Quantitative Characterization of Cholesterol Partitioning Between

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Quantitative Characterization of Cholesterol Partitioning Between Binary Bilayers Soohyung Park, and Wonpil Im J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.8b00140 • Publication Date (Web): 07 May 2018 Downloaded from http://pubs.acs.org on May 7, 2018

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Journal of Chemical Theory and Computation

Quantitative Characterization of Cholesterol Partitioning Between Binary Bilayers

Soohyung Park and Wonpil Im* Departments of Biological Sciences and Bioengineering, Lehigh University, Bethlehem, Pennsylvania

Corresponding Author *[email protected]

ACS Paragon Plus Environment

Journal of Chemical Theory and Computation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT We have devised a practical simulation protocol for quantitative characterization of cholesterol (Chol) partitioning between bilayers with different lipid types. The simulation model contains two patches of laterally contacting lipid bilayers, where the host lipids of each bilayer are allowed to self-adjust their packing. For two combinations of bilayers with different lipid types, 1,2-dioleoyl-sn-glycero-3phosphocholine (DOPC)/1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and 1,2-dipalmitoylsn-glycero-3-phosphocholine (DPPC), the simulation model has been verified by self-adjusted lipid packing in each bilayer, convergence of Chol partitioning between different Chol initial distributions, and relative diffusion coefficients consistent to those from experiments. The calculated Chol partition coefficient between POPC and DOPC bilayers from the Chol partitioning simulations in the POPC-DPPC and DOPC-DPPC binary bilayer systems shows an excellent agreement with that from available Chol exchange experiments between 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine(SOPC)/DOPC vesicles and β-cyclodextrins, which further validates the simulation protocol and illustrates its applicability to any molecular partitioning in the binary bilayer system.

KEYWORDS Partition coefficient; Molecular dynamics; Lateral diffusion coefficient


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Cholesterol (Chol) is abundant and an indispensable component in cell membranes (up to ~50%).1 It maintains the membrane integrity and fluidity and helps secure membrane proteins by forming nano- or micro-sized ordered domains (so-called rafts) together with sphingolipids in the cell membrane. These domains serve as platforms for many important biological processes, such as membrane trafficking, signaling, and protein sequestration.1,2 Such important roles of Chol in cell membranes are regulated by Chol-lipid interactions, which have been qualitatively understood by the hydrophobic interactions between Chol and lipids and are maximized when the acyl chains complement the planar sterol ring, resulting in tight packing.3 Molecular dynamics (MD) have provided molecular description of Chol-lipid interactions,4–6 which have successfully reproduced experimental findings, such as the condensing effects of Chol on bilayers, Chol’s preference to sphingomyelin over phospholipids, and their roles in raft-like membranes. Quantitatively, differences in Chol-lipid interactions between two lipid bilayers (B1 and B2) can be characterized by the partition free energy, ln , where kB is the Boltzmann constant, T is the temperature, and Chol / Chol is the Chol partition coefficient between B1 and B2. In a recently proposed experimental method,7 Chol partitioning was quantitatively determined between vesicles of different lipid types and β-cyclodextrin (β-CD),8–10 where β-CD was used as a reference state to elegantly resolve the known issues of the low Chol exchange rate between vesicles and the difficulties in separating donor vesicles from acceptor vesicles due to vesicle fusion in previous approaches.11–13 However, it still remains challenging to reliably estimate the partition coefficient from MD simulations. Quantitative characterization of Chol-lipid interaction free energies has appeared only recently (using transfer free energies from bilayer to water14,15 or to β-CD16,17), where computationally expensive umbrella sampling18 (containing many windows) is required to restrain Chol’s position along the transfer pathway. The Chol partition function is a thermodynamic property and dependent on the force field (FF). With increasing interest in biologically relevant membranes, it is important to know how well lipid partitioning is captured by the FF. Considering these, it is desirable to have a practical method that allows accurate estimation of Chol partitioning between bilayers while avoiding expensive free energy simulations. In this study, we have devised a binary bilayer system (BBS) (Figure 1A), where two patches of (laterally contacting) bilayers composed of different lipid types are embedded in bulk water. To allow self-adjusted lipid packing in each bilayer without lipid mixing between them, a soft restraint potential is applied if a B1 lipid (but not Chol) from B1 diffuses into B2, and vice versa. Thus, the bilayer properties will be the same to those from pure bilayers. The other components (e.g., Chol in the present work) are allowed to freely diffuse across binary bilayers and partition into B1 and B2, so that the chemical potentials are matched. Therefore, this simulation approach allows accurate estimation of without the need of a reference state (such as β-CD or bulk water) and/or computationally intensive free energy simulations.

Figure 1. (A) Schematic description of a binary bilayer system (top view). The mixing of different types of host lipids is prevented by soft restraint potentials (dashed lines in different colors) near the interfaces



between bilayers, while the other components (e.g., Chol: green circle) are allowed to diffuse freely across bilayers. (B and C) Initial snapshots of two initial cholesterol distributions (top view): (B) delta or (C) random distributions, where the Chol molecules are placed at the X-center of each bilayer or distributed randomly across the binary bilayer system. Different types of lipids are represented in different colors and Chol molecules are shown as green spheres. Water molecules and ions are omitted for clarity. (D) Number of lipids (NRES) in each bilayer that are under the influence of the restraints. Number of lipids under restraint potentials higher than 2kBT (NH-RES) were shown in lighter color. The number of lipids were averaged over the last 300-ns trajectories of 20 replicas for each BBS. To validate this simulation approach and illustrate its efficacy, we considered three simple lipid bilayers composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), 1-palmitoyl-2-oleoyl-sn-glycero-3phosphocholine (POPC), and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC). From these bilayers, we chose two combinations of lipid bilayers DOPC-DPPC and POPC-DPPC for the BBS, where Chol are embedded at 20 mol% (DO-CH-DP and PO-CH-DP: 160 (DO, PO, or DP) lipids and 40 Chol). For each of DO-CH-DP and PO-CH-DP, we considered two initial Chol distributions: 1) a delta distribution where Chol are initially located at each bilayer center (Figure 1B) and 2) a random distribution of Chol across the binary bilayer (Figure 1C). For each (tetragonal) BBS with each initial Chol distribution, we prepared the simulation systems with the initial size of ~ 110×110×80 Å3 by following the five-step procedure employed in CHARMM-GUI’s Membrane Builder.19–22 Then, we carried out 10 independent 400-ns simulations under constant pressure (p = 1 atm) and temperature (T = 318 K) conditions (NPT ensemble, see Simulation details in Supporting Information (SI) for details). Our simulation approach was verified for 1) self-adjusted lipid packing, 2) convergence of Chol partitioning between two different initial Chol distributions, 3) relative diffusion coefficients of Chol and lipids in each BBS, and 4) Chol partition coefficient between POPC and DOPC bilayers. The excellent agreement between the calculated values and the available experimental values illustrates the efficacy of the simulation approach for quantitative calculations of Chol partitioning between bilayers and its general applicability to any molecular partitioning. Self-adjusted lipid packing The restraints applied in the BBS act on lipids that diffuse deep into the other bilayer from its original one. To be a valid simulation model in terms of self-adjusted lipid packing, the number of lipids under the influence of the restraints (NRES) in the BBS should be kept minimal and the restraint energy applied to the lipids should be small (< 2kBT, thermally accessible energy23). Otherwise, the bilayer properties would be distorted due to unphysical lipid packing from high number of lipids under the restraints. In such cases, Chol diffusion across the bilayer-bilayer interfaces would be also affected by these lipids (hindered due to lipids that would push Chol back to its original bilayer). The number of lipids under the influence of the restraints (NRES) were kept small as shown in Figure 1D (see also Table S1 in SI). About 7 out of 160 DOPC (and POPC) molecules (~ 4%) and 4 out of 160 DPPC molecules (~ 3%) were under the influence of the restraints, among which about 0.3 DOPC/POPC molecules (~ 0.2%) and 0.2 DPPC molecules (~ 0.2%) were under the restraint energy greater than 2kBT. These numbers are sufficiently smaller than an approximate number of boundary molecules (NB1-B2 ≈ 57, see Analysis in the SI), from which we infer that the self-adjusted lipid packing is not altered by the restraints. Convergence of Chol partitioning between two initial Chol distributions With the correct self-adjusted lipid packing, Chol partitions into B1 and B2 until the chemical potentials of both bilayers match. Partitioning is a thermodynamic property that should be independent of the initial Chol distribution. Therefore, the simulations from two different initial Chol distributions must converge. Such convergence can be shown in the following ways. First, as shown in Movie S1 in the SI, one-dimensional Chol number density distributions appear to converge after 200 ns. Second, as shown in snapshots of Voronoi tessellation (Figure 2), Chol in DOPC or POPC bilayers are depleted and accumulated in DPPC bilayers. To be more quantitative, from the Voronoi tessellations of simulation trajectories, we calculated the mole


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fraction of Chol (XChol) in each bilayer and the number of interfacial Chol (NChol) (see Analysis in the SI for details). As shown in Figure 3, NChol converges after 250 ns, while XChol converges at later time (> 300 ns, see also Table S2 in the SI). The convergence of XChol and NChol between two initial Chol distributions verifies that Chol partitioning is well represented in the simulation model.

Figure 2. Voronoi tessellations of the top leaflet of a DO-CH-DP BBS containing 20 mol% Chol for (A) delta and (B) random initial Chol distributions at t = 0.01 ns (top panels) and at t = 380 ns (bottom panels). The Chol molecules in DOPC and DPPC bilayers are shown in red and blue, respectively, while the interfacial Chol molecules are shown in green. DOPC and DPPC are shown in pink and cyan. The borders between molecules are shown in grey and the primary simulation box is shown in red.

Figure 3. Time series of Chol mole fraction (XChol) in each bilayer and the number of interfacial Chol (NChol) for (A and B) DO-CH-DP and (C and D) PO-CH-DP. In (A) and (C), XChol in DPPC bilayers and that in DOPC and POPC bilayers are shown in blue and red lines for initial delta Chol distribution,



whereas those for initial random Chol distributions are shown in cyan and pink lines. The time series for each initial Chol distribution were averaged over 10 simulation systems and their standard errors were shown as grey area. Lateral diffusion coefficient As the (self-adjusted) lipid packing is not influenced significantly by the restraints, the other bilayer properties, such as diffusion coefficients of lipids in each bilayer in the BBS, should be consistent to those from a bilayer with Chol embedded. The lateral diffusion coefficients (DL) of Chol, DOPC, POPC, and DPPC from the simulations are summarized in Table 1 (see Analysis in the SI for details). Recently, it was reported that the DL calculated from membrane simulations under the periodic boundary conditions show system-dependent finite-size effects.24 In addition, it was also reported that DL of DOPC and DPPC were overestimated compared to the experimental values in different extents. As the finite-size effects on the DL (under periodic boundary conditions) prevents direct comparison, we compare the ratio of diffusion coefficients (with corrected experimental data25–27 for bilayers with 50 wt % D2O). Before comparison, it should be noted the effect of Chol concentration on the phase of bilayers. The global Chol concentration of 20 mol% in this study was chosen for statistical reason and could be rather high. At the simulation temperature (T = 318 K), DOPC-Chol (at 13 mol% Chol) and POPC-Chol (at 15 mol% Chol) bilayers have been reported to be in liquid disordered phase (ld).25 However, DPPC-Chol bilayers (at 27 and 25 mol% Chol) would show a different phase, the coexistence of liquid disordered and lipid ordered phases (ld + lo).28,29 Due to different phases between DOPC/POPC-Chol and DPPC-Chol bilayers and heterogeneity in the extents of the overestimation in DL for DOPC and DPPC, we did not compare the ratio of DL between DOPC/POPC and DPPC. Assuming that the extents of the finite size effects are comparable, the ratio of DL between DOPC (with 13 mol% Chol) and POPC (with 15 mol% Chol) in our simulations is 1.13, which agrees excellently with the estimate of 1.08 from the experimental data25 (Table 1). The ratios of DL between Chol and DPPC are 1.26 and 1.21 in DO-CH-DP and PO-CH-DP (at 27 and 25 mol% Chol, respectively), which are again in excellent agreement with the estimates from the experimental data (1.26 and 1.22, respectively).26 Because experimental DL of Chol in DOPC and POPC bilayers are not available, the ratio between DOPC/POPC and Chol was not compared. Overall, the ratios of DL from the binary bilayer simulations agree excellently with those from the experiments, which further supports that the BBS is a valid simulation model and keeps the transport properties of each bilayer intact. Table 1. Estimated lateral diffusion coefficient (DL in Å2/ns) of Chol and lipids† BBS Bilayer XChol Component DL Expt.

DO-CH-DP DOPC DPPC 0.13 0.27 DOPC Chol DPPC Chol 0.75 1.49 0.46 0.47 a b 1.65 0.57 0.72b

PO-CH-DP POPC DPPC 0.15 0.25 POPC Chol DPPC Chol 0.66 1.12 0.42 0.51 a b 1.53 0.61 0.74b

†

Average over all 20 independent simulations for each BBS. The standard errors are smaller than 0.03 Å2/ns except those for Chol in DOPC (0.11 Å2/ns) and POPC bilayers (0.09 Å2/ns). aEstimates were calculated from DL measured by pulse filed gradient NMR for oriented bilayers with 30 wt % D2O25 and corrected to those with 50 wt % D2O using calibration curve.27 bEstimates were calculated from DL of each component (DPPC and Chol) measured by pulse field gradient NMR for oriented bilayers with 50 wt % D2O at various temperatures.26


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Estimate of partition coefficient (free energy) So far, we verified that the BBS is a reliable simulation model, where the lipid packing and diffusion are consistent with those from pure lipid bilayers, and thus Chol partitioning is well described by binary bilayer simulations. The remaining verification for the simulation approach is the accuracy of the partition coefficient (or free energy) from the binary bilayer simulations. The partition coefficients of Chol between DPPC and DOPC/POPC bilayers were calculated from the XChol (Table 2). Then, the Chol partition coefficient between POPC and DOPC was calculated by thermodynamic relation, / . The calculated =1.35 ± 0.04 (at T = 318 K) agrees excellently with available experimental data, 1.40 ± 0.11 (partition coefficient between 1-stearoyl-2oleoyl-sn-glycero-3-phosphocholine (SOPC) and DOPC at T = 310.15 K), although there is a chain length difference in POPC (simulation) and SOPC (experiment).7 This result illustrates the efficacy of the simulation approach for quantitative estimation of Chol partitioning between bilayers and further support the validity of the simulation model. Table 2. Estimated partition coefficient and free energy of cholesterol between bilayers. Sim.

a

∆G (kcal/mol)

Expt.

2.25 ± 0.14

-0.51 ± 0.04

1.66 ± 0.05 1.35 ± 0.04

-0.32 ± 0.02 1.40 ± 0.11

b

-0.19 ± 0.02

The partition coefficient was estimated from and at T = 318 K. bPartition coefficient of Chol between 1-stearoly-2-oleoly-sn-glycero-3-phsphocholine (SOPC) and DOPC at T = 310.15 K.7 a

In the present work, we have devised an efficient MD simulation approach for Chol partitioning. The simulation model is composed of binary bilayers of different lipid types embedded in bulk water, where the host lipids self-adjust their packing. The mixing of host lipids of two bilayers is prevented by soft restraint potentials applied near the bilayer-bilayer interfaces, while Chol molecules can freely diffuse across the bilayers. The simulation model was validated by (1) self-adjusted lipid packing (i.e., minimum numbers of lipids under the restraints), (2) the convergence of mole fraction of Chol and the number of interfacial Chol, and (3) diffusion coefficients of lipids and cholesterol in each bilayer. The efficacy of the simulation method is shown by an accurate estimate of Chol partition coefficients between bilayers. It should be noted that our simulation method is flexible in that it can be readily applicable to any lipid membrane of interest and is not limited to two membranes with a single lipid and cholesterol. i.e., any molecular partitioning between complex bilayer membranes (including ternary mixed bilayers) for characterization of protein/lipid-lipid interactions. Also, perhaps more importantly, the simulation approach can be an effective computational method for drug solubility by a straight forward generalization of the BBS, where a simulation system consists of two bulk solvents, binary solvent system, and mixing of solvent molecules between two bulk solvents is prevented by the same type of restraints. From the simulations of the binary solvent systems, one can estimate the partition coefficient of small (drug-like) molecules without the need of (expensive) free energy simulations. ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge.



Section S1, Computational methods; Figure S1, Diffusion coefficient along X for the cholesterol and lipids; Table S1, Number of lipids under the influence of restraints; Table S2, mole fraction of cholesterol and the number of interfacial cholesterol (PDF) Movie S1, Time evolution of the number density of cholesterol along X for DO-CH-DP and PO-CH-DP (MP4). AUTHOR INFORMATION Corresponding Author *(W. I.) Tel: +1-610-758-4524. Fax: +1-610-758-4004. E-mail: [email protected].

Notes The authors declare no competing financial interests. ACKNOWLEDGEMENT

We are grateful to Richard Pastor, Bernard Brooks, and Aurelia Honerkamp-Smith for valuable comments and suggestions. This work was supported by NSF MCB-1727508 and XSEDE MCB070009.

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TOC GRAPHICS Cholesterol Partitioning Experiment

Binary Bilayer Simulation

K VV 12 V1

V1 K CD

V2

CD

V2 K CD

B1

B2


Quantitative Characterization of Cholesterol Partitioning Between

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