Effect of Cholesterol on Membrane Dipole Potential: Atomistic and

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Biomolecular Systems

Effect of Cholesterol on Membrane Dipole Potential: Atomistic and Coarse-Grained Molecular Dynamics Simulations Hujun Shen, Mingsen Deng, zhenhua wu, Jihua Zhang, Yachao Zhang, Chengui Gao, and chao cen J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.8b00092 • Publication Date (Web): 23 May 2018 Downloaded from http://pubs.acs.org on May 23, 2018

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Journal of Chemical Theory and Computation

Effect of Cholesterol on Membrane Dipole Potential: Atomistic and Coarse-Grained Molecular Dynamics Simulations Hujun Shen1,2*, Mingsen Deng1,2, Zhenhua Wu2, Jihua Zhang1, Yachao Zhang1, Chengui Gao1, Cao Cen1 1

Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Synergetic Innovation Center of Scientific Big Data for Advanced Manufacturing Technology, Guizhou Education University No.115, Gaoxin Road, Guiyang, Guizhou, 550018, P. R. China

2. Guizhou University of Finance and Economics, School of Information, University City of Huaxi District, Guiyang, Guizhou, 550025, P. R. China

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ABSTRACT The effect of cholesterol on membrane dipole potential has been the subject of a great number of experimental and theoretical investigations, but these studies have yielded different findings and interpretations at high cholesterol concentrations. This suggests that the underlying mechanism of the cholesterol effect is not well addressed. Moreover, as far as we know, none of the previously proposed coarse-grained (CG) models (including MARTINI and its improved versions) has been successfully used to probe the effect of cholesterol on membrane dipole potential, owing to either an inaccurate description of water-cholesterol electrostatics or the neglect of the contribution of cholesterol to membrane dipole potential. In our previous works, we proposed a CG model CAVS (charge attached to virtual site) for lipid and water, showing the advantage of the CAVS model in the calculations of membrane dipole potential as compared to the MARTINI model. In this work, we present the CAVS model for cholesterol in order to enable us to investigate the effect of cholesterol on membrane dipole potential at large spatial scale. Our works showed that the CAVS and CHARMM models produced similar results in the study of the effects of cholesterol on lipid bilayer structures and membrane dipole potential. In particular, by combining the CHARMM and CAVS simulations, we explicitly calculated the individual contributions of membrane components (cholesterol, water, and lipid) to membrane dipole potential at different cholesterol concentrations, and we discovered that an increase in cholesterol content would result in a non-linear variation of the individual contributions of water and lipid with cholesterol concentration. On the other side, we observed that the individual contribution of cholesterol to membrane dipole potential would non-linearly increase with increasing cholesterol concentration. Thus, the effect of cholesterol on membrane dipole potential is complicated owing to the different variation of individual contributions of membrane components (water, lipid, and cholesterol) with cholesterol concentration.


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INTRODUCTION Cholesterol is a vital component in cell membranes, and it has diverse functions including the modulation of the membrane permeability and fluidity.1 This is ascribed to the condensing effect 2-3 of cholesterol in lipid bilayer, which is characterized by an increase in bilayer thickness and order parameter. In particular, the presence of cholesterol in lipid bilayer would induce the formation of cholesterol-mediated microdomains (called “lipid raft”),4-7 which are widely considered to play critical roles in membrane protein localization, cell signal transduction, and some other relevant biological functions. A great number of computational studies on the mixtures of phospholipids with cholesterol have provided valuable insights into the condensing effect of cholesterol in lipid bilayers. Meyer et al.8,9 employed a coarse-grained (CG) model to study the temperature-composition dependence of the lateral organization of cholesterol in dimyristoylglycero-phosphocholine (DMPC) lipid bilayers, providing a microscopic interpretation of the condensing effect of cholesterol. Khelashvili et al.10 carried out atomistic molecular dynamics (MD) simulations to investigate the effect of cholesterol on the cholesterol tilt in DMPC bilayers at various cholesterol concentrations, providing the first computational estimates of the cholesterol tilt modulus. Zhang et al.11 determined the potentials of mean force (PMFs) for transferring cholesterol from lipid bilayer center to bulk water region using atomistic MD simulations, finding that the affinity of cholesterol to saturated lipid bilayers is higher than to unsaturated lipid bilayers. Marrrink and coworkers have developed a popular CG model (namely MARTINI) for lipids and cholesterol,12-14 showing a nice performance in predicting the structural, mechanical, and dynamic properties of cholesterol-containing lipid bilayers. However, the MARTINI model does not report the expected plateau or decrease in bilayer thickness at high cholesterol concentrations, which is observed in experiment or in atomistic MD simulations. To solve this problem, Daily et al.15 presented an angle-corrected MARTINI model (AC-MARTINI) for lipid-cholesterol mixtures, demonstrating that the improved CG



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model captured the expected plateau or decrease in bilayer thickness at high cholesterol concentrations. Apart from the condensing effect of cholesterol, an increase in cholesterol content would substantially influence membrane dipole potential of lipid bilayer. The electric field generated by the dipole potential is estimated to be 108-109 V/m, which is at least one order of magnitude greater than other electric fields (106 -107 V/m) generated by the transmembrane and surface potentials.16 It has been realized that membrane dipole potential greatly influences a variety of biological processes associated with cell membranes, including formation of gramicidin channels,17 drug binding with phospholipid membranes,18 amphiphilic peptide folding within membranes,19 proton conductance through gramicidin channel,20 virus fusion with membranes,21 voltage gating in ion channels,22 phospholipase A2 activity in glycosphingolipid monolayers,23 binding affinity of ErbB proteins to cell membranes,24 and redox reactions on lipid bilayer surfaces.25 Therefore, the effect of cholesterol on membrane dipole potential has been the important subject of a great number of experimental and theoretical investigations. Unfortunately, these studies yielded inconsistent findings and interpretations at high cholesterol concentrations. Szabo26 showed that in the presence of cholesterol the dipole potential of monoolein bilayers was estimated to increase by 30%, leading to a substantial change in membrane permeability. Similarly, McIntosh et al.27 observed that increasing cholesterol content in egg phosphatidylcholine (EPC) monolayers would result in a monotonic increase in membrane dipole potential. Smondyrev et al.28

carried

out

MD

simulations

of

binary

mixtures

of

dipalmitoylglycero-phosphocholine (DPPC) with cholesterol at low and high cholesterol concentrations, demonstrating a significant increase in membrane dipole potential (from about 0.6 V in pure DPPC bilayers to about 1.0 V in bilayers with 50% cholesterol). However, Hofsäß et al.29 performed MD simulations of DPPC/ cholesterol membranes, presenting a different finding: 1) at low cholesterol concentrations, the dipole potential of DPPC/cholesterol bilayers increases with increasing cholesterol content; 2) at high cholesterol concentrations, adding more ACS Paragon Plus Environment

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cholesterol into the DPPC/cholesterol lipid bilayer would even decrease membrane dipole potential. This is consistent with the experimental observation by Starke-Peterkovic et al.,30 who used the voltage-sensitive fluorescent probe di-8-ANEPPS to explore the effect of sterols (cholesterol and its derivatives) on membrane dipole potential of DMPC/cholesterol lipid bilayers. Meanwhile, a recent experimental work by Shrestha et al.31 presented a similar result for the dipole potential of DMPC/cholesterol lipid bilayers at various cholesterol concentrations. It has been suggested that the effect of cholesterol on membrane dipole potential is associated with the orientation and magnitude of molecular dipoles at the membrane interface.16,26,32 McIntosh et al.27 pointed out that cholesterol influences membrane dipole potential by altering the orientation of interfacial water and lipid head groups. Smondyrev et al.28 argued that the change in membrane dipole potential should be attributed to the variation of cholesterol tilt angle with respect to bilayer normal. Starke-Peterkovic et al. 30 showed that the magnitude of the cholesterol effect is associated with the dipole moment of cholesterol parallel to the bilayer normal. Based on the combined monte carlo (MC) and MD simulations of DPPC-cholesterol bilayers, Chiu et al. 33 suggested that the presence of the cholesterol hydroxyl group allows water molecules to penetrate more deeply into DPPC lipid bilayers, adding a contribution to membrane dipole potential. However, as far as we know, there is no work to explicitly measure the individual contributions of cholesterol, water, and lipids at various cholesterol concentrations, required to understand the underlying mechanism of the cholesterol effect on membrane dipole potential. In our previous works,34,35 we proposed the CAVS (charge attached to virtual site) model for water and phospholipids. In the CAVS model for water (Figure S1 of Supporting Information),34 each CG unit (representing four real water molecules) is composed of one van der Waals (vdW) interaction center (CGM), two positively charged sites (CGPs) and one negatively charged virtual site (CGN). Distance constraint is applied to the bonds formed between CGM and CGPs. A virtual site, which carries a negative charge, is determined by the locations of CGPs and CGM. In the CAVS model for lipid,35 we adopted a similar CG mapping scheme as used in the ACS Paragon Plus Environment


MARTINI model. In addition, two electrostatic interaction sites were embedded into each ester group of PC lipids in order to consider the contributions of the ester dipoles, which are ignored in the MARTINI model. The CAVS model is designed not only to correctly reproduce the positive values for the dipole potential inside PC lipid bilayers but also to properly balance the individual contributions from the ester dipoles and water, surmounting the limitations of current CG models (including MARTINI,36 ELBA,37 and BMW/MARTINI,38 etc.) in the calculations of dipole potential. Furthermore, the electrostatic interactions between cholesterol and lipids are ignored in the MARTINI model12,13 as well as in its improved versions for cholesterol.14,15 In this work, we endeavor to propose a CG model for cholesterol by including electrostatic interaction sites, such that the contribution of cholesterol to membrane dipole potential is taken into account. First, we parameterized the CG force field for cholesterol (Chol) by fitting to the atomistic simulations of DMPC lipid bilayers at various cholesterol concentrations. Then, we examined the transferability of the CG force field in other phospholipid-cholesterol mixtures (such as DOPC/Chol, POPC/Chol, and DPPC/Chol). The CAVS simulations displayed that the CG model reproduced the results for the structural properties of lipid bilayers, which were obtained from atomistic simulations and experiment. Third, we determined the potential of mean force (PMF) of transferring cholesterol from bulk water region to DPPC bilayer center at two different concentrations (0% and 40% Chol), showing that the CAVS model reproduced the effect of cholesterol concentration on the energetics of cholesterol transfer between lipid bilayer and aqueous phase while the MARTINI model failed. Finally, we calculated the dipole potential of lipid bilayers at various cholesterol concentrations as well as the individual contributions of membrane components (cholesterol, water, and lipid). Our work showed that the CAVS and CHARMM models produced consistent results in the study of the effect of cholesterol on membrane dipole potential. By combining the CHARMM and CAVS simulations, we discovered for the first time that, at high cholesterol concentrations, adding more cholesterol into lipid bilayers would non-linearly decrease the individual contributions ACS Paragon Plus Environment

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of water and lipid to membrane dipole potential. In contrast, the individual contribution of cholesterol increases non-linearly with increasing cholesterol content. Owing to the different variation (non-linear decrease or increase) of the individual contributions of membrane components (cholesterol, water, and lipids) with cholesterol concentration, the effect of cholesterol on membrane dipole potential is more complicated than we expected.

METHODS Atomistic MD Simulations Atomistic MD simulations of PC lipid bilayers (including DMPC, DOPC, POPC and DPPC) with cholesterol were carried out using the CHARMM36 force field39 in the simulation package GROMACS 4.6.7.40 For each case, the PACKMOL program41 was employed to generate a mixture containing a lipid bilayer, cholesterol and 10000 SPC/E water molecules.42 In each MD simulation, 256 lipid molecules (including phospholipid and cholesterol) were used at various cholesterol concentrations (ranging from 5% Chol to 60% Chol). Each starting conformation was minimized proceeding to the step of heating the system from 200 K to 300 K over a period of 200 ps under NVT condition. Then, a subsequent NPT simulation was performed for at least 200 ns and the simulation data collected from last 180 ns were used for final analysis. During all NPT simulations, the semi-isotropic pressure of 1 bar (in the z direction and x/y plane respectively) was maintained using the Parrinello-Rahman algorithm43 while the velocity rescaling method44 was used to control the constant temperature of 303 K (for DOPC, POPC, DMPC), or 323 K (for DPPC) in order to mimic experimental conditions. All bonds involving hydrogen atoms were constrained using the linear constraint solver (LINC) algorithm45 such that an integration time step of 2 fs could be adopted. Electrostatic interactions with a cutoff value of 1.2 nm were calculated based on the particle mesh Ewald (PME) method46 while van der Waals (vdW) interactions were truncated at a cutoff value of 1.2 nm. Coarse-Grained MD Simulations



All CG simulations were carried out in the simulation package GROMACS 4.5.540 and the starting configurations were created using the PACKMOL software.41 In each CG simulation, an energy minimization was performed before the system was equilibrated for tens of nanoseconds under NPT condition, and a subsequent NPT simulation was carried out for at least 1.5 µs. For each case, three independent NPT simulations were carried out such that the total simulation of 4.5 µs was used for final analysis. To measure the statistic error, the 4.5 µs simulation was equally divided into 15 windows. In each CG simulation, 512 lipid molecules (including phospholipid and cholesterol) were used at various cholesterol concentrations (ranging from 10% Chol to 60% Chol). For all NPT simulations, the velocity rescaling method44 (with a time constant of 1.0 ps) was employed to govern the constant temperature when the Parrinello-Rahman43 (with a time constant of 3.0 ps) was used to maintain the semi-isotropic pressure at 1 bar in the z direction and in the (x, y) plane respectively. A shift scheme (shifted from 1.2 nm to 1.6 nm) was adopted for computing vdW interactions while the PME method46 was employed for calculating electrostatic interactions with a cut-off value of 1.6 nm. The LINC algorithm 45 as used to constrain the bonds inside a CG unit and the integration time step of 15 fs was used for all CG simulations since an acceptable balance can be made between the stability and computational efficiency, which has been discussed in our previous work.34 Potential of Mean Force Calculations An umbrella sampling technique47 was successfully employed to measure the free energies of cholesterol removal from the centers of sphingomyelin (SM) and unsaturated phosphatidylcholine (PC) bilayers.11 To estimate the free energies of transferring cholesterol from bulk water region to bilayer center, we used the umbrella sampling method47 to calculate the potentials of mean force (PMFs) as a function of distance between the mass center of cholesterol and the mass center of lipid bilayer. Then, the free energies of cholesterol transfer can be determined by the difference in the PMF values. In the PMF calculations, we simulated a DPPC-0%Chol bilayer (containing 511 DPPC lipids and 1 cholesterol) and a DPPC-40%Chol bilayer ACS Paragon Plus Environment

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(containing 308 DPPC lipids and 204 cholesterols). For each bilayer system, we simulated 41 windows. For each window, six independent NPT simulations (three simulations were performed for one leaflet and the other three were done for the opposite leaflet) were respectively carried out for 200 ns (1.2 µs simulation in total). In the first window, one cholesterol molecule was placed in bulk water region. In subsequent windows, we moved the cholesterol molecule towards the bilayer center along the bilayer normal (z-axis) at an interval of 0.1 nm, and the final window had the cholesterol at the bilayer center. During all NPT simulations, we restrained the mass center of cholesterol with respect to the mass center of the bilayer, using a harmonic restraint with a force constant of 3000 kJ mol-1 nm-2. PMFs were calculated using the weighted histogram analysis method (WHAM)48, which was implemented in the GROMACS simulation package.40 For each bilayer system, we determined the mean PMF values and their standard errors from six independent PMF calculations.

RESULTS AND DISCUSSION Parametrization of Coarse-Grained Model for DMPC

Figure 1. CG mapping for DMPC, the names for interacting sites are indicated in black color and the names for CG units in blue color respectively. The neutral, non-interacting, positively charged, and negatively charged sites are respectively denoted by the black filled, black open, red filled, and blue filled circles.

In our previous work,35 we presented a CG model (namely CAVS) for DPPC,



DOPC, POPC, and POPE, showing the advantage of the CAVS model in the calculations of dipole potential of lipid bilayers as compared to the MARTINI and ELBA models. Similarly, the parameterization of the CAVS model for DMPC (depicted in Figure 1) was done by following the same procedure, which has been illustrated in our previous work.35 Here, we summarize it here for completeness: 1) The vdW interaction parameters for the CG beads (such as C2P, C3P, C3E, CMF, PO4, and N4M) were directly adopted from our previous work.35 Please note that the C1P bead (non-interacting site) only serves to connect two neighboring CG beads. 2) A dipole constructed from two point charges was embedded into each glycerol ester group (represented by CO1 or CO2 bead), which corresponds to methyl formate molecule. Since the dipole moment of methyl formate molecule was measured to be 1.77 Debye, the partial charges of the electrostatic interacting sites (such as CMF and OMF) were given as

= 0.37 and = −0.37 respectively when the distance dCMF-OMF was arbitrarily constrained to 1.0 Å. The PO4 bead carries a negative charge ( = −1) while the N4M bead carries a positive charge ( = +1) 3) The iterative inverse Boltzmann (IIB) approach49 was employed to obtain the bond-stretching and angle-bending parameters through fitting to the bond and angle probability distributions sampled from the atomistic reference simulations (using the CHARMM36 force field). Please see examples in Figure S2 of Supporting Information. 4) The parameters for bond stretching and angle bending was further adjusted (in a trial-and-error fashion) until the CG model can reproduce the structural properties of lipid bilayer (including area per lipid, bilayer thickness, and order parameter) obtained from experiment and the CHARMM simulations. To measure the thickness of DMPC lipid bilayer, the number density profiles were constructed, given in Figure S3 of Supporting Information. The bilayer thickness obtained from our CG simulations is defined as the peak-peak distance ( D ) between the PO4 particles. In the calculations of the number density profiles for the ACS Paragon Plus Environment

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head groups (PO4 and N4M), the comparison was made between the CG and CHARMM results, showing a nice agreement between them (illustrated in Figure S3 of Supporting Information). Finally, the area per lipid A and dipole potential were calculated respectively, and the CG results show a nice agreement with experiment and the CHARMM model (see Table S1 of Supporting Information). Please note that the experimental dipole potential is overestimated by the non-polarizable atomistic model (CHARMM36 force field) owing to the polarization effect, which is treated in a mean-field fashion.50 Parametrization of Coarse-Grained Model for Cholesterol

Figure 2. CG mapping for cholesterol, the names for interacting sites are indicated in black color and the names for CG units in blue color respectively. The neutral, positively charged, and negatively charged sites are respectively denoted by the black filled, red filled, and blue filled circles.

Figure 2 illustrates the CG mapping for cholesterol molecule. In this approach, the cholesterol ring was reduced to four neutral CG particles (namely CI, CR1, CR3, and CR3). In order to preserve the electrostatic nature of cholesterol, a dipole was embedded into the CI bead, in which a vdW interaction center (CIO) carries a positive charge and an electrostatic site (OI) carries a negative charge. Base on the dipole moment of cholesterol estimated around 1.9 Debye,30 the partial charges of the electrostatic interacting sites (CIO and OI) were tentatively set as = 0.25 and



= −0.25 when the distance dCIO-OI was arbitrarily constrained to 1.5 Å. Three neutral particles (CR1, CR2, and CR3) of cholesterol ring were assigned with the particle types C6R and C4R respectively, and the hydrophobic tail was reduced into three neutral CG beads (namely CT1, CT2 and CT3), each of which was assigned with the particle type C3R or C2R respectively. An earlier work51 highlighted the importance of two off-plane methyl groups, which are perpendicular to the cholesterol ring. Thus, the pseudo-methyl groups (denoted by CS1 and CS2 respectively) assigned with the particle type C1R were explicitly attached to the CR1 and CR3 particles respectively, illustrated in Figure 2.

Figure 3. Flowchart shows the steps for the parameterization of the CG force field for cholesterol.

To obtain the CG force field parameters for cholesterol, atomistic reference simulations (using the CHARMM36 force field) of DMPC/Chol bilayers were carried out. The detail process for the parameterization of the CG model for cholesterol is given in Figure 3:


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1) The parameters for bond stretching and angle bending were derived by fitting to the bond and angle probability distributions from the atomistic reference simulations of DMPC/Chol bilayers (please see Figure S4 of Supporting Information). The dihedral angle potential was tentatively not applied to the CG cholesterol model in this work because we found that the CG simulations would yield reasonable results with the neglect of dihedral angle interactions. 2) The iterative inverse Boltzmann (IIB) approach49 was employed to obtain the vdW parameters (the well-depth and range parameters) for the CG particle types (C1R, C2R, C3R, C4R, and C6R), please see Figures S5 and S6 of Supporting Information. 3) The CAVS simulations of DMPC/Chol bilayers were performed for the calculations of the structural properties (such as thickness, area per lipid, and order parameter) at various cholesterol concentrations, and the comparison was made between the CG results and the atomistic results (or the experimental results). 4) Steps 2-3 were repeatedly carried out until the CG model could reproduce the structural properties of lipid bilayers at various cholesterol concentrations (such as thickness,52,53 area per lipid,52 and order parameter53) obtained from experiment and the CHARMM simulations. All CG force field parameters are collected in Tables S2-S4 of Supporting Information. Figure 4A shows the change in bilayer thickness caused by altering cholesterol mole fraction in DMPC membrane. Hung et al.52 determined the bilayer thickness of DMPC membranes as a function of cholesterol mole fraction using X-ray lamellar diffraction method, showing that the phosphate-to-phosphate thickness (dPtP) increases from 3.6 nm at 0% Chol to 4.3 nm at 35% Chol where it reaches a plateau. Using X-ray scattering methods, Pan et al.53 measured the head-to-head thickness (dHH), revealing that the bilayer thickness reaches the plateau starting at 20% Chol. At low cholesterol concentrations (< 20% Chol), the CHARMM36 (red curve) and CAVS (blue curve) simulations qualitatively reproduce the rise in bilayer thickness



with increasing cholesterol concentration. At high cholesterol concentrations (> 20% Chol), it appears that the CAVS model can predict the plateau in agreement with the experimental data of Hung et al.52 while the CHARMM prediction of the plateau is consistent with the experiment by Pan et al.53 Meanwhile, it is interesting that the CHARMM and CAVS simulations consistently reveal a decrease in bilayer thickness following the plateau, which is not observed in these two experiments.

Figure 4. Effect of cholesterol on bilayer thickness in (A) DMPC/Chol, (B) DPPC/Chol, (C) POPC/Chol, and (D) DOPC/Chol bilayers, and the comparison between experiment and calculated results (CHARMM, CAVS, and AC-MARTINI). Experimental phosphate-to-phosphate distance (dPtP) in DMPC and DOPC bilayers were determined by Hung et al.52 using X-ray lamellar diffraction method and experimental head-to-head distance (dHH) in DMPC and DOPC bilayers were measured by Pan et al.53 using X-ray scattering methods. Experimental head-to-head distance (dHH) in POPC bilayers were measured by Hodzic et al.54 using small angle X-ray scattering. Since no data is available for the DPPC/Chol bilayers, experimental phosphate-to-phosphate distance (dPtP) in DPPC bilayers can be obtained approximately by shifting the experimental DMPC values53 up by 0.3 nm.


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Figure 5. Lipid area condensation induced by increasing cholesterol concentration in (A) DMPC/Chol, (B) DOPC/Chol, (C) POPC/Chol, and (D) DOPC/Chol bilayers, and the comparison between experiment and calculated results (CHARMM, CAVS, and AC-MARTINI). Experimental data for DMPC and DOPC bilayers were determined by Hung et al.52 using X-ray lamellar diffraction method. Experimental Am for DOPC and POPC monolayers were obtained by Smaby et al.57 at a surface pressure of 30 mN/m. Experimental Am in DPPC bilayers were obtained by Ipsen et al.58

Figure 5A shows the lipid area condensation induced by increasing cholesterol mole fraction in DMPC bilayers. Hung et al.52 calculated the cholesterol-induced area condensation from 0% to 50% Chol, showing a steep decline in area per molecule at low cholesterol concentrations. The CHARMM and CAVS models qualitatively capture this experimental trend. Panels A and B in Figure 6 show the CAVS and CHARMM calculations for lipid tail order parameters as well as their comparison to experiment. Pan et al.53 determined the orientational order parameter (Sx-ray) of DMPC/Chol bilayers using X-ray scattering methods, showing that Sx-ray monotonically increases as the function of cholesterol concentration below 20% Chol



and reaches a plateau above 20% Chol. In the CHARMM and CAVS simulations, the order parameters (SCC) were measured for the consecutive bonds between two beads in each lipid tail. However, the order parameters (SCC) obtained from the simulations cannot be directly compared to experiment. In order to make a comparison between experiment and simulation, we used relative order parameter D(Chol)/D0, where D(Chol) represents the lipid order parameters at various cholesterol concentrations and D0 corresponds to the lipid order parameter at 0% Chol. From the panels A and B in Figure 6, one can see that the CHARMM and CAVS models nicely reproduce the experimental trend. Meanwhile, the CHARMM and CAVS models consistently reveal a slight decrease in tail order parameter at high cholesterol concentrations, which is not observed in experiment. Transferability of Cholesterol Model in Other Lipid Bilayers To test the transferability of the CG force field for cholesterol, we carried out the simulations of DOPC/Chol, POPC/Chol, and DPPC/Chol bilayers with the same parameters. Figures 4B-D show the comparison between the experimental and calculated values of bilayer thickness in the DOPC/Chol, POPC/Chol, and DPPC/Chol bilayers. These figures illustrate that the CAVS and CHARMM simulations can reasonably capture the variation of bilayer thickness with cholesterol concentration as compared to experiment: 1) at low cholesterol concentrations, increasing cholesterol content would increase bilayer thickness; 2) at high cholesterol concentrations, increasing cholesterol content would have a limited influence on bilayer thickness Meanwhile, the CAVS simulations report the decrease in bilayer thickness at high cholesterol concentrations, and this prediction is in an agreement with the CHARMM and AC-MARTINI calculations. Since no experimental data is available for the DPPC/Chol bilayer thickness at various cholesterol concentrations, experimental data for DPPC/Chol bilayer thickness can be derived approximately by scaling the experimental values of DMPC/Chol bilayer thickness52 up by 0.3 nm (based on the experimental values of pure DMPC and DPPC bilayer thickness, which were determined to be 3.53 nm55 and 3.83 nm56 respectively).


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Figure 6. Relative lipid order parameter D(Chol)/D0 as a function of cholesterol concentration in (A) DMPC, (B) DPPC, (C) POPC, and (D) DOPC bilayers, and the comparison between experiment and MD results (CHARMM, CAVS, and AC-MARTINI). D(Chol) represents the lipid order parameter at various cholesterol (Chol) concentrations and D0 corresponds to the lipid order parameter at 0% Chol. Experimental relative order parameters in DMPC and DOPC bilayers were calculated based on the orientational order parameters (Sx-ray) determined by Pan et al.53 using X-ray scattering methods. Experimental relative order parameters in POPC bilayers were derived based on experimental SCH data from Ferreira et al.59 using NMR. Experimental relative order parameters in DPPC bilayers were obtained based on the orientational order parameters (Sx-ray) determined by Mills et al.60 using wide angle X-ray scattering (WAXS).



Figures 5B-C show that the CG (CAVS and AC-MARTINI) and CHARMM predictions of area per molecule (Am) can nicely reproduce the experimental trend in the case of DOPC/Chol and POPC/Chol bilayers. Similarly, in the case of DPPC/Chol bilayer, experimental values are reliably predicted by the CAVS and CHARMM models, shown in Figure 5D. Figures 6C-H show the relative order parameters for the DOPC/Chol, POPC/Chol, and DPPC/ Chol bilayers. It appears that the CHARMM and CG models (CAVS or AC-MARTINI) can reasonably reproduce the experimental variation of order parameter with cholesterol concentration: order parameter increases significantly at low cholesterol concentrations and is slightly influenced at high cholesterol concentrations. Effect of Cholesterol on Cholesterol Tilt in Lipid Bilayers

Figure 7. Variation of average cholesterol tilt angle with cholesterol concentration in (A) DMPC/Chol, (B) DOPC/Chol, (C) POPC/Chol, and (D) DOPC/Chol bilayers, and the comparison between the CAVS and CHARMM results.


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Using an improved united atom GROMOS force-field,61 Khelashvili et al.62 determined the tilt distribution for cholesterol in DMPC/Chol bilayers with various compositions, showing that increasing cholesterol content in the lipid bilayers would decrease average cholesterol tilt angle as well as narrow down cholesterol tilt distribution. Similarly, we calculated the average cholesterol tilt angle 〈〉 according to the following equation: "#

〈〉 = ∙ ! 1 #

and represent the cholesterol tilt angle and tilt distribution respectively. In this work, the cholesterol tilt is defined as the angle between a vector in cholesterol model and the bilayer normal (z-axis), and the vector is considered to be the C17-C3 vector in the CHARMM model and the vector CI-CR3 in the CAVS model respectively. By this definition, = 0# denotes that the orientation of cholesterol is

parallel to the bilayer normal and = 90# indicates that the orientation of cholesterol molecule is perpendicular to the bilayer normal. One can see from Figure

7 that the CAVS model can qualitatively capture the variation of cholesterol tilt with cholesterol concentration as compared to the CHARMM model: 1) at low cholesterol concentrations, increasing cholesterol content would result in a significant decrease in cholesterol tilt; 2) at high cholesterol concentrations, increasing cholesterol content has an insignificant effect on cholesterol tilt. Figure 8 shows the normalized cholesterol tilt distributions in DMPC/Chol bilayers at four different cholesterol concentrations. In addition, we used the violin plot (presented in Figure S7 of Supporting Information) for the further comparison between the CHARMM and CAVS distributions, which were constructed by combining the normalized cholesterol tilt distributions (given in Figure 8) in DMPC/Chol bilayers at four different cholesterol concentrations (10%, 20%, 40%, and 50% Chol). In general, these figures show that the CAVS calculations yield a broader distribution as compared to the CHARMM calculations. Nevertheless, it is shown that the CAVS model can qualitatively reproduce the variation of cholesterol



tilt distribution with cholesterol concentration (please see Figure S8 of Supporting Information): 1) at low cholesterol concentrations, increasing cholesterol content would narrow down the cholesterol tilt distribution; 2) at high cholesterol concentrations, increasing cholesterol content has a limited influence on cholesterol tilt distribution. This is consistent with the previous works done by Khelashvili et al.10,62,63 and Aittoniemi et al.64

Figure 8. Normalized cholesterol tilt distributions in DMPC/Chol bilayers at four different cholesterol concentrations: (A)10% Chol, (B) 20% Chol, (C) 40% Chol, and (D) 50% Chol, and the comparison between the CAVS and CHARMM models.

Effect of Cholesterol on Cholesterol Transfer in Lipid Bilayers Cholesterol translocation within a phospholipid membrane consists of lateral diffusion and transverse diffusion (or flip-flop motion) between leaflets.65 Comparing to the lateral diffusion, the transverse motion is typically considered to be a slower process. However, a great number of experimental studies provided inconsistent results for the cholesterol flip-flop rate ranging from milliseconds to hours.66-70


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Meanwhile, the cholesterol transfer between lipid bilayers has been investigated by considerable molecular dynamics (MD) studies. In particular, the energetics of cholesterol flip-flop were measured from umbrella sampling in terms of one-dimensional (1-D)11,71 or two-dimensional (2-D)72 potential of mean force (PMF).

Figure 9. PMFs for cholesterol transfer between bulk water region and the center of DPPC/Chol lipid bilayers at two cholesterol concentrations (0% Chol and 40% Chol). Error bars are the standard error from six independent PMF calculations (three for each leaflet).

In an earlier work, Bennett et al.71 calculated the PMFs for transferring cholesterol from bulk water region to the center of DPPC bilayers by using GROMOS87 force field with minor changes73 and the MARTINI model.13 Similarly, we used the CAVS model to determine the energetics of cholesterol transfer in DPPC/Chol bilayers at two different cholesterol concentrations (0% Chol and 40% Chol). The PMFs calculated from CAVS simulations (given in Figure 9) display a similar pattern as those obtained from atomistic and MARTINI simulations: 1) there is



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a steep slope ranging from equilibrium position (the lowest free energy state) toward bulk water region in the PMF profiles; 2) cholesterol’s equilibrium position is located between bilayer center and bulk water region; 3) increasing cholesterol content would cause the shift of the equilibrium position away from the bilayer center.

Table 1. Structural and thermodynamic properties of DPPC/Chol bilayers obtained from the CAVS simulations, and the comparison to the united atom (UA) and MARTINI coarse-grained simulations.67 θeq represents the average cholesterol tilt angle in the lipid bilayers, ∆Gd represents the free energy barrier (determined by the difference in the PMF values) for moving cholesterol from its equilibrium position in lipid bilayers to bulk water region (or desorption from the lipid bilayer), ∆Gf indicates the free energy barrier (determined by the difference in the PMF values) for moving cholesterol from its equilibrium position to the center of lipid bilayers, and ∆Zeq corresponds to the distance between equilibrium position and bilayer center. Lipid Bilayer Systems

θeq (degree)

∆Gd (kJ/mol)

∆Gf (kJ/mol)

∆Zeq (nm)

UA DPPC (0% Chol)

29

80

24

1.5

MARTINI DPPC (0%Chol)

23

88

16

1.6

CAVS DPPC (0%Chol)

34

78

14

1.7

UA DPPC (40%Chol)

13

89

41

1.8

MARTINI DPPC (40%Chol)

15

86

25

1.7

CAVS DPPC-40%Chol

21

95

27

2.0

Table 1 summarizes the major features in the PMF profiles calculated from UA, MARTIN, and CAVS simulations. The CAVS results show that the cholesterol desorption (∆Gd) from the DPPC-0%Chol bilayer would be more favorable (by 17 kJ/mol) than from the DPPC-40%Chol bilayer. This is qualitatively consistent with the united atom (UA) estimation (about 9 kJ/mol). In contrast, the MARTINI model fails to capture the effect of cholesterol on the cholesterol desorption from DPPC/Chol bilayer. Nevertheless, in term of the free energy barrier for flip-flop motion (∆Gf), the CAVS and MARTINI models yield a comparable result to that


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obtained from UA simulations, showing that moving cholesterol from its equilibration position to the DPPC-0% Chol bilayer center would be more favorable (by 13 kJ/mol and 9 kJ/mol respectively) than to the DPPC-40%Chol bilayer center. Furthermore, the CAVS model demonstrates that cholesterol’s equilibrium position (∆Zeq) is shifted away from the bilayer center about 0.3 nm when increasing the cholesterol concentration from 0% Chol to 40% Chol. This nicely reproduce the UA result (0.3 nm), shown in Table 1. Effect of Cholesterol on Membrane Dipole Potential By setting z-axis as the bilayer normal, the dipole potential ϕ& along the bilayer normal can be calculated from a double integration of local charge density ρz : -

, 1 , ϕ& z = − dz + ρz ++ dz ++ 2 ε# # #

where ε# is the vacuum permittivity. Figure 10 shows the total dipole potential profiles for the DMPC/Chol, DOPC/Chol, POPC/Chol and DPPC/Chol bilayers at various cholesterol concentrations. Owing to the mean-field treatment of the polarization at the membrane/water interface, one can see that the CHARMM model overestimates the experimental values. However, it is encouraging that the CHARMM model can capture the experimental trend of the variation of dipole potential with cholesterol concentration when shifting the CHARMM results down by 0.4 V (shown in Figure S9 of Supporting Information). In the case of unsaturated lipid bilayers (such as DOPC and POPC), the CAVS and CHARMM results show that the dipole potential increases with increasing cholesterol content, reasonably capturing the experimental trend.30,74 In the case of saturated lipid bilayers (DMPC and DPPC), the CAVS and CHARMM models consistently show the increase of dipole potential with increasing cholesterol concentration in the range of 0%-30% Chol, which is in an agreement with experiment.30 However, the CAVS curves demonstrate a decline in a concave manner in the range of 30%-60% Chol, where the convex curvature is observed in the experimental and CHARMM curves. This difference should be ascribed to the different variation of individual contributions of membrane



components (water, lipid, and cholesterol) with cholesterol concentration (shown in Figures 11 and 12), which will be discussed below.

Figure 10. Variation of membrane dipole potential with cholesterol concentration in (A) DMPC/Chol, (B) DOPC/Chol, (C) POPC/Chol, and (D) DOPC/Chol bilayers, and the comparison is made between the calculated and experimental results. Experimental values in DMPC and DOPC bilayers was determined by Starke-Peterkovic et al.30 and in POPC bilayers were measured by Haldar et al.74

It has been recognized that the dipole potential of pure PC lipid bilayers is mainly influenced by the orientation of water and lipid dipoles at membrane/water interface. In a PC lipid bilayer, the positive contribution of water to total dipole potential is greater than the negative contribution of PC lipids, leading to the positive total dipole potential. For instance, Figure 11 shows the net positive contribution of water and lipid dipoles as the function of cholesterol concentration. Meanwhile, the CHARMM and CAVS models consistently demonstrates that: 1) cholesterol influences the individual contributions of water and lipid significantly at high cholesterol


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concentrations; 2) at high cholesterol concentrations (> 30% Chol), the individual contributions of water and lipids decrease with increasing cholesterol concentration. However, the CAVS curves generally show a slight decline with increasing cholesterol content the range of 0%-30% Chol, where the CHARMM curves show a slight increase with increasing cholesterol concentration.

Figure 11. Net contribution of water and lipids to total dipole potential in (A) DMPC, (B) DOPC, (C) POPC, and (D) DOPC bilayers at various cholesterol concentrations, and the comparison between the CHARMM and CAVS results.

On the other side, the CHARMM and CAVS results reveal that the contribution of cholesterol to total dipole potential increases non-linearly as the cholesterol concentration increases (shown in Figure 12). This finding suggests that the effect of cholesterol on membrane dipole potential would be more complicated than we thought. In addition, Figure 12 shows that in the case of DMPC/Chol and DPPC/Chol bilayers, the CAVS curves are more wiggly than the CHARMM curves. This might explain the concave decline in the CAVS curves for total dipole potential at high cholesterol concentrations (shown respectively in Figures 10A and 10D).



Figure 12. Contribution of cholesterol to total dipole potential in (A) DMPC, (B) DOPC, (C) POPC, and (D) DOPC bilayers at various cholesterol concentrations, and the comparison is made between the CHARMM and CAVS results.

Figure 13. Number density profiles of components in DMPC/Chol bilayer systems at two concentrations: 30% and 40% Chol, including water (black), phosphate (red), choline (blue), cholesterol head group ROH (magenta), and comparison is made between the CHARMM and CAVS results: (A) CHARMM calculations at 30% Chol, (B) CHARMM calculations at 40% Chol, (C) CAVS calculations at 30% Chol, and (B) CAVS calculations at 40% Chol. Phosphate carries a negative charge (red) and choline carries a positive charge (blue), indicating that the lipid dipole is orientated toward aqueous phase, creating a negative dipole potential in the membrane center.


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Figure 14. Individual contributions of water and lipids to total dipole potential in DMPC bilayers at two cholesterol concentrations (30% Chol and 40% Chol), and the comparison is made between the CHARMM (left panel) and CAVS (right panel) calculations. Upper panel represents the contribution of water and lower.

Chiu et al.33 argued the interaction between cholesterol and water allows water molecules to penetrate more deeply into the bilayer, adding a contribution to membrane dipole potential. Similarly, the CAVS and CHARMM simulations consistently show that, at high cholesterol concentrations, increasing cholesterol content would increase the interactions between cholesterol and water, presented in Figure 13 and Figures S10 and S11 of Supporting Information. In fact, this is consistent with the PMF calculations, showing that cholesterol’s equilibrium position (∆Zeq) is shifted towards the membrane/water when increasing cholesterol concentration (given in Table 1). Meanwhile, it is clear to see from Figure S11 of Supporting Information that the cholesterol dipole is orientated in such a way that it creates a positive dipole potential in the membrane center. Thus, the increased interactions between cholesterol and water could influence the orientation of water at membrane/water interface.



However, one can see from Figure 13 that the orientation of water at membrane/water interface should be influenced by lipid head groups (phosphate and choline) more significantly than by cholesterol since water number density is much higher in the region of phosphate (P) and choline (N) than in the region of cholesterol. Please note that P corresponds to the center of phosphate group and N corresponds to the center of choline group, such that the P-N vector angle can represent the orientation of lipid head groups. Figure S12 of Supporting Information illustrates that at a high cholesterol concentration, increasing cholesterol content would result in the increase of P-N vector angle in the lipid head, which reduces the negative contribution of lipids to the dipole potential (shown in Figure 14C and 14D). In turn, the increased P-N vector angle would affect the orientation of water at membrane/water interface, leading to the decrease in the contribution of water to total dipole potential (shown in Figures 14A and 14B).

CONCLUSIONS To investigate the effect of cholesterol on membrane dipole potential using MD simulations, it is required to obtain an accurate description of the orientation of molecular dipoles (contributed from water, lipid, and cholesterol) with respect to bilayer normal. Unfortunately, the popular MARTINI CG model and its improved versions fail to capture the effect of cholesterol on membrane dipole potential since they disregard the individual contribution of cholesterol as well as the cholesterol effect on the orientation of water dipoles at membrane/water interface. To overcome this issue, we presented a CG model for cholesterol with an embedded a dipole constructed from two point charges. The CG force field for cholesterol model was parameterized by matching CG results (including bilayer thickness, area per lipid, and lipid order parameter) to atomistic simulations of DMPC-cholesterol bilayers at different cholesterol concentrations. Subsequently, the transferability of the CG force field has been tested in the MD simulations of different lipid-cholesterol mixtures (such as DOPC/Chol, POPC/Chol, and DPPC/Chol), showing that the CAVS model successfully reproduced ACS Paragon Plus Environment

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the condensing effect of cholesterol in lipid bilayers as compared to atomistic simulations and experiment. Using the CAVS model, we investigated the effect of cholesterol on cholesterol tilt in lipid bilayers, showing that the CAVS model qualitatively reproduced the variation of average cholesterol tilt angle and tilt distribution with cholesterol concentration when comparing to the CHARMM model. Furthermore, the CAVS model captured the atomistic results for the energetics of moving cholesterol from aqueous phase to DPPC bilayer center at two different concentrations (0% Chol and 40% Chol), revealing that the cholesterol desorption from the DPPC-Chol bilayer would be more favorable at low cholesterol concentration than at high cholesterol concentration. Finally, we measured the dipole potential of lipid bilayers at various cholesterol concentrations as well as the individual contributions of water, cholesterol, and lipids. The CAVS and CHARMM models consistently showed: 1) the cholesterol effect on membrane dipole potential was more obvious at low cholesterol concentrations than at high cholesterol concentrations; 2) the individual contribution of cholesterol to total dipole potential would increase non-linearly as the cholesterol concentration increases; 3) at high cholesterol concentrations, adding more cholesterol would decrease the individual contributions of water and lipid. Owing to the non-linear decrease or increase of the individual contributions of membrane components (cholesterol, water, and lipids) with increasing cholesterol concentration, the effect of cholesterol on membrane dipole potential is complicated at high cholesterol concentrations. In addition, at high cholesterol concentrations, increasing cholesterol concentration in a lipid bilayer would increase the interactions between cholesterol and water as well as increase the P-N vector angles at membrane/water interface. These result in the change in the orientation of water at membrane/water interface. However, the number density profiles showed that the orientation of water should be mainly influenced by the orientation of lipid head groups instead of cholesterol.



AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected], Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS This work is supported by the Plan Project for Guizhou Provincial Science and Technology (No. QKHJC[2016]1109), the start-up fund from the Guizhou Education University, the construction project for Guizhou Provincial Key Disciplines (No. ZDXK[2015]10), the science foundation from the Guizhou Education University (2017YB045). We would like to thank Professor Luo Yi (Heifei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China) for helpful discussions.

SUPPORTING INFORMATION Supporting Information contains the force field parameters for cholesterol and the comparison between the CHARMM and CAVS results in the calculations of the properties of lipid bilayers. This information is available free of charge via the Internet at http://pubs.acs.org.


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Effect of Cholesterol on Membrane Dipole Potential: Atomistic and

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