Different effects of cholesterol on membrane permeation of arginine and tryptophan revealed by bias-exchange metadynamics simulations

Experiments have shown that cholesterol influences the membrane permeability of small molecules, amino acids, and cellpenetrating peptides. However, their exact translocation mechanisms under the influence of cholesterol remain poorly understood. Given the practical importance of cell-penetrating peptides and the existence of varied cholesterol contents in different cell types, it is necessary to examine the permeation of amino acids in cholesterol-containing membranes at atomic level of details. Here, bias-exchange metadynamics simulations were employed to investigate the molecular mechanism of the membrane permeation of two amino acids Arg and Trp important for cell-penetrating peptides in the presence of different concentrations of cholesterol. We found that the free energy barrier of Arg+ (the protonated form) permeation increased linearly as the cholesterol concentration increased, whereas the barrier of Trp permeation had a rapid increase from 0 mol. % to 20 mol. % cholesterol-containing membranes and nearly unchanged from 20 mol. % to 40 mol. % cholesterol-containing membranes. Arg0 becomes slightly more stable than Arg+ at the center of the dipalmitoylphosphatidylcholine (DPPC) membrane with 40 mol. % cholesterol concentrations. As a result, Arg+ has a similar permeability as Trp at 0 mol. % and 20 mol. % cholesterol, but a significantly lower permeability than Trp at 40 mol. % cholesterol. This difference is caused by the gradual reduction of water defects for Arg+ as the cholesterol concentration increases but lack of water defects for Trp in cholesterol-containing membranes. Strong but different orientation dependence between Arg+ and Trp permeations is observed. These results provide an improved microscopic understanding of amino-acid permeation through cholesterol-containing DPPC membrane systems. © 2019 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/1.5082351


I. INTRODUCTION
All living cells have plasma membranes that are made up of phospholipids, interweaved with cholesterol and proteins.Cholesterol is the most common and important sterol in mammalian plasma membranes with its concentration ranging from 20% to 40%. 1,2Cholesterol, a small molecule composed of hydrophobic steroidal rings with a hydrophilic hydroxyl group, can strongly affect membrane's structural and physical properties. 3,4This includes reduction of the The Journal of Chemical Physics ARTICLE scitation.org/journal/jcpfree area and volume of a bilayer 5 and enhancement of the bilayer order 6 and stiffness.The membranes of different cell types can vary in molecular composition, including the level of cholesterol. 7As the cholesterol level in cell membranes plays an essential role in health and disease, 8,9 it is essential to employ cholesterol-containing phospholipid membranes, rather than phospholipid-based membranes alone to investigate the mechanism of cell penetration.
In this study, we focus on the effects of the cholesterol level on membrane permeation of two amino acids: arginine and tryptophan.These two amino acids are the key amino acid residues in cell-penetrating peptides (CPPs), 10,11 the peptides that can permeate cell membranes.CPPs vary greatly in amino acid compositions and hydrophobicity with some patterned in an amphipathic manner.The positively charged arginine (Arg+) amino acid is often enriched in the non-amphipathic CPPs. 12,13Its binding to a cell membrane permits insertion of other hydrophobic residues more deeply into the membrane. 12Tryptophan (Trp) is one of the most hydrophobic residues.Its importance in cell penetrating has been demonstrated by the fact that its mutation to Leu 14 or Phe 15 will abolish the cell-penetrating capability of the peptide RW9, a peptide that is made of arginine (R) and tryptophan (W) only with a sequence of RRWWRRWRR-NH 2 .Understanding cell-penetrating capability of important amino acid residues such as Arg+ and Trp is the first step for understanding the cell-penetrating mechanism of peptides.
The role of cholesterol in the uptake of amino acids [16][17][18] has been studied by several experiments.Naoi et al. 16 found that the permeability of alanine decreases with an increase of cholesterol in the phosphatidylcholine liposome.Sada et al. 17 also found that increasing the concentration of cholesterol in the small unilamellar vesicles composed of dimyristoylphosphatidylcholine (DMPC) decreased the permeabilities of alanine, lysine, glutamate, and arginine.Chakrabarti et al. 18 reviewed the overall trend of decreasing permeation of a few amino acids in the presence of cholesterol.However, the exact translocation mechanism and possible structural changes in the membrane and amino acids during cell permeation remain poorly understood.
The effects of cholesterol on membrane permeability of a few small solute molecules [19][20][21][22][23] or a peptide 24 have also been studied by molecular dynamics (MD) simulations.Hub et al. 19 have performed umbrella sampling simulations on the influence of cholesterol on cell permeability of six different solutes (ethanol, ammonia, propane, benzene, nitric oxide, and neopentane) in different biological membranes [palmitoyloleoylphosphatidylcholine (POPC), DMPC, palmitoyloleoylphosphatidylethanolamine (POPE), dipalmitoylphosphatidylcholine (DPPC)] with cholesterol contents varying from 0 mol.% to 50 mol.%.The simulations showed that cholesterol reduced the permeability of solute.Tyrone et al. 20 calculated the free energy barrier for an anticancer drug doxorubicin across the DPPC membrane composed of 0, 15, and 30 mol. % cholesterol by using umbrella sampling MD simulations and the distance between doxorubicin and the bilayer was used as reaction coordinate.Consistent with the experimental trend, these simulations showed that cholesterol increased the free energy barriers of permeation.Moreover, they showed that doxorubicin permeation relied on the bilayer deformation and water leakage due to the attraction between doxorubicin and headgroups of DPPC.Zhang et al. showed that cholesterol acts as a barrier for the uptake of cancer drug pirarubicin but not for cancer drug ellipticine due to different polar propensities of the two drugs according to umbrella sampling MD simulations. 21Also using umbrella sampling MD simulations, Khajeh et al. calculated the free energy barrier for the hydrophilic anticancer drug 5-fluorouracil 22 and the hydrophobic drug ibuprofen 23 across the DMPC membrane with 0, 25, and 50 mol.% cholesterol.The free energy barrier for translocation increases along with the increase in cholesterol concentration for hydrophilic 5-fluorouracil but does not change much for ibuprofen for the membrane with 25 mol.% cholesterol and increases significantly for the membrane with 50 mol.% cholesterol.MD simulations also provided valuable insight on the structures and translocation thermodynamics of the MARTINI coarse-grained model of the TAT peptide across a series of membranes in the presence of 0-30 mol.% cholesterol 24 by using umbrella sampling along the distance between the peptide and the bilayer.A high cholesterol concentration in the membrane impedes peptide translocation.These studies highlight the usefulness of MD simulations to elucidate molecular-level mechanisms of cell permeation through a cholesterol-containing lipid bilayer.
However, all existing studies of free energy barriers for molecular permeation of a cholesterol-containing lipid bilayer employed one-dimensional umbrella sampling MD simulations along the distance between a solute molecule and a bilayer (z-direction).Although umbrella sampling is an efficient method for obtaining free energy changes along with a single reaction coordinate, more than a single reaction coordinate is required for an accurate description of Arg+ and Trp in cell permeation due to orientation dependence. 25Moreover, strong lipid headgroup-solute electrostatic interactions require long equilibration simulation times to explore the large conformational space. 26In our previous study, 27 we found that bias-exchange metadynamics (BE-MetD) simulations with both directional and orientational collective variables (CVs) allow efficient sampling of conformational space 26 and produce highly reproducible free energy surfaces (FESs) of common 20 amino acid transfer from water to the pure DPPC bilayer.
Here, BE-MetD simulations were performed to investigate the permeation of Arg+ and Trp in the cholesterolcontaining dipalmitoylphosphatidylcholine (DPPC) membrane system.DPPC is a commonly used model membrane for mammals. 28Three cholesterol concentrations (0, 20, and 40 mol.%) were used in the simulations.To the best of our knowledge, this is the first MD simulations to investigate the effects of cholesterol on amino-acid membrane permeation.We employed the commonly used z component of the distance between the amino acid and the bilayer, the backbone dihedral angles ϕ and ψ of the amino acid as collective variables, and Gaussian potentials to bias against the previously visited regions. 29We found that Arg permeation is affected II.METHODS

A. MD simulation of amino acid-cholesterol-lipid bilayer systems
We performed four sets of simulations to investigate the permeation of Trp and Arg+ in neutral zwitterionic DPPC membranes in the presence of 20 and 40 mol.% cholesterol and compared with 0 mol.% cholesterol simulations obtained previously. 27For investigating the protonation state of arginine, we also performed two sets of simulations to analyze the permeation of Arg0 (the neutral deprotonated form arginine) in pure DPPC membrane and 40 mol.% cholesterol DPPC membrane.The initial lipid bilayer systems of the zwitterionic DPPC with different cholesterol contents 19 were obtained from https://biophys.uni-saarland.de/cholmembranes.html.For each simulation system, a single amino acid Arg+, Arg0, or Trp was placed on the top leaflet of the membrane surface with a distance about 1.4 nm.The amino acid was capped with the acetyl (ACE) group at the N terminus and the NH 2 (CT2) group at the C terminus.All MD simulations were performed under the periodic boundary condition in a rectangular box.The GROningen MOlecular Simulation (GROMOS) 53A6 force field for Arg+, Arg0, or Trp with the single point charge (SPC) 30 water model, Berger et al. 31 united atom force field for the DPPC bilayer, and the parameters from Höltje et al. for cholesterol. 32fter we have solvated the amino acid-cholesterol-lipid bilayer system, one Cl − anion was added to neutralize the +1 charge of Arg+ and none was added for Arg0 and Trp.The initial simulation systems for Arg+ are shown in Fig. 1.The composition of each simulation system is summarized in Table I.Then, extensive energy minimization was performed, followed by equilibration simulations in the NVT ensemble for 2 ns and in the NPT ensemble for 5 ns.Temperature was maintained at 323 K (which is slightly higher than the DPPC phase transition temperature 315 K 33 ) using a velocity rescaling and a coupling time of 0.1 ps.The pressure was fixed at 1 atm using a semi-isotropic Parrinello-Rahman barostat with a time Long-range electrostatic interactions were computed using the particle mesh Ewald method with a grid spacing of 0.12 nm. 35Bond lengths were constrained by using the Linear Constraint Solver (LINCS) algorithm.van der Waals interactions were calculated using a cutoff of 1.2 nm.

B. Bias-exchange metadynamics (BE-MetD) simulations
All BE-MetD simulations were carried out by using the GROMACS 4.6.2package 36 with PLUMED 1.3 plugin. 37BE-MetD 38 is an integrated tool based on the combined use of replica exchange and metadynamics.In BE-MetD, the dynamics of the walkers (the replicas of the system) are run in parallel biased with a history-dependent potential energy constructed as a sum of Gaussian functions or hills.The bias potential acts on one collective variable (CV) or a few selected CVs.As the simulation proceeds, more Gaussians are added until the system explores the full energy landscape.The repulsive potential makes it possible for the system to diffuse freely between states after about 100 ns or less.These simulations were performed with four replicas, one replica without any bias and other three replicas biased on three separate collective variables (CVs).The three CVs were employed as the z component of the distance between the center of the amino acid and the center of bilayer molecules (CV1), the backbone dihedral angles ϕ (CV2) and ψ (CV3) of an amino acid.During BE-MetD simulations, velocities and conformations of the four different walkers (the replicas of the system) were exchanged every 30 ps according to a Metropolis criterion periodically. 39The Gaussian height is 0.04 kJ/mol per ps, and  the Gaussian widths for z, ϕ, and ψ are 0.2 nm, 0.314 rad, and 0.314 rad, respectively.The simulation time of each replica is 200 ns.

A. Examination of convergence
In our previous study on membrane permeation of 20 different amino acids, 27 the convergence of free energy surfaces (FESs) of Arg+ and Trp for the cholesterol-free system was confirmed by the similarities among the FESs generated from different simulation lengths and from the simulations with different initial velocities and conformations.Here, we employed the same simulation lengths for cholesterol-containing systems.The convergence of BE-MetD simulations is illustrated by repeated sampling of the whole conformational space during the time evolution of CV1 for Arg+ and Trp at different cholesterol contents (Fig. S1 of the supplementary material).For example, the free-energy minimum for Arg+ at the DPPC bilayer with 40 mol.% of cholesterol is quickly filled by biased Gaussian potentials after ∼70 ns.This is illustrated by the mobility of Arg + across the membrane.After ∼100 ns, the motion of the system becomes diffusive and unbound in the region of CV1 space between ∼−2 and 5 nm.

B. FESs for transferring an amino acid from water to the lipid bilayer
Figure 2 shows the FESs of translocating Arg+ and Arg0 [Fig.2(a)] and Trp [Fig.2(b)] into the bilayer along the z direction at 0, 20, and 40 mol.% of cholesterol where the cholesterol-free results were obtained previously for Arg+. 27The error bars were calculated based on the FESs TABLE II.The free energy costs (in units of kJ/mol) of translocating two amino acids across the DPPC membrane with different concentrations of cholesterol, including the free energy barrier from water to the center of the bilayer; and the interfacial free energy minima and the free energy barrier from the free energy minimum to the center of the bilayer (location of the maximum).

From water
From  generated from different lengths of the simulation after excluding the equilibration period.Small error bars confirm sufficient exploration of the whole conformational space.Figure 2 reveals interesting similarity and difference between the FES of Arg+ and that of Trp.Arg+ and Trp have similar shift of free energy minima when comparing cholesterol-free to cholesterol-containing systems.The positions of minimal free energy for Arg+ are located at 1.4, 2.0, and 2.0 nm from the center of the bilayer for 0, 20, and 40 mol.% cholesterol, respectively.The corresponding values for Trp are 1.4,1.9, and 1.8 nm, respectively.This shift is largely due to the shift of the central location of the phosphate group as shown from the density of a phosphate group in Figs.2(c) and 2(d), respectively.In other words, the free energy minimum is located where the interaction between Arg+ and the negatively charged phosphate group is expected at the maximum.However, the minimum for Trp shifts slightly deeper inside of the most probable location of the phosphate group.This free energy minimum is located where the interaction between Trp, negatively charged phosphate group in the lipid, and the hydrophilic hydroxyl group in the cholesterol is expected at the maximum.Arg+ has a lower free energy minimum than Trp because Arg+ has a stronger electrostatic interaction with the negatively charged phosphate group.
All maximal values of the free energy barrier of permeation are located at the center of the lipids.The main difference between Arg+ and Trp is the free-energy maximum in response to the change in the cholesterol concentration.The free-energy maximal values for both Arg+ and Trp increase significantly as the concentration of cholesterol increases from 0 to 20 mol.%, but only the maximal value of Arg+ continues to increase as the concentration of cholesterol further increases to 40 mol.%.In contrast, the maximal freeenergy value of Trp decreases somewhat as the concentration of cholesterol increases from 20 mol.% to 40 mol.%.Thus, even for Trp, a hydrophobic amino acid, our analysis showed a substantial energy cost for transfer from water to the bilayer center for 0 mol.% cholesterol concentration (Table II), which was much higher than that compared to −4.9 kJ/mol reported by MacCallum et al. 40 This discrepancy is likely caused by our use of acetyl and amino groups as the caps of the termini, whereas the side chain analogue was used in the work of MacCallum et al.
To quantify the permeability, we define the free energy barrier as the difference in the FESs from the minimum to the maximum (Table II).For Arg+, the free energy barriers of permeation are 60, 84, and 120 kJ/mol for 0, 20, and 40 mol.% cholesterol concentrations, respectively.The free energy barrier height is close to be linearly dependent on the cholesterol concentration (about 40% increase as the cholesterol concentration changes from 0 mol.% to 20 mol.% and from 20 mol.% to 40 mol.%).However, the free-energy barrier height for Trp increases by about 70% from 40 kJ/mol at 0 mol.% to 67 kJ/mol (∼70% increase) at 20 mol.% cholesterol concentrations, but only 7% from 67 kJ/mol at 20 mol.% to 72 kJ/mol at 40 mol.% cholesterol concentrations.In other words, the impact of cholesterol concentration on Trp permeation is more limited than that on Arg+ permeation after the initial dramatic increase.As shown in Table II, the level of difficulty for Arg+ permeation from water to inside the membrane is similar to that of Trp with 23 versus 18 kJ/mol free energy cost at 0 mol.% and 44 versus 47 kJ/mol free energy cost at 20 mol.% cholesterol.However, Arg+ is significantly more difficult to penetrate at 40 mol.% cholesterol with a free-energy loss at 67 kJ/mol for Arg+, but only 42 kJ/mol for Trp.
To investigate the stabilities of different protonation states of arginine, we have obtained the FESs of ionized (Arg+) and neutral (Arg0) forms of arginine.In Fig. 2, the FES of Arg0 is shifted by the free energy for arginine protonation (upward about 31 kJ/mol). 40Arginine is in the ionized (Arg+) form even at the hydrophobic core of the pure DPPC membrane.However, the neutral (Arg0) form becomes slightly more stable than the ionized (Arg+) form at the center of the DPPC membrane with 40 mol.% cholesterol concentrations.

C. Molecular mechanism of permeation
To further elucidate the molecular mechanisms of membrane permeation, we employed METAGUI3 41 software (downloaded from the website https://github.com/metagui/metagui3), which is a Visual Molecular Dynamics (VMD) 42 interface for calculating the free energy landscape as a function of a subset of the CVs.First, the trajectory frames after equilibration were grouped into microstates in the selected CV space.Then, the equilibrium free energy of each microstate is calculated by the weighted-histogram method 43 by removing the effect of the history-dependent bias potential.The 2D free energy landscapes were obtained along the z-projection distance (X-axis) and the number of hydrogen bonds between an amino acid and water molecules (Y-axis) (Fig. 3) and along the z-projection distance (X-axis) and the number of hydrogen bonds between an amino acid and the headgroup of lipids (Y-axis) (Fig. 4).
According to 2D free energy landscapes, the cell permeating process of the amino acids can be described as follows.For Arg+ in the cholesterol-free membrane, some water molecules can enter through the bilayer with the amino acid as a part of the hydration shell (the top panels of Fig. 3), even reaching the center of the bilayers.A large number of hydrogen bonds between Arg+ and the headgroup of lipid (up to 7, top panels of Fig. 4) are due to a large water defect and penetration of DPPC headgroups into the center of the bilayer for the pure DPPC system (snapshots of Arg+ at the center of the bilayer are shown in Fig. 5).For the cholesterolcontaining membrane, Arg+ continues to cause a significant inward bend of the membrane surface without DPPC penetration.This inward bend allows Arg+ to continue its strong interactions with lipids and waters, even at the center of lipids.However, such a bend is more difficult to form as the cholesterol concentration increases.The difficulty may be the cause of a near-linear dependence of the free-energy barrier on the cholesterol concentration.
On the other hand, the interaction between Trp and the membrane is not strong enough to bend the lipid bilayer.In the pure DPPC bilayer, some water molecules may move through the bilayer with Trp, even at the center of the bilayers (the bottom panels of Fig. 3).However, nearly no water molecules accompany the membrane permeation of Trp for 20 and 40 mol.% cholesterol-containing bilayers (snapshots of Trp at the center of bilayer are shown in Fig. 6).Moreover, Trp has few interactions with lipid headgroups for 20 and 40 mol.% cholesterol-containing bilayers [up to 2 hydrogen bonds, Fig. 4 (bottom panels)].Together, this is likely the reason for a dramatic change in the free energy barrier at 20 mol.%, but not at 40 mol.% cholesterol-containing bilayer.
In addition, a clustering method 44 was also used to evaluate the pore formation.This method calculated the minimal distance between the top and bottom leaflet phosphorus and Trp (right panels) permeation along the distance from the center of the membrane.The amino acid orientation is defined by the angle between the membrane normal and the amino acid vector, a vector connecting the mass center of backbone atoms and that of the side chain atoms.
atoms.Two phosphorus atoms are identified as one cluster if the distance is less than 1.2 nm.We define that if only one phosphorus-atom cluster exists, a pore is formed.We found that water pore formation in the lipid bilayer occurs only for Arg+ permeation of the pure DPPC bilayer (shown in Fig. 5).Arginine-rich peptides [such as HIV-1 TAT peptide 45 and cyclic Arg(9) peptide 46 ] were also reported to translocate across the pure DOPC bilayer by forming a water pore.The free energy barrier for translocation by pore formation is lower than that by a pore-free path. 46For 20 mol.% and 40 mol.% cholesterol bilayers, the pore formation is not observed due to the rigidification of the bilayer by cholesterol (see Figs. 5 and 6).As a result, Arg+ can only lead to water defect during membrane permeation.Although different lipid force fields have much different energetic barriers for the bilayer to form pores, the free energy for membrane defect formation can be reconciled by shifting the free energy profiles to account for membrane thickness differences among different force fields. 47In particular, even if single amino acid molecule penetration may not usually be accompanied by water pore formation, it seems possible that a peptide rich in Arg and/or Trp may have a higher possibility to form water pores.

D. Spatial orientation distribution
It is meaningful to examine if there is an orientation dependence of amino acid during membrane permeation.The positively charged side chain of Arg+ interacts strongly with the headgroups of lipids and causes the structural deformation of the membrane.Here, we measure the orientation dependence by the angle between the membrane normal (z-direction) and the amino acid vector defined as a vector connecting the mass center of backbone atoms and the side chain atoms.Figure 7 shows the angle distribution as a function of the distance from the center of the membrane.Each conformation of an amino acid is a dot.In the water layer, the angle has a wide near-random distribution from 0

IV. CONCLUSION
Atomistic BE-MetD simulations and free energy calculations for the two amino acids [Arg (Arg+ and Arg0) and Trp] across DPPC bilayers with and without cholesterol provided detailed insights into the effect of cholesterol on the membrane transport of these two amino acids.We observed that Arg+ and Trp behave differently for membranes with different concentrations of cholesterol.There is a nearlinear increase in the barrier height for Arg+, but a rapid increase followed by a nearly flat free energy profile for Trp as the concentration of cholesterol changes from 0, 20 to 40 mol.%.
The above observed difference is due to lack of water defects in Trp permeation at both 20 mol.% and 40 mol.% cholesterol concentrations but a gradual depletion of water defects in Arg+ permeation.The stronger interaction between Arg+ and the headgroup of the lipid layer leads to the persistent increase in the free energy barrier as the membrane becomes more rigid and difficult to deform for a watermediated permeation.On the other hand, Trp does not deform the membrane and its water-free permeation has a similar free energy cost for 20 mol.% and 40 mol.% cholesterol concentrations.Our results are consistent with the different effects of cholesterol on membrane permeation found for anticancer drugs pirarubicin and ellipticine. 21For pirarubicin, the free energy barrier was strongly increased when cholesterol was present because the translocation mechanism changes from water defect to dehydration.However, for nonploar ellipticine, the free energy barrier remained similar because the translocation mechanism is associated with dehydration with and without cholesterol.That is to say, hydrophobic and hydrophilic molecules respond differently toward increases in cholesterol concentrations.
Direct permeation (without pore formation) in the presence of cholesterol for Arg+ and Trp is consistent with the previous MD simulations. 51No pore formation was observed in the thermodynamic studies of the DPPC membrane in the presence of 20 and 40 mol.% cholesterol.Obviously, pores are more difficult, if not impossible, to form given the fact that cholesterol increases the rigidity of the membrane. 3In all cases, we showed that cholesterol reduces membrane permeation in general for Arg+ and Trp.This is consistent with the previous experimental studies. 16,17his work confirms that atomistic BE-MetD simulations and free energy calculations are a powerful tool for evaluating the molecular permeation through the lipid bilayer.More importantly, it allows the use of multiple reaction coordinates so that both distance and orientation dependence can be accounted for.In our simulations, we employed three CVs: the commonly used z-projection distance between the center of the amino acid and the center of the bilayer and the backbone dihedral angles ϕ and ψ of an amino acid.The conformational distribution along the distance from the center of the membrane and the amino acid orientation (Fig. 7) suggests that the sampling is sufficient.Arg+ orientation is transited from 0 (side chain pointed inward), 90 • (parallel to the water/bilayer interface) to 180 • (main chain pointed inward) as the Arg+ permeates through the bilayer.A strong orientation dependence was also observed for Trp.0]52

FIG. 1 .
FIG. 1.The starting configurations of Arg+ in (a) 20% cholesterol and (b) 40% cholesterol.In the snapshots, the amino acid is shown in green.The lipid nitrogen and phosphorus atoms are shown as blue and orange spheres, respectively.The lipid tails are shown as thin gray lines.The hydrophobic steroidal rings of cholesterols are shown as purple lines.The hydrophilic hydroxyl group of cholesterols is shown as cyan spheres.Water molecules are shown as red (oxygen) and gray (hydrogen) sticks.

FIG. 3 .FIG. 4 .FIG. 5 .
FIG.3.Two-dimensional free energy surfaces for Arg+ (top panels) and Trp (bottom panels) along the z-projection and the number of hydrogen bonds between an amino acid and water molecules.The free energy unit is kJ/mol.

FIG. 6 .
FIG.6.Same as in Fig.5but for Trp at the center of the bilayer with water defect for the pure DPPC bilayer (a), but not at 20% [(b) and (c)] or 40% (d) cholesterol-containing bilayers.In the snapshot, the amino acid is shown in green.The lipid nitrogen and phosphorus atoms are shown as blue and yellow spheres, respectively.The lipid tails are shown as thin gray lines.The hydrophobic steroidal rings of cholesterols are shown as purple lines.The hydrophilic hydroxyl group of cholesterols is shown as cyan spheres.Water is shown as red (oxygen) and gray (hydrogen) cylinders.

FIG. 7 .
FIG. 7.The orientation dependence of Arg+ (left panels) and Trp (right panels) permeation along the distance from the center of the membrane.The amino acid orientation is defined by the angle between the membrane normal and the amino acid vector, a vector connecting the mass center of backbone atoms and that of the side chain atoms.

FIG. 8 . 7 .
FIG.8.Snapshots of (a) Arg+ beginning to enter a bilayer from water (3 nm in the x-axis of Fig.7), (b) Arg+ at the position of the minimal free energy (2 nm in the x-axis of Fig.7), (c) Arg+ at the position of ∼1 nm in the x-axis of Fig.7, (d)Arg+ at the center of the bilayer, (e) Trp at the position of the minimal free energy (1.8 nm in the x-axis of Fig.7), and (f) Trp at the position of ∼1.2 nm in the x-axis of Fig.7.In the snapshot, the side chain of the amino acid is shown in red and the other portion of the amino acid is shown in green.The lipid nitrogen and phosphorus atoms are shown as blue and yellow spheres, respectively.The lipid tails are shown as thin gray lines.The hydrophobic steroidal rings of cholesterols are shown as purple lines.The hydrophilic hydroxyl group of cholesterols is shown as cyan spheres.All water molecules are removed for clarity.

TABLE I .
34mpositions of two simulation systems at different concentrations of cholesterol in term of the numbers of DPPC, cholesterol, and water molecules.×10 −5 bar −1 .34