Channel Opening Motion of α7 Nicotinic Acetylcholine Receptor as Suggested by Normal Mode Analysis

doi:10.1016/j.jmb.2005.10.039 J. Mol. Biol. (2006) 355, 310–324

Channel Opening Motion of a7 Nicotinic AcetylcholineReceptor as Suggested by Normal Mode Analysis

Xiaolin Cheng2,4*, Benzhuo Lu1,2, Barry Grant1,2, Richard J. Law2,4,5

and J. Andrew McCammon1,2,3,4

1Department of Chemistry andBiochemistry, University ofCalifornia at San Diego, La JollaCA 92093-0365, USA

2Center for Theoretical Bio-logical Physics, University ofCalifornia at San Diego, LaJolla, CA 92093-0365, USA

3Department of PharmacologyUniversity of California at SanDiego, La Jolla, CA 92093-0365USA

4Howard Hughes MedicalInstitute, University ofCalifornia at San Diego, LaJolla, CA 92093-0365, USA

5Biosciences Division, LawrenceLivermore National Labs7000 East Avenue, LivermoreCA 94550, USA

0022-2836/$ - see front matter q 2005 E

Abbreviations used: nAChR, nicoreceptor; AChBP, acetylcholine bindextracellular; TM, transmembrane; Mdynamics; NMA, normal mode anatranslational block; RMSF, root-meaRMSD, root-mean-square deviation

E-mail address of the [email protected]

The gating motion of the human nicotinic acetylcholine receptor (nAChR)a7 was investigated with normal mode analysis (NMA) of two homologymodels. The first model, referred to as model I, was built from both theLymnaea stagnalis acetylcholine binding protein (AChBP) and the trans-membrane (TM) domain of the Torpedo marmorata nAChR. The secondmodel, referred to as model C, was based solely on the recent electronmicroscopy structure of the T. marmorata nAChR. Despite structuraldifferences, both models exhibit nearly identical patterns of flexibility andcorrelated motions. In addition, both models show a similar global twistingmotion that may represent channel gating. The similar results obtained forthe two models indicate that NMA is most sensitive to the contact topologyof the structure rather than its finer detail. The major difference between thelow-frequency motions sampled for the two models is that a symmetricalpore-breathing motion, favoring channel opening, is present as the secondmost dominant motion in model I, whilst largely absent from model C. Theabsence of this mode in model C can be attributed to its less symmetricalarchitecture. Finally, as a further goal of the present study, an approximateopen channel model, consistent with many experimental findings, has beenproduced.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: acetylcholine receptor; ion channel; normal mode analysis;allosteric mechanism
*Corresponding author
Introduction

The nicotinic acetylcholine receptor (nAChR) is aligand-gated ion channel responsible for fast signaltransduction across different synapses.1–3 Thechannel is opened transiently in response to thebinding of neurotransmitter molecules such asacetylcholine. Structurally, nAChR is composed ofa pentameric assembly of five homologous mem-brane-spanning subunits oriented around a centralpore. Each of the subunits is composed of an

lsevier Ltd. All rights reserve

tinic acetylcholineing protein; EC,

D, molecularlysis; RTB, rotational-n-square fluctuation;.ing author:

extracellular (EC) ligand-binding domain and fourtransmembrane (TM) helical segments M1–M4, thesecond of which, M2, forms the channel lumen.Each EC domain contains a core of ten b-strandsarranged as a curled b-sandwich. Strands b1 to b6form an inner sheet, while strands b7 to b10 form asecond outer sheet. A signature Cys loop, locatedtowards the bottom of the EC domain, joins theinner and outer sheets. The acetylcholine-bindingsites lie at the subunit interfaces, and are formedmainly by residues from loops A, B and C of onesubunit (the principal side) and loops D, E and F ofthe other (the complementary side).

Earlier kinetic studies established that nAChRcan exist in at least three conformations withdifferent functional properties: closed, open anddesensitized.4,5 However, molecular detailsremained somewhat elusive until the crystallo-graphic structure of an acetylcholine bindingprotein (AChBP) from Lymnaea stagnalis became

d.

Channel Opening Motion of nAChR 311

available.6 This water-soluble homolog of thenAChR EC domain serves as a useful high-resolution structural model for the nAChRligand-binding domain. A number of crystalstructures of AChBPs complexed with differentligands such as N-2-hydroxyethylpiperazine-N 0-2-ethanesulfonate acid (Hepes6), agonist (nicotine,carbamoylcholine7) and antagonist (a-cobratoxin,8

a-conotoxin9) have now been solved. From acomparison of these structures it seems that onlyloops C and F undergo significant conformationalchange with the presence of different ligands andthat the relative orientation of the subunits, withinthe pentamer, remains unchanged. However, howthese structural changes, observed in AChBPs,relate to those in nAChRs during the gatingprocess is currently unclear. Recently, the structureof nAChR from Torpedo marmorata was determinedby electron microcopy to a resolution of 4 A.10 Thisrefined structure provides a detailed model of boththe EC and the TM domains of the receptor in aclosed state. Further, by fitting the Hepes-boundAChBP structure into the electron density ofTorpedo nAChR, Unwin et al. were able to suggesthow the EC domain might respond to agonistbinding. Together with evidence for the rotation ofthe M2 helix during gating, as indicated by earlierlow-resolution electron microscopy data11 and latersupported by disulphide bond trapping experi-ments,12 Unwin et al. proposed a model for thegating mechanism, in which the acetylcholine-triggered rotations in the EC domains of a subunitsare transmitted to the pore gate through the M2helices.

Although the general framework governing thegating mechanism provided by the recent electronmicroscopy experiments has been very satisfactoryin integrating a large body of structural dataobtained by techniques such as mutagenesis,13,14

photo-labeling15 and fluorescence,16 the detaileddynamics of the transition, including the essentialinteractions involved, has not been determined,partly due to the unavailability of a high-resolutionopen channel structure. Molecular dynamics (MD)simulations have proven to be useful in piecingtogether the data collected from various sourcesand bridging the gap between two or more staticstructures.17,18 Previous MD studies of the ECdomain of the a7 nAChR revealed that the bindingof agonist induces a symmetrical expansion of thefive subunits, whereas a more closed and asym-metrical arrangement was seen for the apo andantagonist binding.19 More recently, a twist-to-closemotion that correlates movements of the C-loopwith the 108 rotation and inward movement of thesubunits A and D was observed in a 15 nssimulation of the a7 receptor.20

Despite having many successful applications,conventional MD simulations are generally limitedto submicrosecond time periods. This makes itdifficult to explore directly conformational changeswith significant kinetic barriers, such as thegating transitions of nAChR. Special simulation

techniques such as targeted MD21 and steeredMD22 have been devised to address this difficulty.In these methods, in addition to the forces derivedfrom potential functions, an external biased force isapplied to guide the system toward the desiredend structure. It should be noted that by removingthe artificial forces using the weighted-histogrammethod23 or Jarzynski’s equality,24 the equilibriumthermodynamic and kinetic quantities such as thepotential of mean force and the transition rate canbe estimated from these biased simulations.

A major goal of our research on the human a7nAChR is to carry out advanced MD simulations tocharacterize the detailed dynamics during channelgating. However, before undertaking such large-scale simulations, it is essential to have an insightinto the nature of the transition. It is for this reasonthat we first performed normal mode analysis(NMA) to examine the intrinsic flexibility of thereceptor, and to identify the most probable directionof the gating transition. NMA, which is based on theharmonic approximation of the system, has pre-viously been demonstrated to be useful in studyinglarge-scale motions in supramolecular complexessuch as the GroEL chaperonin,25 hemoglobin,26

F1-ATPase,27 ribosome,28 and others.29,30 A recentimprovement of NMA31 based on the rotational-translational block (RTB) method32 described byTama et al. has allowed it to be used in biomolecularassemblies of w10,000 residues (conventional NMAis usually limited to systems composed of less than300 residues). The major assumption behind theRTB is that low-frequency normal modes ofproteins can be described as pure rigid-bodymotions of blocks of consecutive amino acidresidues. Because of this simplification, the size ofthe Hessian matrix is reduced, such that thecomputational cost associated with its storageand diagonalization are greatly decreased. As thecurrent study focuses on a few low-frequencymodes of the a7 receptor, the RTB method seemsto be an appropriate choice.

Now we turn to the possible a7 structural modelsthat can be used in the RTB studies. Early on, ahomology model (called model I) based on thecombination of the AChBP structure and channelpore of Torpedo nAChR was constructed andstudied with theoretical methods such as elasticnetwork NMA33 and MD simulations.20 However,there are certain concerns about the accuracy of thismodel: the interface region between the EC and TMdomains is not sufficiently addressed; additionallythe AChBP-derived EC domain may representan activated/desensitized state, whereas the TMdomain from the nAChR is in the closed/restingstate. Consequently, the merged structure could bemismatched or represent an intermediate structure,provided gating occurs in a step-wise process andstructural change in the EC domain precedes themovement of the channel pore.34

The recent 4.0 A resolution electron microscopystructure of the Torpedo nAChR with both theEC and TM domains should provide a better

312 Channel Opening Motion of nAChR

template for modeling nAChRs.10 However, com-plications arise, as Torpedo nAChR is a hetero-pentamer with only two active a subunits. Thus itis not known whether all five subunits of thehomopentameric a7 assume the same confor-mation, or if only two of the subunits are a-likeas in the Torpedo structure. Here, we have chosen tobuild a homology model, which will be referred toas model C below, on Torpedo nAChR withoutimposing 5-fold symmetry.

Here, we report the application of the RTBnormal mode analysis to the above-mentionedstructural models. We compute the root-mean-square fluctuations (RMSF) to examine the overallflexibility of the receptor, and construct cross-correlation maps to identify the interactions thatmay play a role in mediating the channel gatingprocess. Results indicate that the opening of thechannel most likely involves a global twistingmotion. Two lines of evidence support this view:first, the majority of results for the I and C modelsare similar except for some modest differences in afew low-frequency motions; namely, a symmetricalexpansion motion that is the second dominantmotion in model I is changed considerably in modelC. Second, our normal mode results are consistentwith a large body of previous experimental datadeduced from cysteine accessibility,1 affinity label-ing,35 mutagenesis36 and electron microscopyexperiments.11 Moreover, the significant motion ofthe C-loop regions and the asymmetrical expan-sions agree well with MD simulations of the a7 ECdomain.19,37 A similar global twisting motion hasalso been observed recently both in an elastic

network model33 and in a MD simulation of thea7 nAChR.20

Results and Discussion

Comparison of two a7 models

The AChBP derived model I has been used in anumber of earlier computational studies.20,33 Withthe availability of a second, potentially moreaccurate, model based on the recent Torpedoreceptor structure, it is of interest to make a detailedstructural comparison of the two models.A superposition of the two structures based on thebackbone atoms of their EC domains (residues20–205) is displayed in Figure 1(a). Overall, thestructures were found to be highly similar in theirEC domains (with a root-mean-square deviation(RMSD) of 2.7 A). The major structural differenceswere found to reside in loops C and F. These twoloops are the main components of the principal andcomplementary faces of the subunit interface. Inmodel C, both loops appear more loosely struc-tured. For example, the tip of the C-loop is slightlydislodged from its conformation close to the ligand-binding site in model I. These alternate loopconformations reflect the differences between thetwo model template structures.

Additional differences between the models occurin the Cys and b1–b2 loops, located at the bottom ofthe EC domain. Superposition of the structures onthe backbone atoms of their TM domains, as shownin Figure 1(b), reveals that the Cys and b1–b2 loops

Figure 1. Comparison of asubunits in the C model (inorange) and in the I model (ingreen), as viewed parallel with themembrane plane from the peri-phery of the channel. The bluebroken line divides the subunitinto two parts, the EC domain andthe TM domain. (a) Superpositionon the EC domain except the a1helix. (b) Superposition on the TMdomain.


are not in equivalent locations relative to the M2–M3 linkers. Relative to model C, the loops aremarkedly displaced, bringing the Cys loop (1–2 A)and the b1–b2 loop (3–4 A) closer to the M2–M3linker.

In conclusion, the major structural elements ofmodel I should be considered as reasonablyaccurate. This extends to the Cys loop (with anRMSD of 2.7 A between two models) despite the lowsequence identity of a7 and AChBP. However,differences between the models in the positioningof the EC and TM domains may indicate an error inmodel I or may be an outcome of ligand-binding.Differences are particularly evident in the b1–b2region, which is shifted away from the membranesurface by 3–4 A in model C. Regardless of the originof these differences, it is interesting to examine howtheir different interactions might affect the dynamicsof the receptor. The following sections detail theresults of RTB analysis of both models, in which eachresidue is considered as a block.

Root-mean-square fluctuations (RMSF)

Figure 2 illustrates the RMSFs for models I (redline) and C (green line) along with the experimentaldata derived from B-factors for AChBP (black line).Residue equivalences between the EC domain of thea7 and AChBP are as denoted by Henchman et al.37

For clarity, only the average RMSFs for all fivesubunits are shown. The fluctuation profile for bothmodels is very similar (correlation coefficient of0.96). Despite differences in the Cys and b1–b2 loops,the overall flexibility of the whole receptor does notseem to depend on the finer structural details of thisregion and indicates that both models have a level ofaccuracy suitable for coarse-grained NMA studies.

Figure 2. The RMSFs of the Ca atoms at 300 K for the Cmodel (green line) and the I model (red line) calculatedfrom the RTB normal mode analysis, as compared to theexperimental data (black line) of the equivalent region ofthe AChBP. The experimental RMSFs were calculatedfrom the B-factors of the AChBP (PDB code: 1I9B) usingRMSFZ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið3=8p2Þ=Bfactor

p. For clarity, the RMSFs are

averaged over five subunits.

The magnitude of B-factor-derived data wasfound to be much larger than those obtained fromRTB calculations. It should be noted, however, thatthe fluctuation pattern is more relevant than theabsolute thermal amplitude and, in this sense, areasonable agreement is evident (correlation coeffi-cient of 0.64). With NMA, it has been demonstratedthat although fairly robust results can be obtainedfor the fluctuation pattern, the magnitude offluctuation is very sensitive to the energy functionand solvation model employed.38

Differences between AChBP B-factors and simu-lation results are most pronounced in the vicinity ofthe C-loop (residues 180–197). This region wasfound to fluctuate significantly about its initialposition in simulations of both models. However, asagonist interactions help to stabilize the C-loop inthe AChBP structure, it is not surprising to see suchdifferences, since the simulations were performedin the absence of ligand. This result is consistentwith previous experimental studies that indicatethat the C-loop is flexible when the ligand is notpresent.39 A similar observation has also beenobtained in a recent simulation of the a7 receptorincluding a membrane bilayer model.20 Anotherregion that was found to display slight differenceswas the N terminus, which has a short a-helicalstructure. RTB calculations on both modelsindicated a greater mobility in this region than theexperimental B-factor data implied. The origin ofthis difference remains unclear, but may be due tocrystal contacts restricting movement of this regionin the AChBP structure. The final difference of noteoccurs around residues 158–160 (in F-loop), whichmove significantly in AChBP relative to the sameregion in a7 nAChR. We find that Gln160 forms twoover-stabilized salt-bridges with Phe32 and Ser33in our calculations, causing the decreased mobilityfor a7 nAChR.

In the TM domain, helices M1, M2 and M3 aremostly responsible for the inter-subunit contacts,whilst the M4 helix constitutes the outer layer of thechannel. In our RTB calculation, the M4 helix(residues 299–333) exhibits the greatest mobility,which involves a rotation and an outward trans-lation. Although this greater flexibility could beexplained by the lack of lipid bilayer in our model,the recent electron microscopy structure of theTorpedo nAChR shows helix M4 to be less preciselypositioned than the other helices (individual sub-units are aligned by positioning them into a strict5-fold register) suggesting that M4 is indeed moreflexible.10

As expected, most secondary structure elements,such as b strands in the EC domain, exhibit lowflexibility (Figure 2). In addition, four loops alsoshow minimal displacements, namely residues 45–50(b1–b2 loop), 92–96 (A-loop, which makes closecontacts with the binding site), 120–124 (centered atCys121 in Cys loop) and 145–150 (centered at Cys147in Cys loop). This is in agreement with previous MDsimulations, which indicated that of the six loopsshaping the ligand-binding site, loops A and D are


the mosty rigid, whereas loops B, C and F (b8–b9)appear more flexible.37 The rigidity of the b1–b2 andCys loops is consistent with previous experimentalresults2,3 and may be important in transmitting theEC domain motion to the TM domain.

Cross-correlation maps

Central in understanding the allosteric gatingmechanism of nAChRs is a description of howstructural changes induced at the ligand-bindingsite are propagated over large distances (w45 A)resulting in the modulation of channel openingevents. What are the key residue interactionsinvolved in this structural transmission? Since thisquestion is dynamic in nature, even if two end statecrystal structures (in the closed and open confor-mations) are available, there is still a degree ofuncertainty about how the conformational changeoccurs. In previous applications of NMA, theexamination of cross-correlation maps has providedimportant insight into how a local residue fluctuationcorrelates with the movement of another distantresidue.26

The correlation maps for one subunit are shown inFigure 3. Similar intra-subunit correlation maps wereobserved for both models (Figure 3(a) and (b)).Figure 3(c) illustrates the inter-subunit correlationfor model I, the results for the C model being almostindistinguishable (data not shown). The similarresults obtained for two models again lend supportto the appropriateness of using low-resolution

homology models in NMA studies. In the followingsections, discussion is restricted to results obtainedfor model I, which are highly similar to those obtainedfor model C.

As shown in Figure 3(a) and (c), residues withineach subunit were found to exhibit cooperativemotions, whereas residues in adjacent subunitswere relatively uncorrelated, the exception beingseveral residues located at subunit interfaces, suchas Asp24 (in a1-b1), Asn46 (in b1–b2), Asp96 (inloop A), Leu247 and Cys300 (both residing in theM2 and M4 helices) (see also Figure 3(d)).

In the intra-subunit map (Figure 3(a)), yellowlines divide the map into two regions: the ECdomain (bottom left, where the correlation isparticularly strong, probably arising from its morecompact structure), and TM helices (upper right).Dynamic coupling of these regions stems largelyfrom residues 270–274 (the M2–M3 linker), whichare coupled to both residues 43–45 (b1–b2 loop) andresidues 133–135 (Cys loop) (red box in Figure 3(a)).Although the high level of sequence conservation ofthe Cys loop suggests that it might play animportant role in channel gating, Unwin et al.propose that the b1–b2 region functions as anactuator, acting on the M2–M3 linker.40 A recentexperiment with the GABAA receptor has indicatedan alternative possibility; namely, that the b1–b2and Cys loops might act together to coordinate thecommunication between the ligand-bindingdomain and TM helices.36 The current correlationanalysis seems to favor this last proposal, indicating

Figure 3. The correlated fluctu-ations of the Ca atoms in the a7receptor calculated from the RTBanalysis. The correlation maps areshown in (a) the intra-subunitcorrelations in the I model, (b) theintra-subunit correlations in the Cmodel, (c) the correlations betweenthe adjacent subunits in the C/Imodel. The grey level indicatesthe strength of the correlation.(d) Structural model of the a7nAChR with one of the subunitsshown in the ribbon represen-tation. Two highly correlated clus-ters of residues are marked withred boxes, one of which is close tothe acetylcholine binding siteshown as orange van der Waalsspheres (see also the orange box in(a) and (b)). The other is in theM2–M3 linker region shown asgreen and red van der Waalsspheres (see also the red box in (a)and (b)). Two purple van der Waalsspheres located in the TM helicesdenote Leu247 and Val301, whichare also indicated in (c), showingnotable correlated motions withthe residues in other subunits.Also labeled are the locations ofthe b1–b2 loop, the M2–M3 linkerand the A, B, C and Cys loops.


that both the Cys and b1–b2 loops undergo highlyconcerted movements with the M2–M3 linker.

The EC domain can be further divided into twosubdomains (Figure 3(a)). The first corresponds toresidues 127–205 or strands b7–b10 (encircled by ablue ellipse), with the second region encompassingresidues 1–127 or strands b1–b6. Each subdomainessentially undergoes an independent movement asimplicated by a clear separation between these twoblocks. We note that strands b1–b6 form the inner partof the EC domain and have been described by Unwinto undergo a w108 rigid-body rotation relative to theouter sheets upon agonist binding.10 The correlatedmotions observed here are therefore consistent withUnwin’s observation. The independent motion of theinner EC domain b-strands was found to be one of themost dominant global motions of an isolated subunitand will be discussed in more detail below.

Recently, combined MD simulation and trypto-phan fluorescence studies39 have demonstrated thatthe allosteric effect of agonist binding was initiatedfrom the inward motion of the C-loop. However, a fullunderstanding of how this local conformationalchange propagates to the pore domain remains tobe established. In an effort to shed some light on thisissue, we examined the correlated motions of ligand-binding site residues. As highlighted in the orangebox in Figure 3(a), Tyr194 and Tyr187 in the C-loopare highly correlated to Tyr92 in the A-loop andTrp153 in the B-loop (orange spheres in Figure 3(d)).

Figure 4. The RTB normal mode analysis of an isolatedcompared to those from the entire receptor calculation (blacklowest frequency mode. The regions of minimum displacemethe middle indicates important secondary structural elementsthe subunits shown in ribbon representation. The red and greminimum displacements as circled in (b) using the same colorresidues is a possible axis around which the rotation within

This cluster of residues has been confirmed byexperiments to form the principal side of theacetylcholine-binding site.6,7 In effect, the concertedmovement of these residues facilitates the precisepositioning of the ligand. Also evident is the couplingof the Cys loop with the A-loop (residues 92–96) andwith the D-loop (b2, residues 53–56) (green box inFigure 3(a)). As noted previously, at the membraneinterface the Cys loop and the M2–M3 linker arehighly correlated, where together with the b1–b2 loopthey form another strongly related cluster of residues(green and red spheres in Figure 3(d)). Taken togetherwith earlier findings, the current correlation analysisis suggestive of a rough sequential picture for theligand-gated process. That is, agonist binding firstinduces an inward motion of the C-loop, which isthen transmitted to the Cys loop via structuralrearrangements around the binding site, such as A,D-loop movement. Finally, channel gating resultsfrom the interactions of the Cys loop and b1–b2 regionon either side of the M2–M3 linker.

Normal modes of an isolated a subunit

Unwin et al. have proposed that rotation of theinner b sheets of the EC domain initiates TM poreopening.41 The rotation within the EC domain wasdetermined from a rigid-body fitting of the Hepes-bound AChBP structure to the electron density mapof the closed acetylcholine receptor. However, such

a subunit. (a) The RMSFs of the Ca atoms (red line) asline). (b) The RMSFs of the Ca atoms calculated from thents are marked with red or green circles. The color bar in. (c) Schematic diagram of the whole receptor with one ofen van der Waals spheres correspond to the residues with-coding. The vertical line passing through two pairs of redthe subunit occurs.


a rotational movement was not observed in therecently reported AChBP structures.7–9 In an effortto assess the intrinsic flexibility of the a subunit, weperformed an NMA study on an isolated a subunit.Figure 4(a) depicts the RMSFs for the isolated subunitin comparison with results obtained for a singlesubunit from the full a7 receptor. As expected, theRMSFs of the isolated subunit are of greatermagnitude than those observed for the entirereceptor, especially in the C-loop, A-loop and b8–b9regions. Residues in these regions maintain contactswith neighboring subunits in the full receptor, whichare absent in the isolated subunit. The M4 helices alsodisplay greater fluctuations in the isolated subunit.The reason for this difference is not obvious, as the M4helix makes no direct van der Waals contacts with anyother subunits.

The lowest frequency modes of proteins are oftenvery important and potentially related to biologicalfunction.38,42 The RMSFs for the first mode aredisplayed in Figure 4(b), indicating large, correlatedfluctuations of the inner portion of the EC domain(blue box) relative to the outer portion (orange box).Dynamic domains and possible hinge residues wereidentified with the aid of the Dyndom program.43

This analysis indicated that the overall motion of thefirst mode could be described approximately as arigid-body rotation around the hinge residues Ile89,Ser147, Cys127 and Cys141 (red spheres in Figure 4(c)).These positions correspond to points of minimumdisplacement in Figure 4(b) (labeled with red circlesalong the horizontal axis). They form two residuepairs, Ile89-Ser147 and Cys127-Cys141, that

rotation around the long axis passing through two residue(brown spheres). (d) The EC and TM interface, indicating cResidues Leu254 and Ile280, which have minimal displacemspheres. These residues show some increased tendency toby different movement directions around these regions.

maintain close contact at the interface of the innerand outer regions of the EC domain. Thesepositions are speculated to define an axis of rotationwithin the EC domain (orange vertical line inFigure 4(c)). The rotation of the inner region aroundthe axis running through the center of the disulfidebridge has been described by Unwin et al.,41 whospeculated that the highly conserved Cys127 andCys141 (red circle in Figure 4(b)) might act as ahinge point. Additionally, we propose that residuesIle89 and Ser147 might function as a secondstationary point for the rotation. Both Ile89, whichsits on the b4 strand, and Ser147, which is located inthe B loop, are in close proximity to the ligand-binding pocket and may serve as efficient mediatorsof rotation-activation once the ligand is loaded.

In addition to the four hinge residues describedabove, we note several other residues displayingminimal RMSF values (Figure 4(b)). These residuesare Phe32, Met57, Gly121, Cys218, Met253, Ile280and Cys317, which have been marked with greencircles in Figure 4(b) and highlighted as green vander Waals spheres in Figure 4(c). All these residuesare located at the center of secondary structureelements. The former three residues are in the ECdomain while the remaining four are in the TMdomain. A closer examination of the TM domainresidues reveals that there are some kinks formed inthese regions after rotation, particularly in M2 andM3. The kinked structure in the vicinity of Leu247was observed in the closed structure of the TorpedonAChR. However, the M2 and M3 helices appear tobe more kinked after the transition toward the open

Figure 5. The global motion of asingle a7 subunit as suggested bythe lowest frequency mode. (a) and(b) Superposition of two structuresbefore (in blue) and after (in brown)a small displacement along the firstnormal mode. The TM helices areshown as ribbons. The inner set ofthe EC domain (b1–b6) is shown assolid surface representation whilethe outer set (b7–b10) is shown astubes. A schematic diagram on topof (a) and (b) illustrates the direc-tions of the views. (a) Front view,parallel with the membrane plane.(b) Side view, rotated w1508around the pore axis from (a).(c) and (d) The first mode vectorsmapped onto the subunit surface.(c) The EC domain with the innerb1–b6 in blue and the outer b7–b10in orange, as viewed parallel withthe membrane plane from theinside of the channel. As indicatedby the arrows, the motion can bedescribed approximately as a

pairs Ile89, Ser147 (green spheres) and Cys127, Cys141oncerted motions of the b1–b2, M2–M3, and Cys loops.ents (see also Figure 4(b) and (c)), are shown as greenkink during the conformational change as suggested


structure (as indicated by the moving directionalteration around residues Leu254 and Ile180,shown as green spheres in Figure 5(d)).

Figure 5(a) and (b) shows a comparison of the twostructures before (in blue) and after (in orange) asmall rotation along the normal mode direction. Thesuperposition is made based on the backbone atomsof residues in the outer b7–b10 strands. The overallmovement of the first mode corresponds to therotation of the inner set of the EC domain (shown asblue and orange filled representation) except theshort N-terminal a helix, whereas the outer sectionremains relatively stationary (shown as blue andorange tubes). The absence of significant structuralchange in the outer b sheets can be confirmed by theclose fitting of residues in this region (RMSD of1.2 A on 63 Ca atoms) between two structures. Therotation of the inner part is coupled with motion inthe N-terminal region, leading to larger differencesat the top of the subunit (Figure 5(a) and (b)). InFigure 5(c), we also show this rotation by mappingthe normal mode vector for each Ca onto the meshsurface of the EC domain.

Importantly, the rotation extends from the ECdomain to the TM pore region through theinteraction of the M2–M3 linker, b1–b2 and Cysloops, similar to what has been proposed byUnwin.41 Using charge mutations in the GABAA

36

and Gly receptors,2 several groups have demon-strated the importance of molecular interactionsbetween these three loops in imparting cooperativityin Cys loop receptors. However, due to the limitedresolution of the currently available structures, thedetailed mechanical role of the b1–b2 and Cys loopsis still unclear.3 Here, the b1–b2, Cys loops and M2–M3 linker appear to rotate in the same direction(Figure 5(d)). But according to the spatial relation-ship of these three loops, it seems that b1–b2 shouldfunction as an actuator. This does not exclude thepossibility that the Cys loop may act as a stator,bracketing the rotation of the M2–M3 linker whenthe receptor is activated. The role of the Cys loop asa stator may indicate why the rigidity of the Cysloop is so important. Without the disulphide bondbridging two Cys residues, the 15 residue loopwould likely be quite flexible, thus losing itsfunctional role.

Global motion of the entire receptor

In the above RMSF plots and correlation maps,nearly identical results were observed for the twomodels. Structural differences between the modelswere found to have a more significant effect on thethree primary modes of motion; namely, twisting,symmetrical pore-expansion and asymmetricalpore-expansion. These three types of motion havebeen identified from model I, each of themcorresponding to the first three low-frequencymodes, respectively (discussed in detail below). Inmodel C, two major differences were found forthese modes. First, the symmetrical pore-expansionmotion now becomes the fifth mode, and has a low

correlation (!0.3) with that obtained for model I.The asymmetrical pore-expansion motion becomesthe second dominant motion for model C. Second,although the twisting motion remains largelyunchanged (correlation w0.6), the modest differ-ence seen at the interface of the EC and TM domainsinduces a slightly disconcerted motion of b1–b2relative to the M2, M3 helices in model C.

Twisting motion (the first mode in model I)

In both the I and C models, the lowest-frequencymode of the entire receptor involves a globaltwisting motion of the EC domain relative to theTM domain. The two domains undergo a concerted,opposite-direction rotation around the pore axis.An illustration of this motion is given in Figure 6(a)and (b). Several residues that may act as hingepoints for the twisting motion were identified withthe aid of the Dyndom program;43 namely, residues40–51 (b1–b2), 170–174 (b8–b9 loop), 205–210 (b10-M1 linker) and 258–267 (M2–M3 linker). All of theseresidues are located at the EC and TM interface, andmay be interesting targets for mutagenesis. Themotion of all five subunits is very similar, which isalso highly related to the rocking-type rotation seenin the isolated subunit. The correlation coefficientfor this mode, relative to that in the single subunit,is w0.9, suggesting that the combination of the fiveindividual motions intrinsic to each subunit leads tothe symmetrical closing/opening of the wholechannel. Earlier electron microscopy studies havesuggested that all five M2 regions undergo a similargating motion during channel opening.11 A similarmotion has also been observed in a computationalstudy using an elastic network model.33 Morerecently, an all-atom MD simulation has suggestedthe occurrence of a twist-to-close motion.20 How-ever, this seemly opposite result is actually consist-ent with the current observation, since under theharmonic approximation, a conformational changecan occur with the same probability in eitherdirection along a given eigenvector.

In order to assess the functional implication of theidentified twisting motion and to determinewhether it could possibly contribute to the channelopening process, a model structure was generatedby displacing the initial closed structure along themode vector. Figure 7(b) details the pore radiusprofile as a function of pore axis for the recon-figured structure. As indicated by the red line inFigure 7(b), the first mode of motion tends toincrease the width of the pore in the vicinity ofLeu247 and Val251, whereas the pore radiuschanges little for other parts of the channel. Low-resolution electron microscopy studies of nAChRhave also indicated that the channel opens only inthe middle of membrane,11 with Leu247 and Val251acting as two possible gates.40 Mutational studiesby Labarca et al. also indicate that channel gating ofnicotinic receptors is governed symmetrically byconserved Leu residues in the M2 domains.35

Both studies add weight to the presently observed


channel open motion, where each of the fiveLeu247 residues participates independently andsymmetrically in a rotation step in the structuraltransition between the closed and open states.

Although the twisting motion appears to be quitesimilar in the two a7 models, it is still of interest toexamine to what extent these modes are correlated.We therefore compute the correlation between thefirst mode of model I and the eigenvectorsassociated with the first 50 modes obtained frommodel C (Supplementary Data Figure 1S). The firstmodes from two structures are indeed quantitativelysimilar, as indicated by the correlation coefficient ofw0.6. The difference between the modes is due tothe slightly disconcerted motion seen in themembrane interface in model C. We suspect thatthe b1–b2 and Cys loops, that contact the M2–M3region, are slightly displaced in the C model, givingrise to the observed differences.

Symmetrical pore-expansion (the second modein model I)

In contrast to the common twisting motion of thefirst mode, the motion described by the secondmode is different between each of the structures.With model I, the second mode corresponds to asymmetrical pore-expansion of the whole receptor(Figure 6(c)). However, with model C, the secondmode corresponds to an asymmetrical expansion(Figure 6(d)). Generally, the eigenvectors obtainedfor model C show a weaker correlation with thesecond mode than with the first (Supplementary

Data Figure 1S). We suspect that the decreasedsymmetrical motion in model C is because theAChBP derived model I is structurally moresymmetrical than model C.

As shown in Figure 7(b) (green line), thecontribution of the symmetrical pore-expansionmotion to channel opening is evident, albeit to alesser extent than that of the first twisting mode.The pore-breathing motion is also coupled with thestretching/compressing motion along the channelaxis (see Supplementary Data). This explains whythe green line is dramatically shifted in Figure 7(b).We note that a similar pore-breathing motion of theAplysia AChBP upon agonist binding has beenobserved recently (P. Taylor, personal communi-cation). An indirect comparison of the apo TorpedonAChR10 with the liganded AChBP6 also indicates astretching/compressing motion along the channeldirection. However, evidence for the latter is notcompletely convincing, as a more compressedstructure could also be attributed to crystal contactsin the AChBP.

Asymmetrical pore-expansion (the third modein model I)

The asymmetrical pore-expansion motion of thereceptor is observed in both models I and C.Consistent with the structural differences betweenmodels, this motion is the third lowest mode formodel I, whilst it corresponds to the seconddominant motion in model C. As shown inFigure 6(d), two subunits, A and D, move outward

Figure 6. Ribbon diagrams of thea7 receptor, as viewed along thechannel axis from the cytoplasm.(a) The starting closed-channelstructure. (b)–(d) Model structuresgenerated from a small displace-ment along the lowest (twisting),the second lowest (symmetricalpore-expansion) and the third low-est (asymmetrical pore-expansion)normal mode vectors of the Imodel. The broken circles indicatethe size of the pore in the closedstructure. The five arrowheadspoint to the corresponding subunitsin the closed structure using thesame color-coding. These circlesand arrowheads help to illustratethe expanding/rotating motions.

Figure 7. Pore radius profile as a function of the poreaxis. Displacements along the first two modes of the Imodel both tend to increase the minimum pore radius.(a) Cartoon view of the closed structure with the channelpore shown as a blue solid surface representation. Thepore radius profile and the solid surface representationare generated using the HOLE program.59 (b) Pore radiusprofiles of two structural models (see also Figure 6(b) and(c)) as compared to that of the closed structure (PDB code:2BG9). The colors are: the closed, black; mode 1, red;mode 2, green. The shift of the green line is due to thecompression of the receptor along the pore axis.


while three other subunits B, C, and E move inward.Such an asymmetric motion has been observedpreviously in the EC domain and whole receptorsimulations.20,37 Although an asymmetrical two-site-activation seems to be characteristic formembers of the nicotinic receptor family, our resultssuggest that this manner of motion should notcontribute to channel opening (displacementextrapolated from this motion does not result in awider pore). Moreover, a recent comparison of alow-resolution open structure with a closed channelstructure suggested that the pore opened upsymmetrically in the middle of the membrane.40

Thus, the biological significance of this motion forchannel gating remains unclear.

RTB analysis with restraints on the M4 helices

It is well established that the TM domain can bepartitioned into two sets of walls: the inner wall(primarily composed of five M2 helices functioningas the channel lumen), and the outer wall

(composed of the remaining M1, M3 and M4 helicesthat contact the membrane).40 Previously it has beensuggested that only the inner portion (M2 andpossibly part of M1) might move when the receptoris activated.40 However, this is in contrast to thelarge-scale movements of the outer M4 region seenin the current calculations (Figures 2 and 4(a)). Wehypothesize that the absence of a membraneenvironment in the simulation leads to the exag-gerated motion of outer wall. The surroundingenvironment, composed of well-packed lipid mole-cules, would tend to hinder the movement of theouter wall, whereas the M2 region would still beallowed to move due to its minimal contact withother outer helices. The importance of van derWaals interactions between the lipid bilayer and theM4 segment for allosteric movement of the wholereceptor has been recently demonstrated in a 35 nsMD simulation of the Torpedo nAChR TM pore.44 Inaddition, mutagensis experiments of M4 residues aswell as the pharmacological role of several ligandsthat bind in lipid bilayer also seem to support thispostulate.45,46 To further test this hypothesis, weperformed an additional RTB normal mode analysison model I, in which a harmonic restraint, with aforce constant of 3 kcal molK1 AK1, was applied toeach pair of equivalent Ca atoms in the neighboringsubunits (Supplementary Data Figure 2S). Thissimple procedure was designed to mimic therestriction effect of the membrane environment.Remarkably, results indicate that the twistingmotion remains as the dominant mode, in whichonly the interior M2 helices undergo a concertedmotion within the EC domain (see SupplementaryData). The survival of the twisting mode in thecurrent restrained RTB analysis confirms that thetwist-to-open motion is an intrinsic property ofthe receptor, and that it is insensitive to thetreatment of the bilayer environment.

Proposed open-channel models

Although an atomic-resolution closed-channelstructure has emerged recently,10 the low resolutionof the open-channel structure has limited the fittingof secondary structural elements to the electrondensities. In an effort to produce an approximateopen structure for further study, we sought toperturb the closed structure toward an openconformation along the directions of both thetwisting and the symmetrical pore-expansionmodes. It should be noted that, although the resultsfrom a few low-frequency modes have beensuccessfully used in many previous studies todrive the transition between structures,26,47 thistype of extrapolation is not always possible.Significant deformation can occur when the energylandscape is complex i.e. the two end states areseparated by multiple minima. However, in therecently refined Torpedo nAChR structure, it hasbeen shown that the open configuration could begenerated from the closed structure through a w108rotation of the inner b sheets of the EC domain.10

Figure 8. The proposed open-channel models generated by dis-placing the closed structure alongthe two lowest frequency modes.(a) Pore radius profiles (poreregions only) of six representativemodels with backbone RMSD lessthan 3 A from the closed structure(model 1, xZ0.8, yZ150; model 2,xZ0.8, yZ100; model 3, xZ0.9, yZ150; model 4, xZ0.9, yZ100; model5, xZ1.0, yZ150; model 6, xZ1.0,yZ100). These profiles are differ-ent from those shown in Figure 7,since the non-polar hydrogenatoms are not added to the modelsthat we show here. The red andblack lines correspond to theclosed and open structures,respectively, where the closedstructure represents a recentlyrefined electron microscopy struc-ture (PDB code: 2BG9) while theopen structure coordinates areprovided by Unwin based on alow-resolution electron microscopy

image.11 (b) Simplified Ca trace representation of the best candidate model for the open channel. Its pore radius profile isthe closest match to that of Unwin’s open structure. Two elements of the pore gate in the closed channel, the Leu ring (9 0)and the Val ring (13 0), are shown as red and green van der Waals spheres. (c) and (d) The channel is viewed in cross-section. The rotations of Val and Leu rings cause the pore to open up. The structures before and after the rotation areshown as green and red licorice model, respectively.


This relatively small gating motion might thereforejustify the extrapolation of normal modes con-sidered here.

Six candidate open structure models wereproduced using the protocol described in Materialsand Methods. Due to the limited resolution of theexperimentally determined open structure (TM partonly),11 it is not possible to perform direct RMSD-based comparisons with the resulting modelstructures. As an alternative, pore radius profileswere calculated for the six models (shown inFigure 8(a)) and used to select the most represen-tative structure. In Figure 8(a) the red and blacklines correspond to the closed and open structures,respectively. The green line, which corresponds tomodel 3 (with xZ0.9, yZ150, see Materials andMethods), shows the closest similarity to that of theopen structure. A trace representation of this modelstructure is shown in Figure 8(b). The increase ofpore radius occurs in the vicinity of two proposedpore gates, namely the Leu ring (9 0) and the Valring (13 0). We determined that the TM helices,particularly in the L ring and V ring regions(Figure 8(c) and (d)), underwent a clockwiserotation of w128 from the closed structure toproduce this putative “open” structure model. Itwas also noted that a counter-clockwise rotationcontributed differently to the pore radius width,creating a more closed structure (data not shown),as occurred in the MD simulation by Law et al.20

The current open-channel model indicates thatthe opening of the channel is caused primarily byrotation of the M2 domains. This finding is in

agreement with Unwin’s channel gating model,40

and also supported by a recent study, in which afluorescent group attached near the top of the M2helix moves into a more hydrophobic environmentwhen the channel opens.48 In this open-channelmodel, the angular rotation of the inner b strandsrelative to the outer portion of the ligand-bindingdomain is about 128, which is similar to the 108rotation described by Unwin,10 although there isstill a lack of other independent experimentalsupport for this type of rotation. In addition,when moving from the closed-channel nAChRstructure toward a putative open-channel model(e.g. model 3), residue Leu212 (equivalent to Val229in the b subunit of the mouse muscle receptor) isfound to change from a buried state to a more water-accessible state, which is consistent with Zhang andKarlin’s SCAM experiments49 and in agreement witha recent elastic network model calculation.33

Conclusions

RTB normal mode analysis was used to explorepossible mechanisms for the gating motion in thea7 acetylcholine receptor. The two homologymodels investigated displayed nearly identicalRMSFs and cross-correlation patterns. The simi-larity of results indicates that the earlier and moreapproximate I model20,33 can be used withconfidence in coarse-grained normal mode studies.Previous applications of normal mode analysishave shown that the large-scale global motions


captured by the lowest frequency modes aresomewhat insensitive to the finer details ofstructure.27 Consistent with this view, the globaltwisting motion is similar in both models (corre-lation coefficient w0.6), whilst less similar resultsare found for the following modes of motion.

At the tertiary level, the global twisting motioncan be described as a synthesis of five similar,rotational movements within each subunit. Thisrotational motion is an intrinsic property of a singlesubunit, being present in both monomeric andpentameric forms (correlation coefficient w0.9).Although there is nothing intrinsic in the simulationto induce channel gating (i.e. binding of agonists tothe receptor), it is believed that the observed twist-to-open motion may be highly relevant for thegating process, as it is consistent with a number ofrecent experimental results.10,35,40,48,49

The current simulations also suggest that theb1–b2, M2–M3 and Cys loops may play importantroles in the gating movement. Cross-correlationanalysis indicates that the motions of b1–b2, M2–M3and Cys loop regions are highly correlated. Indeed,the lowest frequency mode obtained for a singlesubunit corresponds to the concerted motion of theseloops. Closer examination suggests that the rotationof TM helices is likely to be driven by the b1–b2 loopthrough its interaction with the M2–M3 linker. TheCys loop, on the other hand, may act as a statortogether with b1–b2 to bracket the rotation of M2–M3.

In summary, the present study demonstrates thatthe gating motion deduced experimentally40 isplausible from a theoretical perspective, and alsoprovides a putative open-channel model that isconsistent with a body of experimental data. Furtherstudies of this open-channel model using non-equilibrium MD methods are currently underway.

Materials and Methods

Homology model building

Two homology models of human a7 receptor were builtwith Modeller v4.0.50,51 The first model, model I, wasconstructed by combining the 2.7 A resolution X-raystructure of AChBP6 (PDB code: 1I9B) from L. stagnalisand the 4.6 A resolution TM domain of the TorpedonAChR40 (PDB code: 1OED). The second model, modelC, was built from the recent 4.0 A resolution electronmicroscopy structure of Torpedo nAChR10 (PDB code:2BG9). The homology modeling of model I has beendescribed in detail.20 Briefly, the modeled structurecontains 1665 residues comprising both the EC and TMdomains but excluding the cytoplasmic vestibule domainbetween M3 and M4. 5-Fold symmetry was imposedwhen modeling the pentamer structure. The twotemplates were joined together by using an overlaid all-a-subunit makeup for the TM domain.

Construction of model C was more straightforward,since a single Torpedo nAChR PDB structure was used asthe template. The 29 residues in the MA domain wereexcluded to be consistent with model I. All subunits weremodeled simultaneously to help maintain complemen-tarity between subunit interfaces. 5-Fold symmetry was

not imposed, as we did not expect all the subunits to be inthe same conformation. Due to either the existence ofgaps between the target and template sequences or thelow resolution of the template structure, several loopregions required special attention. Missing residueslocated in the b7–b8 loops of the non-a subunits werepositioned using coordinates from the a subunits. Theb8–b9 linkers were modeled based on loops from AChBP.Modeling the C-loop region required extra care. Thisregion is known to be highly variable and can adopt atleast three conformations, corresponding to apo, agonistor antagonist occupied. Also, since sequence homologyfor this region is low between a7 and non-a subunits ofTorpedo nAChR, models based on non-a templates provedto be unreliable. In the final model, the C-loops in twoalternating subunits had the open conformation, accord-ing to the a subunits of the Torpedo structure, while theremaining subunits had the closed conformation basedon AChBP. The final models were evaluated withPROCHECK52 and Prosa 2003.53

Rotational-translational block normal mode (RTB)

The application of conventional NMA to large bio-molecular systems is limited by the computational costassociated with the storage and diagonalization of all-atom Hessian matrix. The RTB (rotations-translations ofblocks) method, proposed by Tama et al., employs asimplified representation of the system effectively redu-cing the dimensions of the Hessian matrix. In thisrepresentation the protein is broken into nb blocks, eachcomposed of one or more consecutive residues. The overalldynamic behavior is then described by the rigid-body(translational/rotational) motion of these blocks. In theoriginal implementation of RTB,32 the all-atom Hessianmatrix H is first computed explicitly. The block rotational-translational (T/R) matrix Hb is then obtained from H as:

Hb Z PTHP (1)

where P is the so-called projection matrix and PT is itstranspose. The projection matrix is obtained by transform-ing the derivatives of potential function, V, in the atomicspace to those in the block T/R space using the chainproduct, i.e.:

vV

vXi;a

ZX X

jZ1;2;3

vxj

vXi;a

vV

vxj

a Z 1; 2;.; 6 (2)

where the first sum is over all the atoms in block i; Xi,a arethe translational (aZ1, 2, 3) and rotational (aZ4, 5, 6)degrees of freedom for block i; and xj are the Cartesiancoordinates.

Once the block T/R matrix Hb is constructed, theapproximate low-frequency normal modes of the proteincan be obtained by diagonalizing Hb. Since the size ofmatrix Hb, namely 6nb!6nb, is greatly reduced whencompared to that of the original all-atom Hessian matrixH, namely 3N!3N, the RTB method can be employed tostudy much larger proteins than the standard NMA.Another advantage of the block-based method is that, dueto the self-averaging effects within each block, the energysurface in block T/R space is smoother than that in atomicspace. It has been shown that on a rugged energy surfacewith many local minima, the normal mode method,which expands the potential about a single localminimum, does not necessarily capture the desiredtransition from one minimum to another. Thus, thesmoother energy surface resulting from the RTB model


should make it easier to observe large-scale confor-mational transitions.

It should be noted, however, in the RTB describedabove, the need for storing the full Hessian matrix at thefirst step somehow compromises the advantage of themethod. In the current implementation in AMBER8†, theblock T/R Hessian matrix is constructed in a directfashion. That is, once the second derivatives for each pairof atoms are calculated, they are directly projected ontothe corresponding block Hessian elements. This idea hasbeen pursued previously by Cui et al.,31 where “superblocks” were used to avoid the repetitive evaluation of theatomic second derivatives.

In our work, the main loop runs over each pair ofatoms; for each pairwise interaction between atoms i andj, we first calculate its associated all-atom Hessian matrixelements, such as {(3(iK1)Ca, 3(iK1)Cb), (3(iK1)Ca,3(iK1)Cb), (3(iK1)Ca, 3(jK1)Cb), a, bZ1, 2, 3}. Each ofthe 36 atomic derivatives is then converted to blockmatrix elements according to the chain rule given inequation (2). It is worth noting that the interactions fromany pair of atoms, which belong to the blocks I, J,respectively, only contribute to the corresponding matrixelements {(6(IK1)Ci, 6(IK1)Cj), (6(IK1)Ci, 6(JK1)Cj),(6(JK1)Ci, 6(JK1)Cj), iZ1, 2, ., 6; jZ1, 2, ., 6} of theblock T/R Hessian, while the interactions within theblock contribute nothing to the block Hessian, thus can beneglected during the calculation. As the currentimplementation forgoes the need to store the large atomicHessian matrix, it can be routinely used to study largeproteins while still using a standard atomic potential.Compared to other more approximate methods such asthe Gaussian network model42 and elastic networkmodel,54 the use of an all-atom potential should providea more realistic description of the system, especially forhighly charged or heterogeneous ones.

Equilibration and minimization

Before running NMA, the modeled structures wereequilibrated with a 1 ns MD simulation with positionalrestraints on all Ca atoms. The equilibration utilized thegeneralized Born implicit solvent model55 asimplemented in AMBER8. The equilibrated structurewas then subjected to three rounds of energy minimi-zation. The system first underwent 500 steps of steepestdescent minimization with restraints on all backboneatoms. This was followed by 5000 steps of conjugate-gradient minimization with steadily decreasing restraintson Ca atoms. The restraints were applied to preventunrealistic perturbations from the initial structure.Finally, the structure was minimized for another 3000steps with the conjugate-gradient algorithm and norestraints until a root-mean-square gradient ofw0.01 kcal molK1 AK1 was reached. The heavy-atomRMSDs of the final minimized structures for the modelsI and C were w1.1 A and w1.6 A, respectively, from theircorresponding starting structures. It should be noted thatalthough the gradient threshold was much greater thanthat typically required for conventional NMA (w10K6

kcal molK1 AK1), this gradient range was found to besufficient for obtaining well-converged results with block-based NMA.31 The RTB calculations were performed witha modified AMBER8 program using the AMBER ff94force field.56 A distance-dependent dielectric (1/4r) wasused with no cutoff for non-bonded interactions. All

† http://amber.scripps.edu

calculations and analyses were performed on a Dell dual2.0 GHz Pentium4 desktop machine with 2 GB ofmemory.

Root-mean-square fluctuations

The root-mean-square atomic fluctuations (RMSF) forthe ith atom are given by57:

hDr2i i Z

kBT

miuk

a2ik for the kth normal mode (3)

hDr2i i Z

kBT

mi

X3NK6

kZ1

a2ik

uk

for all the normal modes (4)

where mi is the mass for atom i; uk is the vibrationfrequency of mode k; whilst aik is the ith component of thekth eigenvector.

Correlation analysis

The cross-correlation coefficient Cij, between atoms iand j, is a measure of the correlated nature of their atomicfluctuations and is computed as follows:57

hDri$Drji ZX3NK6

kZ1

kBT

u2k

aikajkffiffiffiffiffimi

p ffiffiffiffiffimj

p (5)

Cij Z hDri$Drji=ðhDri$DriihDrj$DrjiÞ1=2 (6)

the summation is over all 3N–6 normal modes; mi and mj

are the masses for atoms i and j; uk is the vibrationfrequency of mode k; whilst aik and ajk are the ith and jthcomponents of the kth eigenvector.

Comparison of normal modes

The overlap of two sets of normal modes ai and aj isdefined by the inner product of the two modes as follows:58

Rij Zai$aj

jaijjajj(7)

The values of Rij should range from K1 to 1. A large Rij

value indicates that the two modes are highly similar.

Generating an open-channel model

Starting from the closed-channel structure10 (PDB code:2BG9), 25 model structures were generated by displacingthe initial structure along the two most dominanteigenvectors DR(1) and DR(2) obtained for model I. If thecoordinates for the closed structure are represented byRclose, then the new set of the coordinates after displace-ment would be Rnew ZRclose CyðxDRð1ÞC ð1KxÞDRð2ÞÞ,where x and y are two adjustable parameters that controlthe amplitude of the displacement. The process wasrepeated several times by varying the values of x and y.To ensure a smooth structure, the backbone RMSD wasused as a restraint. If the new structure deviated more than4 A from the closed structure, a reduced y would be used.Previously, an iterative procedure was used to ensure asmall conformational change in each step.47 However, inthe current work a one-step treatment seemed sufficient toyield smooth structures. The generated structures wereminimized within AMBER8. Of these, six structures had abackbone RMSD within 3 A of the closed structure andunderwent pore-radius profile analysis with the aid of the

http://amber.scripps.edu


HOLE program.59 The reason for using a 3 A thresholdwas that the gating movements were believed to berelatively small so as to preserve the energetically favoredhydrophobic cores.

Acknowledgements

Support for this project was provided partly byNSF, NIH, SDSC, HHMI, NBCR and by the NSFCenter for Theoretical Biological Physics. We thankDr N. Unwin for providing us a low-resolutionopen channel structure.

Supplementary Data

Supplementary data associated with this articlecan be found, in the online version, at doi:10.1016/j.jmb.2005.10.039

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Edited by G. von Heijne

(Received 12 September 2005; received in revised form 11 October 2005; accepted 12 October 2005)Available online 8 November 2005

Documents

Channel Opening Motion of α7 Nicotinic Acetylcholine Receptor as Suggested by Normal Mode Analysis