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Ž .Current Opinion in Colloid & Interface Science 00 2000 00]00

Molecular dynamics simulations of lipid bilayers

Scott E. FellerU

Department of Chemistry, Wabash College, 301 W. Wabash, Crawfords̈ ille, IN 47933, USA

Received 26 June 2000; accepted 4 August 2000

Abstract

Computer simulation methods are becoming increasingly widespread as tools for studying the structure and dynamics oflipid bilayer membranes. The length scale and time scale accessible to atomic-level molecular dynamics simulations are rapidlyincreasing, providing insight into the relatively slow motions of molecular reorientation and translation and demonstrating thateffects due to the finite size of the simulation cell can influence simulation results. Additionally, significant advances havebeen made in the complexity of membrane systems studied, including bilayers with cholesterol, small solute molecules, andlipid-protein and lipid-DNA complexes. Especially promising is the progress that continues to be made in the comparison ofsimulation results with experiment, both to validate the simulation algorithms and to aid in the interpretation of existingexperimental data. Q 2000 Elsevier Science Ltd. All rights reserved.

Keywords: Molecular dynamics; Simulation; Force-field; Algorithm; Interactions

1. Introduction

The structure of a lipid bilayer in its biologicallyrelevant, liquid-crystalline, state cannot be describedby any single conformation of the molecules makingup the membrane assembly. This inherent disorderleads to difficulties in developing simple models thatcan be used to visualize the system and to interpretexperimental results. In the past decade, atomic-levelmodels of the lipid bilayer have been developed as auseful tool for accomplishing these tasks. Molecular

Ž .dynamics MD simulation, where particles represent-

Abbre¨iations: DPPC, dipalmitoylphosphatidylcholine; DMPC,dimyristoylphosphatidylcholine; MD, molecular dynamics; NMR,nuclear magnetic resonance; PC, phosphatidylcholine; POPC,palmitoyloleoylphosphatidylcholine

U Tel.: q1-765-361-6175; fax: q1-765-361-6340.Ž .E-mail address: fellers@wabash.edu S.E. Feller .

ing lipid, water, and solute atoms are followed throughtime, has been used extensively because it simultane-ously provides information on both the spatial organi-zation and temporal dynamics of the system. Thisreview will focus on MD simulations of lipid bilayermembranes described in the literature during theperiod from early 1999 to early 2000. For earlierreviews of the field of membrane simulation, the

w xreader is referred to the following literature 1]7 . Anoverview of bilayer structure in general, coveringmostly experimental results but also discussing bilayersimulations, is given by Nagle and Tristram-Naglew v x8 .

The following discussion has been organized aroundŽ .the topics of: 1 pure lipid simulations, focusing on

insights into lipid structure and dynamics and metho-Ž .dological developments; 2 membrane solute simula-

tions, focusing on the interactions of small solutemolecules and cholesterol, with their membrane envi-

Ž .ronments; and 3 membrane-biopolymer simulations,

1359-0294r00r$ - see front matter Q 2000 Elsevier Science Ltd. All rights reserved.Ž .PII: S 1 3 5 9 - 0 2 9 4 0 0 0 0 0 5 8 - 3

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( )S.E. Feller r Current Opinion in Colloid & Interface Science 00 2000 00]002

focusing on complex membranes containing proteinsand DNA.

2. Pure lipid simulations

Increases in processor speed and the availability ofparallel computers allowed major advances to be madein increasing the length scale and time scale accessi-ble to bilayer MD simulations during the period ofthis review. With this increase in simulation duration,a growing number of reports have analyzed motionson the nanosecond time scale. Essmann and Berkowitzw v x9 detailed the slow motion of the PC headgroupatoms and found that the orientation of watermolecules compensates for the headgroup fluctua-tions to maintain a nearly constant membrane dipolepotential. The long time scale of these headgroupmotions was also emphasized in studies of headgroupinteractions through charge pairing and water bridg-ing in DMPC, where contact lifetimes on the order of

w xa nanosecond were observed 10 . In a simulation ofan especially large membrane patch, Lindahl and

w vv xEdholm 11 estimated the relaxation time of collec-tive udulatory and peristaltic modes of motion. Thelong time scale for lipid reorganization, observed inthese simulations, has important consequences in thestudy of the more complex membranes discussed inSection 5 of this review because the molecular trans-lations and reorientations required to solvate incor-porated species is presumably also on the multi-nanosecond time scale.

Membrane simulations with durations of 10 nsw v v x9 ,12 and system sizes reaching 1024 lipids were

w vv xreported 11 , allowing new comparisons betweensimulation results and experimental data. Examplesinclude the calculation of Nuclear Overhauser En-

Ž .hancement Spectroscopy NOESY cross-relaxationrates from a 10-ns simulation of DPPC and the subse-quent interpretation of the underlying correlation

w v xfunctions in terms of lipid motions 12 , the determi-nation of the diffusion coefficients for molecular rota-tion about the lipid long axis and for lateral transla-

w v xtions 9 , and the computation of the bending modu-w vv x w vv v xlus 11 and area compressibility modulus 11 ,13 .

An especially interesting comparison between simula-tion and experiment was the work of Tobias thatfocused on the wide variety of experimental data

w vv xavailable from neutron scattering techniques 14 .The interpretation of the relationship between lipidsurface area and NMR S order parameters wasCDreconsidered based on the results of a DPPC simula-tion, where a new formula was proposed that repro-

w v xduced the simulation area per lipid 15 . A secondstudy of the order parameters in DPPC, this one

w v xfocusing on the S order parameter 16 and moti-CC

vated by recent experimental results for this quantityw x17 , found significant differences between the confor-mations of the sn-1 and sn-2 fatty acid chains. Otherinteresting simulations motivated by specific experi-mental systems include a study of a hybrid bilayerformed from a DPPC monolayer and an alkanethiol

w xself-assembled monolayer 18 , and a study of solventeffects where water was replaced by dimethylsulfoxideŽ . w xDMSO in a simulation of DPPC 19 . An interestingobservation from the latter simulation was that thedipole potential changed sign when comparing theaqueous and DMSO systems, a result that has impli-cations for theories of the hydration force actingbetween membranes.

Several important methodological issues were ad-w v xdressed in the past year. Chiu et al. 20 ,21 described

a hybrid equilibration procedure combining configu-Ž .rational bias Monte Carlo CBMC with MD simula-

tion to improve sampling efficiency. These methodscould be especially useful for generating initial condi-tions of complex membranes where one wishes toequilibrate the lipids surrounding an incorporatedsolute. The same group also developed a hydrocarbonparameter set, by fitting to molecular volumes andheats of vaporization over a range of chain lengths,

w v xfor use in lipid simulations 22 . Especially encourag-ing was their finding that a single set of hydrocarbonparameters could reproduce both short chain andlong chain experimental data. In a study to testparameterization, quantum mechanical calculationson indole and N-methylindole were carried out tostudy whether cation-p interactions, thought to becrucial in describing the attraction of aromatic aminoacids for the membrane interface, can be describedusing simple point charges placed on atomic centersw x23 . The authors concluded that much of the interac-tion is captured for point charges approaching per-pendicular to the aromatic ring, however, agreementbetween the quantum mechanical results and forcefield calculations were less satisfactory for other di-rections of approach.

Most MD simulations of lipid bilayers have focusedon the liquid crystalline state, however, one simula-tion of gel state DPPC was reported where the au-thors carried out a systematic study of the effects offorce truncation and boundary conditions on struc-tural parameters such as area per molecule, bilayerrepeat spacing, chain tilt, and fraction gauche bondsw v x24 . They concluded that gel phase simulations re-quire a fully flexible simulation cell during the equili-bration period and that Ewald summation techniquesare superior to truncation methods, and showed thatequilibration of chain torsions near the headgroupregion can be a very long process in the gel state.

The most pressing issue in the development ofbilayer simulation methods over the past 5 years has

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been the choice of boundary conditions in constantpressure simulations, where the size andror shape ofthe simulation cell is allowed to adjust. In principle,this type of simulation can provide a powerful tech-nique for determining membrane structural parame-ters, such as the surface area per molecule. Theargument among practitioners of membrane simula-tion has centered on the appropriateness of applying

Ž .an isotropic pressure typically 1 atm in both thedirections parallel and perpendicular to the mem-brane surface. Employing an isotropic pressure tensoris equivalent to imposing a condition of zero surfacetension, g, on the lipid interface. It has been sug-gested that zero surface tension is the appropriatestate for an unstressed bilayer at its free energyminimum and thus that an isotropic pressure is the

w xcorrect ensemble for MD bilayer simulations 25 .Others have argued, based on the confining effects of

w xperiodic boundary conditions 26]28 or comparisonw x Žwith monolayer systems 29 , that a bilayer at least on

.the length scale of a typical MD simulation may havea finite surface tension at the surface area permolecule that minimizes its free energy. Unfortu-nately, there is little guide from experiment or else-where on its precise value, and the value of g calcu-lated from constant area simulations has beenobserved to depend sensitively on the force field em-ployed and the method of calculating long-range cou-

w xlombic interactions 30 . Consequently, the majority ofconstant pressure lipid simulations have been donewith gs0, or with only the cell dimension perpendic-ular to the membrane allowed to adjust against atmo-

Žspheric pressure the NPAT ensemble, for constantparticle number, normal pressure, surface area, and

.temperature . Substantial progress on this problemhas been achieved recently. Feller and Pastor showed,via a series of DPPC simulations differing only intheir value of the applied surface tension, that thearea per molecule and other structural parameters

w v xdepended sensitively on the value of g applied 13 .Importantly, their comparisons with fixed area simula-tions showed that, when systems at approximatelyequal surface areas were examined, there was nodifference in structural or dynamic properties due tochoice of ensemble. Thus, the value of the applied

Ž .surface tension or fixed surface area is much moreimportant than whether one uses a fully flexible simu-lation cell or one with a fixed area. Lindahl andEdholm carried out a series of fixed area simulationsand analyzed the calculated surface tensions in termsof the energetic and entropic contributions from vari-ous interactions between lipid headgroups, fatty acid

w v xchains, and water 31 . They find the surface tensioncalculated from simulation to be a sum of large termsof opposing signs and interpret this result as explain-ing the sensitivity of g to simulation setup. Finally, in

an ambitious series of simulations where 64, 256, and1024 DPPC molecules were simulated under isotropicpressure, Lindahl and Edholm observed that the areaper molecule increased uniformly as the number of

w vv xlipid molecules was raised 11 . This explicit demon-stration of system size-dependent behavior in a con-stant pressure simulation is consistent with earlier

w xobservations of Feller and Pastor 26 where the cal-culated surface tension decreased with larger systemsize in a series of constant area simulations. Combin-ing the work of the two groups results in clear evi-dence for a size-dependent surface tension present inlipid simulations over the range from 18 to 1024molecules. By extrapolating to infinite sized mem-branes, Lindahl and Edholm estimate that a standardsized membrane simulation consisting of 64 lipids will

˚2have an area per molecule that is ;2]3 A too smallwhen simulated at gs0. The results of Feller andPastor, using smaller systems, suggest the effect couldbe somewhat larger. Clearly, constant pressure simu-lations of lipid bilayers are more complicated thanthose on isotropic systems and the artifacts inherentin a uniform pressure tensor, while only a few percentof the total area, are large enough to influence lipidstructure and dynamics.

3. Membrane-solute simulations

Both the transport of small solutes and their effectson membrane structure have been studied extensively

w v xwith MD simulation. Pohorille and colleagues 6,32have recently published a review of their work andothers in the field, providing a useful overview of thetheories and simulation strategies that have beenapplied to membrane permeation. Many simulationstudies have focused on the role of spontaneouslyarising free volume with the membrane, including the

w x w xworks of Xiang 33 and Xiang and Anderson 34where MD simulations of noble gases in a modelmembrane were used to study the fundamentalproperties of membrane transport. Another target ofmembrane simulation has been the interaction ofanesthetics, such as a recent study of halothane in a

w v xDPPC bilayer 35 . The halothane was observed tolocalize within the hydrocarbon core and to changethe bilayer structure, lowering the fatty acid chainorder parameters at the center of the membrane.

Several simulations of phospholipid bilayers con-taining cholesterol were reported during the period of

w xthis review. Smodyrev and Berkowitz 36 performedsimulations with DPPCrcholesterol ratios of 8:1 and1:1 and compared these results with those of a pureDPPC bilayer under indentical conditions of tempera-ture and hydration. They found a significant decreasein lipid surface area, thus reproducing the experimen-

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tally observed ‘condensing’ effect that cholesterol hason membrane lipids, along with an increase in chainorder as measured by the deuterium order parame-ters and a decrease in the gauche fraction. This samegroup also examined the differences between a 1:1mol ratio mixture of DPPC and cholesterol sulfateand the aforementioned 1:1 mixture of DPPC andcholesterol, and found the condensing effect and or-dering of alkyl chains was less pronounced with

w xcholesterol sulfate 37 . A study of a DMPCrcholesterol bilayer, focusing on the effects of choles-terol on the membranerwater interface, suggests thatthe addition of cholesterol disrupts Coulombic inter-actions between lipid headgroups and increases

w xlipid]water interactions 38 .

4. Membrane-biopolymer simulations

The number of complex membrane simulations re-ported in the literature has exploded recently, andnow likely surpasses the reports of ‘simple’ bilayer

Ž .systems described in the previous sections in mostjournals. Simulations of lipid bilayers containing pep-tides species have recently been thoroughly reviewed

w xby Forrest and Sansom 7 , thus we will not attempt tocover all published works but focus only on a fewobservations.

Two studies of melittin in phospholipid bilayershave recently been reported. A single peptide wasfollowed for 500 ps and observed to induce disorderin the lipid chains, with the magnitude of this effect

w xdifferent for the two halves of the bilayer 39 . Asecond MD simulation studied a membrane poreformed by four melittin molecules initially embeddedin a lipid bilayer, however, over the course of thesimulation the aggregate decayed into a trimer and an

w xisolated monomer 40 . This relatively long melittinŽ .simulation 5.8 ns in length shows convincingly that

significant trajectory must be obtained before con-cluding that an initial membrane structure is thermo-dynamically stable. Another important methodologi-cal issue is raised by the melitin simulation in Bachar

w xand Becker 39 , that is how does one allow surfacedensities on the upper and lower monolayer to adjustindependently when the peptide insertion is not sym-metrical? Some bilayer simulations have employed

w xfully flexible simulation cells 41 , but the majorityimposed orthorhombic symmetry on the system thatcould introduce artifacts into the membrane struc-ture.

An especially active area of research has been thestudy of proteins forming ion channels spanning thelipid membrane. During the period of this review,

w xsimulations of a gramicidin channel 42 , a variety ofq w v xK channels 43 ,44,45 , a synthetic Leucine-Serine

w x w xion channel 46 , a proton channel 47 , and otherhelical peptides that associate in lipid bilayers to form

w xion channels 48]50 , have been reported. A numberof these simulations have explicitly followed the dy-namics of ion or water permeation through the chan-

w v xnel 43,45,51 and identified structurally significantfeatures that influence this process. Molecular dy-namics simulations have also been used to test chan-nel protein structures generated by homology model-

w xing 52,53 , to compare the effect of a bilayer mem-w v xbrane with other solvent environments 54 , and to

investigate alternative model-built structures as initialw v xconditions 55 . In the latter it was observed that

simulation results for the protein structure are sensi-tive to details of the starting structure, at least on thenanosecond time scale.

Finally, the first report describing an MD simula-tion of a lipid]DNA complex was reported by Bandy-

w v xopadhyay et al. 56 . This system, a hydrated lipidbilayer composed of a mixture of the cationic lipid

Ž .dimyristoyltrimethylammonium propane DMTAPand the neutral lipid DMPC, with a DNA strandintercalated between bilayers, was motivated by ex-perimental studies on these compounds and the po-tential application of lipids as DNA carriers for genetransfer therapies.

5. Conclusions

Improvements in simulation protocol, such as theŽ .particle mesh Ewald summation PME that allows

w xefficient calculation of Coulombic interactions 57 ,and constant pressure methods that allow flexibility in

w xthe size and shape of the simulation cell 58 , havedramatically improved the accuracy of membranesimulations in the recent past. These tools, as well asthe continual refinement of potential energy parame-ters, have advanced the field of bilayer simulation tothe point where quantitative agreement betweensimulation and experiment has been achieved bynumerous groups for most positions of the fatty acid

Žchain order parameters the quantity most often used.to benchmark lipid simulations . Further progress is

likely needed before similar convergence will beobserved in headgroup and water structure. As exam-ples, few if any simulations have been able to repro-duce the splitting of the two unique order parametersobserved experimentally for C2 of the sn-2 chain, andthe magnitudes and origins of the membrane dipolepotential have varied widely among reported simula-tions.

A review of lipid bilayer simulations in this journalfrom 3 years past predicted orders of magnitude in-creases in the length scale and time scale accessible

w xto atomic-level MD simulation 2 . Certainly this pre-

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diction has come true and at present it seems clearthat the increased computational power and algo-rithmic advances needed to sustain this growth willcontinue, at least for the near future. This increase incomputational power will be especially useful instudying the lipid]protein complexes of significantbiological interest. These simulations suffer not onlyfrom poor sampling due to the small number of solutemolecules being followed, but also from long relax-ation times inherent in equilibrating a lipid solventenvironment. It is critical that in the drive to increasethe complexity of systems under study, the accumu-lated knowledge gained from pure lipid simulations,e.g. long equilibration times and sensitivity of resultsto treatment of electrostatic interactions, is not over-looked.

Acknowledgements

The author gratefully acknowledges the support ofthe National Science Foundation through grant MCB-9896211.

References and recommended reading

v of special interestvv of outstanding interest

w x1 Pastor RW. Molecular dynamics and Monte Carlo simula-tions of lipid bilayers. Curr Opin Struct Biol 1994;4:486]492.

w x2 Tobias DJ, Tu KC, Klein ML. Atomic-scale molecular dy-namics simulations of lipid membranes. Curr Opin Coll Inter-face Sci 1997;2:15]26.

w x3 Tieleman DP, Marrink SJ, Berendsen HJC. A computerperspective of membranes: molecular dynamics studies oflipid bilayer systems. Biochim Biophys Acta 1997;1331:235]270.

w x4 Jakobsson E. Computer simulation studies of biological mem-branes: progress, promise and pitfalls. Trends Biol Sci1997;22:339]344.

w x5 Berendsen HJC, Tieleman DP. Molecular dynamics: studiesof lipid bilayers. In: Schleyer R, editor. Encyclopedia ofcomputational chemistry. Wiley and Sons, 1998:1639]1650.

w x6 Pohorille A, Wilson MA, Chipot C, New MH, SchweighoferK. Interactions of small molecules and peptides with mem-branes. In: Lesczynski J, editor. Computational molecularbiology, theoretical and computational chemistry. Elsevier,1999:485]526.

w x7 Forrest LR, Sansom MSP. Membrane simulations: bigger andbetter? Curr Opin Struct Biol 2000;10:174]181.

w x8 Nagle JF, Tristram-Nagle S. Lipid bilayer structure. Currv Opin Struct Biol 2000, in press.

Reviews experimental methods for determining lipid surface areas.Several quantities are discussed that may be interesting to calculatefrom simulation.w x9 Essmann U, Berkowitz ML. Dynamical properties of phos-v pholipid bilayers from computer simulation. Biophys J

1999;76:2081]2089.A long DPPC simulation is analyzed in terms of nanosecond scaledynamics. The difficulty in defining molecular rotation is discussedand one method for defining a molecular frame is presented.

w x10 Pasenkiewicz-Gierula M, Takaoka Y, Miyagawa H, KitamuraK, Kusumi A. Charge pairing of headgroups in phosphatidyl-choline membranes: a molecular dynamics simulation study.Biophys J 1999;76:1228]1240.

w x11 Lindahl E, Edholm O. Mesoscopic undulations and thicknessvv fluctuations in lipid bilayers from molecular dynamics simula-

tions. Biophys J 2000.Long simulations of DPPC bilayers containing up to 1024 moleculesare analyzed in terms of collective motions of the lipids. Figure 2 ofthe paper demonstrates the system-size dependence of simulationresults for the molecular surface area.w x12 Feller SE, Huster D, Gawrisch K. Interpretation of NOESY

v cross-relaxation rates from molecular dynamics simulation ofa lipid bilayer. J Am Chem Soc 1999;121:8963]8964.

Simulation is used to understand the motions underlying the corre-lation functions that determine NOESY cross relaxation rates andto verify the assertion that the lipid NOESY experiment primarilyprobes inter-molecular contacts.w x13 Feller SE, Pastor RW. Constant surface tension simulations

v of lipid bilayers: the sensitivity of surface areas and compress-ibilities. J Chem Phys 1999;111:1281]1287.

Methods for calculating the area compressibility modulus are re-ported, as well as a comparison of constant pressure and constantsurface area ensembles.w x14 Tobias DJ. Membrane simulations. In: Becker OH, Mac-

vv Kerell Jr. AD, Roux B, Watanabe M, editors. ComputationalBiochemistry and Biophysics. New York: Marcel Dekker,

w x2000. in press .The focus here is on lipid and water dynamics and the types ofexperimental measurements that probe these motions.w x15 Petrache HI, Tu K, Nagle JF. Analysis of simulated NMR

v order parameters for lipid bilayer structure determination.Biophys J 1999;76:2479]2487.

The formula relating order parameters to chain length and area permolecule is reconsidered based on a DPPC simulation and analternative relationship is proposed.w x16 Smondyrev AM, Berkowitz ML. Molecular dynamics study of

v sn-1 and sn-2 chain conformations in dipalmitoylphos-phatidylcholine membranes. J Chem Phys 1999;110:3981]3985.

The relationship between CC and CD order parameters are testedin a DPPC simulation and differences between sn-1 and sn-2chains are demonstrated using the CC order parameter.w x17 Douliez JP, Leonard A, Dufourc EJ. Conformational order of

DMPC sn-1 and sn-2 chains and membrane thickness: anapproach to molecular protrusion by solid state 2H-NMR andneutron diffraction. J Phys Chem 1996;100:18450]18457.

w x18 Tarek M, Tu K, Klein ML, Tobias DJ. Molecular dynamicssimulations of supported phospholipidralkanethiol bilayers

Ž .on a gold 111 surface. Biophys J 1999;77:964]972.w x19 Smondyrev AM, Berkowitz ML. Molecular dynamics simula-

tion of DPPC bilayer in DMSO. Biophys J 1999;76:2472]2478.w x20 Chiu SW, Jakobsson E, Subramaniam S, Scott HL. Combined

v Monte Carlo and molecular dynamics simulation of fullyhydrated dioleyl and palmitoyl-oleyl phosphatidylcholine lipidbilayers. Biophys J 1999;77:2462]2469.

A novel technique is presented that efficiently explores conforma-tional space, and thus reduces equilibration time, is presented.w x21 Chiu SW, Clark MM, Jakobsson E, Subramaniam S, Scott

HL. Application of combined Monte Carlo and moleculardynamics method to simulation of dipalmitoylphosphatidyl-choline lipid bilayer. J Comp Chem 1999;20:1153]1164. See

w v xChiu et al. 20 .w x22 Chiu SW, Clark MM, Jakobsson E, Subramanium S, Scott

v HL. Optimization of hydrocarbon chain interaction parame-ters: application to the simulation of fluid phase lipid bilay-ers. J Phys Chem B 1999;103:6323]6327.

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( )S.E. Feller r Current Opinion in Colloid & Interface Science 00 2000 00]006

The linear relationship between molecular volume and chain lengthis used as the basis for choosing Lennard-Jones parameters forsaturated alkanes.w x23 Woolf TB, Grossfield A, Pearson JG. Indoles at interfaces:

calculations of electrostatic effects with density functionaland molecular dynamics methods. Int J Quantum Chem1999;75:197]206.

w x24 Venable RM, Brooks BR, Pastor RW. Molecular dynamicsŽ .v simulations of gel L phase lipid bilayers in constantBI

pressure and constant surface area ensembles. J Chem Phys2000:4822]4832.

One of only a handful of simulation reports on the gel phase oflipid bilayers. Important methodological issues are addressed andthe dynamics of the chain dihedrals are described and related torelevant experimental measurements.w x25 Jahnig F. What is the surface tension of a lipid bilayer

membrane? Biophys J 1996;71:1348]1349.w x26 Feller SE, Pastor RW. On simulating lipid bilayers with an

applied surface tension: periodic boundary conditions andundulations. Biophys J 1996;71:1350]1355.

w x27 Feller SE, Pastor RW. Length scales of lipid dynamics andmolecular dynamics. In: Altman RB, Dunker AK, Hunter L,Klein TE, editors. Proceedings of the Pacific symposium onbiocomputing. Singapore: World Scientific, 1997:142]150.

w x28 Marsh D. Renormalization of the tension and area expansionmodulus in fluid membranes. Biophys J 1997;73:865]869.

w x29 Chiu SW, Clark M, Balaji V, Scott HL, Jakobssen E. Incor-poration of surface tension into molecular dynamics simula-tion of an interface: a fluid phase lipid bilayer membrane.Biophys J 1995;69:1230]1245.

w x30 Feller SE, Pastor RW, Rojnuckarin A, Bogusz S, Brooks BR.Effect of electrostatic force truncation on interfacial andtransport properties of water. J Phys Chem 1996;100:17011]17020.

w x31 Lindahl E, Edholm O. Spatial and energetic-entropic decom-v position of surface tension in a lipid bilayer by molecular

dynamics simulations. J Chem Phys 2000.The energetic contribution to the surface tension is calculated fromthe linear change in internal energy with respect to area and theentropic contribution determined as the difference between totalsurface tension and energetic contribution. These quantities arefurther broken down into contributions from various parts of thelipidrwater system.w x32 Pohorille A, New MH, Schweighofer K, Wilson MA. Insights

v from computer simulations into the interaction of smallmolecules with lipid bilayers. Curr Top Membr 1999;48:49]76.

A number of simulation approaches to the study of permeation arereviewed.w x33 Xiang T. Translational diffusion in lipid bilayers: dynamic

free-volume theory and molecular dynamics simulation. JPhys Chem B 1999;103:385]394.

w x34 Xiang T, Anderson BD. Molecular dissolution processes inlipid bilayers: a molecular dynamics simulation. J Chem Phys1999;110:1807]1818.

w x35 Koubi L, Tarek M, Klein ML, Scharf D. Distribution ofv halothane in a dipalmitoylphosphatidylcholine bilayer from

molecular dynamics calculations. Biophys J 2000;78:800]811.Description of the behavior of an anesthetic in various regions of alipid bilayer. The simulation is analyzed with regards to severaldifferent experimental measurements.w x36 Smondyrev AM, Berkowitz ML. Structure of dipalmitoylphos-

phatidylcholinercholesterol bilayer at low and high choles-terol concentrations: molecular dynamics simulation. BiophysJ 1999;77:2075]2089.

w x37 Smondyrev AM, Berkowitz ML. Molecular dynamics simula-tion of dipalmitoylphosphatidylcholine membrane withcholesterol sulfate. Biophys J 2000;78:1672]1680.

w x38 Pasenkiewicz-Gierula M, Rog T, Kitamura K, Kusumi A.Cholesterol effect on the phosphatidylcholine bilayer polarregion: a molecular simulation study. Biophys J 2000;76:1376]1389.

w x39 Bachar M, Becker OM. Protein-induced membrane disorder:a molecular dynamics study of lemittin in a dipalmitoylphos-phatidylcholine bilayer. Biophys J 2000;78:1359]1375.

w x40 Lin JH, Baumgaertner A. Stability of a melittin pore in alipid bilayer: a molecular dynamics study. Biophys J 2000;78:1714]1724.

w x41 Tu K, Tobias DJ, Klein ML. Constant pressure and tempera-ture molecular dynamics simulation of a fully hydrated liquidcrystal phase dipalmitoylphosphatidylcholine bilayer. BiophysJ 1995;69:2558]2562.

w x42 Chiu SW, Subramanium S, Jakobsson E. Simulation study ofa gramicidinrlipid bilayer system in excess water and lipid. I.Structure of the molecular complex. Biophys J 1999;76:

w x1929]1938. See Chiu et al. 51 .w x43 Berneche S, Roux B. Large molecular dynamics of the KcsA

v Kq channel in a bilayer membrane. Biophys J 2000;78:2900]2917.

Over 40 000 atoms are represented in this simulation of the KcsAchannel in a DPPC bilayer solvated by explicit electrolyte solution.w x44 Shrivasta IH, Capener CE, Forrest LR, Sansom MSP. Struc-

ture and dynamics of K channel pore-lining helices: a com-parative simulation study. Biophys J 2000;78:79]92.

w x45 Shrivasta IH, Sansom MSP. Simulations of ion permeationthrough a potassium channel: molecular dynamics of KcsA ina phospholipid bilayer. Biophys J 2000;78:557]570.

The motion of water and potassium ions are followed in thissimulation of the KcsA channel based on the experimentally de-termined channel structure. Concerted motions of water and ionsare observed in the channel.w x46 Randa HS, Forrest LR, Voth GA, Sansom MSP. Molecular

dynamics of synthetic leucine]serine ion channels in a phos-pholipid membrane. Biophys J 1999: 2400]2410.

w x47 Schweighofer KJ, Pohorille A. Computer simulation of ionchannel gating: the M2 channel of influenza A virus in a lipidbilayer. Biophys J 2000:150]163.

Simulations are used to investigate mechanisms for proton transportacross a DMPC bilayer.w x48 Law RJ, Forrest LR, Ranatunga KM, La Rocca P, Tieleman

DP, Sansom MSP. Structure and dynamics of the pore-lininghelix of the nicotinic receptor: MD simulations in water lipidbilayers, and transbilayer bundles. Proteins 2000;39:47]55.

w x49 Tieleman DP, Berendsen HJC, Sansom MSP. Surface bindingof alamethicin stabilizes its helical structure: molecular dy-namics simulations. Biophys J 1999;76:3186]3191.

w x50 Tieleman DP, Berendsen HJC, Sansom MSP. An alamethicinchannel in a lipid bilayer: molecular dynamics simulations.Biophys J 1999;76:1757]1769.

w x51 Chiu SW, Subramanium S, Jakobsson E. Simulation study ofv a gramicidinrlipid bilayer system in excess water and lipid. II.

Rates and mechanisms of water transport. Biophys J1999;76:1939]1950.

Water molecules are followed as they move through the gramicidinchannel and the trajectory is used to calculate permeation ratesthat are then discussed in terms of experimental measurements.w x52 Forrest LR, Tieleman DP, Sansom MSP. Defining the tran-

smembrane helix of M2 protein from influenza A by molecu-lar dynamics simulations in a lipid bilayer. Biophys J 1999:1886]1896.

w x53 Capener CE, Shrivastava IH, Ranatunga KM, Forrest LR,Smith GR, Sansom MSP. Homology modeling and moleculardynamics simulation studies of an inward rectifier potassiumchannel. Biophys J 2000;78:2929]2942.

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( )S.E. Feller r Current Opinion in Colloid & Interface Science 00 2000 00]00 7

w x54 Tieleman DP, Sansom MSP, Berendsen HJC. Alamethicinv helices in a bilayer and in solution: molecular dynamics

simulations. Biophys J 1999;76:40]49.The effect of environment on the peptide structure and dynamics isinvestigated using simulation in water, in methanol, and in a POPCbilayer.w x55 Forrest LR, Kukol A, Arkin IT, Tieleman DP, Sansom MSP.

v Exploring models of the influenza A M2 channel: MD simu-lations in a phospholipid bilayer. Biophys J 2000;78:55]69.

Simulation in explicit lipid is used to test several different modelsof this proton-selective channel. The results demonstrate that simu-lation results can be extremely sensitive to the choice of startingstructure.

w x56 Bandyopadhyay S, Tarek M, Klein ML. Molecular dynamicsv study of a lipid-DNA complex. J Phys Chem B

1999;103:10075]10080.Simulation of a lipid DNA complex containing a mixture of chargedand neutral lipids, a DNA duplex, and explicit water. Both chargedand neutral lipids are observed to neutralize the charged DNAphosphate groups.w x57 Essmann U, Perera L, Berkowitz ML, Darden T, Lee H,

Pedersen LG. A smooth particle mesh Ewald method. JChem Phys 1995;103:8577]8593.

w x58 Zhang Y, Feller SE, Brooks BR, Pastor RW. Computersimulation of liquidrliquid interfaces. I. Theory and applica-tion to octanerwater. J Chem Phys 1995;103:10252]10266.