Molecular dynamics simulations of ionic concentration ... · and entropic constraints on hydration shell structure, and may thus play a signiﬁcant role in membrane protein struc-ture

JOURNAL OF CHEMICAL PHYSICS VOLUME 118, NUMBER 4 22 JANUARY 2003

Molecular dynamics simulations of ionic concentration gradients acrossmodel bilayers

Jonathan N. Sachsa)

Department of Biomedical Engineering, The Johns Hopkins University School of Medicine, Baltimore,Maryland 21205

Horia I. PetracheLaboratory of Physical and Structural Biology, NICHD, National Institutes of Health, Bethesda,Maryland 20892

Daniel M. ZuckermanCenter for Computational Biology and Bioinformatics, School of Medicine, University of Pittsburgh,Pittsburgh, Pennsylvania 15213

Thomas B. Woolfb)

Department of Biomedical Engineering, The Johns Hopkins University School of Medicine, Baltimore,Maryland 21205 and Department of Physiology, The Johns Hopkins University School of Medicine,Baltimore, Maryland 21205

~Received 2 July 2002; accepted 29 October 2002!

To model a concentration gradient across a biomembrane, we have performed all-atom moleculardynamics simulations of NaCl solutions separated by two oppositely charged plates. We haveemployed the recently formulated three-dimensional Ewald summation with correction~EW3DC!technique for calculations of long-range electrostatics in two-dimensionally periodic systems,allowing for different salt concentrations on the two sides of the plates. Six simulations were run,varying the salt concentrations and plate surface charge density in a biologically relevant range. Thesimulations reveal well-defined, atomic-level asymmetries between the two sides: distincttranslational and rotational orderings of water molecules; differing ion residency times; a clearwetting layer adjacent only to the negative plate; and marked differences in charge density/potentialprofiles which reflect the microscopic behavior. These phenomena, which may play important rolesin membrane and ion channel physiology, result primarily from the electrostatics and asymmetry ofwater molecules, and not from the salt ions. In order to establish that EW3DC can accurately capturefundamental electrostatic interactions important to asymmetric biomembrane systems, theCHARMM

force-field~with the corrected Ewald sum! has been used. Comparison of the results with previouslypublished simulations of electrolyte near charged surfaces, which employed different force-fields,shows the robustness of theCHARMM potential and gives confidence in future all-atom bilayersimulations using EW3DC andCHARMM. © 2003 American Institute of Physics.@DOI: 10.1063/1.1531589#

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I. INTRODUCTION

Understanding the behavior of ions and water nearpores of ion channels, in the so-called electrical double-lais of prime importance in elucidating ion channel functioIon channels are among the most important transmembproteins involved in signal transduction. Among the mafunctional questions raised by ion channel researchers ision selectivity is achieved. One hypothesis is that themoval of waters from ion-hydration shells, as is requiredion conductivity, may be the rate-limiting step in selectivity1

Therefore, it becomes necessary to understand the strucand dynamic properties of hydrated ions, especially atmembrane–electrolyte interface. The importance of studyion and water behavior at the membrane surface is furhighlighted by experimental data on lipid headgroup confmational dynamics. The degree to which ions disrupt hyd

a!Electronic mail: [email protected]

b!Electronic mail: [email protected]

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tion shell structure—which is sensitive to ion type acharge—affects fluctuations in headgroup structure.2,3 Bi-layer structural properties, including headgroup dynaminfluence transmembrane protein structure and function4–9

and thus we must understand the behavior of hydratednear these surfaces.

Despite the complexity of the membrane–electrolyinterface7—which includes proteins, lipids, water, and salt—there are concrete properties of this region which mayexploited in constructing models of the membrane. Forample, it has been well established that functional properof ion channels, such as conductance level, are quite setive to bilayer surface charge, which is biologically regulatvia the ratio of charged to uncharged lipids. This has beshown extensively in the gramicidin A channel,10–12 thealamethicin channel,13 and K1 channels.14 Further, modelsof bilayers need not be symmetric, as biological membraare known to be asymmetric in lipid composition, and henin charge density. The asymmetric lipid distribution coulddue to a different ratio of negative phosphatidylserine~PS!

7 © 2003 American Institute of Physics

license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

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1958 J. Chem. Phys., Vol. 118, No. 4, 22 January 2003 Sachs et al.

and neutral phosphatidylcholine~PC! lipids in the two leaf-lets. This, in principle, leads to an asymmetry in local ording of water and salt in the double-layer, which could haprofound consequences for the biophysical processesvolved in transmembrane signaling. In addition, one recnizes that the water molecule itself is asymmetric, bothgeometry and in partial charge distribution. The nonsphcal, asymmetric nature of water molecules at the surfacmembranes may play a significant role in influencing hegroup conformations, as well as in determining the strenof interactions between headgroups and ions. Finally, difences in ionic radii may influence the balance of enthaand entropic constraints on hydration shell structure,may thus play a significant role in membrane protein strture and function.

Experimentally, related questions regarding the influeof molecular level interactions, dynamics, and structurebe addressed using spectroscopic and scattering method15,16

In addition, theoretical treatment has provided insight.17,18

Supplementing these techniques are computational simtions, which provide atomic-level descriptions. Both MonCarlo19 and molecular dynamics~MD!20–26simulations havebeen used extensively to study the behavior of water andnext to both charged and uncharged surfaces. Surface chdensity and molecular roughness have been shown to athe orientational distribution of water molecules. Theserameters are directly related to the charge state and chemstructure of lipid headgroups, and thus are relevant to stuof biomembranes. There is extensive literature devotedMD simulations of biomembranes27–33 and transmebraneproteins, including ion channels.34–39 All-atom representa-tion of the bilayer, however, is computationally expensivand hence prohibitive for exploring new methodologieshas been shown that reduced representations of the bilaywhich are computationally more efficient than all-atorepresentations—can provide important insight into funmental properties dictating the biophysical nature of mebrane systems. For example, it has been shown that a laof inducible dipoles can be used to represent the electrosenvironment and for calculations of transmembrane prosolvation free energies.40 The work presented here utilizeMD to simulate a model transmembrane concentration gdient, in which the membrane is represented as two opsitely charged surfaces. Such a reduced representation afor efficient investigation of the detailed behavior of watand salt in this novel, biologically relevant geometry.

Because all-atom simulations that cut off electrostainteractions have well known artifacts,41–44 including severereductions of salt mobility, we apply the Ewald summatitechnique. One methodological aspect of simulationsutilize the Ewald sum is that the system must be replicaperiodically in all three dimensions. Simulations of a tranmembrane concentration gradient have two-dimensioperiodicity, and thus have not been previously performOne solution would be to simulate more than one bilayerunit cell, but this is currently computationally prohibitiveThe problem of simulating systems with two-dimensionperiodicity has been similarly challenging for simulatioof electrical double layers between oppositely charg


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electrodes.23–26,45,46 A rigorously convergent two-dimensional Ewald sum~EW2D! does exist, and is thoughto be the ideal method for long-range electrostatic calcutions in such systems.47–49 While simulations utilizing thismethod have been shown to give good agreement withperimental results,50 the implementation of EW2D is prohibitively slow.23,51,52 One successful alternative adds a shadependent correction term53,54 to the traditional Ewald sumThe corrected method~EW3DC! and EW2D have demonstrated quantitative agreement.24,55 Because the implementation of EW3DC was found to be ten times faster, we adophere. The increase in computational efficiency is crucialstudies of large systems such as biological membranes.

It is important to note that the effectiveness of EW3Dapplied to a bilayerlike setting, as is presented here,yet to be tested. Among the goals of this study is to shthat fundamental properties of the system, such as wateder and hydration, are correctly calculated underCHARMM force-field with EW3DC. Methodologically, thework represents an important modification to previosimulations19,20,24,55,56,as it applies the EW3DC technique ta more biologically relevant geometry, incorporating a cocentration gradient in which electrolyte species interacross a model bilayer. As is discussed below, the mobilayer consists of charged Lennard-Jones spheres, faciing efficient evaluation of the effectiveness of EW3Dthrough a comparison of our results with these other relasystems. Having shown the viability of simulations in thgeometry, it is believed that application of the EW3DC meodology should prove valuable in future all-atom simulatioof biological membranes solvated by electrolyte.

We present here simulations of two NaCl solutions serated by two oppositely charged plates, as shown in FigThe system is constructed to mimic bilayer geometry, wdisparate salt concentrations~in the range of 250 mM to 1M!on the two sides of the plates. The plates are separate34 Å, the approximate width of a typical biologicamembrane.57 The choice of oppositely charged plates modan asymmetric distribution of lipid types between oppos

FIG. 1. Schematic of system setup. Two plates composed of discretespheres~see Methods! are separated by 34 Å of empty space. Concentions on the negative plate side are varied~see Table I!, while they are keptconstant at 250 mM on the positive plate side in all systems. Vacuumgions are placed at the ends of the electrolyte regions to allow for apption of the EW3DC technique for calculation of electrostatic interactioExcess counterions are added, making each side~including the plate! elec-trically neutral.


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1959J. Chem. Phys., Vol. 118, No. 4, 22 January 2003 Ionic concentration gradients across bilayers

monolayers. The plates consist of a square lattice of tigpacked van der Waals~vdW! spheres, which also carry poincharges at their centers, modeling both the roughnessbilayer surface and the discreteness of charge. The surcharge values were chosen to approximate that of biologmembranes, in the range of 0 C/m2 to 0.2 C/m2, which cor-responds to a biologically realistic ratio of charged to ucharged lipids.

Water ordering~both translational and orientational!, iondistributions, and electrostatic potential profiles are analyas functions of plate surface charge density and salt contration. We find asymmetric ordering of water moleculesthe two plates, which is explained as a manifestation ofgeometric and electrostatic asymmetry of the water molecitself. Specific interactions between the oppositely charhydrogens and oxygens, with the oppositely charged plalead to better defined water layers and hydration shell stture on the negative plate side, both of which are in accdance with previously published results.20–22 Simulation de-tails are presented in the next section, followed by resultswater and salt ordering, as well as electrostatic potential pfiles in Sec. III. A discussion of the asymmetries in themolecular orderings follows in Sec. IV.

II. METHODS

A. Simulation setup

Figure 1 shows the general setup for the simulationsorder to establish the viability and efficacy of applyinEW3DC to membrane systems, the design of the systemchosen to match as closely as possible that of Crozieret al.55

with the intention of comparing the results against thosean electrodelike system. The cathode, or negatively chaplate, was placed atz5117 Å, while the anode, or positively charged plate, was placed atz5217 Å. Each 25.5 Å325.5 Å plate was a 17317 lattice of tightly packed vdWspheres of radius 0.75 Å. Single point charges were placethe center of each sphere, the magnitude of which weretermined by the overall plate surface charge density,6s.The position of the spheres was fixed throughout the simlations. Adjacent to each plate, electrolyte regions were beach extending 42.5 Å from the plates, making the total vume of each electrolyte region 27 636 Å3. Vacuum regions2.5 times the cumulative length of the electrolyte and plregions were placed adjacent to the electrolyte regions. Tthe overall dimensions of the simulation cell were 25Å325.5 Å3714 Å. In all simulations the total number oparticles~waters, Na1 and Cl2) per side was kept constant1000.

Four classes of simulation are presented, distinguisby the value ofs, as shown in Table I. Classs50 C/m2 wasa system with neutral plates, while the plates were chargeclassess560.05 C/m2, s560.1 C/m2, and s560.2C/m2. The ionic concentration on the positive plate side wheld constant at 250 mM for all classes. Classs50.1 C/m2

consisted of three separate sets of simulations, in whichnegative plate side concentration was set to either 250 m500 mM, or 1 M. These correspond to 4, 8, and 16 iorespectively. Excess counterions were added to each


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which neutralized the charge on the plate. However, unwith an ideal parallel plate capacitor, in which the externelectric fields are zero everywhere, the discreteness ofplate charges and the explicit treatment of the electrosolutions allows for interactions between the two sides aaffects their dynamics. Thistrans-bilayer interaction is influ-enced by the concentration gradient and is therefore unamong systems previously described.19,20,24,26,58However,the time-averaged structure approaches that of isolated sin the long time limit. Thus, while the system presented hdoes capture side–side interactions on short time scalessumed relevant to biomembrane dynamics, the long timeerage structure should be comparable with simulationselectrolytes confined within parallel plates.

Electrolyte regions were prepared by starting with twpre-equilibrated water boxes~100 ps of dynamics with nosalt!, followed by a random placement of ions within eabox, each ion replacing a water molecule. The systemconstructed as described above, and the whole systemthen subject to a minimization and dynamics~110 ps! cyclefor further equilibration. Ten starting configurations weconstructed for each system presented, with the initialplacements varying between them. Data were averagedall ten configurations, and over 1 ns of dynamics per cfiguration. Hence, a total of 10 ns of dynamics is presenfor each setup. Simulations were performed usingCHARMM

software,59 version 26. Periodic boundary conditions weused with constant number of atoms~N!, temperature~T5298 K!, and volume~V! to generate NVT ensembles.cutoff of 12 Å was used for van der Waals interactions. Ttime step was 2 fs, and all bonds involving hydrogens wfixed using the SHAKE algorithm, with a tolerance~relativedeviation! of 1026. The frequency of regenerating the nobonded list was set with a heuristic testing algorithm thupdates based on the distance each atom moved since thupdate.

CHARMM utilizes the TIP3P water model60 which con-sists of three partially charged sites, and agrees well wexperimental data regarding hydration and energetics.parameterization of the ions was based upon comparwith solvation free energy data and quantum mechancalculations.58 The CHARMM parameterization has bee

TABLE I. Configurational parameters for the six sets of simulations psented. Four classes of system are defined based upon the plate scharge density. Positive plate side ionic concentrations were fixed atmM, while the negative plate side concentrations were varied as shoThree simulations withs50.1 C/m2 provided information regarding theeffect of changing negative plate side concentration. Note that, as descin the text, excess counterions were added to each side in the non-neplate systems.

Positive plate side Negative plate sidesplate NWat NNa1 NCl2 NWat NNa1 NCl2 @NaCl#

0.0 C/m2 992 4 4 992 4 4 250 mM60.05 C/m2 990 4 6 990 6 4 250 mM60.1 C/m2 988 4 8 988 8 4 250 mM60.1 C/m2 988 4 8 980 12 8 500 mM60.1 C/m2 988 4 8 964 20 16 1 M60.2 C/m2 984 4 12 984 12 4 250 mM


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extensive61,62and in addition to small molecule quantum caculations is focused upon biomolecular interactions~e.g.,water–protein, water–lipid and lipid–lipid interactions!.

In order to use EW3DC, we made a modification to tCHARMM implementation of the particle mesh Ewald~PME!sum following Yeh et al.24 to account for the two-dimensional periodicity. Following previous work,23,24 wetested this implementation by calculating the force actbetween two oppositely charged point charges as a funcof separation distance. As with previous results, the resulforce profile plateaud at long separations under the curimplementation of EW3DC, but diverged under EW3Such consistency with previous results showed that therent implementation was reliable. The method also requplacement of vacuum regions in thez-dimension, in order toreduce interactions between the two boundaries. In ordeinsure that waters did not evaporate into the vacuum regia force was applied using a miscellaneous mean field potial ~MMFP!.63 This acted at the water–vacuum boundainhibiting evaporation and also minimizing artifactual ordeing.

We have run 10 ns of dynamics for each of the setpresented in Table I, a total of 60 ns for the work presenhere. As discussed below, thes50 C/m2 simulations consistof two perfectly symmetric sides. In the case of perfect sapling, therefore, we expect the properties of these two sto be the same. As shown below, this is in fact the case,we take this as evidence that 10 ns is indeed sufficient silation time for each system. Each configuration~1 ns! wasrun for 65 h on 8 processors of an IBM SP3.

B. Density and electrostatic potential profiles

Average number density profiles of water and salt, afunction of distance from the plates, were calculated aslows. Each electrolyte region was divided into volumetslices of length 0.2 Å in thez-dimension. A histogram ofzpositions was then constructed as a trajectory averaged qtity for water hydrogen and oxygens, as well as for Na1 andCl2. Number densities are therefore in units of atoms/Å3.Normalized ionic concentration profiles were obtained byviding by bulk concentrations.

Poisson’s equation gives the electrostatic potentF(z), as

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C. Residency times

In order to investigate the local dynamic behaviorions near the plates, residency times for ions,t, at a givenzposition were calculated from fits to the time correlatifunction

^N~ t1Dt !& t5^N~ t !& t expS 2Dt

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whereN(t) is the number of ions present at timet andN(t1Dt) is the number of ions still present at timet1Dt. Thebrackets indicate averaging over all time frames withinsimulation. As was done in Ref. 64, thez-dimension wasbroken into 4 Å regions, and the averagez for that region isgiven in the plots.

D. Volumetric calculations

Calculation of thermally accessible volumes for the wter and ions was done using a Voronoi procedure providedGersteinet al.65 Briefly, given a distribution of atoms, thestandard Voronoi procedure constructs a polyhedron aroeach atom, that has the property that all interior pointscloser to the central atom than to any others. The resulpartitioning fills the entire space in the simulation box~i.e.,allows no voids!. The reported volumes are averages ovtrajectories and configurations.

III. RESULTS

Table I lists the simulation details for the four classessystem presented here. For simplicity, we adopt a nomenture as follows: for example,s50 C/m2 ~250 mM, 1 M!refers to the system which has positive plate side concention of 250 mM, and negative plate side concentration1 M. In what follows, we present the trajectory averagresults for the six sets of simulations. We first provide resufor macroscopic and microscopic water properties, followby salt properties, including evidence that the EW3DC tenique has enabled appropriate salt mobility. Finally,present the macroscopic electrostatic potential profiwhich results from the combined properties of the water asalt.

A. Water ordering

As we will discuss the interactions between the solv~water! and solute~salt! with the plates, we first present thdistribution profiles for water. Figure 2~A! shows the waternumber density profile,n(z), for the neutral plates simulation (s50 C/m2), with hydrogen,nhyd(z), and oxygen,noxy(z), shown separately. Data are presented as a funcof distance from the charged plates~negative distances fothe positively charged plate side are simply meant to reflthe geometry of the system!. Hydrogen distribution tails ap-proach the plates roughly 1 Å closer than do those for oxygen. Two strong peaks are seen in the plots, followed bthird less clear peak. These oscillations are due to localdering of the waters, as known from experimental measuments and previous simulations.20,24,55,66Typically, the peaksare used to define water hydration layers. Beyond appr


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FIG. 2. Effect of plate surface charge density,s, onoxygen noxy(z) and hydrogennhyd(z) number densityprofiles. Note that the bulk water density is 0.033waters/Å3. ~A! For s50.0 C/m2, oxygen ~solid line!and hydrogen~dashed line! profiles. ~B! The first oxy-gen peaks fors50.0 C/m2, 60.05 C/m2, 60.1 C/m2,and60.2 C/m2. ~C! The first hydrogen peaks, systemas in~B!. Data in parts~B! and~C! have been shifted upfor clarity. The vertical, dotted black line indicates thposition of the surface of the plate vdW spheres,z50.75 Å.

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mately 10 Å from each plate, the profiles reach a consvalue, signaling no influence from the plates. Thus, for splicity, data is presented only out to 15 Å from each plat

Consistent with previous simulations,55 water numberdensity profiles are relatively insensitive to the varied cocentration of salt on the negative plate side in thes56 0.1C/m2 simulations~data not shown!. However, these densitievary quite profoundly with changing the plate charges.Thus, we next consider the effect ofs on these profiles, andfocus on the first water layer. Figure 2~B! shows that ass isincreased from 0 to6 0.2 C/m2, the peak positions remairelatively constant. Increasings has a more profound effecon the hydrogen profiles. Figure 2~C! shows that there is anadditional structure in the first hydrogen layer on the netive plate side, seen in the emergence of a second peak


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proximately 1 Å closer to the plate than the original peak. Nsuch second peak is seen on the positive plate side.

There are two factors which determine the shapes ofdistributions shown in Fig. 2, namely, the relative positionwater molecules and their relative orientation. The latterfluences the hydrogen distributions,nhyd(z), more pro-foundly, as is now discussed. We observe that the distabetween the two hydrogen peaks on the negative plate sidless than the 1.6 Å hydrogen–hydrogen~HH! distance foreach water molecule. This suggests that the HH vector iaverage tilted with respect toz, meaning there is as inducedreorientation of the water. Previous simulations of water nplatinum surfaces20 showed clear, electrostatically induceorientations of water molecules near surfaces. These simtions used a different water model and potential funct


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than is employed here. However, comparison with thesesults is informative. As such, the distributions P(cosu) ofanglesu between the HH vector and thez-axis for waters inthe first water layers next to the plates are plotted in FigCorresponding water orientations foru50° ~perpendicular!,45°, and 90°~parallel! are shown for illustrative purposesNote that there is an inherent ambiguity in the definition

FIG. 3. Effect ofs on the orientation of first layer water molecules, as givby the probability distribution ofucosuu, the angle between the HH vectoand thez-axis, for~A! the positive plate side and~B! the negative plate sides50.0 C/m2 ~solid line! ands560.2 C/m2 ~dashed line! are shown. Datais binned in 0.2 Å increments. Corresponding water orientations are shfor illustrative purposes. Note that the distribution for a bulk, isotropic waunder no influence from the plates is a flat line.


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u590°, in that the water molecule plane~defined by the OHbonds! can be either parallel or perpendicular to the plaThe distribution for bulk water, that is at locations away frothe plates, is expected to be flat. Thus, we can understanshapes of these distributions in each case in terms of detions from the bulk case. Starting with the neutral plate cathe distributions on both sides are identical, and are clenot flat, suggesting that the plates have introduced restions in the orientational freedom of the waters. This is mlikely due to excluded volume effects, since the plates bno charge. There is a greater probability of the HH vecbeing parallel to the plate (u590°) than perpendicula(u50°), which is geometrically consistent with the presenof only one hydrogen peak in the profiles shown in Fig.The distributions P(cosu) are quite broad, with significanprobability of the HH vector being perpendicular to the pla

Next we focus on the effects of charging the platessÞ0!, starting with the positive plate side@Fig. 3~A!#. Themaximum value for P(cosu) is still at 90°, but population ofthis state has increased, while theu50° state has becomless populated with the increase ins. This indicates an electrostatically induced restriction in rotational freedom for twaters. Figure 3~B! shows the distribution for the negativelcharged plate side. Increasings generates a maximum oP(cosu) at u545° ~waters tilted away from the plates!, con-sistent with previous simulations.19 This preferred orientationgenerates the double peak innhyd(z) shown before in Fig.2~C!. The average position of this peak is shiftedtowardstheu590° orientation with increasings ~data not shown!. In-terestingly, the orientation of these water molecule nextthe negative plate reflects an atomic-scale double-lawithin the first water layer comprising the more typicaldescribed ionic double-layer. Data for intermediate surfacharge densities is omitted for clarity, but interpolate btween the extremes. These results are in remarkable agment with previous simulations,20 endowing an at least moderate degree of confidence in the EW3DC/CHARMM

potential.We have seen that water molecules next to the pla

pack differently than in bulk. We further investigated this bcalculating the thermally accessible volumes of the wamolecules utilizing the Voronoi algorithm~see Methods!.Figure 4 shows the results of these calculations, fors50 ands560.2 C/m2, as a function of distance from the plateThe figure highlights the volumetric restriction imposeupon the water molecules as they approach the plates,the available volume decreasing by approximately 30% aÅ from the plates, essentially approaching the steric packlimit 67 ~shown by the dashed lines in Fig. 4!. On the negativeplate side, increasings induces a decrease in relative watvolume near the plates. There is, on the other hand, minivolumetric response on the positive plate side. Data froms560.05 and60.1 C/m2 cases is omitted but follows thtrends shown.

B. Salt properties

Having shown the results for the solvent~water! behav-ior, we now turn to the solute~salt!. The results for salt arepresented in two sections. The first section gives time av

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FIG. 4. There is a decrease in the thermally accessvolumes per water molecule near the plates, which issdependent on the negative plate side only. Calculavia the Voronoi procedure~see Methods!, these vol-umes are plotted as a function of distance~in z) fromthe plates fors50 C/m2 ~solid line! and s56 0.2C/m2 ~dashed line!. Horizontal dashed lines indicatewater bare volume~steric limit!.

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aged results, in the spirit of those presented above forwater. The second section gives time dependent resultorder to address the mobility of the salt.

1. Spatial distribution

In order to show the effects ofs on salt behavior, wehave plotted the position dependent counter-ion concentions for thes560.05 C/m2, s560.1 C/m2 ands560.2C/m2 cases in Fig. 5. Note that the absolute distance of ecounterion type from its corresponding plate is plotted.counterion profiles show two well-defined layers. The potion of the peaks is different for the two counterion typbetween the two sides, with the Cl2 peak being approxi-mately 0.8 Å closer to the positive plate than the Na1 peak isto the negative plate. The first Cl2 peak is larger in magni-tude than the first Na1 peak, while this trend is reversed fothe second peaks. As opposed to the counterions, we seintervening peaks in co-ion density on either side. Bulk cocentrations are reached by approximately 20 Å from the pfor both ion types. Peak heights increases dramatically asis increased, and peak positions are shifted such that cou

FIG. 5. Effect ofs on counterion concentration profiles. Solid lines areNa1 ions on the negative plate side and dashed lines are for Cl2 ions on thepositive plate side. Note that the distances are shown as absolute valuedata has been shifted up for clarity.


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rions approach closer to the more highly charged platesthe case of neutral plates (s50! there is no peak in the iondistributions next to the plates~data not shown!. Similar tothe water, increasing the NaCl concentration on the negaplate side changes neither the peak heights nor the peaksitions, as we have tested for all threes50.1 C/m2 simula-tions ~data not shown!.

2. Range of motion

As mentioned in the Introduction, salt mobility has beof concern for MD simulations. Among the motivations fothe use of the Ewald sum in calculating long-range elecstatics is the fact that under cutoffs there are thought toartifacts in salt mobility.41–44Thus, it was necessary to verifmobility of ions in the simulations. Figure 6 shows a typictime series for thez-position of an arbitrarily selected Na1

and Cl2 on ~A! the negative plate side and~B! the positiveplate side from thes560.1 C/m2 ~250 mM, 250 mM! simu-lations. Due to the vdW exclusion radii of the plate spherno particle can penetrate closer than approximately 0.7plus its vdW radius from each sphere. Because the platrough, there are ‘‘dimpled’’ regions between the sphewhere particles may get closer than this. The figure showclear ion exclusion zone of approximately 3.0 Å from thplates, attributed to an intervening water layer. The figualso show that co-ions freely traverse thez-dimension, popu-lating the entire range in less than 1 ns. Counterions, onother hand, have a tendency to adsorb to the plate for speriods, as expected.26 Similar mobility is observed in thex-andy-dimensions and in all six simulated systems~data notshown!.

In order to quantitatively characterize the adsorptiphenomena, ion residency times,t, were calculated~seeMethods! and are shown in Fig. 7. For both Na1 and Cl2,there is a peak int located 4 Å from the plates, which isroughly 1 Å from the exclusion zone. Peak residency timfor Na1 next to the negative plate~273 ps! is greater thanthat of Cl2 ~171 ps! next to the positive plate, each approxmately one order of magnitude less than the length ofsimulation. Both Figs. 6 and 7 demonstrate, however, thatadsorption of counterions is a transient process withinsimulations, as ions are not permanently bound to theface. The falloff oft to zero beyond the adsorption zone

and


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quite rapid, due to less restricted ion mobility in thesegions. Similarly, co-ions~data not shown! have uniformlylow residency times.

C. Electrostatic potential

Understanding atomic level ordering of waters and ioprovides a unique backdrop for interpretation of macroscomeasurements such as the electrostatic potential. Havingamined the properties of water and salt individually, we nturn to the charge density distribution as a whole. Figurshows first layer charge distributions,rc(z), for s50 C/m2

ands56 0.2 C/m2. Results fors50 C/m2 are, as expectedsymmetric for the two sides. The results fors560.2 C/m2,however, are asymmetric, with the negative plate side shing more and better-defined alternating positive and negapeaks. On the negative plate side, the peaks ofrc(z) closestto the plate are positive, and based on the hydrogen numdensity,nhyd(z) @see Fig. 2~C!#, are most likely due to hy-drogen. Note that this first peak, which is approximately 1

FIG. 6. Time series of distance from the plates for two arbitrarily selecNa1 ~thin, dashed line! and Cl2 ~thick, solid line! ions showing a widerange of ionic mobility under EW3DC.~A! the positive plate side and~B!the negative plate side of thes50.1 C/m2 ~250 mM, 250 mM! simulation.Similar motions are seen for all other systems, as well as for thex- andy-dimensions.


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in width, has a broad shoulder which is a manifestationthe double peak innhyd(z). The first peak inrc(z) on thepositive plate side is positive, due to the fact that hydrogapproach the plate more closely than oxygens. This trenreduced ass increases to 0.2 C/m2, though it is not fullyabsent even in that high charge case. Fors560.2 C/m2

there are two additional, well-defined water layers onnegative plate side~data not shown!, which are absent on thepositive plate side.

Using Eq.~2.2!, we can now calculate electrostatic ptential profiles,F(z), which are given in Fig. 9~A!. Again,oscillations result from the molecular ordering discussabove. Results fors50 C/m2 are perfectly symmetric. Aswas the case withnhyd(z) andnoxy(z), the potential is insen-sitive to changes in the negative plate side NaCl concention. The positions of the first peak and valley in the negatplate side potential profiles correspond exactly with the fiand second hydrogen number density peaks. The peaksvalleys for the positive plate side are less coincident. It wbe seen that this is due to a more well-defined countehydration layer on the negative plate side.

In order to compare the potential profiles on the twsides, we choose to calculate the potential drop fromcenter of the plate vdW spheres to the bulk. In principle, ocould also choose the surface of the spheres as the stapoint for the calculation. Choosing thez 5 0 point accountsfor the possibility of atomic penetration into the dimpleregions of the lattice. It should be noted that this choiwhile affecting the magnitude of the potential drop,DF(z),did not affect the underlying asymmetry in the data. Figu9~B! plots DF(z) from each plate to the bulk as a functioof s. The change in magnitude of the drop is more thdouble on the positive plate side. As discussed above, tis an exclusion zone immediately adjacent to the plates,therefore the potential changes linearly over this region. Tdifference in the overall potential drop is due to the differemolecular ordering on the two sides. The length of theclusion zone on each side, which is less for the negative pand is defined by the vdW ‘‘roughness’’ of the plate surfaand the vdW radii of approaching atoms, also influencDF(z).

IV. DISCUSSION

Membrane proteins are influenced by the membranevironment which, complex and heterogeneous, includesids, water, and salt. In this paper we have chosen to invegate the interactions of water and salt in the vicinitycharged plates, which are intended as a model of the mbrane. The main focus has been in determining how theand water behavior is different next to the plates than in buwhich may ultimately lead to understanding how hydratsalt affects lipid–protein interactions. There is a good deaexperimental evidence which suggests that regulationmembrane surface charge density is a mechanism fortrolling transmembrane protein structure and function.10–14

One possible explanation is that there is an indirect biophcal pathway, which goes from the lipid, through the orderiof interfacial water and salt, to the protein. Therefore, itimportant to study the details of water and salt behavior n

d


ted


FIG. 7. Residency times,t, for counterions as a func-tion of distance from the charged plates, as calculafrom Eq. ~2.3!. Shows sensitivity to changes ins, butnot to changes in negative plate side concentration.~A!Cl2 ions on the positive plate side~filled! and~B! Na1

ions on the negative plate side~open!. s560.1 C/m2

~250 mM, 250 mM! ~diamonds!, s56 0.1 C/m2 ~250mM, 1 M! ~triangles!, ands560.2 C/m2 ~squares! areshown.

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membranes. Molecular dynamics simulations have beensuited for such studies. The charge densities used inpresent study are realistic for biological membranes. Tsimulated 25.5 Å325.5 Å area corresponds to two monolaers of approximately 9 lipid molecules each, which wouhave a charge density of20.014e/Å 2, or 20.22 C/m2, ifcomposed entirely of PS lipids. Thus, the molecular orderwhich we have investigated in this work is presumabpresent in biomembrane systems as well. Such orderinwell documented in similar systems of electrolyte near sincharged surfaces,17–20,24,55,56and provides the context for oudiscussion.


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A. Asymmetric molecular ordering

The dominant electrostatic properties in these systeare the asymmetric partial charge distribution of the wamolecule and the water–plate interactions. In a 250 mNaCl solution there are only four salt molecules for eve988 water molecules, and hence one can easily see theportance of examining the role of water ordering and orietation. Water orientation probability distributions plottedFig. 3 agree with previously published simulation results19,20

and it is remarkable that such agreement is seen despitenificant differences in water parameters. Our system provi

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FIG. 8. Trajectory averaged charge density profileused to calculate the electrostatic potential profiles,most sensitive to changes ins. Note that, as describedin the text, these distributions are dominated by wapartial charges.~A! Positive plate side and~B! negativeplate side charge density profiles as a functiondistance from the plates fors50 C/m2 ~solid line! ands560.2 C/m2 ~dashed line!.


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FIG. 9. Asymmetries are evident in the potential prfiles calculated from Eq.~2!. Potential as a function ofdistance from each plate is given in part~A! for fourvalues ofs. Data has been shifted up for clarity.~B!Overall potential drop from the charged plate to bulka function ofs. The arrows highlight the asymmetrimagnitude in potential drop from the oppositecharged plates.

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the opportunity to investigate the behavior near two differsurfaces within the same simulation, and as a result we hshown multiple examples of how the water geometric aelectrostatic asymmetry results in asymmetry betweentwo sides.

The most obvious asymmetries between the two sioccur in the first layer of water and salt. Figure 10 recadata from Figs. 2 and 5 to show an overlay of first layoxygen, hydrogen, and counterion densities (Na1 for thenegative plate side, and Cl2 for the positive plate side!. Onthe negative plate side, the Na1 peak is clearly shifted awayfrom the first layer water peaks, demonstrating that a wdefined water layer intervenes between the plate and theNa1 layer. On the positive plate side, however, the Cl2 peakoverlaps much more with the water peaks, suggesting adiscrete hydration layer. In order to more fully investigathe relative arrangements of the water and ions, and in o

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to compare the behavior with the previous simulationsSpohret al.,21 Fig. 10~C! plots the distribution of oxygen–ion–oxygen angles (z) within the first hydrationshell ofeach ion in these first waterlayers. The hydration shells aredefined by the location of the minima in theg(r ) functions~data not shown!. There is a clear geometric arrangementwaters around the Na1 ions next to the negative plate, witthe peak at cosz5 0 being consistent with an octahedrarrangement.21 The water arrangement around the Cl2 ionson the positive plate side is much less well-defined, whichalso consistent with the previous simulation results. As wthe other asymmetric trends discussed above, the differein hydration behavior increases withs.

Understanding this asymmetric ordering of water asalt next to oppositely charged surfaces must include acussion of how the insertion of neutral plates perturbs isopic, bulk water. Under the influence of neither electrostanor vdW forces imposed by the plates, a bulk water molecundergoes full isotropic rotational motion in the long-tim license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

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FIG. 10. Combined spatial distributions of water ansalt reveal asymmetric ordering on the two sides of tsystem. Overlayed oxygen~—!, hydrogen ( – – – ),~A!Cl2 ~positive plate side, filled diamonds! and ~B! Na1

~negative plate side, open diamonds! from thes560.1C/m2 ~250 mM, 250 mM! simulation. ~C! Probabilitydistribution of the O–ion–O angle in the first hydrations shell of the counterions in the first layer nexteach plate@symbols as in parts~A! and ~B!#.

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limit. It is important to point out that the resulting moleculdistributions are dependent upon the reference point. Ifreference is moved from the lab frame~plates, in this case! toa given water molecule, as is done for radial distributifunctions,g(r ), oscillations are seen due to local water odering. In fact, any insertion experiences the inherent loordering of water. The resulting density distributions,g(r ),depend upon molecular interactions as well as molecsizes. In this framework, one can think of the plates as intions with infinite radii of curvature. Thus, we understand torigin of the oscillations in thes50 C/m2 simulation, asreflecting this intrinsic property of the water–insertion inteaction. In addition, we have seen that the smaller hydroatoms populate locations approximately 1 Å closer to theplates than do the oxygens, due to their smaller sizeshould be noted that this hydrogen-plate packing is liksensitive to the size and shape of the spheres which makthe plates, and by analogy the specific molecular naturevarious biologically relevant lipid headgroups.

Oscillations in the number density profiles thereforeflect a translational ordering of the water molecules witrespect to the plates. Beyond this type of ordering, we sawFig. 3 that waters respond to the insertion of the plates worientationalordering as well. With no preferred orientatiofor bulk waters, the probability distribution of HH angles,in Fig. 3, would be flat. Given that the insertion of neutrplates causes water reorientation, the question becoHow does charging the plates affect this order? Figure 3~A!showed that the effect of increasings on the positive plate


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side was to increase the population of waters withu590°~parallel to the plate!. Such an orientation is favorable eletrostatically, as it decreases the interaction between the ptively charged hydrogen and the positive plate. Note thatambiguity in this state~viz., H–O–H plane! is resolved bythe charge density profile,rc(z) shown in Fig. 8, in that thefirst peak became more negative with increasings.

In contrast, the behavior seen in Fig. 3~B! for the nega-tive plate side, showed a decrease in the water populawith u590°, suggesting that the favorable electrostatic intaction between the positively charged hydrogens and netively charge plate is, surprisingly, diminished with increaing s. However, the emerging peak in the P(cosu)distribution atu545° shifted towards theu590° state withincreasings ~data not shown!. This is consistent with anincreased electrostatic attraction of the hydrogen to the plThus, there is clearly a delicate balance in forces actingthe water molecules on the negative plate side. The subtleof this behavior may potentially be explained via a competion between sterics and electrostatic interactions. One nthat water is more cylindrical than spherical, with a lengto-width ratio of approximately 1.6 Å. The extent to whicsuch a geometric asymmetry may influence entropic degof freedom, and hence the relative free energies of spewater orientations/packing arrangements, may depend uthe charge state of the plates~both sign and magnitude!.

The asymmetry between the positive and negative plawas also seen in the salt behavior, again due to the interbetween ionic size and charge with water geometry and


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larity. Na1 residency times were significantly longer thathose for Cl2 next to their respective counter-charged platHowever, Cl2 approaches its counter-charged plate mclosely. Further, the water layers on the negative platewere more well defined than those on the positive plate sThese phenomena may be explained by the formationmore well-defined hydration layers next to the Na1, presum-ably facilitated by its smaller ionic radius. The presencethis more well-defined layer on the negative plate sidecreased Na1 residency time and prevented Na1 penetrationto the plate. On the other hand, the larger Cl2 ions disruptedthese structures on the positive plate side, explainingcloser approach and shorter residency times.

B. Comparison to continuum theory

Efforts to capture water and salt behavior and intertions at the bilayer interface have been made using comtationally efficient models such as the Gouy–Chapmantension of Poisson–Boltzmann theory. While continuumodels have been quite illuminating,68 we have seen that thmolecular structure of water molecules, and subsequendering, has a dramatic influence on the shape of the elecstatic potential profiles. Such models do not capture thecillations because of the dielectric treatment of the solveDespite this, continuum models have been extensively,successfully, used to describe relevant experimental pareters, such as the Debye screening length of solvents of ving ionic strength. It is interesting, therefore, to attemptextract related parameters from the oscillating profiles psented above in Fig. 9. As was done by Israelachvili66 forcalculating oscillations in solvation pressures acting asolid–liquid interface, and elsewhere,69 we have fit the po-tential as the product of an exponential decay and a pericosine function as follows:

F~z!5A expS 2z

dD cosS 2p~z2s!

p D , ~4.1!

whereA is the amplitude,d is a decay length, inspired by thDebye length,p is the period of the oscillations~giving peakspacing!, and s is a phase shift setting the position of thpeaks relative to the plate. Figure 11 compares the negaplate side potential profile fors520.2 C/m2 with this em-pirical model of the potential, with values ofA52.0 V,d53.0 Å, s51.1 Å, andp52.5 Å. This value forp, it shouldbe noted, is approximately the width of one water laywhich is consistent with the picture of water layering ascause of the oscillations in the number density profiles. Fther, the shift,s, can be related to the length of the exclusizone in the vicinity of the plates. This empirical modclearly misses several details of the data, most notablysurface potential. It is interesting, nonetheless, to compthe value ofd to the actual Debye length value, which is 6.Å for a 250 mM NaCl solution at 298 K. The value ofd isthus approximately half of this in our model, which maythe result of the discreteness of water partial charges prein an all-atom representation of water, which is absent incontinuum model. Further refinements of these ideas arerently being explored in a new set of simulations.


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V. CONCLUSIONS

We have achieved two primary goals in the presstudy. First, we have applied the EW3DC methodologycalculating long-range electrostatics to a system with blogically relevant membrane geometry. We have successfperformed an all-atom simulation of a concentration gradiin such a geometry. Our results on water ordering are csistent with those from nonbilayer like systems, givingconfidence that the implementation of the EW3DC in thcontext successfully avoids interactions in thez-dimension,as is necessary for systems with two-dimensional periodicSecond, with the viability of the method established, we ato understand macroscopic features, such as the electrospotential, in terms of molecular-level ordering. We hashown that the geometric and electrostatic asymmetry ofwater molecule is the fundamental basis for the macroscoasymmetry between the two sides of a membranelike sys

The key role of molecular asymmetry in water orderimay impact upon the understanding of biological mebranes. As we have performed simulations in the biologirange of surface charge (s50–0.2 C/m2), our results aresuggestive of the effect of changing the ratio of chargeduncharged lipids in biological membranes. As water structaround ions at the headgroup region of biological mebranes has a profound impact on the fluctuations in hegroup order, our results regarding asymmetries are of inest.

We have initiated a series of related simulations in whthe overall charge on each side of the system is nonzThese new simulations, which will be discussed in a futureport, should provide useful insight into how interactiobetween water and salt on opposite sides affect molecordering.

FIG. 11. A possible connection between the simulated results andtinuum theory. Comparison of potential profile from thes560.2 C/m2

simulation and the theoretical prediction calculated from Eq.~4.1!. Param-eters used are given in the text.


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ACKNOWLEDGMENTS

The authors wish to thank Dr. Paul Crozier, Dr. LuForrest, Dr. Alex Hodges, as well as Hirsh Nanda, for helpdiscussions. Special thanks to Dr. Michael Miller and Dr. RWinslow of the Johns Hopkins University Center for Imaing Sciences for use of the SP3 computer. J.N.S. thanksWhitaker Foundation for Biomedical Engineering for gradate fellowship support.

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Documents

Molecular dynamics simulations of ionic concentration ... · and entropic constraints on hydration shell structure, and may thus play a signiﬁcant role in membrane protein struc-ture