Surface Tension Parameterization in Molecular Dynamics Simulations of a Phospholipid-bilayer Membrane: Calibration and Effects

Surface Tension Parameterization in Molecular Dynamics Simulations of aPhospholipid-bilayer Membrane: Calibration and Effects

Ramasubbu Sankararamakrishnan* and Harel Weinstein*

Department of Physiology and Biophysics, Mount Sinai School of Medicine, New York, New York 10029 andWeill Medical College of Cornell UniVersity, New York, New York 10021

ReceiVed: March 8, 2004; In Final Form: May 11, 2004

Molecular dynamics simulations of interfacial systems such as phospholipid bilayers require experimentalestimates of either the surface area per lipid or the surface tension (γ). To investigate the mode of selectionof γ values, we have carried out the molecular dynamics (MD) simulations described here for a neat DMPCbilayer comprising 90 lipids using NPNγT and NPNAT ensembles. Influence ofγ values coupled with theeffect of force truncation for both NPNγT and NPNAT ensembles was analyzed in multiple simulations. Themembrane structural properties were studied comparatively using differentγ values in NPNγT ensembleswith a spherical cutoff of 18 Å and particle mesh Ewald method (PME) that takes long-range electrostaticinteractions into account. In parallel, we tested the sensitivity of calculatedγ value in simulations usingNPNAT ensembles with four different spherical cutoffs and PME. Our studies suggest that when PME isused to calculate the nonbonded forces, the value of surface tension for the system ofthis sizeshould be inthe range of 25 to 30 dyn/cm (per interface). On the other hand, for simulations with a cutoff of 18 Å,shrinkage of box size of about 7-10% is observed forγ values ranging from 0 to 85 dyn/cm. The surfacetension value has to be raised to 625 dyn/cm to keep the surface area/lipid close to the experimental estimatefor neat DMPC bilayers. Molecular dynamics simulations were also carried out with the opioid peptidedynorphin A(1-13) embedded within the DMPC bilayers. Severalγ values were tested with two electrostaticschemes. Our results demonstrated that forγ values 0, 45, and 65 dyn/cm, due to the shrinkage of box size,the R-helical structure in the N-terminal region of the peptide is distorted with an 18 Å cutoff. When theγvalue is increased to 625 dyn/cm with an 18 Å cutoff or when PME is used withγ ) 25 dyn/cm, the peptide’sR-helical structure is maintained and its orientation is similar to that obtained from earlier simulations35 usingNVE ensembles. The aromatic side chains in the peptide (Tyr-1 and Phe-4) interacted similarly in all thesimulations except whenγ)0 is used with a cutoff of 18 Å. All constant surface tension simulations werecompared with constant area ensembles in which the surface area/lipid remains fixed. Our results suggestthat neglect of long-ranged electrostatic interactions and/or incorrect surface tension value results in seriousartifacts in membrane simulations and suggest that caution is required when constant surface tension simulationsare carried out on neat bilayers. In simulations of membranes with an embedded solute, the choice of anappropriateγ value is more complex, as it will affect both the structure and the interactions of the solutewithin the bilayer.

Introduction

The central role of membrane proteins in the function ofbiological systems has increased the interest in moleculardynamics simulation studies of such systems. A key elementin such studies is the representation of the lipid bilayers in thebiologically relevant liquid-crystalline state. Therefore, it wasvery gratifying to note that MD simulations are now capableof reproducing a number of important structural and dynamicparameters observed experimentally, such as bilayer thicknessand order parameter profiles.1-9 Analysis showed that amongthe most important issues in the simulation methodology of lipidbilayers are the nature of the force field, the boundary conditions,

and the treatment of nonbonded interactions. Thus, force fieldssuch as CHARMM10,11and GROMACS12-15 have been devel-oped for both saturated and unsaturated phospholipids and theapproaches are being improved continuously, for example, withthe inclusion of the Particle Mesh Ewald (PME) algorithm16 inthe calculation of Coulombic forces in lipid simulations. ThePME algorithm has significant advantages over traditionalspherical cutoff methods because it is efficient and effectivelytakes into account all interactions by calculating the long-distance nonbonded forces in reciprocal space. For boundaryconditions, the majority of the membrane simulations have usedPeriodic Boundary Conditions (PBC),1,2,5,7either with constantvolume or constant pressure algorithms. In the constant volumeensembles NVE and NVT, the energy and temperature are keptconstant, respectively, and the dimensions of the box are fixedthroughout the simulations. However, for interfacial systemssuch as lipid bilayers, it is often advantageous to simulate aflexible cell. This is possible in constant-pressure ensembles,

* Correspondence: Dr. R. Sankararamakrishnan; Department of Biologi-cal Sciences & Bioengineering, Indian Institute of Technology, Kanpur208016, India; Email: [email protected]; Tel:+91 512 2594014; Fax:+91 512 2594010. Dr. Harel Weinstein, Department of Physiology andBiophysics, Box 75, Weill Medical College of Cornell University, 1300York Avenue, New York, NY 10021; E.mail: [email protected];Tel: (212) 241 7018; Fax: (212) 860 3369.

11802 J. Phys. Chem. B2004,108,11802-11811

10.1021/jp048969n CCC: $27.50 © 2004 American Chemical SocietyPublished on Web 07/02/2004

in which a pressure tensorP is specified. The commonly usedapproaches include the NPNAT and NPNγT ensembles, in whicha constant normal pressure (PN) is applied with a fixed surfacearea (A) or a constant surface tension (γ). In both theseensembles, the length of the unit cell along theZ-axis (bilayernormal) is adjusted to maintain the constant normal pressurePN. In an NPNγT ensemble, the surface area is allowed tofluctuate in addition to theZ-axis, to keep a constant nonzerosurface tension. In the NPT ensemble, the surface tension iszero and an isotropic pressure tensor is applied. In both NPNγTand NPT simulations, the simulation cell is fully flexible.

In constant volume and NPNAT ensembles, an experimentalestimate of the surface area per molecule is needed to set upthe simulations. This parameter can be obtained from gravimetricdata, X-ray diffraction, or NMR experiments.17,18However, thesurface area determined from different experiments over theyears has an enormous range, and it has been shown that thisquantity can vary as much as 25% for the biologically relevantfully hydrated liquid crystalline dipalmitoylphosphatidylcholine(DPPC) bilayers.17 On the other hand, in the NPNγT ensemble,it is the surface tension that must be specified. Surface tensionis a macroscopic quantity and the precise value ofγ is thesubject of debate in the recent literature.19-22 It has been arguedthat the surface tension must be zero for an unstressed bilayerat its free energy minimum,20 and hence an NPT ensemble hasbeen used in many simulations.6,9 Although direct determinationof γ for bilayers is not available, based on the values obtainedfrom analogous systems (oil/water and fatty acid/water) and alsofrom monolayer data,23-27 a finite surface tension value has beensuggested for microscopic membrane patches typically used inthe simulations.2,19 The membrane patches in the simulationsare only a few nanometers long, whereas the actual size of themembrane is∼ 1 µm. Feller and Pastor21 argued that in orderto produce macroscopic features, simulations of microscopicmembrane patches should be carried out with a nonzero appliedsurface tension even if the macroscopic surface tension is zeroor close to zero. A compromise has been implemented in severalsimulations by using the NPNAT ensemble in which the surfacearea of the lipid was taken from experimental values and onlytheZ-axis was adjusted against the atmospheric pressure.7,28Theresults of these simulation studies obviously depend on theaccuracy of the experimental estimate of the surface area.

Simulations with a fully flexible cell should, in principle, yieldthe membrane dimensions (and hence the surface area per lipid)directly from the results. Allowing this flexibility in theparameters of the system is especially important since membrane-bound compounds such as peptides, proteins, and other mol-ecules that are often included in the simulated systems are likelyto influence their surface area and other membrane properties.Estimating the surface area per lipid in such complex hetero-geneous systems will be complicated, and in these cases theuse of an NPNγT ensemble seems appropriate. In the simulationsof a pure dimyristoylphosphatidylcholine (DMPC) bilayer, Chiuet al.19 have used the NPNγT ensemble and applied a negativetangential pressure that corresponds to 28 dyn/cm per interface.Feller and Pastor2 simulated a membrane patch of 72 DPPClipids and showed that the value of applied surface tension forthis system should be 35-45 dyn/cm per interface. It shouldbe noted that the choice ofγ value is sensitive to the potentialenergy function in the force field, to the method of forcetruncation, and to system size.22

To investigate the mode of selection ofγ values, we havecarried out the molecular dynamics simulations described herefor a neat DMPC bilayer comprising 90 lipids using NPNγT

and NPNAT ensembles. We have analyzed the effect of forcetruncation for both NPNγT and NPNAT ensembles. The mem-brane structural properties were studied comparatively in NPNγTensembles with a spherical cutoff of 18 Å and PME, usingdifferent γ values. In parallel, we tested the sensitivity of thecalculatedγ value in NPNAT ensembles for four differentspherical cutoffs and compared theγ values with that obtainedfrom the PME simulation. In addition to the neat bilayersimulations, simulations are also presented here for the membrane-bound opioid peptide dynorphin A(1-13), in which the structureand peptide orientation in the membrane were investigated withdifferentγ values in NPNγT simulations using a spherical cutoffof 18 Å and PME. In total, 18 simulations of neat bilayers and6 simulations of the peptide in the bilayers were carried out forperiods of 2 ns to 4 ns. While the results of neat bilayersimulations using PME agree with the earlier simulation studiesusing a CHARMM force field2 utilizing similar γ values, butthe sameγ values with cutoff 18 Å in NPNγT ensembles yieldsignificantly different membrane properties. Notably, theγ valueobtained from the NPNAT ensemble using the 18 Å cutoff ismore than 1 order of magnitude higher than that obtained usingPME. Our results demonstrate that long-ranged electrostaticinteractions with the proper choice ofγ value are needed toproduce membrane structural and physical properties that arein good agreement with experiment. Spherical cutoffs as longas 18 or 21 Å still result in serious artifacts. In the simulationsof the membrane-bound peptide, theγ values are critical,because those that produce smaller surface area per lipid werefound to give rise to distortions of the peptide structure, or tounlikely orientations of peptide side chains.

Methods. The program CHARMM10 was used with the all-atom PARM22b4b parameter set29 that includes parameters forphospholipids11 and TIP3P water potentials.30 The CPT (constantpressure and temperature) module of CHARMM was used forthe constant pressure/temperature simulations. The simulationswere carried out at 330 K (57°C) and the temperature wasmaintained by means of the Hoover thermostat.31 The membranenormal was oriented along theZ axis with the center of thebilayer atZ ) 0. The SHAKE32 algorithm was used to fix thebond lengths involving all hydrogen atoms. A time step of 0.002ps was used. The initial structure of pure bilayers and themembrane-bound peptide dynorphin A(1-13) were constructedusing the protocol developed by Woolf and Roux.33

Neat Bilayers. NPNγT Ensembles. The periodic simulationcell contained 90 DMPC molecules (45 per monolayer) and∼30 water molecules per lipid amounting to a full hydration ofthe bilayer (total:∼ 18 700 atoms). In the NPNγT ensemble, afully flexible simulation cell was employed with theZ-directionadjusted to maintain the normal pressure of 1 atm. TheX andY dimensions were varied to maintain the desiredγ value.Pressure and surface tensions were maintained at their chosenvalues by means of the Langevin Piston algorithm that is avariant of the extended system formalism.34 A piston mass of500 amu and a collision frequency of 5 ps-1 were used in thesimulations. The initial area of the phospholipid was set at 63.1Å2, a value close to the recent experimental estimate18 for DMPCbilayers at 50°C. This estimate for the value at 50°C wasobtained by Nagle and Tristram-Nagle18 by using the area perDMPC molecule at 30°C and the thermal expansion adjustment;notably, this value is quite close to the experimentally deter-mined area per DPPC molecule at 50°C. The periodic systemconsisted of a rectangular box with dimensions 53.3× 53.3×62.4 Å3. Two schemes were used to calculate the nonbondedinteractions, namely a spherical cutoff at 18 Å and PME.

Surface Tension Parameterization in Simulations J. Phys. Chem. B, Vol. 108, No. 31, 200411803

For “spherical cutoff 18 Å”, the nonbonded list was generatedusing a group-based cutoff of 18 Å. Both the electrostatic andvan der Waals interactions were smoothly switched to zero from14.0 to 17.0 Å.

In the PME scheme, the Lennard-Jones (LJ) potential wasswitched smoothly to zero over the region from 10 to 12 Å.PME was used to calculate the electrostatic interactions with aB-spline order of 4 and a FFT grid of 64× 64 × 81. A real-space Gaussian-width kappa of 0.32 Å-1 was used. A neighborlist, used for calculating the LJ potential and the real spaceportion of the Ewald sum, was kept to 14 Å using an atom-based cutoff and updated every 10 fs.

For a spherical cutoff of 18 Å, we used a series ofγ values:0, 10, 20, 45, 65, and 85 dyn/cm. A higherγ value of 625 dyn/cm (see below) was also used with a spherical cutoff of 18 Å.Surface tensions of 0, 20, 25, 30, and 45 dyn/cm were used inthe PME simulations (Table 1). The values of surface tensionare given on a per-interface basis throughout this paper.

To investigate the influence of van der Waals (vdW)contributions on membrane properties, an additional simulationwas carried out in the PME scheme with the LJ potentialswitched smoothly to zero over the region 14.0 to 17.0 Å aswas done in the spherical cutoff simulations. Aγ value of 45dyn/cm was used in this simulation (PME-I in Table 1).

NPNAT Ensembles. Five NPNAT simulations were carried outusing PME and four different spherical cutoffs. The lateraldimensions of the simulation cell, X and Y, were fixed in thesesimulations so that the surface area per lipid remains close tothe recent experimental estimate of 63.1 Å218 throughout thesimulations. Cutoff values used to calculate the nonbondedinteractions were 12, 15, 18, and 21 Å. The nonbonded listswere generated using a group-based cutoff and they weresmoothly switched from 8 to 11, 11 to 14, 14 to 17, and 17 to20 Å for cutoffs 12, 15, 18, and 21 Å respectively (Table 1).The details of PME simulations are the same as those in theNPNγT simulations above.

The surface tensionγ (per interface) was calculated for eachof the NPNAT simulations from the pressure tensor using theequation

whereLz denotes the length of the unit cell along the bilayernormal andPzz is the component of the pressure tensor normalto the membrane surface.Pxx andPyy are tangential componentsof the pressure tensor.

Dynorphin A(1-13) in DMPC Bilayers. In the periodicsystem, the top layer contained 41 DMPC lipids and the opioidpeptide dynorphin A(1-13) [Dyn A(1-13)], and the bottomlayer contained 45 lipids. The construction of the dynorphinpeptide-lipid complex has been described in detail.35,36 Theamino acid sequence of this peptide is YGGFLRRIRPKLK. TheNMR conformation of dynorphin in DPC micelles37 was usedas a structural template for the peptide in which the first nineresidues assumed anR-helical conformation. Previous simula-tions of this peptide were carried out using an NVE ensemble.35

Here, effects of the flexible cell in influencing the peptidestructure and orientation were investigated using NPNγTensembles. As in the case of neat bilayers, two different schemeswere used to calculate the nonbonded interactions, namely thespherical cutoff of 18 Å and PME. When PME was used in thesimulations, 5 chloride ions (Cl-) were added near the site ofthe basic residues so that the entire system was electricallyneutral.

Surface tension values used in the 18 Å cutoff simulationswere 0, 45, 65, and 625 dyn/cm. Theγ value used in the PMEsimulation is 25 dyn/cm. For comparison purpose, a simulationusing the NPNAT ensemble was also carried out with thespherical cutoff of 18 Å. The details of simulations using thespherical cutoff of 18 Å and PME are the same as those usedin the neat bilayer simulations.

The summary of all the simulations performed for neatbilayers and the membrane-bound peptide is given in Table 1.

Simulation Details. Initial structures of neat bilayers werefirst coupled to a heat bath at 330 K, and Langevin dynamicssimulations of 100 ps were carried out at constant volume. Aplanar harmonic restraint was applied on the center of mass(CM) of the lipid atoms to maintain the planarity of themembrane. A further 150 ps of simulation were carried out usingan NVE ensemble during which time the restraints weregradually removed.

In the case of the Dyn A(1-13)-lipid system, in addition tothe restraints on the lipid atoms, positional harmonic restraintswere applied on the peptide atoms during the 100 ps Langevindynamics at constant volume. During the subsequent 150 pssimulations in the NVE ensemble, a cylindrical harmonicrestraint was applied on the CM of theR-helical residues 1-9and, as in the neat bilayers, a planar harmonic restraint wasapplied on the CM of lipid atoms. At the end of the 150 pssimulations, all of the restraints were removed.

The systems were then simulated using NPNγT or NPNATensembles for a period of 2 to 4 ns. The first nanosecond wasconsidered the equilibration phase and hence all the analyseswere done on the structures saved after 1 ns. To facilitatecomparison, the results from the analyses are presented from 1to 2 ns for all the simulations.

Results

Neat Bilayers: Cutoff 18 Å vs PME in NPNγT Ensembles.Surface Area. Knowledge of surface area per lipid can becorrelated with many of the membrane structural and physicalproperties (e.g., order parameters, bilayer thickness, conforma-tion of acyl chains, etc.) and hence this is considered to be themost central structural quantity. Molecular dynamics trajectoriesof surface area per lipid are plotted for simulations using aspherical cutoff of 18 Å (Figure 1a) and PME (Figure 1b). Useof γ ) 0 results in contraction of the box in both the cutoff 18Å and PME simulations. In PME, this effect is much moredramatic, as observed in earlier studies.2 The nonzeroγ values

TABLE 1: Summary of the Simulations Performed on NeatBilayers (90 DMPC lipids) and Dyn A(1-13)-bilayer Systems

system cutoff/PME ensemble γ (dyn/cm)

neat bilayers cutoff 18 Å NPNγT 0, 10, 20, 45, 65, 85, 625neat bilayers PME NPNγT 0, 20, 25, 30, 45neat bilayers PME-Ia NPNγT 45neat bilayers cutoff 12 Å NPNATneat bilayers cutoff 15 Å NPNATneat bilayers cutoff 18 Å NPNATneat bilayers cutoff 21 Å NPNATneat bilayers PME NPNATdyn A(1-13) - bilayers cutoff 18 Å NPNγT 0, 45, 65, 625dyn A(1-13) - bilayers PME NPNγT 25dyn A(1-13) - bilayers cutoff 18 Å NPNAT

a A neighbor list, used for calculating the LJ potential and the realspace portion of the Ewald sum, was kept to 18 Å using an atom-based cutoff and updated every 10 fs. LJ potential was switchedsmoothly to zero over the region from 14 to 17 Å. In all other PMEsimulations, a neighbor list was kept to 14 Å using an atom-based cutoffand the LJ potential was switched to zero from 10 to 12 Å.

γ ) 1/2 {<LZ × (Pzz - 1/2 Pxx - 1/2 Pyy)>} (1)

11804 J. Phys. Chem. B, Vol. 108, No. 31, 2004 Sankararamakrishnan and Weinstein

yield significantly different results in PME compared to thecutoff 18 Å simulations.

In PME, the surface area becomes larger (> 70 Å2) at theend of the 2 ns simulation forγ ) 30. Forγ ) 45, the areaexpansion is sudden and very large right from the beginning ofthe simulation, reaching a value of more than 75 Å2 within thefirst 500 ps of the simulation. The average value of the surfacearea becomes much larger (∼ 110 Å2) at the end of the 2 nssimulation indicating that the system no longer represents theliquid crystalline state of a DMPC bilayer. Forγ ) 20, the areastays reasonably close to the experimental estimate of∼ 63 Å2

during the first 1 ns of the simulation, but later drifts to∼ 55Å2. Forγ ) 25, the area remains close to the experimental valuefor the major part of the simulation. Even here, at the end ofthe 2 ns simulation, a drop is observed in the value of the surfacearea.

With all theγ values tested,γ ) 25 appears to give the mostreasonable value for the surface area. This agrees well withsimilar studies carried out for a system of 72 DPPC lipids.2

For that system, the correct surface tension to apply wasrecommended in the range of 35-45 dyn/cm. The presentsystem of 90 lipids is larger and hence a smaller value of surfacetension is anticipated.21 With the results from the reasonablylong simulations of 2 ns, our studies suggest that theValue ofsurface tension for the system containing 90 lipids should bein the range of 25 to 30 dyn/cm when PME is used to calculatethe nonbonded forces.

In the simulations using a cutoff of 18 Å, theγ values rangingfrom 0 to 85 dyn/cm yield properties that are significantlydifferent from those observed in PME simulations. Even withγ ) 85, the simulation results in a smaller box size in cutoff18 Å simulations. The average surface area at the end of thesesimulations lies between∼ 57 to∼ 59 Å2, a decrease of 4-6Å2 from the experimental estimate of 63 Å2.18 When thesimulation forγ ) 45 dyn/cm was extended for an additional2 ns, no change was observed in the area that remained closeto 57 Å2 (data not shown).

Surface tension values were calculated from NPNAT simula-tions using Equation 1 (see Methods). Trajectories of surfacetension are plotted for a cutoff of 18 Å and PME simulationsin Figure 2. Using 50 ps block averages to estimateγ values,PME simulation yields values between 15 and 35 dyn/cm duringthe last 500 ps of simulation. For the same period, the averageγ values calculated for cut off 18 Å simulations is close to 625dyn/cm, more than 1 order of magnitude higher than thatcalculated from PME simulations. When theγ ) 625 dyn/cmvalue is used with 18 Å cutoff, the surface area per lipid remainsclose to the experimental value (Figure 1a).

The average surface area and the tangential pressure calcu-lated from the last 500 ps of simulations are plotted againsttheir respective surface tensions for both the spherical cutoffof 18 Å (Figure 3a) and PME (Figure 3b). The curves wereobtained using a polynomial curve fitting procedure.38 Clearly,only a slight increase in the surface area is observed in the 18Å cutoff when the surface tension was increased from 0 to 85dyn/cm; the decrease of the tangential pressure is morepronounced. In PME, both the increase in surface area and adecline in tangential pressure were steep whenγ was raisedfrom 20 to 45 dyn/cm. The tangential pressure was close to-80 atm forγ ) 25 dyn/cm (PME) and∼ -1950 atm forγ )625 dyn/cm (cutoff of 18 Å). It should be noted that a tangentialpressure value of-100 atm for a system of 100 DMPC lipidswith the hydrated lipid thickness of 55 Å was derived usingmonolayer data.19 The γ value of 25 to 30 dyn/cm obtainedfrom the PME simulations for the system of 90 lipids is similarto the surface tension value derived from MD simulations fora system of 72 lipids.2

Bilayer Thickness. The average bilayer and hydrophobicthickness calculated during the last 1 ns production runs aregiven in Table 2 for all the neat bilayer simulations. It is clearthat for cutoff 18 Å simulations the bilayer thickness is about2 Å higher when the value ofγ is between 0 and 85 dyn/ cm.For PME simulations, whenγ ) 0 (or 45), the thickness is toohigh (or low), indicating that the system no longer represents aliquid-crystalline state. The bilayer and hydrophobic thickness

Figure 1. Molecular dynamics trajectories of surface area per lipidfor the neat bilayers using NPNγT ensembles. (A) Spherical cutoff of18 Å and (B) PME.γ ) 0 results in contraction of the box length inboth a cutoff of 18 Å and PME simulations. The results show thatvalue ofγ for a system of 90 lipids should be in the range of 25 to 30dyn/cm when PME is used in the simulations. In the simulations usinga cutoff of 18 Å, theγ value has to be increased to 625 dyn/cm tokeep the surface area per lipid close to the experimental estimate of 63Å2. This is more than an order of magnitude higher than that used inthe PME simulations. In the case of NPNAT ensembles, the surfacearea per lipid was taken close to the experimental estimate for the neatDMPC bilayers.


evaluated forγ ) 625 dyn/cm with a cutoff of 18 Å and forthe two NPNAT simulations are very close to the values obtainedfrom experiments and previous molecular dynamics simulationsfor DMPC bilayers.5,39-41 Analysis for the PME simulationsagain confirms that the appropriateγ value for simulations islikely to be between 25 and 30 dyn/cm for the system consideredin the present study.

Order Parameters. The values of the order parameters forthe sn-2 chain are given in Figure 4 for the simulations usingγ ) 25 and 30 (PME) and 625 (cutoff of 18 Å). Data from thetwo NPNAT simulations are also plotted in the same figure. Itis clear that the general features observed experimentally arepresent in the NPNAT simulations and for the analyzedγ values.For PME,γ ) 30 dyn/cm shows the best agreement with theexperimentally observed profiles.42

Long-range Electrostatics orVan der Waals?The significantdifferences observed for the sameγ value in the two sets ofsimulations (spherical cutoff of 18 Å and PME) point clearlyto the fact that the neglect of long-range interactions lead toserious artifacts. In simulations where long-range electrostaticinteractions are explicitly included, a 12 Å cutoff was used tocalculate the van der Waals (vdW) interactions. In sphericalcutoff simulations, vdW interactions were truncated at 17 Å.Beyond the contact distance, vdW interactions are alwaysnegative and this may give rise to a speculation that the increasedvdW cutoff in spherical cutoff simulations might be the causeof the shrinkage of area for a givenγ value. To investigate thecontribution of vdW interactions, we carried out an additionalPME simulation withγ ) 45 dyn/cm. In this simulation, aneighbor list to calculate the LJ potential and the real spaceportion of the Ewald sum was kept to 18 Å using an atom-

Figure 2. MD trajectories of surface tension calculated for the neatbilayer simulations using NPNAT ensembles. (A) Cutoff of 18 Å and(B) PME. Both 1 ps (black) and 50 ps (white) block averages areplotted.

Figure 3. Average surface area (b) and the tangential pressure (9)calculated for the last 500 ps are plotted against the surface tension forthe neat bilayer simulations using NPNγT ensembles. (A) Sphericalcutoff of 18 Å and (B) PME method. A polynomial curve fittingavailable in the KaleidaGraph package was used to obtain the curves.


based cutoff and the LJ potential was switched smoothly to zeroover the region from 14 to 17 Å, as was done in spherical cutoffsimulations. All other parameters were same as that of the otherPME simulation with the sameγ value. Comparison of MDtrajectories of surface-area per lipid (Figure 1b) shows that thetwo PME simulations withγ ) 45 dyn/cm are almost similar,although the vdW cutoff to calculate the LJ potential is increasedby 4 Å. If the neglected long-ranged vdW forces are responsiblefor the shrinkage of area, then the PME simulation with a longerreal-space cutoff (PME-I) would have resulted in a smallersurface area per lipid. This clearly demonstrates that theshrinkage of area observed in the simulation using an 18 Åcutoff with γ ) 45 dyn/cm is NOT due to the increased vdWinteractions and is due to the neglect of long-ranged electrostaticinteractions.

Clearly, the surface tension of 625 dyn/cm that can maintainthe experimental area of the lipid in the cutoff 18 Å simulationsis too high, and this must be an artifact of the spherical cutoffmethod. When PME is used for a system of 90 lipids, a valueof γ between 25 and 30 dyn/cm is expected to keep the surfacearea per lipid, other membrane structural properties, and lateralpressure. Thus the above set of simulations demonstrates thatthe neglect of long-range electrostatic interactions will haveserious shortcomings in lipid simulations.

NPNAT Ensembles: Cutoffs 12, 15, 18, and 21 Å, and PME.Influence of force-truncation methods in determining the surfacetension values was investigated in simulations with NPNATensembles. Surface area (A) in these simulations was maintainedclose to the experimentally determined value.18 Average ((standard error) values of surface tension, tangential, and normalpressure were analyzed (Table 3). The values from the cutoffsimulations were compared with that of PME simulation usingthe same NPNAT boundary conditions. Calculated surfacetension values for different NPNAT ensembles range from∼300 (for 12 Å) to 625 (for 15 and 18 Å) dyn/cm with no cleartrend available. This is true also for average tangential andnormal pressure values. Even when the cutoff is increased to21 Å, the surface tension value is still high, and higher thanthat obtained from a smaller cutoff of 12 Å. However, thecalculated surface tension for NPNAT simulation with PME is28.6 dyn/cm and the tangential pressure is-92.8 atm. For asystem of 90 lipids, these values appears very reasonable.2,19

Also from the set of NPNγT simulations with differentγ values,when long-ranged electrostatic interactions were explicitlyincluded, aγ value between 25 and 30 dyn/cm is expected tomaintain the membrane fluid-phase properties for the systemconsidered here (see above).

Dyn A(1-13) in DMPC Bilayers NPNγT Ensembles.Theopioid peptide Dyn A(1-13), like other peptide hormones, isbelieved to bind the membrane first before reaching the targetreceptors.43,44We have previously simulated this peptide in theNVE ensemble and studied the membrane-binding propertiesof this peptide.36 The results of these simulations have shownthat theR-helical region of the peptide is stabilized within thebilayers by special interactions that are due to the nature andposition of the aromatic and the basic residues in the peptide.The long side chains of the arginine residues interact with allcomponents of the lipids, giving rise to a type of interactionsidentified as the “snorkel-model”. The aromatic residues Tyr-1and Phe-4 are key for the positioning of the peptide in thebilayer,36 but behave differently. Thus, the simulations showedTyr-1 interacting with the lipid headgroups, while the side chainof Phe-4 prefers to be close to the more hydrophobic membraneinterior. The N-terminalR-helical structure of the peptideremained stable from residues 4 to 9 throughout the simulations.

To evaluate the effect of surface tension on the calculatedproperties of the membrane-bound peptide, we simulated DynA(1-13) in DMPC bilayers using NPNγT ensembles. A fully

Figure 4. Order parameter profiles for the sn-2 chain from the neatbilayer simulations using NPNγT and NPNAT ensembles. Only thoseNPNγT simulations in which theγ value keeps the surface area perlipid close to the experimental value are included (625 dyn/cm with acutoff of 18 Å; 25 and 30 dyn/cm with PME). For NPNAT simulations,data are shown both for a cutoff of 18 Å and PME.

TABLE 2: Average and Root-mean-squared Fluctuations ofBilayer and Hydrophobic Thickness. The Parameters AreCalculated for the Last 1 ns Production Runs for All NeatBilayer Simulations

γ (dyn/cm) -cutoff of 18 Å

bilayerthickness (Å)

hydrocarbonthickness (Å)

0 37.7 (0.2) 26.6 (0.2)10 37.8 (0.2) 27.0 (0.2)20 37.1 (0.3) 25.8 (0.2)45 37.3 (0.2) 26.5 (0.2)65 37.2 (0.2) 26.7 (0.2)85 37.0 (0.2) 26.2 (0.2)

625 35.1 (0.2) 24.4 (0.2)NPNAT 34.8 (0.3) 24.0 (0.2)

γ (dyn/cm) - PME0 40.8 (0.2) 28.3 (0.2)

20 38.5 (0.5) 26.4 (0.4)25 37.0 (0.5) 24.9 (0.5)30 33.0 (0.8) 21.2 (0.8)45 25.5 (1.9) 14.5 (1.8)

NPNAT 35.2 (0.3) 23.7 (0.2)

TABLE 3: Average (Standard Error) Surface Tension (γ),Tangential (Ptangential), and Normal (Pnormal) PressureCalculated from the NPNAT Simulationsa

cutoff γ (dyn/cm) Ptangential(atm) Pnormal (atm)

12 Å 297.4 (3.7) -942.2 (7.9) -0.9 (10.3)15 Å 622.9 (3.9) -1997.6 (8.3) 0.1 (10.1)18 Å 625.6 (3.6) -1981.7 (8.1) 12.6 (10.2)21 Å 486.2 (4.1) -1568.7 (8.3) -13.6 (11.0)PME 28.6 (3.3) -92.8 (6.9) -2.9 (10.0)

a The parameters were calculated for the last 500 ps of 2 nsproduction runs.


flexible simulation cell will allow the lipid bilayer to expandor contract when a peptide is added so that the peptide canassume an optimum orientation inside the bilayers. Here again,an estimate of surface tension value is necessary to use NPNγTensembles. This becomes more complicated due to the fact thataddition of compounds in the membrane is expected to influencethe surface tension of the bilayer. As in the neat bilayersimulations, we have carried out simulations using NPNγTensembles for differentγ values. Two schemes (cutoff of 18 Åand PME) to calculate the nonbonded forces were used in thesimulations as described above. For comparison purposes, DynA(1-13) in the DMPC bilayers was simulated using the NPN-AT ensemble with a cutoff of 18 Å, and the surface area/lipidused in NPNAT simulations was taken from the experimentalestimate for the neat bilayers.18 The influence ofγ on thestructure and orientation of the peptide is studied in comparisonto the neat membranes. The simulation results of NPNγTensembles are also compared with simulations using NPNATand NVE35,36 ensembles.

The molecular dynamics trajectories of surface area areplotted for simulations with differentγ values in Figure 5. Asobserved in the neat bilayers, the area decreased rapidly beforethe first 500 ps simulations forγ ) 0, 45, and 65 dyn/cm whena spherical truncation was used. The average area for the last500 ps simulations is in the range of 57-59 Å2. This is about4-6 Å2 less than the experimental value estimated for the neatbilayers.18 For γ ) 625 dyn/cm (a value obtained from NPNATneat bilayer simulations with a cutoff of 18 Å) the area ismaintained close to the experimental estimate for neat bilayers.For the system of 90 DMPC lipids studied here,γ ) 25 dyn/cm, and the use of PME yields a surface area close to the experi-

mental estimate for neat bilayers. It is also clear that the fluctua-tion in the surface area is larger in PME simulation. In all thesesimulations of the peptide-bilayer system, the surface area/lipid is similar to that observed in neat bilayers in NPNγTensembles.

Dyn A(1-13) Peptide Structure in Bilayers. The structuresof Dyn A(1-13) peptides at the end of 2 ns production runsfrom all the simulations are plotted in Figure 6. For comparison,Figure 6 includes the previously published initial structure, andthe structure saved at the end of 8 ns production run from NVEsimulation.36 It is clear that the N-terminal helical region of thepeptide remained within the bilayers in all the simulations. InNVE simulations, residues 4 to 9 retained anR-helical structureat the end of 8 ns production run.36 However, closer examinationreveals that the helix is distorted for some of theγ values usedin the simulations. The average values of backbone dihedralanglesφ andψ for residues 4 to 9 are plotted for all simulationsin Figure 7. Averageφ andψ values calculated from the first500 ps of the production runs (Figure 7a and 7b) are comparedto those from the last 500 ps of 2 ns productions runs (Figure7c and 7d) in all the simulations. Forγ ) 0, 45, and 65 thatresulted in shrinkage of the box size, theφ, and ψ valuesdeviated significantly from theR-helical structure (Figure 7c).The γ values that maintained the lipid surface area (625 for acutoff of 18 Å and 25 for PME), or the NPNAT simulations inwhich the area is fixed to the experimental value, maintainedthe helical structure (Figure 7d). Even a distortion in theC-terminal end of the helix observed in the first 500 ps of theproduction run in theγ ) 625 dyn/cm with an 18 Å cutoffsimulation (Figure 7b) disappeared during the last 500 ps ofthe 2 ns production run (Figure 7d). It appears that the smaller

Figure 5. Molecular dynamics trajectories of surface area per lipid for the bilayers in which Dyn A(1-13) is imbedded. Data are for four differentγ values (0, 45, 65, and 625 dyn/cm) that used a cutoff of 18 Å, andγ ) 25 dyn/cm with PME using NPNγT. Results from simulations using anNPNAT ensemble in which the surface area is close to the experimental value for the neat bilayer are shown for comparison.


surface area leaves little breathing space for the peptide, and asa result a structural distortion is observed forγ ) 0, 45, and 65dyn/cm.

In previous NVE simulations,35,36 the two aromatic residuesTyr-1 and Phe-4 showed different behavior that reflected thechemical nature of the side chains. The side chains of Tyr-1

and Phe-4 pointed toward the membrane-water interface andthe bilayer interior, respectively. Whenγ ) 0 dyn/cm was usedwith a cutoff of 18 Å, the smaller box size appears to haverestricted the movement of the peptide helix(Figure 5). As aresult, instead of moving upward toward the lipid headgroupregion, the side chain of the Tyr-1 residue moved in this

Figure 6. Structures of Dyn A(1-13) at the end of 2 ns production runs are plotted for all the peptide-bilayer simulations. For comparison, theinitial structure and the structure saved at the end of the 8 ns production run from the previous NVE simulation are also shown. Theγ values usedin the simulations, and the use of PME, are indicated in each plot as appropriate (all other simulations use the cutoff of 18 Å). For details of NVEsimulation, see.35,36 For clarity, lipid molecules are not shown in this figure.

Figure 7. Average backbone dihedral anglesφ (blue) andψ (red) calculated for the first (Figure 7a and 7b) and last (Figure 7c and 7d) 500 ps ofproduction runs. Simulations using NPNγT ensembles with a cutoff of 18 Å are plotted forγ values 0 (b), 45 (9), and 65(2) in the left. Data forNPNγT ensembles with a cutoff of 18 Å and PME are plotted forγ values 625 dyn/cm (b) and 25 dyn/cm (2). For comparison, results fromNPNAT ensembles using a cutoff of 18 Å (9) are also shown.


simulation to the opposite side, toward the other half of thebilayer, and attracted water molecules from that side.

Discussion

The importance of achieving an accurate representation ofthe phospholipid membrane environment in simulations of cell-surface systems is well established. Among the parameters thatdetermine the quality of the representation in such simulations,the surface tension is being recognized as playing a key role.Thus, while experimentally based surface area/lipid knowledgehas improved over the years and the value obtained for thisquantity is more reliable from improved experimental techniquesand MD simulations, the surface tension value is still debatedand estimated indirectly. As demonstrated in this study and inprevious work on such systems,2,21 it depends sensitively onvarious factors. The results show that the influence of force-truncation methods on the surface tension is serious and cannotbe overlooked.

To evaluate the specifics of the dependence of simulationresults on this key parameter, we have carried out 13 simulationsof neat bilayers of 90 DMPC lipids using NPNγT ensembleswith a cutoff of 18 Å and PME. Another 5 simulations of thesame system were carried out using NPNAT ensembles withPME and four different truncation schemes. The results of thesesimulations show significant differences between a cutoff of18 Å and PME. Although 18 Å is generally considered as asufficiently long cutoff, the calculated surface tension value,lateral pressure (in NPNAT simulation), surface area per lipid,and other membrane structural properties (in NPNγT simula-tions) are significantly different from the experimental results18,27

or from other computational studies.2,19 Comparison of PMEsimulations with differentγ values and different real spacecutoffs clearly demonstrates the role of long-ranged electrostaticinteractions in membrane simulations. In PME simulations, thesurface tension value that maintains the properties of the bilayerof this size (90 lipids) is expected to be between 25 and 30dyn/cm. On the other hand, surface tension value of more thanan order of magnitude is required for 18 Å cutoff simulationsto maintain the membrane fluid-phase properties. Differencesbetween cutoff and PME simulations have been observed inearlier simulations also using the CHARMM force field.45

Simulations of DPPC bilayers have shown that theγ valuecalculated from a cutoff of 12 Å is about 20 dyn/cm larger thanthat from Ewald potentials. This is a very small differencecompared to the present studies and may be due to the largersurface area considered during NPNAT ensembles. In general,the results obtained from PME simulations for the system of90 DMPC lipids (withγ ) 25-30 dyn/cm) agreed with theexperimental results and earlier simulation studies on 72 DPPClipids.2 It should also be noted that the present simulations havebeen carried out for a longer duration of 2 ns with the first 1nanosecond considered as an equilibration phase.

Our simulation results with the CHARMM force field havebeen compared here to previous simulation studies from Fellerand Pastor.2,21Comparison of simulations using CHARMM andGROMACS force fields and between different GROMACSsimulations has been much more difficult due to various factors.First, the CHARMM simulations include all atoms, whileGROMACS uses a united atoms model for nonpolar hydrogens.In GROMACS simulations, Chiu et al.19 have used a nonzerosurface tension for neat bilayers while Lindahl and Edholm6

advocated an NPT ensemble with zero surface tension. Inaddition to different van der Waals parameters used in the lattersimulations, the 1,4 electrostatic interactions and the van der

Waals interactions were reduced by factors of 2 and 8,respectively. Two recent papers have studied the influence oftruncating electrostatic interactions in DPPC bilayers using theGROMACS force field.46,47 They support the conclusion fromthe present studies that long-ranged electrostatic interactions areneeded to maintain the fluidlike properties of bilayer membranes.Both studies used an NPT ensemble with a surface tension valueof 0. A lateral and normal pressure of 1 bar was applied. Patraet al.46 have studied DPPC bilayers over a time scale of 20 nsusing three different truncation schemes (18, 20, and 25 Å) andPME. In the simulations that used truncation schemes, theobservations included small surface areas per lipid, enhancedordering of acyl chains, and artificial ordering of lipids in theplane of the membrane; the lipid bilayer was no longer in atruly fluidlike state. Comparison with PME simulations led Patraet al.46 to conclude that truncation of electrostatic propertiescan have serious consequences for the structural and electrostaticproperties of lipid bilayer systems. Studies of Anezo et al.47

reached the similar conclusion that for the simulation of fluid-phase bilayers Ewald techniques are more appropriate thanstraight cutoff methods. In this series of simulations, increasingthe electrostatic cutoff resulted in further decrease in the surfacearea per lipid. The area contraction observed in the straightcutoff techniques is attributed to the small lateral dipolemoments of lipid headgroups.

Notably, the significant difference between the studies of Patraet al.46 and Anezo et al.47 is in the treatment of surface tensionvalue. While simulation studies with GROMACS parametersused a surface tension value of 0,46,47 we investigated here theinfluence of truncation on this crucial parameter with a nonzerovalue in membrane simulations (see Introduction). Previouslysuggested surface tension values for finite size membrane patchsimulations typically lie in the range of 20 to 45 dyn/cm.2,19 Arange of nonzero surface tension values was used in the presentsimulations coupled with different schemes to calculate thenonbonded interactions. It is evident that neglect of long-rangedelectrostatic interactions results in serious artifacts forγ valuesless than 100 dyn/cm. With the truncation method, only anonzero value of several hundred dyn/cm can maintain thestructural and physical properties of the membrane. If long-ranged electrostatic interactions are taken fully into account, asurface tension value between 25 and 30 dyn/cm is expected tomaintain the experimentally observed membrane properties fora system size of 90 lipids. This is also supported by NPNATsimulations with PME in which the calculatedγ value is 28.6dyn/cm. The lateral pressure calculated from these simulationsis also close to the value derived from monolayer experimentaldata.19,27The present studies also reveal a steep surface tensiondependence if PME is used in combination with the NPNγTensemble in bilayer simulations.

Our simulations of Dyn A(1-13) in DMPC bilayers showthat surface tension values that result in a smaller area/lipid arelikely to affect the structure of the peptide embedded in themembrane. With zero surface tension, the residues of the peptidedid not appear to have enough freedom to move due to theshrinkage of the box. All other simulations with nonzero surfacetension show the characteristic interactions of aromatic residues.Chiu et al.41 have simulated the gramicidin channel in a DMPCbilayer using an NPNγT ensemble with a nonzero surfacetension. Simulations of bacterial membrane proteins, KcSApotassium channel, and FhuA show less drift in the initialstructure if PME is used to treat the long-range electrostaticinteractions.48 Recent simulation studies on a potassium chan-nel,49 aquaporin,50 and glycophorin A51 have all been performed


with an NPNAT ensemble and a fixed surface area. Only theZ-direction (bilayer normal) was allowed to vary to maintainthe constant normal pressure. It is clear from this work thatinclusion of peptides and other compounds complicates thesituation, and that the inserts have a direct bearing on themembrane properties such as surface area and surface tension.Results from the simulations of the membrane-bound com-pounds in NPNγT ensembles have to be treated with cautionand preferably compared with simulations using NPNATensembles.

Acknowledgment. This work was supported by NIH grantsP01 DA-11470, DA-12923, and K05 DA-00060. Computationalsupport was provided by the National Science FoundationTerascale Computing System at the Pittsburgh SupercomputingCenter.

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Documents

Surface Tension Parameterization in Molecular Dynamics Simulations of a Phospholipid-bilayer Membrane: Calibration and Effects