Molecular Dynamics Studies of the Molecular Structure and

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J. Phys. Chem. B 2007, 111, 11021-11031

11021

Molecular Dynamics Studies of the Molecular Structure and Interactions of Cholesterol Superlattices and Random Domains in an Unsaturated Phosphatidylcholine Bilayer Membrane Qing Zhu,† Kwan H. Cheng,‡ and Mark W. Vaughn*,† Departments of Chemical Engineering and Physics, Department of Chemical Engineering, Texas Tech UniVersity, P.O. Box 43121, Lubbock, Texas 79409-3121 ReceiVed: January 19, 2007; In Final Form: June 28, 2007

The effect of the molecular organization of lipid components on the properties of the bilayer membrane has been a topic of increasing interest. Several experimental and theoretical studies have suggested that cholesterol is not randomly distributed in the fluid-state lipid bilayer but forms nanoscale domains. Several cholesterolenriched nanodomain structures have been proposed, including rafts, regular or maze arrays, complexes, and superlattices. At present, the molecular mechanisms by which lipid composition influences the formation and stability of lipid nanodomains remain unclear. In this study, we have used molecular dynamics (MD) simulations to investigate the effects of the molecular organization of cholesterolssuperlattice versus randomson the structure of and interactions between lipids and water in lipid bilayers of cholesterol and 1-palmitoyl-2oleoylphosphatidylcholine (cholesterol/POPC) at a fixed cholesterol mole fraction of 0.40. On the basis of four independent replicates of 200-ns MD simulations for a superlattice or random bilayer, statistically significant differences were observed in the lipid structural parameters, area per lipid, density profile, and acyl chain order profile, as well as the hydrogen bonding between various pairs (POPC and water, cholesterol and water, and POPC and cholesterol). The time evolution of the radial distribution of the cholesterol hydroxy oxygen suggests that the lateral distribution of cholesterol in the superlattice bilayer is more stable than that in the random bilayer. Furthermore, the results indicate that a relatively long simulation time, more than 100 ns, is required for these two-component bilayers to reach equilibrium and that this time is influenced by the initial lateral distribution of lipid components.

1. Introduction Lipid membranes play an important role in cellular processes such as cell signaling, membrane fusion, virus entry, protein sorting, and ion transport. Computer simulation techniques such as molecular dynamics (MD) have become powerful tools in lipid membrane studies.1-6 This is because of the unique potential of simulation in revealing the details of the molecular mechanisms underlying the biological and physical properties of the lipid membranes at the atomic level. The multicomponent lipid bilayer provides an important model for studying biological membranes. Most computational investigations of lipid membranes have focused on singlecomponent lipid bilayers. However, the relationship between composition and structure in biological membranes is likely to be complex, involving not only lipids of different chemical structures but also heterogeneous distributions of those lipids. As a result, the properties and functions of biological membranes will depend on both the lipid composition and the distribution of the components. In recent years, lipid bilayers containing cholesterol and one or more phospholipids have received much attention. Cholesterol is an important component in mammalian cell membranes, particularly in the plasma membrane.5,7 In addition, it is an important component of lipid rafts, which appear to play a critical role in cell signaling and protein sorting on the membrane surface.8-11 The overall effect of cholesterol on the mechanical and thermodynamic properties of lipid bilayers has been established * Address correspondence to this author. Phone: (806) 742-0451. Fax: (806) 742-3552. E-mail: [email protected]. † Department of Chemical Engineering. ‡ Department of Physics.

by both experiment and simulation. Membranes that contain cholesterol can form lipid raft microdomains rich in cholesterol, glycolipids, and sphingolipids.12-14 Cholesterol profoundly affects a variety of bilayer properties. Cholesterol can increase the order of phospholipid acyl chains15-19 as well as induce a condensing effect that decreases the surface area per molecule of fluid-phase lipid bilayer.16,20-22 When the cholesterol concentration of a bilayer membrane is increased, the membrane mechanical strength is increased,23 but the passive permeability24-26 and the phospholipid lateral diffusion19,27,28 are reduced. The relationship between the lateral organization of cholesterol in lipid membranes and these properties is not known. However, the lateral organization of lipid molecules is known to be important for biological membrane function. Membrane organization has been actively investigated in recent years, especially the context of the formation of domains with distinct composition, such as “rafts”.10,12,29-36 For cholesterol-containing lipid bilayers, several experimental studies have reported that certain membrane properties do not change smoothly, but display discontinuities as a function of cholesterol concentration.7,15,16,37-41 These appear as dips or peaks in experimental data and occur at well-defined or critical cholesterol mole fractions, for example at Xchol ) 0.118, 0.154, 0.20, 0.25, 0.33, 0.40, and 0.50 in binary cholesterol/lipid mixtures. The presence of property changes at the critical compositions has been interpreted as evidence for the “superlattice” (SL) theory or regular distribution model.30,33,37,42 For cholesterol-containing bilayers, this model was originally proposed by Chong,37 based on fluorescence intensity changes observed at certain sterol mole fractions, in the study of lateral organization of sterols in liquid crystalline phosphatidylcholine

10.1021/jp070487z CCC: $37.00 © 2007 American Chemical Society Published on Web 08/25/2007

11022 J. Phys. Chem. B, Vol. 111, No. 37, 2007 bilayers. The superlattice model states that for certain critical compositions cholesterol will be located at sites predicted by either a hexagonal or a centered-rectangular (CR) structure: the cholesterol superlattice (SL) theory does not suggest that the entire membrane is regularly ordered, but that there are regions of order that are surrounded by coexisting regions of disorder and packing defects. One of the key predictions of SL theory is that the membrane lateral order attains a local maximum at each superlattice (critical) composition and the bilayer area covered by randomly organized lipids increases when the composition moves away from the critical SL composition. Another key prediction is that coexisting lateral packing defects surrounding the SL domain boundaries form at or near the SL compositions.15,30,42 Superlattices may form at either the head group or tail group level. As recently demonstrated,7 a tail group cholesterol SL and a head group SL may coexist in fluid bilayers that contain phospholipids of different head group size. While several experimental studies support the SL model, only a few computer simulation studies have addressed the SL theory.18,43-45 Suga´r and co-workers43 used Monte Carlo simulations to investigate the formation of superlattice patterns by introducing a pairwise-additive repulsive interaction that can promote superlattice arrangement at Xchol ) 0.5. However, it should be noted that MC simulations of cholesterol containing membranes often treat the acyl-tails of the lipid separately and independently, which may allow configurations that are physically unrealizable. Huang and Feigenson44,46 developed an “umbrella” model for multibody cholesterol/phospholipid interactions. Their model proposed that nonpolar cholesterol molecules are covered by the phospholipid head groups, thereby avoiding energetically unfavorable interactions with water. They found multibody interactions can generate regular distribution of cholesterol at high cholesterol mole fractions, Xchol ) 0.57, 0.67. These Monte Carlo simulations modeled cholesterol molecules and phospholipid acyl chains as single spheres, so the atomic detail of the interaction was lost. Chiu and co-workers18,45 combined Monte Carlo and MD technique to study the lipid-cholesterol atomic interactions of the cholesterol-dipalmitoyl phosphatidylcholine (DPPC) bilayer at various cholesterol concentrations. Their starting structures were roughly hexagonal lattices. Smondyrev and Berkowitz47 also performed MD simulations on the DPPCcholesterol-containing bilayer at Xchol ) 0.11 and 0.50. They compared the behavior of two different structures of DPPCcholesterol bilayers in 2 ns simulations: One structure had a roughly superlattice-like cholesterol distribution. The other structure contained randomly distributed cholesterol. Other multicomponent MD simulation studies5,19,48,49 have focused on phospholipid-cholesterol systems, but did not consider SL or SL-like structures. Computational resources often limit MD simulations in time (typically tens of nanoseconds) and system size (typical dimensions of 5 to 10 nm). These are serious limitations for observing evolution in multicomponent heterogeneous systems. The molecular dynamics simulations used here explore the cholesterolSL theory by comparing the behavior of cholesterol/POPC in a bilayer system with an initial regularly distributed cholesterol SL to that of a randomly distributed bilayer system of identical composition. In both systems, the mole fraction of cholesterol was Xchol ) 0.40, a predicted SL composition. To minimize system size and time limitations of previous studies, we used a system size sufficient to allow several repeating SL structures and an extended computational time of 200 ns. Both the simulation time and system size exceeded available studies.5,18,19

Zhu et al.

Figure 1. Schematic of cholesterol (left) and POPC (right). The cholesterol hydroxy oxygen is designated O6. The double bond of the sn-2 chain occurs between carbons C24 and C25.

In addition, artifacts from sampling in the simulation were minimized by performing four replicate simulations for each system from the same initial configuration, but different initial velocities. Bilayer properties were evaluated for each of the four runs to provide confidence levels for the system differences. 2. Methods 2.1. Model and Simulation Details. The numbering schemes of the cholesterol and POPC used in the simulation are shown in Figure 1. Two Xchol ) 0.40 bilayer membranes were constructed. The initial configuration of the SL membrane was determined by computing the position for each phospholipid tail and cholesterol that was consistent with a 2D tail group superlattice representation.7 The random membrane was constructed similarly, but with the lipid and cholesterol positions randomly selected from sites in a 2D lattice representing the tail groups, with the constraint that the lipid tails of a single lipid molecule had to occupy adjacent positions. In this idealized 2D model, each of the two lipid tail groups occupies one position and each cholesterol occupied one position, see Figure 2. A single POPC structure in protein data bank (pdb) format50 was constructed as compactly as possible, then energy minimized by using Hyperchem (Hypercube, Inc., Gainesville, FL). The cholesterol structure of Ho¨ltje et al.51 was obtained from the GROMACS website.52 The membrane starting structure was prepared from the 2D lattice coordinates of the individual lipids by using home-written software to translate and rotate the individual lipid coordinates to the desired center of mass locations. The rotation angle and the density of the initial structures were chosen to ensure that there were no overlaps. The resulting lipid membrane, which had a density of about 600 kg m-3, was then compressed to a density of 1000 kg m-3, by scaling the simulation box using the editconf program from the GROMACS53,54 molecular dynamics package. This membrane was energy-minimized, combined with two boxes of water to form a starting structure for MD simulation of a hydrated binary lipid membrane, and subjected to a 1 ns preequilibration in a NPT (constant number of atoms, constant pressure and temperature) ensemble to relax compression-induced stresses. It should be noted that the SL model predicts three possible configurations of the tail group SLs at Xchol ) 0.40: hexagonal,

Effect of Molecular Organization of Lipid Components

Figure 2. Idealized and initial 2-dimensional membrane structure. Shown are the molecular organization of the center rectangular (CR) superlattice domain at the acyl chain levels at the theoretical critical composition of Xchol ) 0.40. Several unit cells of the superlattice are shown outlined, and the black bar indicates corresponding tail groups of individual POPC molecules. For this composition, the hexagonal and CR bilayers have the same configuration. To implement this configuration in an MD simulation, each POPC molecule must be mapped to its tail group locations, as shown in panel B. This is the membrane structure prior to compression. Here the 2D convex hull of single compact POPC molecules is shown in dark gray and the convex hull of cholesterol molecules is shown in light gray. Panel C shows the corresponding random structure.

center-rectangular (CR), and rectangular.7 Figure 2 shows the center-rectangular (CR) symmetry in the tail group lipid/ cholesterol superlattice that is our focus here. For this composition, the CR structure is identical, except for choice of the unit cell, to the hexagonal SL structure. The equilibration and time evolution of two different lipid membrane models were simulated by using the GROMACS 3.3 package.53,54 Lipid parameters were described before by Berger et al.,55 and cholesterol parameters were taken from Holtje et al.51 The simple point charge (SPC) model56 was used for water. The two membrane systems were simulated by using an NPT ensemble with an isotropic pressure tensor of 1 bar. The temperature of each component was separately coupled to a bath at 300 K, using a Berendsen thermostat.57 A leapfrog58 integrator was used with a 2 fs time step. The electrostatic interactions were determined by using the particle-mesh Ewald (PME) method.59,60 The van der Waals (VDW) interactions were evaluated by use of a twin-range cutoff, with interactions within 1.0 nm evaluated every step and interactions between 1.0 and 1.5 nm evaluated every 10 steps. Bond lengths were constrained by the linear constraint solver (LINCS) algorithm.61 Both of the membranes were formed from POPC/cholesterol at a 60:40 mole ratio. In the superlattice system there were 144 POPC lipids, 96 cholesterol molecules, and 6888 water molecules; the system contained 30 936 total atoms in a 6.9 × 8.2 × 7.6 nm3 initial simulation box. The randomly arranged system had 144 POPC lipids, 96 cholesterol molecules, and 6924 water

J. Phys. Chem. B, Vol. 111, No. 37, 2007 11023 molecules (31 044 total atoms) in a 7.5 × 7.5 × 7.6 nm3 initial box. The starting structures described above were reached after energy minimization and 1 ns NPT equilibration. These starting structures were used for four separate 200 ns NPT simulations for each system. Each of these simulations used the same starting structure, but different distributions of the initial velocities. Replicate simulations are discussed in more detail in the following section. To quantify the effect of cholesterol on the POPC, a simulation of a pure hydrated POPC bilayer was performed. This hydrated pure POPC bilayer was constructed from the ending structure of the 200 ns simulation of CR-SL membrane by removing the cholesterol. There were 144 POPC molecules and 6888 water molecules in the single-component lipid bilayer system. All other simulation parameters were the same as for the binary system. The resulting membrane structure was allowed to evolve for 20 ns in an NPT simulation. The bilayer equilibrium area was reached after a few nanoseconds of contracting, and remained constant for the remainder of the simulation. Three separate simulations of the pure POPC system were run. For one of these simulations, the bond lengths were constrained by the LINCS algorithm.61 Analysis of membrane structural differences focused on area per molecule, number density profile, hydrogen bonding, order parameters, and radial distribution functions. These computations were done by use of the GROMACS analysis tools. Graphical images and trajectory visualization employed the VMD software package.62 2.2. Statistical Analysis. To obtain statistically relevant comparisons between the superlattice and random membranes, we ran replicate simulations. As previously noted,6 because of the sample size limitations of MD simulations, the properties of interest may not reveal statistically significant differences when systems are compared. Even for 200 ns simulations, system properties resulting from different initial velocity conditions can vary considerably, so comparisons between the single simulations can be misleading. To directly compare the superlattice and random systems, we performed four replicate runs using different random seeds for each system. Results from all four runs were used in the statistical analysis of the differences of the systems. A number of statistical tests were applied. The two-sample t-test63 is frequently used in experimental work to assess whether the means of two different groups of measurements differ. But in MD simulations, it is not clear whether the simulation results, mainly time-dependent parameters, are normally distributed. Although 200 ns is a relatively long time in MD bilayer lipid membrane simulations, currently, it is still very short compared to many biological processes. To determine if the behavior of superlattice and random membranes was statistically different, the Mann-Whitney two-sample nonparametric rank test was used.6,64 This test is much more powerful when the assumptions of the t-test are violated. Even for normally distributed data, it is 95% as powerful as the t-test.64 Even at equilibrium, there may be large fluctuations of a parameter about its mean value that make determination of a steady state difficult. To verify the time at which the number of hydrogen bonds and distance between the centers of mass of the cholesterol and POPC reached a steady state, linear regression was used. The apparent steady-state time was selected by visual inspection of the parameter plotted as a function of time. Then linear regression was used to determine the slope of the best-fit straight line through the parameter values of the proposed steady state. The p-value of the slope was computed.

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Figure 3. Surface molecular structure of the CR-SL and random POPC/cholesterol systems. Blue spheres represent the polar head group of POPC, and yellow spheres represent the polar 3-β hydroxy groups of cholesterol. (A) CR-SL starting structure with 1 ns preequilibration. The system is somewhat perturbed from the ideal SL of Figure 2 during membrane compression. (B) Final CR-SL structure after 200 ns NPT run. (C) Random starting structure with 1 ns preequilibration. (D) Final random structure after 200 ns NPT run. Each image is of four simulation cells.

If p > 0.5 compared to the null hypothesis of zero slope, then the value of the slope was indistinguishable from zero, and the parameter was considered to be at equilibrium. In the simulations performed here, both leaflets of the bilayer membrane were identical. The behavior of the upper and the bottom layer was considered separately when calculating order parameters and hydrogen bonds. As a result, there were eight observations for each system. For quantities that varied little from their steady state, such as density and order parameters, the time-averaged value was used for the statistical test. For dynamic time-dependent quantities, such as hydrogen bonds, the last 10 ns of the time-dependent curve was averaged, and this average value was then used to compute the significance. For statistical comparisons, we consider results significant at the 90% level. Values are reported as mean ( standard deviation, computed from the four replicate simulations. 3. Results and Discussion 3.1. System Overview and Equilibration. The starting structures of the lipid bilayer surfaces after 1 ns relaxation and final structures after 200 ns MD simulations of SL and random systems are presented in Figure 3. For clarity in displaying the lateral organizations of the two different systems, only the polar head group of POPC and the polar 3-β hydroxy of cholesterol (O6 of Figure 1) are shown. Although the compression process perturbs both structures, these images suggest that the superlattice-like distribution of cholesterol and the POPC head group appears to be preserved on the membrane surface, but in the random system the cholesterol molecules in cholesterol-rich regions appear to diffuse into the POPC-rich regions. This suggests that the cholesterol-POPC interactions are more

Zhu et al.

Figure 4. Area per molecule as a function of time: (A) area per POPC molecule for the CR-SL and random systems and (B) area per cholesterol molecule for the CR-SL and random systems.

favorable than cholesterol-cholesterol interactions, consistent with current SL theory and with previous studies.15,16,45 To determine the equilibration of the two systems, several structural properties of the systems were examined. The method of Hofsa¨ss et al.48 was used to compute the temporal behavior of the area per molecule, shown in Figure 4. According to their approach, the area per POPC molecule at Xchol ) 0.40 is given by

APOPC )

(

)

0.4NlipidVchol 2A 10.6Nlipid V - N wV w

(1)

where A is the area of a simulation cell in the x - y dimension, Nlipid is the total number of lipid molecules in the system including POPC and cholesterol, Nw is the number of water molecules in the system, Vchol is 0.593 nm3, the volume per cholesterol molecule, and Vw is 0.030 nm3, the volume per water molecule. The values of Vchol and Vw were given by Hofsa¨ss et al.48 Similarly, the area per cholesterol molecule can be determined from48

Achol )

2AVchol V - NwVw

(2)

This method assumes that the volume of a cholesterol molecule in a crystal is the average volume of a cholesterol molecule in the bilayer, regardless of the cholesterol mole fraction. Although this assumption has been shown not to be true in general, it appears to be a good approximation for POPC/ cholesterol bilayers.22,65 The value of Vchol used here is smaller than the most recent measurement of 0.630 nm3,22 but it is

Effect of Molecular Organization of Lipid Components

Figure 5. Measures of equilibrium for the random and superlattice membranes. (A) Time-dependent potential energy of the CR-SL and random system, running average over 20 ps; the CR-SL system reaches equilibrium after ∼150 ns, but random system energy decreases over the entire 200 ns simulation. (B) Number of hydrogen bonds between water and the cholesterol hydroxy oxygen. For this measure, equilibrium required ∼150 ns. (C) Distance between the centers of mass (COM) of POPC and cholesterol. For panel C, a plateau was achieved by ∼100 ns for both systems.

consistent with the total lipid and POPC molecular volume calculations, below. Our primary interest in the molecular areas is to compare the temporal evolution of the surface area of CR-SL and random systems. It took approximately 150 ns for these systems to reach a stable lateral area value. The final area per POPC was 0.5716 ( 0.0005 nm2 in the CR-SL system and 0.5819 (

J. Phys. Chem. B, Vol. 111, No. 37, 2007 11025 0.0004 nm2 in the random system. Our pure POPC simulations resulted in a surface area per lipid of 0.709 ( 0.05 nm2 at 300 K. Therefore, both the CR-SL and the random system show considerable cholesterol condensing effect,16,20-22 although less than that of a bilayer of saturated lipids, such as DPPC.48,66 The computed equilibrium area per POPC for the pure POPC bilayer is about 4% larger than the best current experimental value, 0.683 nm2.67 It is also larger than two recent MD simulations of the pure POPC bilayer: an area per lipid of 0.658 nm2 at 310 K and 0.665 nm2 at 303 K.68,69 The larger area may be the result of water trapped near the glycerol backbone69 after cholesterol removal, where it hinders the contraction of the bilayer. For the CR-SL bilayer, the volume per lipid Vlipid and volume per POPC VPOPC in the 40% cholesterol bilayer were 0.9561 ( 0.0027 nm3 and 1.1981 ( 0.0020 nm3, respectively. This is about 5% less than recent measurements.22 Similarly for the random configuration, Vlipid and VPOPC were 0.9484 ( 0.0187 nm3 and 1.1853 ( 0.0031 nm3. From eq 2, the area per cholesterol was found to be 0.2976 ( 0.0002 nm2 in the CR-SL system and 0.3055 ( 0.0003 nm2 in the random system. These values are somewhat larger than the area per cholesterol in DPPC bilayers of 0.22 to 0.28 reported by other studies.5,18,48 These results are contrary to those of Pandit et al.,69 whose computations for a POPC/CHOL bilayer used different forcefield parameters. The area per molecule of both POPC and cholesterol in the CR-SL system are lower than those in the random system. The absolute difference between the two systems is not large, but it is significant, p < 0.01. Figure 5 shows three time-dependent indicators of system equilibrium: system potential energy, hydrogen bonds between water and cholesterol, and the distance between the centers of mass (COM) of the POPC and cholesterol. The potential energy of CR-SL systems reaches equilibrium after ∼150 ns, but does not reach an equilibrium value during the 200 ns simulation for the random system. The number of hydrogen bonds between water and cholesterol appears to reach equilibrium at about 150 ns for both systems, as determined from the slope of the linear regression line between the last 50 ns of the simulation. The distance between the POPC and cholesterol centers of mass of both systems reaches a steady value at approximately 100 ns, as determined from the slope of the regression line. Taken together, these data indicate that care should be exercised when determining the system properties of bilayers with complex composition. Parameters vary in their sensitivity to structural differences, and it may not be obvious which are the best indicators for a complex bilayer. We consider the system at equilibrium for the last 50 ns of the 200 ns simulation. It should be noted, however, that 200 ns is still short compared to the time for total bilayer rearrangement, and further decrease in the values of these parameters could occur. It should be noted that there is a tremendous difference between the equilibration time found for experimental measurements and that of our simulation. For experimental work, the samples are typically allowed to equilibrate from 4 days32,37,40,70 to 10 days.7,15,41,71 The difference in equilibration time between the experiment and simulation is likely a reflection of different system size and different mixing. MD simulations use a single nanometer-size bilayer with periodic boundary conditions and predetermined structure, and for this simple, nanoscale system little diffusion is required to attain the final expected structure. Many microscale processes occur in an experimental system that are not taken into account in a simulation, examples include thermal undulations, capillary waves, vesicle-vesicle interac-

11026 J. Phys. Chem. B, Vol. 111, No. 37, 2007

Figure 6. Number density profiles of POPC, cholesterol, water, POPC acyl chains, POPC head group phosphorus, carbonyl oxygen, 3-β hydroxy polar oxygen in cholesterol, and methyl groups for (A) the CR-SL system and (B) the random system. The density profiles were averaged over last 50 ns.

tions, and sedimentation. Furthermore, for multilaminar vesicles, the interactions between the bilayers could significantly increase the equilibration time. The experimental equilibration time is that required for the formation of the cholesterol superlattice, whereas the simulation equilibration time is that required for a selected property of the premade SL structure to reach a steadystate value. Although structural changes in the random membrane occur during the simulation time frame, the time required for a random structure to form a SL could be far longer than 200 ns. 3.2. Density Profile. Detailed information of the bilayer structure can be found from the number density profiles of the species and atom groups, shown in Figure 6. These groups include the acyl chain, (POPC C17-CA1 and C36-C49), the POPC head group phosphorus (POPC P8), the acyl chain carbonyl oxygens (POPC O16 and O35), the acyl chain methyl groups (POPC CA2 and C50), and the 3-β hydroxy oxygen in the cholesterol (cholesterol O6). See Figure 1 for the atom numbering. The calculated profiles are the averages of the last 50 ns of all replicate simulations. The density profiles from each replicate run are quite similar, but there are differences between the two structures (p < 0.01 for all differences). The first observation is the difference of membrane thickness between the two systems. The thickness is 4.11 nm for the CR-SL membrane, and 3.97 nm for the random membrane (determined from the relative positions of phosphate density peaks). Both systems have wide distributions of the CH3 groups, showing considerable folding back of the lipid carbon tails.72 The full width at half-maximum of the CH3 peaks for the CR-SL bilayer

Zhu et al. (0.64 nm) is less than that for the random bilayer (0.81 nm). This suggests that the thinner random membrane is the result of more lipid tails folding back. In both configurations, the maximum cholesterol density overlaps the POPC acyl chain density curves, indicating that cholesterol is located primarily in the hydrophobic area of the bilayer. This phenomena has been reported in previous studies.19 At the center of the membrane, there is more cholesterol (6.24 atom/nm3) in the random system than in the CR-SL system (4.61 atom/nm3). The distances between the two cholesterol peaks also show significant differences: 2.22 nm for CR-SL, which is 54% of the SL bilayer thickness, and 1.98 nm for random membrane, which is only 50% of the random bilayer thickness. To verify the difference in cholesterol location, we also computed the average distance from the cholesterol COM in each leaflet to the membrane center, 1.03 ( 0.02 nm in CRSL and 0.93 ( 0.02 nm in random bilayer (data not shown). This agrees with the distance between the cholesterol peaks and suggests that the cholesterol stays closer to the membrane center in the random system. The folding back of the acyl chains produces shorter hydrophobic tails in the random structure, which induces the cholesterol to stay at the bilayer center. These results will be found consistent with the radial distribution function, as discussed below. In both systems, the maximum density (the most probable location) of the cholesterol O6 hydroxyl oxygen is near that of the acyl chain carbonyl oxygens (O16, O35) and overlaps with the density peak of the P8 phosphorus. The close proximity suggests the possibility of hydrogen bonding between cholesterol and POPC.5,18 The number density of cholesterol atoms as well as the other differences between the CR-SL and random membranes are summarized in Table 1. 3.3. Deuterium Order Parameters of Acyl Chains. To investigate the lipid ordering, the deuterium order parameters were computed. Experimentally, it is defined as

SCD )

〈23 cos θ - 21〉 2

(3)

where θ is the angle between the CD bond vector and the bilayer normal, and the broken brackets imply averaging over time and molecules. The calculated deuterium order parameters profiles of sn-1 and sn-2 chains of the CR-SL and random systems are shown in Figure 7. Because these simulations used a unitedatom model for the acyl chains, the position that a deuterium associated with a carbon would occupy is determined for each successive triplet of CH2 groups. The carbon labled 1 in Figure 7 corresponds to POPC C17 for the sn-2 chain or C36 for the sn-1 chain (Figure 1). The order parameters allow simulation results to be related to experiment through 2H NMR (deuterium nuclear magnetic resonance) data, and POPC and POPC/cholesterol systems have been measured.73-76 SCD of pure POPC lipids were first obtained by using specially labeled lipids in 2H NMR experiments.73,74 An improved method based on the 2H NMR spectra was introduced by Lafleur et al.75 to determine the order parameters of POPC tails. The order profiles of the sn-1 chain from two different methods agree. Lafleur and co-workers76 extended their 2H NMR studies to POPC/cholesterol systems with various cholesterol concentrations: 0.05, 0.10, 0.20, 0.30, 0.45 mol %. Their results showed that the order parameters of the sn-1 chain increased with increasing cholesterol mole fractions. The addition of cholesterol increased the order parameters of POPC sn-1 middle carbons by a factor of 1.8 at Xchol ) 0.45, 1.55 at Xchol ) 0.30, and 1.29 at Xchol ) 0.20 compared to those of the

Effect of Molecular Organization of Lipid Components

J. Phys. Chem. B, Vol. 111, No. 37, 2007 11027

TABLE 1: Summary of Differences between the CR-SL and Random Membranes, Mean from Four Replicates ( Standard Deviation, as Well as the Statistical Significance of the Difference structural parameter surface area (nm2) membrane thickness, nm CH3 peak fwhm, nm cholesterol density of the membrane center (atoms/nm3) order parameters, sn-1 order parameters, sn-2 no. of H bonds

CR-SL POPC CHOL

C4 C8 C13 C4 C8 C13 CHOL-water POPC-water sn-1 CdO-water sn-2 CdO-water POPC-CHOL

pure POPC bilayer.73,75 Of their compositions, only 0.20 was a critical composition for a SL. In Figure 7, the computed order parameters are compared with experimental values for POPC and POPC/CHOL bilayers.73 Both systems have larger values for the order parameters of the two acyl chains than experimental NMR measurements of the pure POPC bilayer,73 which shows that the effect of cholesterol is to increase the acyl chain order, particularly in the middle of the acyl chains where the cholesterol rings are

Figure 7. Deuterium order parameters SCD of sn-1 chain (A) and sn-2 chain (B) for both the CR-SL and the random system. The experimental data for a pure POPC bilayer were reported by Seelig and Waespe-Sarcevic,73 and the data for a POPC bilayer with 30% cholesterol are from Lafleur et al.76 The increased order of the chains is consistent with experimental data and suggestions that cholesterol increases membrane order.15,16,76,77

0.5716 ( 0.0005 0.2974 ( 0.0002 4.11 ( 0.02 0.64 ( 0.04 4.61 ( 0.23 0.266 ( 0.014 0.264 ( 0.011 0.207 ( 0.021 0.290 ( 0.015 0.295 ( 0.018 0.181 ( 0.027 23.6 ( 4.5 460.0 ( 6.4 45.8 ( 2.1 105.6 ( 1.9 43.7 ( 1.4

random 0.5819 ( 0.0004 0.3055 ( 0.0003 3.97 ( 0.06 0.81 ( 0.02 6.24 ( 0.60 0.242 ( 0.013 0.247 ( 0.017 0.183 ( 0.011 0.262 ( 0.018 0.267 ( 0.012 0.150 ( 0.009 27.7 ( 4.8 471.4 ( 6.3 49.4 ( 1.4 109.5 ( 3.0 40.3 ( 1.3

p< 0.0001 0.0001 0.010 0.010 0.005 0.010 0.050 0.050 0.010 0.005 0.010 0.050 0.005 0.005 0.010 0.050

located.19,48 The order parameters for the sn-1 chain in the CRSL system is significantly (p < 0.05) higher than that in the random system for all tail-group carbons. The order parameters at the carbon 4, 8, and 13 positions for the CR-SL and random bilayers are also compared in Table 1. The sn-2 chain shows less difference between systems, because of the unsaturated double bond (C24dC25 in Figure 1) and because it is further from the bilayer center than the sn-1 chain. Nevertheless, the sn-2 chain in the CR-SL has significantly higher order (p < 0.10) except for the unsaturated double bond carbons. 3.4. Hydrogen Bonding. Hydrogen bonding plays an important role in lipid/water, cholesterol/water, and lipid/ cholesterol interactions.5,18,78 Membrane properties differ between random and CR-SL distributions, possibly a result of differences in hydrogen bonding between the two arrangements of cholesterol. The number of hydrogen bonds for several donor-acceptor species pairs were computed for the last 100 ns of the simulation: cholesterol/water, POPC/water, sn-1 carbonyl oxygen (O35 in Figure 1)/water, sn-2 carbonyl oxygen (O16 in Figure 1)/water, and POPC/cholesterol are shown in Figure 8. In this study, a hydrogen bond was assumed to have formed if the donor-acceptor distance r e rHB ) 0.35 nm and the hydrogen-donor-acceptors angle R e RHB ) 60°.79 Here rHB denotes the length of a hydrogen bond and R denotes angle. To decrease uncertainty, each bilayer leaflet was treated independently, so that eight observations were available for each interacting pair. The Mann-Whitney test was used for significance, and the number of hydrogen bonds was averaged over the last 10 ns of the simulation. The number of hydrogen bonds did not appear to vary appreciably with time, and visual examination of the data suggests that 10 ns is a reasonable time scale for the change in the number of hydrogen bonds. The averaged points provided a single value as the observation for each monolayer. For each system, phosphate oxygen (O7, O9O11) and carbonyl oxygens (O16, O35) were acceptors; cholesterol hydroxyl groups and water could be donors as well as acceptors. Panel A of Figure 8 gives the number of hydrogen bonds between cholesterol and water. In the CR-SL system, the cholesterol forms per bilayer leaflet 23.6 hydrogen bonds with water molecules, but 27.7 bonds in the random system, p < 0.05. Clearly, the cholesterol in the random system is more accessible to water, which suggests that the well-dispersed cholesterol in the CR-SL is shielded by POPC molecules, even though the cholesterol in the CR-SL bilayer is closer to the bilayer/water interface (Figure 6). The cholesterol/water interac-

11028 J. Phys. Chem. B, Vol. 111, No. 37, 2007

Figure 8. Number of hydrogen bonds between different interaction pairs: (A) cholesterol/water, (B) POPC/water, (C) sn-1 carbonyl oxygen (O16)/water, (D) sn-2 carbonyl oxygen (O35)/water, and (E) POPC/ cholesterol (O6). The differences between CR-SL and the random structure are summarized in Table 1.

tion appears dominated by the exposed cholesterol from small clusters formed as a result of random distribution in the membrane. In agreement with the predictions of the umbrella model,44,46 the cholesterol appears to be shielded by the phospholipid head groups to prevent unfavorable interactions between water and the hydrophobic part of the cholesterol. The hydrogen-bonding interactions of all donors and acceptors of POPC: sn-1 carbonyl oxygen, and sn-2 carbonyl oxygen with water are shown in Figure 8, parts B, C, and D, respectively. In every case, the random system has significantly more bonds: 471 to 460 (POPC/water), 49.4 to 45.8 (O35 sn-1-Cd O/water), and 110 to 106 (O16 sn-2-CdO/water), p < 0.01. Apparently, the more ordered structure of the CR-SL system reduces the penetration of small water molecules, which may relate to cholesterol-induced reduction of the passive bilayer permeability.24,25 Because of the double bond (C24dC25 in Figure 1), there is a bend in the sn-2 chain: the segment before C24 lies parallel to the membrane surface and the segment after C25 is perpendicular to the membrane surface.80 So the average position of the sn-2 chain is closer to the membrane/water interface than that of the sn-1 chain. As a result, the sn-2 carbonyl oxygen can form more hydrogen bonds with water than that of the sn-1 chain.

Zhu et al. Panel E of Figure 8 shows the hydrogen bonding between POPC and cholesterol. Here the phosphate oxygens and carbonyl oxygens both form hydrogen bonds with cholesterol hydroxy groups. This behavior is suggested by the density profiles, Figure 6. Cholesterol forms about 10% more bonds with POPC in the CR-SL system (43.7) than in the random system (40.3). At a mole fraction Xchol ) 0.40, cholesterol molecules are well separated in the CR-SL system, so each cholesterol is surrounded by POPC. The wide separation increases the opportunity for hydrogen bond formation. 3.5. Radial Distribution Function. The phospholipidcholesterol association and structural properties of the bilayer can be examined by use of the radial distribution function (rdf) of the appropriate atom pairs. Figure 9 shows the radial distribution function of three atom pairs: (1) cholesterol hydroxy oxygen (O6) and POPC sn-1 carbonyl oxygen (O35), (2) cholesterol hydroxy oxygen (O6) and POPC sn-2 carbonyl oxygen (O16), and (3) cholesterol hydroxy oxygen (O6) and POPC phosphate oxygen (O7, O9-O11). The cholesterol oxygen (O6) and POPC carbonyl oxygens for both CR-SL and random systems have the same rdf curve shape that displays a sharp primary peak at 0.3 nm with a broad secondary peak at 0.5 nm, and little structure after 0.5 nm. At this level, two systems have the same structure. The height of the rdf peak for cholesterol oxygen and sn-1 carbonyl oxygen is much higher (almost four times) than that for cholesterol oxygen and sn-2 carbonyl oxygen, indicating that the cholesterol prefers to stay at the level of the unsaturated sn-2 chain. For the cholesterol oxygen and phosphate oxygens, there is a strong peak within the hydrogen-bonding range of 0.35 nm and a smaller peak near 0.5 nm for the CR-SL system but little structure for the random system. We conclude that the carbonyl oxygens are the only hydrogen bond acceptor in the random system, but both the phosphate oxygens and carbonyl oxygens are acceptors in the CR-SL system. Apparently, cholesterol in the CR-SL membrane has more freedom to populate the head group region but in the random membrane remains closer to the bilayer center. This interpretation is consistent with the results of the density profile and agrees with the predictions of Chong,37 who proposed the cholesterol SL theory to explain the fluorescence intensity drops at critical mole fractions. Similar results were reported by Chiu and co-workers18 in a MD study of a DPPC/cholesterol mixture with 50% cholesterol and rough SL-like structure, although they did not have a random structure for comparison. As suggested above, the increased number of cholesterol-water hydrogen bonds in the random membrane are most likely from cholesterol in POPC-free clusters, rather than from cholesterol dispersed in the POPC. Cholesterol dispersed in POPC would tend to be be found nearer the bilayer center. One question these simulations were intended to address was whether the widely spaced superlattice structure was more stable than a random structure. The stability was investigated by observing the time-evolution of the radial distribution function. Figure 10A,B shows the radial distribution function between pairs of cholesterol hydroxy oxygen. Evolution of the system was examined starting at 150 ns, the time required for equilibration, and at 10 ns increments thereafter. Parts A and B of Figure 10 show that the cholesterol arrangement of the CRSL system undergoes little change, compared to the random structure of panel B. The cholesterol molecules maintain the well-separated 1 nm distance. In Figure 10B, the random system shows a strong peak at approximately 0.6 nm, but there is a smaller peak at about 0.35

Effect of Molecular Organization of Lipid Components

Figure 9. Radial distribution function for atom pairs in the CR-SL and random membrane. Shown is the radial distribution function between (A) cholesterol hydroxy oxygen-POPC sn-1 carbonyl oxygen, (B) cholesterol hydroxy oxygen-POPC sn-2 carbonyl oxygen, and (C) cholesterol hydroxy oxygen-POPC phosphate oxygen.

nm, possibly a result of cholesterol hydroxy groups hydrogen bonding. Interestingly, and most importantly, as the simulation time increases, the height of the strong peak at 0.6 nm decreases and a new peak begins to form. In the random system, the cholesterol molecules appear to diffuse from cholesterol-rich regions into POPC-rich regions, although the simulation is too short to tell if the peak at 1 nm signals the evolution of a superlattice structure. Figure 10C shows the number of contacts between POPC and cholesterol as a function of time. The contacts achieved a stable value after 110 ns in the CR-SL system, but kept

J. Phys. Chem. B, Vol. 111, No. 37, 2007 11029

Figure 10. The radial distribution function between pairs of cholesterol hydroxy oxygen at different time frames for (A) the CR-SL system and (B) the random system, and the number of contacts between POPC and cholesterol within a cutoff distance of 0.6 nm (C). There is less change in the rdf peak magnitude in the ordered CR-SL system than in the random system, over the last 50 ns. The random system evolves with time and appears to be forming a peak at 1 nm, the dominant peak location of the CR-SL system.

increasing during the entire simulation for the random system. Increasing POPC contacts suggest that cholesterol in the random system was entering the POPC-rich regions. Taken together, the information from the time-dependent rdfs and the number of contacts suggests that the structure of the CR-SL membrane was well-maintained during the 200 ns simulation, but the structure of the random membrane evolved, and the cholesterol tended to become more separated. 3.6. Summary and Conclusions. The results of 200 ns MD simulations on POPC/cholesterol bilayers with CR-SL structure and cholesterol-random-distributed structure at Xchol ) 0.4 have been presented. The simulations, 200 ns, were much longer than those of earlier studies. Two important observations result solely from the length of the simulation: (i) The time required for the system to reach equilibrium depends on the initial structure of

11030 J. Phys. Chem. B, Vol. 111, No. 37, 2007 the membrane and (ii) this equilibrium time (as much as 150 ns) was much longer than that required for single-component membrane systems,81-83 even those that contain membrane proteins.84-88 In addition to the relatively long simulation time, replicate runs for each system allow assignment of statistical significance to the properties between the two systems. The significance was computed by use of a nonparametric statistical analysis that used data from all simulations. The structure of the lipid membrane is shown to affect a number of properties of the lipid bilayer. For the area per lipid and average membrane thickness the effect of the membrane structure was small, but statistically significant. The smaller area per molecule and thinner membrane of the CR-SL system was consistent with the cholesterol condensing effect16,20-22 on lipid bilayer. We would expect this effect to be more pronounced for cholesterol distributed uniformly than for the “pockets” rich in cholesterol found when the membrane structure is random. It is believed that the acyl chain order can be increased if cholesterol is present in the bilayer,15,16,76,77 and our computational order parameters are significantly higher in the CR-SL membrane, reflecting that increase. The previous experimental data73-76 predicted that the addition of 40% cholesterol in a POPC bilayer would increase the deuterium order parameters by a factor of 1.55 to 1.8 for acyl chain middle carbons. Compared to POPC 2H NMR experiments,73-75 deuterium order was observed in our simulated CR-SL and random membranes, respectively. The data for the CR-SL membrane were slightly closer to experimental results.76 Hydrogen-bonding results suggest that the CR-SL structure is more likely to prevent small water molecules from diffusing into the bilayer hydrophobic interior. Hydrogen bonding is significantly different between the two systems. The reduced water diffusivity of the CR-SL is consistent with the recent transmembrane diffusion studies.16,24,25 Visualizing the trajectory during the 200 ns simulations by using VMD62 indicates that the CR-SL structure is preserved during the long NPT run, whereas the cholesterol in the random system tended to move to the lipid-rich region. This observation was quantified by use of the time-dependent radial distribution functions. The rdf and POPC/CHOL contacts give direct evidence that the CR-SL structure was well maintained during the simulation, but that cholesterol in the random system diffuses into the POPC-rich region. These results appear consistent with experimental data.7,15,32,37,38,40,41,70 The cholesterol rdf and the POPC-cholesterol contacts also suggest a tendency for cholesterol in the random membrane to become more separated and ordered, although the simulation is too short to determine the final equilibrium cholesterol arrangement. Acknowledgment. Support from National Science Foundation Grant 0134594 to M.W.V. and the Robert A. Welch Research Foundation (D-1158) to K.H.C. is gratefully acknowledged. The authors benefited from enlightening discussions with J. Huang and helpful comments and insight from M. R. Ali. References and Notes (1) Murzyn, K.; Ro´g, T.; Jezierski, G.; Takaoka, Y.; PasenkiewiczGierula, M. Biophys. J. 2001, 81, 170-183. (2) Marrink, S. J.; Sok, R. M.; Berendsen, H. J. C. J. Chem. Phys. 1996, 104, 9090-9099. (3) Feller, S. E.; Pastor, R. W.; Rojnuckarin, A.; Bogusz, S.; Brooks, B. R. J. Phys. Chem. 1996, 100, 17011-17020. (4) Mukhopadhyay, P.; Vogel, H. J.; Tieleman, D. P. Biophys. J. 2004, 86, 337-345.

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