance of n 3 (100 fs) in the desired direction, followingIsralewitz et al.19 The a-carbons of actin’s residues 31, 26,56, 215, 307, and 333 at the front face of the protein (Fig.1a) were held fixed to anchor actin during the forcedseparation of Pi.

The release of Pi in the presence of the Ca21 ion wasperformed in simulations of length 20 ps using a velocityn 5 0.75 Å/ps. The dissociation of Pi in the presence of theCa21 ion was simulated for various velocities n 5 1, 0.5,0.25, 0.125, and 0.0625 Å/ps in calculations of length 16,32, 64, 128, and 256 ps, respectively. The simulations werecarried out for both singly and doubly protonated phos-phate. In the cases involving doubly protonated Pi, thephosphate was protonated after equilibration of the HPO4

22

system. Divalent cation-free actin was simulated by replac-ing the Ca21 ion with a water molecule.

RESULTSb-g Phosphoester Bond Cleavage

To prepare ATP-actin for the extraction of Pi, the b-gphosphoester bond of ATP was cleaved as described inMethods. Figure 2 presents the resulting structure ofADP · Pi complexed with the Ca21 ion after equilibration ofthe system. Pi is in the singly protonated state (HPO4

22)after cleavage of the b-g bond.21,22 Relative to its position inthe ATP-actin crystal structure,12 the phosphate rotated70° about the Ca21 ion. The ion itself moved 1.7 Å into thegap between Pi and the negatively charged b-phosphate ofADP. This displacement of Pi can be attributed to electro-static repulsion away from the b-phosphate. A watermolecule from the surrounding medium was hydrogen-bonded to both Pi and the b-phosphate, forming a bridge.After cleavage of the bond, Pi moved 3.4 Å in the directionof the putative back door exit (Fig. 1c), reducing thedistance to the exit by 25%. A similar cleavage-relatedmovement of Pi of 3.4 Å was observed in crystal structuresof the ATPase fragment of the bovine 70-kDa heat shockcognate protein,37 which is homologous to actin.38

Interactions With the Divalent Cation

The suggested separation path (Fig. 1c) provides theshortest route of Pi to the exterior of the protein. To test theviability of the path for dissociation, the phosphate waspulled along the path in various simulations described inMethods. Four stages of the dissociation process of Pi areshown in Figure 3. After the cleavage of the b-g bond (t 5 0ps, Fig. 3a) and the initial heat-up and equilibration

†The actin coordinates used in this work12 are not deposited in astructure database. PDB entry 1ATN corresponds to the actin-DNase1 complex, in which actin adopts a similar conformation (backbonerms deviation 0.9 Å).

264 W. WRIGGERS AND K. SCHULTEN

(t 5 10 ps, Fig. 3b), the phosphate restraint point wasmoved until the exerted force was strong enough to pullthe doubly protonated Pi off the Ca21 ion at t 5 21.5 ps (Fig.3c). At a displacement of 12 Å on the separation path, Pi

became exposed to the bulk solvent. At the end of thesimulation, at t 5 30 ps, the now exposed Pi was displaced13.5 Å from its position after equilibration (Fig. 3d).

The force applied to the phosphate along its path and itsdisplacement after equilibration depends on the proton-ation state (Fig. 4a). Figure 4b shows the electrostaticenergies governing interactions of the singly and doublyprotonated phosphates with the Ca21 ion. At first, thedissociation of the phosphates in the presence of the Ca21

ion proceeds slowly: the phosphates remain tightly boundto the cation, while the applied forces are steadily increas-ing to values greater than 2,000 pN. In comparison, SMDsimulations of the dissociation of the avidin-biotin com-plex18 and the streptavidin-biotin complex17 involved rup-ture forces lower than 800 pN. The rupture forces mea-sured here are larger because of the strong electrostaticinteraction of the phosphates with the Ca21 ion (Fig. 4b).Eventually, the phosphate ruptures from the ion. Thisrupture event is manifested by a pronounced jump (6 Å) inthe displacement caused by the relaxation of the harmonicrestraints, and by a drop in the Ca21 interaction energies.After the separation from the cation, forces exerted on thephosphates remain below 1,500 pN.

The protonation state of Pi is a significant determinantof its behavior during dissociation. Release of HPO4

22

required a rupture force of 3,100 pN, whereas the libera-tion of H2PO4

2 involved a smaller rupture force of 2,400

pN. Protonation of Pi lowered the electrostatic barrier DEfor separation from the cation from DE 5 440 kcal/mol(HPO4

22) to DE 5 280 kcal/mol (H2PO42). We note that the

Ca21—Pi interaction energies given in Figure 4b representunscreened electrostatic contributions that exclude theeffects of the protein and solvent surrounding the phos-phate. These interaction energies, which would arise in amedium of dielectric permittivity e 5 1 (e.g., in vacuo), areof the same order of magnitude as molar lattice energies ofsalt crystals.39 The actual Ca21—Pi interaction energiesare expected to be considerably lower, as they scale withthe inverse dielectric permittivity of the protein/solventenvironment of the phosphate.39 The exact dielectric prop-erties of proteins are the subject of much debate; suggestedvalues for the dielectric permittivity range from 10–36.40,41

Assuming a low value e 5 15 for the sake of argument, wecan estimate Ca21—Pi interaction energies of DE 5 29kcal/mol (HPO4

22) and DE 5 19 kcal/mol (H2PO42). We

note that this simple estimate does not consider effects ofionic screening and the molecularity of the solvent me-dium. However, the continuum approach does predicttrends surprisingly well in the experimentally observedinteraction energies and solubilities of salt ions.39

The overall kinetics of ligand binding suggests thatligand dissociation occurs typically on a relatively fast,micro- to millisecond timescale,42,43 even in cases wheredissociation involves a diffusive motion of the ligandthrough the receptor protein.42 What could be the rate-limiting step in actin’s slow Pi release (half-time forCa21-actin ,500 s44)? The estimated electrostatic barrierheights DE suggest that the slow release may be due to the

Fig. 2. Cleavage of the b-g phosphoester bond of ATP. ADP (grey), theCa21 ion (black), a water molecule (black), and the g-phosphate/Pi (white)are shown in licorice representation. Also shown is the angle Pb-Ca21-Pg.ATP is rotated by 180° about the vertical axis relative to its orientation in

Figure 1b. a: The structure of ATP in the initial crystal conformation12;b: the structure after 10 ps heat-up/equilibration at 310 K. HPO4

22 isoriented towards the back door exit (see Fig. 1c).

265ACTIN Pi RELEASE

strong Ca21—Pi interaction. According to Kramers/Arrhe-nius theory,45,46 the escape over a potential barrier ofheight DE is retarded by a Boltzmann factor exp (DE/kBT ).For the diffusive motion of Pi in the ion potential (picosec-ond timescale), the above values for the barrier heightswould lead to escape times on the order of 109 s (HPO4

22)and 102 s (H2PO4

2). In this scenario, HPO422 would remain

trapped in the potential well of the Ca21 ion. Only its

protonation would allow the phosphate to escape thecation on the biological timescale.

Interactions With Actin

After liberation from the ion, the simulation path allowsfor the release of the phosphate without significant distur-bance to the structure of actin (Fig. 5). The Ca21-ATP-actinsystem had been simulated earlier for a total simulation

Fig. 3. Actin’s nucleotide vicinity at four stages of Pi release. Theprotein has been rotated by 180° about the vertical axis relative to itsorientation in Figure 1b. ADP (grey), Ca21 ion (black), and Pi (white) areshown in van-der-Waals sphere representation. The protein backbone isshown in tube representation. Water molecules surrounding the protein

are shown in white line representation. a: t 5 0 ps: cleavage of the ATPOb-Pg bond; b: t 5 10 ps, start of the extraction of H2PO4

2; c: t 5 21.5 ps,H2PO4

2 dissociates from the Ca21 ion; d: t 5 30 ps, end of the simulation.The figure was generated using the molecular graphics program VMD.47

266 W. WRIGGERS AND K. SCHULTEN

time of 500 ps.15 This simulation provided a control thatallowed us to assess the effect of Pi separation on thestability and dynamics of the protein. As an example, wecompare the simulation of HPO4

22 release in the presenceof Ca21 to the control simulation; other simulations exhib-ited similar behavior (data not shown). The changes in theprotein structure were monitored through the root meansquare (rms) deviation of the a-carbon atoms from theinitial structure (Fig. 5) and through the temperatureincrease of the system. The rms deviation of the structureduring phosphate dissociation exceeded the rms deviationin the control simulation (1.5 Å) only slightly, i.e., by about0.3 Å (Fig. 5a). SMD simulations of retinal extraction frombacteriorhodopsin resulted in a temperature increase of 40K caused by irreversible work performed on the systemduring separation of the ligand retinal.19 In comparison,

the temperature increased only moderately by 10–15 K inthe simulations described in this work (data not shown).

In addition to the simulations in the presence of Ca21,we performed simulations of Pi release from divalentcation-free actin. These simulations reveal important inter-actions of Pi with amino acid residues in the putativeseparation pathway that would otherwise be obscured bythe pronounced jump in the displacement due to theinteraction with the ion (Fig. 4a). The improved samplingof interactions with actin at intermediate Pi displacementsalso allowed us to distinguish between specific interactionswith protein side chains, and nonspecific, velocity-depen-dent interactions in the separation channel due to friction.To this end, we extracted the phosphate at differentdissociation velocities. The accuracy of the simulation of Pi

motion after its liberation from the ion relies on two

Fig. 4. Characteristics describing the release of Pi in the presence ofCa21. a: Force exerted on Pi by the restraint (solid line) and displacementof Pi from its position after heat-up/equilibration (dotted line) for H2PO4

2

(grey) and HPO422 (black); b: the corresponding electrostatic interaction

energies between Pi and the Ca21 ion. The simulation time excludes thetime of the initial heat-up/equilibration (10 ps).

267ACTIN Pi RELEASE

assumptions: (1) the slow escape of Pi over the ion poten-tial barrier (see above) is stochastic and does not require aconformational change of the protein; (2) the subsequent Pi

release is sufficiently fast, as suggested by the overallkinetics of ligand-receptor binding (see above), such thatconformational changes orthogonal to the pull directionare sampled on the short timescales accessible to SMD.

Does Pi follow a unique separation path in the absence ofthe divalent cation? Figure 6 demonstrates that consider-able variability arises in the forces corresponding to smalldisplacements from the initial position of Pi. An inspectionof the ‘‘animated’’ dynamics of Pi extraction with themolecular graphic program VMD47 revealed that the pro-nounced peaks in the measured forces (Fig. 6) are causedby the breaking of hydrogen bonds when Pi is liberatedfrom its binding pocket. In a given realization of Pi

dissociation, the strength of the hydrogen bonds withcoordinating groups is sensitive to the particular positionof the phosphate relative to neighboring residues. H2PO4

2

was found to interact strongly with actin’s Ser14, Gln137,and Val159. An initial contact of one of the hydrogens witha nearby oxygen of the ADP b-phosphate was also observedin two cases (simulations of length 128 and 256 ps). Incomparison, singly protonated Pi formed strong bondsmainly with the side chain of actin’s Ser14 and withbridging water molecules that coordinated both HPO4

22

and the ADP b-phosphate (see Fig. 2b).The animation of the simulation trajectories identified a

total of ten residues that made contact with the phosphatealong its separation path. The observed number of interac-tions with Pi in each of the two sets of trajectories of like Pi

protonation states are given in Figure 7. Two snapshots(Fig. 8) exemplify the coordination of H2PO4

2 by Ser14,Gln137, and the ADP b-phosphate, and of HPO4

22 byHis73 and Arg177. Initially Pi participates in interactionswith the side chains of Ser14, Gln137, and Val159, with themain chains of glycines 13, 74, and 158 and, transiently,with Ile71. These initial contacts break in the course of thesimulations and, in certain cases, new hydrogen bondswith His73, His161, and Arg177 are formed at a later stageof the dissociation process (Fig. 7). The contact frequenciesreveal that the length of the positively charged Arg177 sidechain allows this residue to interact with the phosphate fornearly the full range of Pi displacement.

The protonation of Pi altered the propensity of thephosphate to form a contact with the side chain of methyl-ated His73. In the simulations involving HPO4

22, His731

formed hydrogen bonds with Pi (Fig. 7b). The contact withH2PO4

2 required a reorientation of His73 (Fig. 8b) relativeto its position in the crystal structure, where the imidazolepoints to the side opposite to the phosphate (Fig. 1). In thesimulations involving H2PO4

2, methylated His731 did notcoordinate the phosphate (Fig. 7a). The protonation of Pi

also weakened the initial interactions with Gly13 andSer14 (Fig. 7). The effect of the protonation on residuesother than Gly13, Ser14, and His73 appears to be lesssignificant.

Solvation Effects

Solvation is likely to influence the forces measured inSMD simulations. In simulations of the streptavidin-biotin complex,17 the binding pocket was exposed to thesolvent. This allowed water molecules to enter the bindingpocket and participate in breaking hydrogen bond net-works between the ligand and the protein during thedissociation. Grubmuller et al.17 observed a decreasingforce with decreasing dissociation velocity n, which wasattributed to a frictional contribution that depends lin-early on n. In this work, Pi is coordinated by three or feweractin residues (Fig. 7) once the displacement of the phos-phate from its position after cleavage exceeded 5 Å. Watermolecules in the solvated back-door channel, which com-pete with actin’s residues for hydrogen bonds, provide theremaining coordination of Pi. We investigated whether ornot the reduced number of interactions with the proteingave rise to frictional contributions to the dissociationforce, which decrease with smaller dissociation velocity n.

Table I presents the averages and standard deviations ofthe exerted force computed from the trajectories of diva-lent cation-free actin for displacements less than 5 Å andfor displacements greater than 5 Å. The average forces, fordisplacements less than 5 Å, exhibited considerable varia-tions (400–930 pN). These force variations are due to thevariability of specific interactions with actin residues inthe initial phase of Pi release (see above). For displace-ments greater than 5 Å, the average forces generallydecreased with smaller dissociation velocities to values aslow as 400 pN (for H2PO4

2) and 510 pN (for HPO422). This

trend was generally observed for both phosphate proton-ation states, albeit HPO4

22 exhibited higher extraction

Fig. 5. RMS deviation of a-carbons from the initial structure. Thevalues shown correspond to the simulation of HPO4

22 release fromCa21-actin (grey) and to the control simulation (black) reported else-where.15

268 W. WRIGGERS AND K. SCHULTEN

Fig. 6. Forces exerted on Pi as a function of its displacement inselected simulations of divalent cation-free actin. The breaking of con-tacts with groups in the Pi binding site, corresponding to peaks in themeasured forces, are marked as follows: ‘‘b’’ indicates the breaking of adirect hydrogen bond between Pi and a b-phosphate oxygen of ADP;

‘‘H2O’’ denotes the breaking of a water bridge between Pi and ab-phosphate oxygen; the breaking of contacts with amino acids areindicated by the respective residue number. The simulation lengthscorrespond to the times of Table I.

Fig. 7. Number of Pi contacts exhibited by residues of divalentcation-free actin as a function of displacement. Displacement-dependenthydrogen bonds with the side chain (Gly: main chain) of Pi -coordinat-ing residues were identified using VMD.47 The number of contacts at

comparable displacements was determined from five simulations of like Piprotonation state (see Table I). a: Number of contacts in five simulationsinvolving H2PO4

2; b: number of contacts in five simulations involvingHPO4

22.

269ACTIN Pi RELEASE

forces than H2PO42 at comparable dissociation velocities.

Hence, after liberation of Pi from its binding pocket, theforces exerted on the phosphate follow a force-velocityrelationship similar to the one described in Grubmuller etal.17 (Table I).

We note that the 32 ps simulation involving HPO422

provided the sole exception to the observed decrease of theaverage force with smaller dissociation velocities. The high

adhesion force of 1,050 pN in this simulation was causedby a stable attachment of the His73 side chain to thedissociating Pi for displacements greater than 4.5 Å, whichinduced a strain in the main chain of the protein (Fig. 8b).

To consider the effect of water mobility on a ligand thatundergoes uniform motion in a narrow, water-filled chan-nel such as present in actin, we estimate the relaxationtime of water molecules in the channel. It is assumed that

Fig. 8. Contacts of Pi with actin residues and with ADP. ADP (grey),Ca21 (black), and the dissociated Pi (white) are shown in van-der-Waalssphere representation. The protein backbone is shown in tube representa-tion. The orientation of the protein corresponds to the view in Figure 3.a: Dissociation of H2PO4

2 from divalent-cation-free actin, after equilibra-

tion. Ser14, Val159 and Gln137 are shown in black licorice style. b:Dissociation of HPO4

22 from divalent-cation-free actin, after 8 ps Pidissociation (total simulation length 32 ps). His73 and Arg177 are shownin black licorice style. The figure was generated using the moleculargraphics program VMD.47

TABLE I. Pi Extraction From Divalent-Cation-FreeActin†

Simulation time (ps)Simulation time (ps)

16 32 64 128 256

H2PO42

Force (pN) ,5 Å 530 6 220 410 6 280 400 6 220 530 6 220 740 6 210Ave. 6 SD .5 Å 640 6 190 570 6 230 550 6 220 470 6 150 400 6 120

HPO422

Force (pN) ,5 Å 670 6 250 680 6 310 520 6 200 930 6 460 640 6 230Ave. 6 SD .5 Å 840 6 180 1,050 6 200 770 6 210 660 6 150 510 6 190

†Shown are the extraction forces observed for displacements less than 5 Å and for displacements greater than 5Å. For each simulation (see Methods) the average and standard deviation (SD) of the forces were computed fromthe trajectories, excluding the initial heat-up/equilibration.

270 W. WRIGGERS AND K. SCHULTEN

the motion of water molecules is governed by one-dimensional diffusion. The diffusion coefficient along thechannel axis, Dz, is then characterized by

7[z(t 1 t) 2 z(t)]28 5 2Dzt, (2)

where 7· · ·8 denotes an average over time origins t and overthe water molecules in the channel, z(t) is the position of awater molecule at the offset time t. We can approximatethe width of a layer of water molecules, d0, by the size of asingle water molecule, d0 5 3.2 Å. The time t0 required toexchange, by diffusion, a water molecule in the layer isthen

t0 5d0

2

2Dz. (3)

The three-dimensional self-diffusion coefficient of bulkwater at 300 K is D 5 0.23 Å2/ps.48 In the case ofone-dimensional diffusion in narrow channels of radius2–3 Å, the coefficient is reduced to a value Dz 5 0.06Å2/ps,49,50 resulting in a water exchange time of t0 5 85 ps.This value is only slightly lower than the shortest experi-mentally observed exchange times of water molecules inthe hydration shell of solvated ions, which can be as low as300 ps.51

With the help of Eq. 3, we can compute a critical pullvelocity ncrit, at which the time required to traverse thedistance d0, t 5 d0/ncrit, equals the diffusive water exchangetime

ncrit 52Dz

d0. (4)

The values of Dz and d0 assumed above yield a criticalvelocity ncrit 5 0.0375 Å/ps. For dissociation velocities n :ncrit, the slow diffusion of water molecules in the systemcan not fill the space freed by fast displacement of theligand, and the separation of the ligand proceeds as thehydrogen-bond network of the surrounding, relativelyimmobile matrix of water molecules is fractured, formingempty cavities in the wake of the ligand. For dissociationvelocities n : ncrit, the diffusing water molecules form alubricating cloud of transient hydrogen bonds. The dissocia-tion velocities in this work, which range from 0.0625 Å/ps(,ncrit) to 1 Å/ps (.ncrit), suggest that the decreasing forcesobserved in slow dissociation simulations are likely due toan increased lubrication effect as the water molecules gainmobility relative to the displaced phosphate.

DISCUSSION

Steered molecular dynamics provides the possibility toinduce relatively large conformational changes in ligand-receptor complexes on the time scales accessible to MDsimulations. The simulations furnish a qualitative pictureof non-covalent dissociation processes. In this work, wehave applied SMD and convential MD to corroborate amodel of Pi release from actin through a separation paththat was found earlier15 to provide solvent access to actin’s

enzymatic site. The forces required for extraction of (dou-bly protonated) Pi after liberation from its binding pocketin divalent cation-free actin are due to friction and do notindicate any significant potential barriers. The separationof Pi proceeds smoothly and the forces exerted on thephosphate settle at low values near 400 pN for lowdissociation velocities n (Table I).

The simulations provide a clear prediction of the time-limiting step of Pi release from actin, namely, the breakingof strong electrostatic interactions of Pi with the divalentcation that is associated with the nucleotide. The resultssuggest also that protonation of Pi promotes dissociationfrom the cation: titration of HPO4

22 to H2PO42 signifi-

cantly lowers the cation-related electrostatic barrier, whichthe phosphate needs to overcome. Assuming a dielectricconstant e 5 15 of the protein/solvent environment inactin’s catalytic site, the estimated electrostatic interac-tion energies with Ca21 are 29 and 19 kcal/mol for HPO4

22

and H2PO42, respectively. Protonation of Pi also lowers the

adhesion to actin residues that line the separation chan-nel, notably, His73.

The simulations in this work were carried out based onthe Ca21-actin structure. In the cell, this ion is most likelyreplaced by Mg21 (reviewed in Estes et al.14). Experimentssuggest that Mg21 binding induces a conformational changein the protein,52 but the structure of Mg21-actin is notknown in atomic detail. The experimental literature dem-onstrates considerable differences between Ca21- and Mg21-actin in terms of ATP hydrolysis and polymerizationbehavior.6,14,53 Due to a smaller van-der-Waals radius ofMg21 (0.65 Å compared to 0.99 Å of Ca21),39 the electro-static metal-Pi interactions should be considerably stron-ger for Mg21. Consistent with this idea, ion-coordinatingligands appear to be held more tightly and the dissociationof the ion from the high-affinity binding site on Mg21-actinis slower.14 By analogy, one would therefore expect a slowerPi release from Mg21-actin relative to Ca21. However, Pi

release as well as ATP hydrolysis are actually promoted byMg21 relative to Ca21.44,54 Thus, the differences in thebehavior of Mg21- and Ca21-actin cannot be explained bythe ionic radius alone. The release of Pi could be enhancedby a conformational change in Mg21-actin that lowers theheight of the electrostatic barrier or stabilizes the proto-nated H2PO4

2.Actin hydrolyzes ATP during the G-F transformation.

The aggregation into filaments may induce a change ofactin’s conformation.24,55 Are the simulations based on aG-actin crystal structure relevant for Pi release fromF-actin? The effect of phalloidin-binding to F-actin sug-gests that a possible conformational change associatedwith the G-F transformation does not alter the describedrelease of the phosphate: Kinetic measurements indicate aphalloidin-induced delay in Pi release.25 This delay isprobably due to steric hindrance, since the exit of thephosphate separation pathway (Wriggers and Schulten15;this work) forms part of actin’s phalloidin binding face.24 Inthe absence of phalloidin, F-actin’s phosphate separationpathway appears viable. Three-dimensional reconstruc-tions of electron micrographs reveal a conformational

271ACTIN Pi RELEASE

difference between ADP-Pi filaments and ADP filaments,and show that the crystal structure used in this work fitsvery well the F-actin data in the presence of ADP-Pi.56

In the absence of divalent cation, the simulations reveala propensity of His731 to form a salt bridge with HPO4

22,but not with H2PO4

2. Interactions with H2PO42 occurred

at displacements as small as 2.5 Å (Fig. 7b), which is closeto the thermally accessible range of conformational fluctua-tions (1.5 Å15) if HPO4

22 were still bound to the Ca21 ion.Although a salt bridge with HPO4

22 was not observed inthe presence of the ion, the His731 side chain came within5 Å of the nearest phosphate oxygen, a distance readilybridged by a water molecule. By analogy to pKa shiftsobserved in a His-Asp salt bridge in T4 lysozyme,57 one canestimate that a direct salt bridge between His731 andHPO4

22 would lower the pKa of H2PO42 by 3–4 units

relative to its value in solution (pKa 5 7.21), i.e., His731

would stabilize singly protonated HPO422. A water bridge

between His73 and Pi would also stabilize HPO422, albeit

to a lesser degree. The methyl group, which in most actinspecies is added to His73 by a posttranslational modifica-tion at the expense of metabolic energy, would promote theability of His73 to assume the charged, Pi-stabilizing state.

The importance of the charge at the position of residue73 is confirmed by His/Tyr mutants that exhibit a slightlygreater critical concentration for polymerization.27 A moredrastic effect was recently described for a His73/Ala mu-tant: ATP turn-over (hydrolysis and/or Pi-release) relativeto net-polymerization was faster than observed for thewild type (T. Nyman and R. Karlsson, personal communica-tion). The difference from wild type actin could be ex-plained by an increased subunit exchange at His73/Alamutant filament ends leading to the hydrolysis of morethan oneATP per actin subunit incorporated. This interpre-tation is consistent with our model: The stabilization ofsingly protonated Pi by His73 would delay its protonationand, thus, its release from actin. Retention of Pi stabilizes,in turn, the elongating filaments in the cytoskeleton.

In addition to His73, our results also suggest a stabiliz-ing function for Arg177. The flexibility of its side chainallowed Arg177 to coordinate Pi along the separationpathway, starting at displacements as low as 1 Å andending at the exit of Pi (Fig. 7). Arg177 may act as a shuttlethat mediates the transport of Pi to a second binding siteon the surface of the protein. The presence of a secondbinding site for Pi is supported by bimodal effects of Pi-likeBeFn on the fluorescence of F-PIA-ADP actin.23 As de-scribed by Allen et al.,23 the two Pi binding sites would besequentially occupied during phosphate release.

New kinetic and mutagenesis experiments will furtherelucidate the mechanism of actin’s phosphate release. Inparticular, we expect that the temperature-dependent Pi

dissociation rate follows the Arrhenius law,46 which wouldconfirm a single rate limiting step (the liberation from thedivalent cation) and reveal the activation energy. Muta-tions of Val159 or Gly74 that positively charge the residueshould decrease the rate of Pi release. A mutation of Val159to Asn uncouples Pi release from a conformational changeobserved in yeast actin56 and confirms a critical role of this

residue in the time-dependent assembly and disassemblyof the cytoskeleton.

ACKNOWLEDGMENTS

We thank Paul McLaughlin for protein coordinates andPeter Rubenstein, Sofia Khaitlina, Barry Isralewitz, Ser-gei Izrailev, Sergey Stepaniants, and Manel Balsera fordiscussions.

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