Modulation of glycophorin A transmembrane helix interactions by lipid bilayers: molecular dynamics...

doi:10.1006/jmbi.2000.4072 available online at http://www.idealibrary.com on J. Mol. Biol. (2000) 302, 727±746

Modulation of Glycophorin A Transmembrane HelixInteractions by Lipid Bilayers: MolecularDynamics Calculations

Horia I. Petrache1, Alan Grossfield2, Kevin R. MacKenzie3

Donald M. Engelman3 and Thomas B. Woolf1,2*

1Department of Physiology and2Department of BiophysicsJohns Hopkins UniversitySchool of Medicine, BaltimoreMD 21205, USA3Department of MolecularBiophysics and BiochemistryYale University, New HavenCT 06520, USA

E-mail address of the [email protected]

Abbreviations used: GpA, glycopdimyristoyl-phosphatidylcholine; Dphosphatidylcholine; DOPC, dioleophosphatidylcholine; POPC, 1-palmphosphatidylcholine; NOE, nuclearenhancement; vdW, van der Waals.

0022-2836/00/030727±20 $35.00/0

Starting from the glycophorin A dimer structure determined by NMR,we performed simulations of both dimer and monomer forms in explicitlipid bilayers with constant normal pressure, lateral area, and tempera-ture using the CHARMM potential. Analysis of the trajectories in fourdifferent lipids reveals how lipid chain length and saturation modulatethe structural and energetic properties of transmembrane helices. Helixtilt, helix-helix crossing angle, and helix accessible volume depend onlipid type in a manner consistent with hydrophobic matching concepts:the most relevant lipid property appears to be the bilayer thickness.Although the net helix-helix interaction enthalpy is strongly attractive,analysis of residue-residue interactions reveals signi®cant unfavorableelectrostatic repulsion between interfacial glycine residues previouslyshown to be critical for dimerization. Peptide volume is nearly conservedupon dimerization in all lipid types, indicating that the monomerichelices pack equally well with lipid as dimer helices do with one another.Enthalpy calculations indicate that the helix-environment interactionenergy is lower in the dimer than in the monomer form, when solvatedby unsaturated lipids. In all lipid environments there is a marked prefer-ence for lipids to interact with peptide predominantly through one ratherthan both acyl chains. Although our trajectories are not long enough toallow a full thermodynamic treatment, these results demonstrate thatmolecular dynamics simulations are a powerful method for investigatingthe protein-protein, protein-lipid, and lipid-lipid interactions that deter-mine the structure, stability and dynamics of transmembrane a-helices inmembranes.

# 2000 Academic Press

Keywords: glycophorin A transmembrane domain; membrane proteins;protein-lipid interactions; a-helix association; dimerization motif
*Corresponding author
Introduction

A large fraction of membrane proteins consist ofbundles of transmembrane a-helices. Despite theirabundance, the process by which these bundlesform is not well understood. One possible mechan-ism for helix association of membrane proteins is

ing author:

horin A; DMPC,PPC, dipalmitoyl-yl-itoyl-2-oleoyl-Overhauser

the two-stage folding model proposed by Popot &Engelman (1990; see also Engelman & Steitz, 1981).In this framework, the transmembrane helices ®rstform independently, then pack together into astable tertiary structure. The transmembranedomain of glycophorin A (GpA) is an excellentmodel system for the study of transmembranehelix association (Bormann & Engelman, 1992;Lemmon & Engelman, 1994). GpA contains asingle transmembrane helix, and forms a homodi-mer under native conditions.

The GpA dimer structure was ®rst predictedcomputationally, by Treutlein et al. (1992), usingthe results of extensive mutagenesis work(Lemmon et al., 1992a,b) to narrow the search. The

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728 Glycophorin A-Lipid Bilayer Simulations

prediction was later re®ned, using an improvedglobal search method (Adams et al., 1996). Morerecently, the structure of the GpA dimer in dodecylphosphocholine micelles was determined usingNMR measurements (MacKenzie et al., 1997). Theclose agreement between the experimental andcomputational results indicated that computationalapproaches can be powerful tools for understand-ing membrane proteins, especially when combinedwith preliminary experimental results.

The previous GpA structure calculations focusedentirely on protein-protein interactions, and com-pletely neglected the interactions between the pro-tein and the micelle or the lipid bilayer. Bycontrast, simulations of soluble proteins have con-sistently demonstrated the importance of solvent inobtaining reasonable structures and dynamics(Novotny et al., 1984; Brooks et al., 1988). Theenvironment effect is likely to be even more pro-nounced in the case of membrane proteins, sincelipid bilayers are strongly anisotropic and thereforegreatly restrict protein motions.

Lipid properties have been shown to modulateprotein folding, structure, and function in manymembrane systems. For example, the role of lipidheadgroup, chain length and unsaturation on thephotochemical behavior of rhodopsin has beendocumented by Brown (1994) and Litman &Mitchell (1996). Koeppe and collaborators haveshown the dependence of gramicidin conformationon lipid chain length, and identi®ed a minimalthreshold for channel formation (Greathouse et al.,1994; Koeppe & Andersen, 1996). The role of head-group interactions has been studied by Gawrischet al. (1993) in the case of the P828 peptide frag-ment from the envelope glycoprotein gp41, whileBezrukov et al. (1998) have determined the effect oflipid packing on alamethicin channel formationand conductance. Many other examples can befound in recent reviews by Killian (1998), Epand(1998), and White & Wimley (1999).

A large body of experimental work hassuggested that lipid properties are in turn modi®edby the presence of the protein (Pink et al., 1981;Keller et al., 1996; de Planque et al., 1998). In par-ticular, a hypothesis has been proposed thatboundary lipids next to the protein are morestrongly perturbed than are the lipids furtherremoved from it (Jost et al., 1973). However, therange of this perturbation effect on the lipidbilayer, as well as the precise effect on the proteinor peptide remain uncertain (Rehorek et al., 1985;Sperotto & Mouritsen, 1991; Chiu et al., 1999;Harroun et al., 1999), and therefore require moreinvestigation.

In general, structural studies of membrane pro-teins are a challenge even for modern experimentaltechniques, owing to the dif®culty of obtainingappropriate samples for X-ray diffraction andNMR spectroscopy (Fu & Cross, 1999). Nonethe-less, it is hoped that a combination of experimentaland theoretical approaches will lead to a full ther-modynamic description of the membrane protein

system (White & Wimley, 1999). To be complete,such a thermodynamic description should includeinformation not only about the average proteinstructure, but also about the range of ¯uctuationsabout this average. In this context, computer simu-lations have become indispensable tools for solvingand understanding complex molecular systems(Brooks et al., 1988). All-atom simulations, whichinclude the lipid bilayer explicitly, are able to givedetailed information on both protein and lipidmolecules. This approach, while computationallyexpensive, can help elucidate the precise mechan-ism by which the lipid bilayer in¯uences the pro-tein free energy surface.

Molecular dynamics simulations of transmem-brane domains in explicit lipid bilayers are becom-ing more common. In one of the earlier efforts,Edholm et al. (1995) simulated a bacteriorhodopsintrimer in an explicit lipid bilayer and studiedenvironmental effects on the protein structure and¯uctuations. Woolf & Roux (1994, 1996) performedsimulations of gramicidin A channel, and of Pf1coat protein (Roux & Woolf, 1996), and showedthe reciprocal effect of the interacting peptide andlipids on their dynamic structure. A recent simu-lation of gramicidin A by Chiu et al. (1999) focusedon the boundary lipids and reported an increasedbilayer thickness adjacent to the gramicidin chan-nel and correspondingly, increased acyl chainorder parameters. Stouch and co-workers simu-lated a polyalanine peptide (Shen et al., 1997),while a number of lipid/protein systems havebeen analyzed in a series of papers from Berend-sen's and Sansom's groups and are summarized byTieleman et al. (1998).

The present set of molecular dynamics calcu-lations addresses the effects of the lipid environ-ment on the GpA transmembrane structure anddynamics, and, in general, the issue of lipid-pep-tide interactions in ¯uid phase lipid bilayers. Thefocus of this paper is on helix association, thesecond stage of the Popot-Engelman model, whichoccurs entirely within the lipid bilayer environ-ment. This study does not therefore discuss thehelix insertion/formation mechanism, assumed tooccur in an earlier distinct stage. We have con-sidered four different lipid types in an attempt toexamine the in¯uence of various lipid properties.The ®rst two of the lipids, dimyristoyl-phospha-tidylcholine (DMPC) and dipalmitoyl-phospha-tidylcholine (DPPC), have two saturated acylchains. The third, dioleoyl-phosphatidylcholine(DOPC) has two unsaturated chains with onedouble bond at position 9, while the fourth, 1-pal-mitoyl-2-oleoyl-phosphatidylcholine (POPC), hasone saturated and one unsaturated chain. All lipidsconsidered have a phosphocholine (PC) head-group. With this minimal set of lipids we attemptto monitor GpA behavior as a function of lipidchain length and saturation. In addition, the POPCruns provide a comparison with mixed-chain sys-tems. Each system consists of a GpA monomer ordimer and 30 lipid molecules. The number of

Figure 1. (a) Time course of box dimension along thebilayer normal for the GpA/DMPC simulations. (b)Root-mean-square (RMS) deviations for GpA backboneatoms in the DMPC trajectories. Global GpA translationand rotation are removed. The RMS deviations are cal-culated relative to the structure at 250 ps, as explainedin the text.

Glycophorin A-Lipid Bilayer Simulations 729

water molecules in each case was chosen based onexperimental measurements of fully hydrated mul-tilamellar vesicles of pure lipid bilayers, asdescribed in Methods.

In the framework of the two-stage model, wehave simulated both monomer and dimer forms ofGpA for the purpose of understanding the role ofhelix-lipid interactions in the stability of helixassociation. The goal of this paper is to set thebasis for a long term systematic investigation ofenvironmental effects on the structure, dynamics,and pair association of the GpA transmembranedomain.

Structural Results

The analysis of an extensive set of moleculardynamics simulations of the glycophorin trans-membrane domain in explicit bilayers is reported.Both GpA monomer and dimer were simulated infour different lipid bilayer environments, for atotal of eight independent simulations. In eachcase, simulations of 1.5 ns duration were com-pleted and analyzed. The results suggest, at leastat this time-scale, modulation of GpA behavior bythe lipid environment.

The simulation results indicate that the trajec-tories sample an equilibrium population of statesin the vicinity of their starting conformation, andthat no dramatic (systematic) drift of the propertiesof interest has occurred, after an initial equili-bration window for each trajectory. While it is dif-®cult to prove that a molecular dynamicssimulation is fully equilibrated at all time scalesand for all degrees of freedom, certain propertieshave traditionally been used in an effort to checkfor reasonable behavior. A necessary test is thestability of the trajectory, as an indication that awell de®ned region in phase space was sampled,and that simulation settings were compatible withthe structure of interest. In this regard, Figure 1(a)shows the box dimension along the bilayer normalas a function of simulation time for the GpA/DMPC simulations. Since the lateral box dimen-sions were kept constant (see Methods), the timeseries shown represent the simulation boxvolumes, up to a factor equal to the lateral area ineach case. Furthermore, all of the current simu-lations reached stable, well-de®ned GpA confor-mations after about 250 ps of full dynamics (seeMethods for a description of earlier equilibrationstages involving restraints). This is demonstratedby the root-mean-square (RMS) deviations of GpAbackbone atoms and by the dynamics of backbonedihedrals. The RMS deviations, shown inFigure 1(b) for a representative trajectory, are cal-culated relative to the ®rst structure after 250 ps oftrajectory production. For all trajectories, the RMSdeviations remained below 1.5 AÊ throughout thesubsequent 1.25 ns simulation times. With regardto equilibration, additional properties are pre-

sented throughout the paper, in particular whenhelix tilt and helix-lipid packing are discussed.

Transmembrane domain structural properties

A ®rst description of the trajectory-averagedGpA structure is given in Figure 2, where we showthe average values and ¯uctuations of backbonedihedral angles. Despite large ¯uctuations (as indi-cated by the vertical bars in Figure 2) the averagebackbone structure remained in a stable a-helicalconformation for both monomer and dimer forms.As expected, backbone ¯uctuations and deviationsfrom ideal a-helix dihedral values were found tobe greater at the helix ends than at the helix center(similar behavior was observed in the moleculardynamics simulations of individual bacteriorho-dopsin helices in DMPC (Woolf, 1997)). This isespecially true in the dimer simulations, where, aswe show later, the individual helices are moretilted relative to the bilayer normal than in thesingle monomer form. Also note that the dihe-

Figure 2. Backbone �- dihedral angles (shown with open squares and ®lled circles, respectively), for monomerand dimer helices. The four solvent media are shown. The error bars represent the root-mean-square ¯uctuations forthe simulated dynamics. The continuous lines at ÿ47 and ÿ57 degrees on each panel represent ideal a-helix values.


dral angles of valine residues (especially V84) nextto glycine residues are more negative in the dimerform. Within the conformational space sampled ineach simulation, different average values and ¯uc-tuations are observed: the structure adopted by thebackbone dihedrals is not exactly identical in eachenvironment. Although statistical signi®cance isuncertain due to limited sampling, these differ-ences suggest that the environment modulates thesubspace of structurally accessible states duringGpA thermal motion, and this fact should bere¯ected in measurements of thermodynamic par-ameters. Note that among the four lipid types, thePOPC simulation shows a more pronounced dis-

tortion of the N terminus, giving an early indi-cation that the sampled GpA dynamics in POPCmay be signi®cantly different than in the othersimulations. This fact is discussed in more detail inInteraction Results.

Of special interest regarding the dimer structureis the nature of the helix-helix interface. A detaileddescription of the dimer structure observed in eachenvironment is provided by a matrix of distancesbetween residue pairs on the two opposed helices.The trajectory averaged distances are presented inFigure 3 as grey scale grids. The darker patterns,representing close residue-residue contacts, ident-ify the motif sequence xLIxxGVxxGVxxT, located

Figure 3. Residue-residue distance matrix between Ca

atoms in the dimer form. The distances vary between4.2 AÊ (dark ®ll) and 27 AÊ (white ®ll). The intermediategray levels have been assigned using a square root func-tional form for better contrast.

Figure 4. Time series of helix tilt from the GpA/DMPC trajectories. The time series shown include theinitial 250 ps equilibration window. The thick grey lineshows the monomer trajectory. The thick black lineshows the global dimer tilt, and the thin lines eachshow individual monomers in the dimer trajectory.


at the dimer interface. These are precisely the criti-cal residues identi®ed by mutagenesis studies(Lemmon et al., 1992a,b). The observed inter-resi-due distances are the result of intermolecular inter-actions that dictate the relative helix-helixorientation. One direct observation from Figure 3is the symmetry of the patterns in each trajectory.This symmetric pattern indicates a symmetrichelix-helix orientation, and in particular, a negli-gible shift along the helical axes in agreement withAdams et al. (1996).

A number of trajectory-averaged geometricalparameters that describe global helix orientationare summarized in Table 1. The root-mean-squaredeviations for each parameter are also given inorder to emphasize the range of ¯uctuations pre-sent in the simulated dynamics. The center of mass(CM) separations were calculated based on allhelix atoms, including hydrogens. Helix orientation(tilt) was obtained by ®nding the axis of a cylindri-cal surface that best ®t the a-carbon atoms in eachhelix (CHARMM subroutine; using the method ofChothia et al., 1981). With this approach, a unitvector is assigned to each helix in each frame. Thedimer tilt is then de®ned as the orientation of thevector sum of individual monomer unit vectors,and the helix crossing angle () as the anglebetween them. Table 1 shows that there is a greater

helix separation in the case of POPC, and a largercrossing angle in DMPC. For the dimer tilt, a lowervalue is seen in DOPC. Interestingly, dimer tilt (asa whole) relative to the bilayer normal is similar inmagnitude and ¯uctuations with the monomer tilt(in the monomer trajectories), despite the fact thatthe dimer has greater cross-sectional area. How-ever, the tilt angle for each individual monomer inthe dimer form is much larger in magnitude, asshown for a typical trajectory (DMPC) in Figure 4.In addition, it is apparent from the time series pre-sented in Figure 4 that the tilt angles of the twomonomers are anticorrelated, meaning that thedimer tilts preferably in the dimer plane (perpen-dicular to the line that connects the centers of thetwo helices).

Lipid bilayer structure

The structure of the lipid bilayer itself is alteredby the presence of the protein. One importantstructural parameter is the distance between thelipid headgroups (DHH) across the bilayer. This dis-tance can be measured experimentally using X-rayscattering, and represents a measure of the bilayerthickness (Lewis & Engelman, 1983). Because thelipid electron density is concentrated at the phos-phorus atom (P), the measured DHH is approxi-mately given by the distance between the averagelocation of the P atoms in the two monolayers(DPP). In Table 2 we report DPP values from ourGpA/lipid simulations and compare them withour neat bilayer simulations (with similar bound-ary conditions and system sizes), and with exper-imental DHH data from fully hydrated lipidsamples, at the same temperatures as the simulatedtrajectories.

Table 1. Helix orientation parameters

Lipid CM (AÊ ) (deg.) Dimer tilt (deg.) Mono tilt (deg.)

DMPC 8.2 � 0.3 ÿ46 � 4 8 � 4 10 � 3DPPC 8.1 � 0.2 ÿ39 � 3 9 � 2 9 � 3DOPC 8.4 � 0.2 ÿ41 � 3 6 � 2 8 � 4POPC 9.4 � 0.3 ÿ40 � 3 11 � 3 9 � 3

Center of mass separation (CM), crossing angle (), global dimer tilt, and monomer tilt (from monomer trajectories). Averagevalues and ¯uctuations over the trajectories are shown.


As a general trend, the bilayer thicknesses in thedimer simulations are smaller than in the monomersimulations. While this can be explained by the lar-ger perturbation imposed by the presence of thehelix dimer, it is worth checking that the result isnot an artifact due to our choice of the lateral area.A ®rst indication would be the presence of unrea-sonable values for the surface tension. The last twocolumns in Table 2 show the calculated surfacetensions for each run, as given by the CHARMMoutput (method by Zhang et al., 1995). Thesevalues for the surface tension are typical for simu-lations of lipid bilayer systems (Feller et al., 1997;Feller & Pastor, 1999). Due to the small systemsize, the ¯uctuations in the surface tension are verylarge. Fluctuations between 50 ps block averagesgave RMS deviations of about 20 dyn/cm for themonomer trajectories, and slightly smaller, ofabout 15 dyn/cm for the dimer trajectories. Fornanosecond time scales, differences on the order of10 dyn/cm in the surface tension are not expectedto cause signi®cant changes in the bilayer structure(Feller & Pastor, 1999). The fact that the magnitudeof the surface tensions observed are reasonable,and that the differences between the monomer anddimer simulations are barely resolvable suggestthat the simulated lipid bilayers are, at least in a®rst approximation, under similar lateral stress.Therefore, the results presented in Table 2 indicatethat the lipid bilayer thickness decreases uponGpA dimerization. We emphasize, however, thatthe magnitude of the effect may depend on theprecise values of the boundary conditions.

Table 2. Lipid bilayer parameters

Lipid DHHneat (exp) DPP

neat DPPmono DPP

dime

DMPC 34.4a 35.9 33.8 (33.0) 32.5 (33DPPC 36.4-39.6b 39.0 36.1 (35.0) 34.4 (35DOPC 35.3c - 35.0 (35.0) 33.2 (33POPC - - 37.8 (36.3) 35.4 (35

Experimental DHHneat are from measurements on pure lipid bilayers

were 30 �C for DMPC and DOPC, and 50 �C for DPPC). Average Dtext (simulations of neat DOPC and POPC were not performed, therin parentheses give the bilayer thickness for boundary lipids. Cothe monomer and the dimer trajectories. The last three columns givtrajectories.

a Petrache et al. (1998a).b Nagle et al. (1996).c Tristram-Nagle et al. (1998).

Besides the average thickness, of special interestis the local effect of GpA on the lipid bilayer. Theboundary DPP values are shown in parentheses inTable 2, next to the average values. With an errormargin of 0.5 AÊ , we ®nd that the boundary thick-ness is larger for the monomer, but smaller for thedimer simulations when compared to the averagevalues in each case. This suggests that the effect onthe boundary lipids depends on the size of theembedded molecule. Indeed, Tieleman et al. (1998)showed that while membrane insertions almostalways in¯uence the bilayer structure, the effectsvary with the properties of the inserted molecule.A systematic study of WALP/lipid systems(Petrache et al., 2000) shows that hydrophobicmatching is a complex mechanism that involves alarge number of degrees of freedom. Besides thebasic peptide and lipid lengths (static properties),the peptide and lipid tilt (dynamic properties) arerelevant.

GpA-lipid packing

The GpA structure and the structure of the lipidbilayer are coupled through intimate molecularpacking. One measure of the lipid-protein packingis the available volume for each molecular com-ponent of the system. For heterogenous systems,these volumes can be calculated from simulationsusing the Voronoi method (Richards, 1985). Wehave used the program developed by Gerstein et al.(1995) to ®rst calculate the accessible volumes forall GpA heavy atoms (see Methods). The volumesfor individual atoms were then summed to obtain

r �DPP/DPP gneat gmono gdimer

.8) ÿ3.8 % 21 29 47

.4) ÿ4.7 % 44 35 27

.8) ÿ5.1 % - 15 12

.1) ÿ6.3 % - 24 19

at full hydration and in the ¯uid lamellar phase (temperatures

PP distances are calculated from simulations, as explained in theefore we report DPP

neat for DMPC and DPPC only). The numberslumn 6 gives the percentage change of average DPP betweene the surface tension (in units of dyn/cm) calculated from the


the total helix volumes. Table 3 gives the totalvolumes for GpA determined by this method ineach lipid bilayer.

Compared to the bare van der Waals volumes,of about 2260 AÊ 3 per GpA monomer, the thermallyaccessible volumes are larger by approximately25 %. While the precise results depend on thechoice of the Voronoi dividing planes (Gersteinet al., 1995), it is clear that the helix volumechanges upon dimerization are of the order of 1 %or less. At atmospheric pressure, the P�V term inthe free energy of helix-helix association is negli-gible (P�V 4 1 cal/mol). In addition, we haveestimated the overall volumetric changes upondimerization by comparing the total volume fromthe monomer simulations and an adjusted volumefrom the dimer simulations. The adjustment in thecase of the dimer consists in subtracting out onemonomer and the corresponding number of watermolecules, in order to have the same GpA-mono-mer/lipid/water ratios as in the monomer sys-tems. We obtained volume changes of the order of0.1 % which are at the limit of the simulation resol-ution. The small volume difference indicates thatoptimal lipid packing around the GpA peptide canbe almost equally achieved in both monomer anddimer form, and in addition, that molecular pack-ing at the helix-helix interface conserves the avail-able volume. The volumes per lipid molecule,calculated by subtracting the peptide and thewater volumes from the total volume of each simu-lation box are also shown in Table 3. The lipidvolume results agree with former calculations(Petrache et al., 1997; Armen et al., 1998) and exper-imental measurements (Nagle et al., 1996; Petracheet al., 1998a; Tristram-Nagle et al., 1998) and showno signi®cant change with peptide insertion.

The molecular packing inside the lipid bilayer,and in particular the precise value of the helixvolume depends on many factors. The mostimportant of these factors is the density gradientalong the bilayer normal (Wiener & White, 1992;Petrache et al., 1997; Armen et al., 1998). Due tothis density gradient, the accessible helix volumesare controlled by an interplay between helix tiltand bilayer thickness. For example, as shown inTable 3, the percentage change in helix volumeupon dimerization is much smaller in DMPC,which has the smallest bilayer thickness (see

Table 3. Thermally accessible volumes calculated using the V

Lipid Vm Vd/2

DMPC 2806 � 44 2809 � 47 (37)DPPC 2848 � 48 2815 � 47 (36)DOPC 2794 � 50 2766 � 43 (33)POPC 2831 � 53 2799 � 44 (33)

Vm represents the monomer volume in the monomer simulationvolume per monomer and the volume ¯uctuations at monomer levvolume ¯uctuations at dimer level. Column 4 gives the percentage cthree columns give the volume per lipid molecule (VL) calculated fdifferent simulations are less or about 0.5 %. The volume units are AÊ

Table 2), than in the other three lipids. Speci®cally,the bilayer thickness decreases from 33.8 AÊ in themono/DMPC trajectory to 32.5 AÊ in the dimer/DMPC trajectory, approaching the GpA helixlength of roughly 32 AÊ . The small bilayer thicknessmight be the reason why the helix crossing angle islarger in DMPC than in the other bilayers. The lar-ger crossing angle, in turn, results in an increase inhelix volume upon dimerization. Moreover, theGpA volume is lowest in the DOPC trajectories,despite the greater area of the simulation box (seeTable 6, below). However, both the GpA tilt andthe bilayer thickness are small in the DOPC trajec-tories, thus implying that the helix ends exploreregions of higher density near the lipid glycerolbackbone. Also note that the POPC trajectorieshave larger volumes than DOPC. This is related tothe greater bilayer thickness and the larger inter-helical distance (see Table 1) in this case.

Another important aspect of the peptide-lipidpacking is the extent of ¯uctuations in the helixvolume. A ®rst observation is that the volume ¯uc-tuations of the two monomers in the dimer formare roughly uncorrelated, as indicated by the factthat the ¯uctuations at dimer level scale as 1=

��2p

relative to the ¯uctuations at monomer level. Theabsence of correlation between monomeric units isbetter seen in Figure 5, which shows the distri-bution of monomer volumes from a representativedimer simulation. A second observation is that,when comparing the different lipid types, the GpAvolume ¯uctuations decrease upon dimer for-mation, in the case of the two unsaturated, asopposed to the two saturated lipids. We note that,in terms of solvent (hydrocarbon) volume units,the magnitude of GpA volume ¯uctuations andchanges upon dimerization are comparable withthe volume of two methylene groups (CH2) in thelipid acyl chains. The lipid methylene volume inthe ¯uid phase, was determined to be about 28 AÊ 3

from both speci®c volume measurements (Nagle &Wilkinson, 1978) and lipid bilayer simulations(Petrache et al., 1997; Armen et al., 1998). This con-nection between the peptide volume changes andsolvent volumes was found to be relevant for esti-mating the energetic cost of packing defects inlipid bilayers. For example, it has been estimatedthat a free energy of about 1.6 kcal/mol is required

oronoi procedure

�V/V (%) VLneat VL

mono VLdimer

0.1 1085 1089 1094ÿ1.1 1223 1219 1224ÿ1.0 - 1298 1294ÿ1.1 - 1251 1256

s. The dimer values (denoted by Vd/2) represent the averageel, in the dimer simulations. The values in parentheses give thehange in volume per monomer upon dimer formation. The lastrom each simulation. For each lipid, volume variations among3.

Figure 5. Instantaneous monomer volumes from theGpA dimer/DOPC simulation.


to create a void volume comparable with twice thelipid methylene volume (White & Wimley, 1999).

In order to give a more detailed description ofthe GpA-lipid packing, we examined volumetricvalues at the residue level, as shown in Figure 6.The reported residue volumes do not include theatoms involved in the peptide bond (N, HN, C,and O), but include the backbone a-carbon atoms.For example, the reported glycine volumes rep-

Figure 6. Trajectory averaged side-chain volumes (includeatoms N, HN, C, or O). Monomer is shown with open circles

resent the CaH2 groups. We note that the smallerresidues (G79, G83, G86, as well as A82) show nosigni®cant volume changes between the monomerand the dimer forms. More importantly, all threeglycine residues have the same volume, regardlessof their location relative to the dimer interface, andin addition, their magnitude is practically equal tothe volume of the methylene group in the lipidhydrocarbon chains.

The largest accessible volumes seen in Figure 6correspond to the aromatic phenylalanine side-chains (F78). These residues are located on the sideopposite to the helix-helix interface, and are there-fore in direct contact with the lipids surroundingthe dimer. On average, the F78 side-chains arelocated inside the lipid hydrocarbon region closerto the lipid carbonyls. The volumes of F78 side-chains are of about 173 AÊ 3 and are comparable inmagnitude with the volumes of lipid headgroupfragments, which for DPPC at 50 �C are 173 AÊ 3 forcarbonyls � glycerol and 153 AÊ 3 for phosphate �choline (Petrache et al., 1997; Armen et al., 1998).Recent studies by Yau et al. (1998) have demon-strated the preference of aromatic groups for theheterogeneous environment of the lipid-waterinterface. This suggests that the location of F78along the bilayer normal (z-axis) is an importantfactor in determining the equilibrium location andorientation of the GpA molecule. Figure 7 showsthe F78 center of mass location within the bilayeras a function of simulation time. The center of themembrane (i.e. the z � 0 level) has been set at the

the backbone Ca and do not include the peptide bond, and dimer is shown with ®lled diamonds.

Figure 7. Center of mass locationalong the bilayer normal for theF78, G83, and T87 side-chains(backbone atoms not includedexcept for Ca). Trajectories fromresidues on each of the two helicesin the dimer form are shown withdifferent line types. The dottedcurves represent the average pos-itions of lipid phosphorus atoms(P) for each monolayer (averagedover all lipids in each frame).


center of mass of the lipids. Figure 7 also showsthe locations of G83 and T87 side-chains, and theaverage positions of the lipid phosphorus atoms,in order to give a reference for the GpA orientationwithin the lipid bilayer. Among the residuesshown, G83 is located at the bilayer center, whileF78 and T87 are closer to the lipid headgroupregions. It is important to note that, while the aver-age position of lipid phosphorus atoms is practi-cally constant during the simulation, individuallipid molecules undergo signi®cant vertical motiongenerating a distribution of the P atoms with awidth of 3-5 AÊ (not shown).

The time series presented in Figure 7 revealimportant aspects of the simulated dynamics. First,the constancy of the bilayer thickness (DPP) duringthe analyzed trajectories con®rms the global stab-ility of the membrane system. Second, the locationsof the GpA residues along the bilayer normal indi-cate a rigid body motion of the dimer of roughly2 AÊ amplitude, within the nanosecond simulationtime. Third, faster ¯uctuations are observed aboutthis slow rigid body motion for all systems.Altogether, these results indicate a degree ofmotional coupling between the two a-helices in thedimer, as a consequence of the strong helix-helixinteractions discussed in the next section.

Finally, we note that the two F78 residues of theGpA dimer are sampling slightly different environ-ments. This is due to the particular way the dimeris tilted relative to the bilayer normal (vide supra).A fully converged molecular dynamics trajectory(probably on microsecond or millisecond timescales) would presumably show a more symmetricensemble of states between the two chemicallyequivalent monomers. We emphasize that inaddition to the motion along the z-axis, there is asigni®cant degree of motion of the GpA peptide in

the membrane plane, that is not captured inFigure 7.

Interaction Results

The structural parameters analyzed in the pre-vious sections are determined by the net balance ofcomplex molecular interactions. The number of rel-evant energy terms required for a complete ther-modynamic description of a peptide/lipid bilayersystem is quite large as emphasized by White &Wimley (1999). These terms include intra andinter-molecular interactions (enthalpies) as well asentropic terms. The formation and stability of thepeptide secondary structure involves an energeticbalance between residue-residue interactions in thepolypeptide chain and interactions with the solventenvironment (Kovacs et al., 1995). While inter-mol-ecular interactions characterize the association ofvarious molecular species, the intra-molecular (self)energies measure the deformations (strains)imposed on the molecular structure by theseassociations. For example, the lipid/water mol-ecules may distort the peptide a-helical structure,and do this differently for an isolated helix thanfor a helix pair. In addition, the process of helixassociation itself may distort the secondary struc-ture of the dimer units and further alter helix selfenergy.

Given that the entropic terms are not easilywithin reach, in what follows we discuss trajectoryaveraged interaction energies (enthalpic terms)between the GpA peptide and the membraneenvironment in order to describe how differentmolecular constituents are coupled within thesimulations. We shall ®rst present intra-helicalinteractions (responsible for secondary structureformation and stability), followed by direct helix-


helix interactions. We then turn to helix-environ-ment and environment-environment interactions.

Intra and inter-helical interactions

The intra-helical interactions (Hintra) per GpAmonomer are shown in Table 4, and are decom-posed into contributions from non-bonded (vander Waals and electrostatic) and bonded terms.The latter include energies associated with bondlength and angle distortions and are basically setby the simulation temperature, as can be seen bycomparing the DPPC run at 50 �C with the otherthree runs at 30 �C. The net change in intra-helicalinteractions (�Hintra) is given in column 6 of Table 4and appears to be marginal (estimated error is1 kcal/mol), except in the case of the POPC simu-lation which shows a signi®cantly higher helix selfenergy for the dimer form.

For a detailed analysis of inter-helical inter-actions, we computed interaction energies betweeninter-molecular residue pairs of the dimer. Eachlipid environment, in principle, can interact differ-ently with the GpA dimer and modulate inter-heli-cal conformations. This fact is revealed in Figure 8,where we present the residue-residue interactionmatrices for all dimer trajectories. The residueinteraction terms include side-chain as well asbackbone atoms. Most residue-residue interactionsare attractive, with values between ÿ2.5 kcal/moland zero, except for a number of glycine-glycineinteractions that are repulsive, and are marked bythe plus signs in Figure 8. The repulsive com-ponent in the glycine-glycine interactions is mostlygiven by the unfavorable electrostatic interactionsbetween both backbone carbonyls and the CaH2

groups. The magnitude of the overall glycine-gly-cine interactions is between 0.1 and 0.5 kcal/mol,with the variations depending on the glycinelocation (G79 or G83) and on the lipid type. Similarto the distance matrix (Figure 3), the dimerizationmotif is clearly demarked by the darker ®ll pat-terns in Figure 8. The slightly lighter ®ll patternin the POPC matrix re¯ects weaker helix-helixinteractions, in accord with a larger inter-helicalseparation.

The global helix-helix interactions (Hinter),obtained as a sum over all residue pairs, are givenin column 7 of Table 4. Overall, helix-helix inter-

Table 4. Trajectory averaged GpA interactions per monomer

Hnbintra Hb

intra

Lipid Mono Dimer Mono Dimer

DMPC ÿ80 ÿ83 302 302DPPC ÿ82 ÿ83 312 313DOPC ÿ83 ÿ81 299 299POPC ÿ79 ÿ76 300 302

Hintra (intra-helical), Hinter (inter-helical), and Henv (net interactand bonded (b) terms to Hintra are given separately. The values in phelical interaction. The energy units are kcal/mol.

actions are strongly favorable, the unfavorable gly-cine-glycine interactions being offset by thefavorable arrangements of other residues. Theinter-helical interactions are roughly ÿ40 kcal/mol,with signi®cant ¯uctuations of about 3 kcal/mol.Note that in the case of POPC, where the distancebetween the dimer helices is larger by 1 AÊ than inDOPC, the helix-helix interaction is weaker byroughly 8 kcal/mol, which is about three times thethermal ¯uctuation level.

Helix-environment interaction

If the interaction with the environment is neg-lected, then only the interaction terms discussedabove would be present and would indicate a verystrong preference for the dimer form, as measuredby the direct helix-helix interaction term Hinter.Practically, this would correspond to a dimer simu-lation in vacuum with, presumably, internalrestraints to preserve peptide secondary structure.The magnitude of Hinter (on the order of ÿ40 kcal/mol) indicates that inter-helical interactions arestrongly favorable (attractive), but, as we shownext, the interaction of the helix with the lipidbilayer is also highly favorable. The question isthen whether the GpA monomer prefers the associ-ation with a second helix over complete exposureto lipid molecules. For this reason, the helix-environment interaction term (Henv) in the dimersimulations is calculated as the sum of the inter-actions between one helix and lipid, water, and theother helix. That is, the energies are reported on aper monomer basis, regardless of the GpA form,and represent the net interaction between onemonomer and everything else in the simulationbox.

Table 4 shows that (for the same helical confor-mations) the monomer interaction with theenvironment is much lower than in vacuum (byabout 200 kcal/mol for the dimer form) due tostrong favorable interactions with the lipid bilayer.However, the interaction with the lipid bilayer issuch that the total interaction of a GpA helix withthe surrounding environment changes by just asmall amount going from complete solvation bysurrounding lipids (monomer) to having a faceexposed to a second helix (dimer). The enthalpygap, �Henv, between monomer and dimer forms is

Henv

�Hintra Hinter Mono Dimer �Henv

ÿ3 ÿ37.0 (3.0) ÿ243 ÿ238 �5ÿ0 ÿ39.5 (3.0) ÿ228 ÿ227 �12 ÿ36.7 (2.5) ÿ229 ÿ239 ÿ105 ÿ28.6 (2.6) ÿ235 ÿ244 ÿ9

ion with environment). Contributions from non-bonded (nb)arentheses respresent root-mean-square ¯uctuations in the inter-

Figure 8. Trajectory averagedresidue-residue interactions. Theinteraction energies vary fromÿ2.5 kcal/mol (dark ®ll) to 0 kcal/mol (white ®ll), except for glycinepairs which interact unfavorably(0.1-0.5 kcal/mol) and which aremarked by the plus signs.


much reduced from that in vacuum. The enthalpygap is in fact reduced to a level where small differ-ences in helical self energies (�Hintra) may becomesigni®cant. Comparing the helix self energiesalone, we observe higher energy levels for thedimer/POPC simulation relative to the monomer/POPC.

At this point, a discussion of the possible arti-facts in the case of our GpA/POPC simulations isrequired. A number of structural parameters,including the strong distortion of the N terminus,the larger center of mass separation between thedimer units, together with weaker inter-helicalinteractions, may indicate artifactual sampling.Note, however, that the POPC simulations areinternally consistent: the increase in the GpA selfenergy in the dimer form relative to the monomerform was accompanied by a larger decrease in theGpA-environment interaction term. In otherwords, the net helix energy decreases at the (rela-tively minor) expense of local structural distortion.It is also important to note that, at present there isno accurate experimental data on the area perPOPC lipid and the corresponding number ofwater molecules. Therefore, there is a likely possi-bility that our choice for these parameters (seeTable 6, below) is not optimal.

Examination of the helix-environment inter-actions (Henv) given in Table 4 suggests that upondimerization, the peptide monomer is driven into asigni®cantly lower enthalpic energy state (dimerversus monomer form) in the case of the unsatu-rated lipids, as opposed to the case of saturatedones. This re¯ects again the differences in GpAbehavior seen in saturated versus unsaturatedlipids, observed previously in the volume analysis.These differences between the effects of saturatedand unsaturated lipids on peptide properties maybe related to the higher degree of lipid chain dis-order typically present in unsaturated lipidbilayers, as indicated experimentally by measure-ments on ¯uid phase lipid bilayers using 2H NMR(Holte et al., 1995), and X-ray scattering (Petracheet al., 1998a).

The range of energy ¯uctuations can be seen indetail from Figure 9, where we present interactionenergies for each monomer unit from the dimer/DMPC trajectories. The interaction between GpAhelix and environment is presented in terms ofindividual contributions from water (c) and lipid(d) interactions, in order to emphasize the differentpartitioning between the two terms. The ¯uctu-ations of the various GpA interaction terms are onthe order of 10-20 kcal/mol, which is to be com-

Figure 9. Instantaneous intra-helical (a) and helix-environment (b) energy terms for individual GpA monomers inthe dimer/DMPC simulations. The values in (b) represent the sum of helix-helix (Table 4), helix-water (c) and helix-lipid (d) energy terms. Note that the energy range on each axis in every panel is the same (150 kcal/mol) for easycomparison of the range of ¯uctuations of the different energy terms.


pared with 3 kcal/mol in the case of helix-helixinteractions. We note that the range of ¯uctuationsin the helix-lipid interaction is slightly narrowerthan the helix self energy ¯uctuations.

Lipid-environment interaction

As emphasized by White & Wimley (1999),when discussing the energetics of the lipid-peptidesystems, the peptide interaction terms are onlypart of the picture. The analysis of the dimer for-mation free energy is complex and requires a con-sistent de®nition and calculation of enthalpic aswell as entropic terms. In addition to the peptiderelated terms (and apart from entropic contri-butions that are not calculated here), the energyterms associated with the perturbation of the lipidbilayer need to be taken into account. A directcomparison of the lipid energy terms across thedifferent lipid bilayer types is not warranted, pri-marily due to the differences in the acyl chain com-position. However, the changes in the lipid energyterms upon interaction with the GpA peptide areable to convey information in regard to the bilayereffects on the energetics of the peptide system. Thecalculated trajectory averaged lipid energies fromneat bilayer and GpA/lipid simulations are givenin Table 5. The values represent averages over all

lipids in each trajectory. Despite the small magni-tude of the effect, there is a clear increment of thelipid energy as the size of the bilayer perturbationincreases from neat systems (pure lipid) to lipid-monomer and to lipid-dimer complexes. It isinstructive to note that even a small perturbationof the lipid energy states is suf®cient to perturb thebilayer thickness signi®cantly (see Table 2). Notethat the increased lipid energies would actuallydisfavor dimer formation, and this result can betaken as an indication that lipid entropic terms,which presumably favor peptide aggregation, playa signi®cant role.

Boundary lipids

The boundary lipid concept implies a localchange of lipid properties near to the peptide orprotein. The precise effect on the lipid molecules,however, and the level of perturbation induced bymembrane insertions, are still debated issues. Cur-rent experimental techniques do not permit a directobservation of boundary lipids, rather, their exist-ence is inferred from a combination of theory andexperimental results (e.g. see Harroun et al., 1999).Simulations, however, have a clear advantage onthis issue, even if results may require complexinterpretation (Chiu et al., 1999) and may strongly

Table 5. Trajectory averaged lipid energies per one lipid molecule

HLintra HL

env

Lipid Neat Mono Dimer �HintraL Neat Mono Dimer �Henv

L

DMPC 94.5 95.2 96.3 1.1 ÿ194.7 ÿ193.7 ÿ193.3 0.4DPPC 108.8 110.5 110.4 ÿ0.1 ÿ197.7 ÿ199.1 ÿ196.4 2.7DOPC - 119.6 119.5 ÿ0.1 ÿ ÿ208.7 ÿ206.6 2.2POPC - 112.3 113.1 0.8 - ÿ206.6 ÿ205.1 1.4

HintraL (self energy), and Henv

L (net interaction with environment). The energy units are kcal/mol.


depend on the nature of the inserted molecule(Tieleman et al., 1998; Petrache et al., 2000). Indeed,our GpA lipid simulations show that in the vicinityof the peptide, the local bilayer thickness differsfrom its value away from the peptide, but does sodifferently for the monomer and for the dimer sys-tems (see Table 2). Developing a detailed descrip-tion of lipid conformations, especially in the ¯uidphase, is in general a dif®cult task and involves theexamination of various lipid degrees of freedom,such as internal chain conformations (trans/gaucheisomerizations) and global chain tilt. This confor-mational analysis is quite complex and it is notincluded in this paper. We do, however, includeresults regarding the energetic aspect of the pro-blem, which may be useful for further understand-ing and modeling of lipid-protein interactions(Woolf, 1998). Speci®cally, we plot the lipid selfenergy (ELS) as a function of its interaction with theGpA peptide (ELG). Figure 10(a) shows a scatterplot of the observed energy states. Each point rep-resents a sampled lipid state in terms of twoinstantaneous energy terms: ELS and ELG. For eachtime frame, every 2 ps, we have recorded the selfenergy term for each lipid and its interaction withthe peptide. The density of points is a measure ofconformational sampling; the majority of states,and the higher density of points, is aroundELG � 0, representing ``bulk lipid'' states. The aver-age self energies from the neat bilayer trajectoriesare also shown in Figure 10(a) with ®lled symbols,together with 1 and 2 standard deviation bars foreasy comparison with the distribution of the ELS

values from the GpA/lipid simulations.Figure 10(a) shows that, even if bilayer structural

properties vary with the distance form the GpAmolecule, there is no noticeable effect on the mag-nitude of the lipid self energies as ELG becomesstronger. This is, however, not very surprising,since the overall changes of lipid energies are small(as seen in Table 5) it is merely a con®rmation thatlipid self energies are highly degenerate. Note thateven though the average lipid self energy does notdepend on ELG, the distribution (width) about theaverage does. In addition, Figure 10(a) suggeststhat the population of states along the ELG dimen-sion is not uniform. In other words, the presence ofthe GpA peptide may have a strong entropic effectrather than a purely enthalpic effect. Unfortu-nately, the sampling of various lipid states duringour 1.25 ns trajectories, especially for large ELG

values, is not suf®cient for a good estimate of theseentropic effects.

Given that most of the GpA-lipid interface islocated in the lipid hydrocarbon region, we haveexamined the interaction between the GpA mol-ecule and the individual lipid acyl chains.Figure 10(b) plots the instantaneous interaction(every 2 ps) between each lipid chain (sn1 or sn2)and the peptide, for all lipids in the simulationbox. In these plots, most of the points are off-diag-onal. This result indicates that lipid-protein inter-actions most likely occur through single chainsof individual lipids, rather than both lipid chainssimultaneously.

Comparison with Experimental Data

NMR structure

The starting point for our calculations was therecently determined NMR structure in dodecylpho-sphocholine micelles by MacKenzie et al. (1997).The NMR structure was solved using a set of NOEdistance restraints along with J-coupling values tolimit dihedral angles. The resulting family of struc-tures, determined via X-PLOR calculations, rep-resents a well de®ned transmembrane domain(0.8 AÊ heavy atom RMS). One important questionthat arises is whether the structure of the GpAtransmembrane domain is in any way different inthe dodecylphosphocholine micelles than in planarlipid bilayers. In particular, structural differenceswould be re¯ected in the values of hydrogen-hydrogen distances. To address this question, wehave ®rst calculated average hydrogen-hydrogendistances from the set of NMR structures, togetherwith their mean square deviations across the set.The hydrogen pairs considered correspond to theassigned NOE signals used as constraints in theNMR structure determination. We then calculatedthe corresponding hydrogen-hydrogen distancesfor each of our four dimer trajectories. In the caseof chemically equivalent hydrogen atoms we tookthe minimum distance in each time frame, in orderto account for side-chain rotations. The results arepresented in Figure 11 and show similar ranges ofhydrogen-hydrogen distances in all four bilayersimulations. Compared to the NMR structures, thesimulations show larger separations at the N termi-nus of the transmembrane domain. It is worth not-ing that the X-PLOR calculations used unrealistic

Figure 10. (a) Instantaneous (every 2 ps) lipid self energy (ELS) versus lipid-GpA interaction energy (ELG). The aver-age values of ELS from the neat DMPC and DPPC trajectories are shown with ®lled circle symbols and with 1s and2s ¯uctuation bars. (b) Instantaneous GpA interactions with the sn1 and the sn2 acyl chains of the same lipid, for alllipids in each simulation box.


(repulsive only) non-bonded terms, which maygenerate more rigid structures.

Additional structural information comes fromsolid-state NMR (rotational resonance) experiments(Smith et al., 1994). One particular result is an aver-age distance of 4.5(�0.5) AÊ between the a-carbonof G83 and the carbonyl carbon of V80, as well asbetween the a-carbon of G83 and the carbonyl car-bon of M81 (the experiments were performed on2H-DMPC bilayers at ÿ50 �C). From our trajec-tories we have calculated average values of4.5(�0.2) AÊ for the ®rst, and 4.5(�0.1) AÊ for the lat-ter distance, where the deviations indicate the RMS¯uctuations during the trajectories. The sameresults were obtained for both monomer anddimer forms, indicating that the region around G83is very stable in both forms, as has been seen in thebehavior of backbone angles (Figure 2). Theseresults further suggest that the range of structuresin all four bilayers are consistent with the

measured NMR restraints. Interestingly, we havealso calculated the corresponding inter-monomerdistances, in addition to the intra-monomer onesreported above, and found very similar results(within the experimental accuracy). The results are4.7(�0.3) AÊ for G83-Ca to V80-C, and 6.8(�0.3) AÊ

for G83-Ca to M81-C distances, with slightly largervalues in the case of POPC.

In sum, these results imply that the micelle-based structure is valid for the bilayer setting.

Dimerization motif

An important ingredient in the GpA structureprediction (Treutlein et al., 1992; Adams et al.,1994) has been the result of replacement mutagen-esis studies that identi®ed the critical residuesinvolved in GpA dimerization (Lemmon et al.,1992a,b). Additional properties of the GpA dimerinterface have been determined based on insertion

Figure 11. H-H distances (among chemically equival-ent H atoms) for residue pairs with assigned NOE sig-nals. Averages and ¯uctuations from the 20 NMRstructures are shown with the thick vertical bars. MDresults are shown with open circles (DMPC), ®lled cir-cles (DPPC), open squares (DOPC), and ®lled squares(POPC), respectively.

Figure 12. Trajectory average interaction energiesbetween each residue and the opposed helix in thedimer form. The absolute values are shown in order toemphasize residue importance, as explained in the text.The grey background bars represent the empirical dia-gram of disruptive effect from Lemmon et al. (1992b)(the diagram is scaled by a factor of 2 for a better com-parison).


mutagenesis (Mingarro et al., 1996, 1999). In thisregard, we have examined our simulation resultsfor possible insights into those residues most criti-cal for dimer stability and thus, presumably, leasttolerant of mutations.

It is clear that one relevant property of thesecritical residues is the interaction strength with theopposite helix. These residue-helix interactionterms are presented in the enthalpy diagramshown in Figure 12. As expected, stronger inter-actions are obtained for the motifxLIxxGVxxGVxxT. Interestingly, the plot inFigure 12 closely resembles the diagram of disrup-tive effect of mutagenesis reported by Lemmonet al. (1992b). The empirical scale from Lemmonet al. is shown by the grey bars in the backgroundof Figure 12.

Note, however, that the enthalpy alone misrepre-sents the importance of smaller residues, glycinesin particular. A mutation from a small residue to alarger one alters the enthalpic contribution, and atthe same time, adds a packing strain at the dimerinterface. In other words, there is a packing penaltyassociated with each particular mutation. Inaddition to the residue interaction strength, asearch for critical residues should consider a num-ber of additional parameters as described byMacKenzie & Engelman (1998). Nevertheless, theenthalpy diagram (Figure 12) by itself reproducesthe mutagenesis pattern very well.

The present simulations con®rmed previouscomputational and experimental work thatsuggested the close proximity of Gly83-Gly83 inthe dimer interface. In fact, all four simulationsshowed an unfavorable (positive) interaction

energy between these glycine residues that wascompensated by other favorable energy termsbetween the helices. A possible rationale for thistype of molecular interaction was suggested by theanalysis of Javadpour et al. (1999) on transmem-brane protein domains. Their analysis suggested apredominance of glycine residues at many structu-rally de®ned helix crossing points. Being the smal-lest residues, glycines facilitate helix-helixinteractions by allowing a close contact betweentwo opposing helices, and thus support a widerange of helix crossing angles (Treutlein et al., 1992;Bowie, 1997). In addition to the role of glycine resi-dues on helix-helix packing, the current simu-lations indicate that the helix crossing angledepends not only on the properties of the helix-helix interface, but is also coupled to the helix tiltrelative to the membrane normal, via helix-lipidbilayer interactions.

Recently, the GxxxG pattern has been shown tofrequently mediate helix-helix transmembraneassociations (Russ & Engelman, 2000; Senes et al.,2000), especially in the presence of b-branched resi-dues at neighboring positions (the pattern isGVxxGV in the case of GpA). Therefore, a detailedanalysis of glycine-glycine interactions is in order,especially since the net glycine-glycine interactionsappear to be unfavorable, at least in the currentCHARMM force ®elds. As mentioned above, wehave found that the repulsive component is due toelectrostatic interactions of backbone carbonyls and


the CaH2 groups. Despite their repulsive inter-actions, the glycine residues seem to accommodatenot only the net helix-helix packing, but also theoverall packing of the GpA dimer within the lipidenvironment. Recall that the glycine volumes (theCaH2 groups) are found to be equal to the volumeof the lipid methylene groups that surround theGpA dimer, regardless of glycine position relativeto the dimer interface.

Conclusions

In the framework of the two-stage model forhelix association, we have analyzed the propertiesof the dimer and the monomer forms of GpA inlipid bilayers. The interaction analysis, based onenthalpic contributions alone, reveals a delicatebalance between various GpA energy terms, andindicates lower dimer energy states in the case ofunsaturated lipids. Among the residues that arecritical for dimer formation, the glycine residues onthe opposed helices interact in an unfavorablefashion. The close packing at these sites, however,facilitates the favorable interaction of the otherinterfacial residues, leading to an overall helix-helix attraction.

Our simulation results indicate that, among lipidbilayer structural properties, the bilayer thicknesshas the most in¯uence on the accessible GpA con-formations. In accord with the hydrophobic match-ing hypothesis (Mouritsen & Bloom, 1984), wefound that the structure of the peptide-lipid com-plex is adjusted by an interplay between bilayerthickness and peptide tilt. The effect is most pro-nounced in the case of DMPC, where the smallbilayer thickness leads to a larger helix crossingangle.

The volumetric analysis shows that the peptideaccessible volume is conserved upon dimerization,indicating that the GpA monomer packs equallywell with the other monomer, as with lipids. Moredetailed analysis reveals that lipid molecules inter-act with the GpA peptide through single chains,rather than both chains at once.

The calculations suggest that the four bilayerenvironments considered do not change the aver-age GpA structure signi®cantly. However, therange of motions and thus ¯uctuations about theaverage are modulated by lipid bilayer properties.This supports the idea that biomolecular systems,and in particular, membrane proteins at physio-logical temperatures, are best described by ¯uctu-ations in the range of their accessible structures. Inorder to understand protein stability, it isespecially important to determine the spectrum ofstructural ¯uctuations, since this knowledge allowsthe determination of ¯exible versus rigid subdo-mains within the protein. Ultimately, this morecomplete thermodynamic description may help usunderstand the complex processes underlying pro-tein function as well as aid structure determi-nation.

Methods

Ensemble choice

For lipid bilayer systems, the choice of the simulatedensemble together with the appropriate thermodynamicparameters is a delicate issue. One such parameter is thelipid ¯uid phase cross-sectional area, for which literaturedata cover a broad range (Nagle et al., 1996). In addition,the lateral area occupied by the peptide itself is notknown precisely. Because of these uncertainties, a con-stant pressure ensemble would be preferable over a con-stant area simulation, since the bilayer patch dimensionswould then be free to adjust and equilibrate during thesimulation run. The complication, however, arises fromthe presence of a surface tension at the lipid water inter-face (JaÈhnig, 1996). It has been argued that a membranepatch that consists of just a small number of lipid mol-ecules has a signi®cant surface tension, on the order of10-50 dyn/cm (Feller & Pastor, 1996; Chiu et al., 1995; fora discussion on this debated issue, also see Tobias et al.,1997). The most appropriate simulation ensemble willthen be NgPNT, i.e., constant number of particles (N),constant surface tension (g), constant normal pressure(PN), and constant temperature (T). Unfortunately, theprecise value of the surface tension is hard to determine,because it depends on many factors, such as lipid typeand system size. Between the two thermodynamicensembles, each with its own set of advantages and dis-advantages, we chose to use the relatively more rigidNAPNT ensemble as a starting point. The area A of eachsimulation box has been chosen in a systematic way asexplained below. The bene®t of constant area ensemblesas a ®rst set of simulation runs is twofold. First, molecu-lar packing is expected to equilibrate faster under a ®xedarea constraint than in a constant surface tension run.Second, having generated a constant area ensemble, thesurface tension can be subsequently calculated and usedfor future constant surface tension runs. Note that evenif the lateral area is ®xed, the volume of the simulationcell in a NAPNT run is not; the vertical dimension of thecell is free to ¯uctuate under the constant normal press-ure (PN) constraint, and in consequence, the densities ofthe different molecular components are free to adjust,eliminating the density artifacts associated with theconstant volume simulations.

Simulation construction

Simulations were performed using CHARMM version26 (Brooks et al., 1983). Each GpA simulation consists ofone monomer or one dimer form of the glycophorin Atransmembrane domain, plus 15 lipids per monolayer(30 lipids in total) and the corresponding number ofwater molecules (see Table 6). Four different lipid typeswere considered: DMPC (dimyristoyl-phosphatidyl-choline), DPPC (dipalmitoyl-phosphatidylcholine),DOPC (dioleoyl-phosphatidylcholine), and POPC (1-palmitoyl-2-oleoyl-phosphatidylcholine). Periodic bound-ary conditions in all three spatial directions were used,with constant normal pressure (PN � 1 atm) and constantlateral area, with different values for different lipids, asshown in Table 6. All simulations were performed at30 �C, except the DPPC systems where trajectories weresimulated at 50 �C. The number of water molecules ineach case was determined starting from experimentaldata on fully hydrated multilamellar vesicles of purelipid bilayers. Speci®cally, using the number of watermolecules per lipid and the lipid cross-sectional area in

Table 6. Simulation setup

Total area Total waters

Lipid Area/lipid Waters/lipid Neat Mono Dimer Neat Mono Dimer

DMPCa 59.8 25.7 1075 1073 1248 925 924 1151DPPCb 62.9 29.1 1132 1121 1296 1048 965 1195DOPCc 72.2 32.5 - 1260 1436 - 1134 1293POPCd 63.0 30.0 - 1122 1298 - 1069 1236

GpA simulations contain 30 lipids, and neat bilayer simulations contain 36 lipids. The area units are AÊ 2.a Petrache et al. (1998a).b Nagle et al. (1996).c Tristram-Nagle et al. (1998).d Estimate.


each lipid bilayer, the number of water molecules perunit area was calculated and then scaled to the total areaof the simulation box. (Note the implicit assumption thatinter-lamellar water spacing does not change with pep-tide insertion, which is clearly an approximation. Therationale, however, is based on inter-bilayer interactionstudies (Petrache et al., 1998b) which show that the waterspacing decreases in the absence of bilayer ¯uctuations.Therefore, using data from fully hydrated, unstressedsamples at most overestimates the number of water mol-ecules required to fully hydrate a small, non-¯uctuatingbilayer patch.) The total area of the simulation boxincludes the peptide cross-sectional area, and was esti-mated as follows. First, the volumes for both GpA mono-mer and dimer were estimated by calculating theexcluded volume for a spherical probe the size of awater molecule. These volumes were then divided byeffective helix lengths to obtain ``bare'' cross-sectionalareas. Tilt averaged areas were estimated by consideringa uniform population of peptide tilt angles between 0and 25 degrees (Bowie, 1997). These results were com-bined with the ``collapsed'' area obtained by translatingall atoms along the helix axis in the z � 0 plane. Esti-mated values of �177 AÊ 2 for the monomer, and �353 AÊ 2

for the dimer form were used. To these results we thenadded the area per lipid measured experimentally at fullhydration, to obtain the total area of each simulationbox. In parallel, we performed neat DMPC and DPPCbilayer simulations, with 18 lipids per monolayer (totalof 36 lipids each). Table 1 summarizes all structuralinformation regarding the molecular dynamics setup.

Initial membrane structures were constructed usingthe procedure proposed by Woolf & Roux (1994, 1996).The NMR structure of GpA (residues 74 to 91) reportedby MacKenzie et al. (1997) was used as a starting point.Lipid molecules were randomly chosen from pre-equili-brated lipid libraries. The DPPC library was provided byHardy & Pastor (1994), and also used to generate DMPCmolecules by deletion of two terminal carbon segmentsfrom each acyl chain. DOPC and POPC libraries wereprovided by Scott Feller (Armen et al., 1998). The lipidplacement around the peptide was ®rst determined by a100 ps simulation of large van der Waals (vdW) spheresconstrained in the vicinity of two parallel planes at theaverage location of the lipid headgroups. Next, lipidmolecules were randomly chosen from the libraries andplaced at the location of the vdW spheres. The lipidswere then systematically rotated and translated aroundthe initial positions, in order to reduce the number ofsteric collisions, followed by a gradual increase of thevdW atom radii and minimization. During this minimiz-ation stage, the peptide atoms were kept ®xed to theirinitial locations, and the lipid glycerol C2 atoms were

restrained to their initial plane using a harmonic poten-tial of 10 kcal molÿ1 AÊ ÿ2 and a drop off cutoff of 1 AÊ .Next, a TIP3 water overlay was performed from the gly-cerol regions on both sides of the membrane. For eachtrajectory, the z-dimension of the box was determined bythe target number of water molecules chosen in Table 6.Water-lipid packing was ®rst relaxed by a series of mini-mization and Langevin dynamics simulations, followedby velocity scaling simulations with electrostatics shiftedand van der Waals switched at 12 AÊ . At this stage, theconstraints on the peptide and the lipid glycerol atomswere kept on. Next, the constraints on the lipid glycerolswere removed, and equilibration continued with 25 ps ofleapfrog constant pressure and constant temperaturedynamics. In the next stage of equilibration, the peptiderestraints were also removed and 25 ps of dynamicswere performed using the particle mesh Ewald methodfor electrostatic interactions (Sagui & Darden, 1999). Acutoff of 12 AÊ was used for van der Waals interactions(Feller & Pastor, 1999). The time step was 2 fs, and allbonds involving hydrogen atoms were ®xed using theSHAKE algorithm, with a tolerance (relative deviation)of 10ÿ6. The frequency of regenerating the non-bondedlist used the heuristic testing algorithm that updatesbased on the distance each atom moved since the last listupdate. Production dynamics simulations were per-formed for 1.5 ns. The results reported in this paper arebased on the last 1.25 ns of dynamics, after a 250 psequilibration window.

Voronoi procedure

A detailed description of the algorithm used is givenby Gerstein et al. (1995). Brie¯y, given a distribution ofatoms, the standard Voronoi procedure constructs apolyhedron around each atom, that has the property thatall interior points are closer to the central atom than toany others. The resulting partitioning ®lls the entirespace in the simulation box (i.e. allows no voids). Thepolyhedron faces are located midway between neighbor-ing atoms, which assumes that all atoms have intrinsi-cally the same size. Gerstein et al. (1995) have consideredmore physical partitioning methods to account for atomsize differences within a molecular system, such as aprotein. These methods calculate the location of thedividing planes based on proportionality relations withthe atom van der Waals radii. The authors suggest theirmethod B as most appropriate dividing procedure,which we have used. It was noted that this procedureintroduces a ``vertex error'' at the intersection of three ormore dividing planes, but estimates the error to besmall. We should also mention that the method uses


heavy atoms only (hydrogen atoms are accounted forimplicitly), and may introduce additional errors. Sinceour main purpose is to estimate volume differencesbetween the GpA peptides in different environments, weexpect that these systematic errors do not in¯uence theresults signi®cantly.

Acknowledgments

We thank Dan Zuckerman for helpful discussion andcritical reading of the manuscript. We also thank the tworeviewers for helpful criticism and suggestions,especially regarding the molecular self energies and theboundary lipid issues. Richard Pastor and Scott Fellerare acknowledged for kindly providing lipid structurelibraries. This research was supported by the NIH andNSF.

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Edited by G. Von Heijne

(Received 5 April 2000; received in revised form 20 July 2000; accepted 23 July 2000)

Modulation of glycophorin A transmembrane helix interactions by lipid bilayers: molecular dynamics...

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