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Letter Cite This: J. Phys. Chem. Lett. 2018, 9, 6529−6535

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Facilitated and Non-Gaussian Diffusion of Cholesterol in Liquid Ordered Phase Bilayers Depends on the Flip-Flop and Spatial Arrangement of Cholesterol Younghoon Oh and Bong June Sung* Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 04107, Republic of Korea

J. Phys. Chem. Lett. 2018.9:6529-6535. Downloaded from pubs.acs.org by EASTERN KENTUCKY UNIV on 01/23/19. For personal use only.

S Supporting Information *

ABSTRACT: The diffusion of cholesterol in biological membranes is critical to cellular processes such as the formation of cholesterol-enriched domains. The cholesterol diffusion may be complicated especially when cholesterol flip-flops and/or stays at the membrane center. Understanding the diffusion mechanism of cholesterol at a molecular level should be, therefore, a topic of interest. We perform molecular dynamics simulations up to 100 μs for lipid bilayers with various concentrations of cholesterol. We find that cholesterol diffusion in the liquid ordered phase depends on whether it is within leaflets or at the bilayer center, is non-Gaussian for several microseconds, and is enhanced significantly compared to that of lipids. Cholesterol at the bilayer center diffuses fast, while cholesterol in the hydrocarbon region with upright orientation diffuses relatively slowly. Such position-dependent dynamics of cholesterol leads to facilitated and non-Gaussian diffusion.

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quite mobile. As more cholesterol is introduced into the lipid bilayers at a given T, the liquid ordered (Lo) phase may appear. In the Lo phase, cholesterol was often found to be stable at the lipid bilayer center, while the cholesterol performed flip-flop between leaflets.39−42 Harroun et al. performed neutron diffraction experiments for polyunsaturated lipid membranes and found that cholesterol resided at the membrane center.43−45 Cholesterol in the membrane center could play important roles in domain registration of lipid membranes.46,47 Other studies reported that small molecules such as methanol diffused faster at the lipid bilayer center than those within the leaflets,48,49 which suggests that the cholesterol diffusion mechanism would be complicated in the Lo phase. We investigate binary component lipid bilayers composed of saturated lipids (dipalmitoylphosphatidylcholine, DPPC) and cholesterol at various temperatures (T = 300−360 K) and compositions (xchol = 0.1−0.5). We perform coarse-grained molecular dynamics simulations using Martini force fields50 and the Gromacs 2016 molecular simulation package.51 There are two different solvent models in Martini (implicit (dry) and explicit (wet) solvent models) and two different cholesterol models (with and without virtual sites). We employ three different Martini models: dry Martini with a virtual site,52 wet Martini with a virtual site, and wet Martini without a virtual site. Unless otherwise noted, we present results obtained by using the dry Martini model and the cholesterol model with virtual sites. We find no qualitative difference in the spatial arrangement and the lateral diffusion of cholesterol between

holesterol is an essential component of biological membranes and plays critical roles in various processes such as cholesterol-enriched domain formation1−13 and signal transduction.14−23 Because the transport of cholesterol affects the rate of the processes, cholesterol transport has been an issue of importance.24−27 Cholesterol travels in lipid bilayers via lateral diffusion and flip-flop between two leaflets. According to a recent study on skin lipid multilayers by Das et al.,28 the lateral diffusion of cholesterol depended on the flipflop: when a cholesterol molecule underwent a flip-flop at least once, the cholesterol traveled a 2.6 times longer distance during 500 ns than cholesterol that never flip-flopped. This indicates that flip-flop would complicate the lateral diffusion of cholesterol. In this study, we perform molecular dynamics simulations for lipid bilayers with cholesterol and find that some cholesterol molecules reside at the bilayer center during flip-flop. We also find that the cholesterol diffusion is dependent on its spatial arrangement, non-Gaussian at a few microseconds, and is enhanced in the liquid ordered (Lo) phase compared to that of lipids. The cholesterol at the bilayer center diffuses quite fast before completing flip-flop, and its subdiffusion appears at short time scales (∼1 ns). On the other hand, other cholesterol within leaflets diffuses slowly, and its subdiffusion regime develops at long times (∼102 ns). Such position-dependent dynamics and flip-flop lead to the facilitated and non-Gaussian diffusion of cholesterol. The phase and the diffusion of lipid bilayers depend on both temperature (T) and the mole fraction (xchol) of cholesterol.8,23,29−38 At relatively low temperature and small xchol, lipid bilayers are in the solid (gel) phase, where both lipids and cholesterol hardly diffuse. As T increases, liquid disordered (Ld) phase develops such that both lipids and cholesterol are © 2018 American Chemical Society

Received: September 27, 2018 Accepted: October 22, 2018 Published: October 22, 2018 6529

DOI: 10.1021/acs.jpclett.8b02982 J. Phys. Chem. Lett. 2018, 9, 6529−6535

Letter

The Journal of Physical Chemistry Letters

cholesterol to the ROH bead and the unit vector along the zaxis (Figure 1C). θ = 0 and 180° correspond to cholesterol with canonical upright orientation, whereas θ ≈ 90° is for cholesterol staying parallel to the bilayer surface. For xchol = 0.1, there are two peaks in P(z,θ) at (z,θ) = (−1.8 nm, 0°) and (1.8 nm, 180°), which indicates that cholesterol is mostly upright with its head group around the bilayer surface. On the other hand, for xchol = 0.5, there are three additional peaks at (z,θ) = (0, 90°), (0, 0°), and (0, 180°). The small peaks at (0,0°) and (0,180°) represent a very small portion of cholesterols of inverted orientation with their head groups located at the membrane center. The peak at (0, 90°) corresponds to some cholesterol lying parallel between two leaflets. Figure 2C depicts a representative simulation snapshot for xchol = 0.5, where cholesterol molecules are placed at both central and leaflet regions. The fraction of cholesterol at the bilayer center depends on the composition (xchol) and temperature of lipid bilayers. We estimate the free energy profile (F(z) = ÅÄ π ÑÉ −kBT lnÅÅÅÅ∫ P(z , θ ) dθ ÑÑÑÑ) for the cholesterol as a function ÅÇ θ = 0 ÑÖ of z. Here, kB denotes the Boltzmann constant. As shown in Figure 2D, when xchol < 0.3 at T = 330 K, there are only two minima in F(z) such that cholesterol molecules reside only within leaflets. As xchol increases, a local minimum begins to appear at z = 0, which indicates that the cholesterol may reside at the bilayer center. The value of F(z = 0) is higher than that of F(z = ±1.8 nm) regardless of xchol, which suggests that z = ±1.8 nm should be thermodynamically stable states for cholesterol. On the other hand, z = 0 is an unstable state for xchol < 0.3, while z = 0 becomes a metastable state for xchol ≥ 0.3. ΔF‡ (a free energy barrier that cholesterol needs to overcome in order to move from z = 0 to ±1.8 nm) is increased as either xchol increases or T decreases (Figure 2E). An increase in ΔF‡ indicates that the state of cholesterol at z = 0 becomes more stable. Therefore, cholesterol at the bilayer center becomes more stable with an increase in xchol and/or a decrease in T. As xchol increases, the chemical potential of cholesterol is increased within the membrane leaflet2 such that there should be an imbalance in the chemical potential between the leaflet and the membrane center. Such an imbalance in the chemical potential would lead to a flux of cholesterol molecules from the leaflet to the center and a local minimum at the membrane center. The presence of a local minimum in the free energy may also depend on the saturation level43,59,61 and the length of lipids.42 The lateral diffusion of lipids and cholesterol depends on the phase and composition of lipid bilayers.31,32,63−65 We present numerical details on how we determine the phase of our systems in the Supporting Information. In order to investigate the lateral diffusion of lipids and cholesterol, we project the tail group (C2A, C2B) of lipids and the ring bead (R2, R3) of cholesterol onto the x−y plane (membrane surface). We calculate the lateral mean-square displacement (⟨(Δr(t))2⟩ ≡ ⟨[r⃗i(t) − r⃗i(0)]2⟩) and the self-part van Hove correlation function (Gs(r,t) ≡ ⟨δ{r − |r⃗(t) − r⃗(t = 0)|}⟩). Here, r⃗(t) is a position vector (on the x−y plane) of either the tail group of a lipid or the ring bead of cholesterol at time t. ⟨···⟩ denotes an ensemble average. According to the Einstein relation, ⟨(Δr(t))2⟩ ≈ t1 in the Fickian regime. Figure 3A,B depicts ⟨(Δr(t))2⟩’s of lipids and cholesterol, respectively. Subdiffusion is observed for both lipids and cholesterol at certain times scales, which agrees with a previous study.26 In the gel phase at

different models (the comparison is provided in the Supporting Information). In order to propagate our systems with the dry Martini model, we use the second-order stochastic dynamics (SD) integrator and a time step of 30 fs. Compressibility in a direction normal to the membranes is set to zero such that the dimension of a simulation cell in the direction is fixed at 30 nm. In order to mimic tensionless bilayers, we allow the dimensions of the simulation cell in the lateral directions to relax with zero reference pressure. We also monitor and correct the motion of centers of mass of lipids in upper and lower leaflets and cholesterol molecules separately.26,53,54 The initial configurations of binary component lipid bilayers are constructed using the insane python script provided by the Marrink group.55 About 720 molecules are inserted into the simulation cell. The lateral dimension of the simulation cell varies from 11 to 15 nm depending on T and xchol. Figure 1A

Figure 1. (A) Representative simulation snapshot for xchol = 0.5 and T = 330 K. Gray and orange molecules represent DPPC and cholesterol, respectively. Only head groups are represented with spherical beads. (B) Structures of Martini model DPPC and cholesterol. (C) Definition of θ, an angle between the vector from the C1 bead to ROH bead and the vector normal to the membrane surface.

depicts a representative simulation snapshot for T = 330 K and xchol = 0.5. Molecular structures of a lipid and a cholesterol are shown in Figure 1B. We equilibrate simulation systems over several hundreds of nanoseconds until the potential energy converges. We use a Berendsen barostat56 during equilibration but employ a Parrinello−Rahman barostat57 during the production run, which is as long as 100 μs. Ensemble averages of properties are performed over up to 20 different sets of simulations for each state point. Some cholesterol molecules in our simulations are found at the bilayer center between two leaflets, which is consistent with previous studies.39−45,58−62 We calculate the density distribution functions (P(z,θ)) of cholesterol molecules for xchol = 0.1 and 0.5 (Figure 2A,B). z denotes the position of the R2 and R3 beads in a direction (z-axis) normal to the bilayer surface, and θ is an angle between the vector from the C1 bead of 6530


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Figure 2. P(z,θ) at T = 330 K and xchol = (A) 0.1 and (B) 0.5. (C) Representative simulation snapshot for xchol = 0.5 and T = 330 K. Blue and red molecules are cholesterol molecules at the bilayer center and within leaflets, respectively. Gray spheres are the head groups of lipids. Tail groups of lipids are omitted for the sake of clarity. (D) Free energy F(z) as a function of z at T = 330 K. (E) Free energy barrier (ΔF‡) required for cholesterol at the bilayer center to travel to leaflets as a function of xchol for various temperatures. Note that F(z) graphs in Figure 2D are shifted for the sake of visibility.

Figure 3. Mean-square displacements (⟨(Δr(t))2⟩) of (A) lipids and (B) cholesterol for different values of xchol. (C) Lateral diffusion coefficient (D) of lipids and cholesterol at T = 330 K. In the inset is the ratio of the values of D of lipids and cholesterol.

T = 300 K and xchol = 0.1, the lateral diffusion is very slow and never reaches a Fickian regime in our simulations until 100 μs. ⟨(Δr(t))2⟩ shows a plateau for orders of magnitude of time for both lipids and cholesterol such that molecules in the gel phase hardly diffuse.

In the Ld and Lo phases at T = 330 K, both lipids and cholesterol exhibit subdiffusion at relatively short time scales but reach the Fickian regime after tens of nanoseconds. As xchol is increased at T = 330 K and a phase transition occurs from the Ld to Lo phase, the lateral diffusion becomes slower with a 6531


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Figure 4. (A−D) Self-part van Hove correlation functions (Gs(r,t)) of lipids and cholesterol at T = 330 K and xchol = 0.1 and 0.5. Solid lines are Gaussian guides. Non-Gaussian parameters (α2(t)) for (E) lipids and (F) cholesterol at T = 330 K and various values of xchol.

Figure 5. (A) Representative trajectory of the value of z as a function of the time t of the cholesterol. The color code represents the value of z of the center of mass of the cholesterol. (B) Trajectory of the center of mass of a single cholesterol molecule projected on the x−y plane (membrane surface). (C) Gs(r,t = 12 ns)’s of cholesterol molecules at the bilayer center (red symbol) and within the leaflets (blue symbol). The yellow solid line represents Gs(r,t = 12 ns) obtained from all cholesterol molecules in the lipid bilayers.

xchol ≤ 0.3. However, in the case of xchol > 0.3, Dchol/Dlipid increases rapidly, which indicates that cholesterol diffusion is facilitated compared to that of lipids. According to the Stokes−Einstein relation, the diffusion coefficient of molecules is determined by the ratio of T and viscosity (η), i.e., D ∝ T/η. Therefore, Dchol/Dlipid is supposed

decrease in the lateral diffusion coefficient D, which is obtained from the Einstein relation. Interesting is that in the Lo phase the D of cholesterol does not decrease as much as that of lipids with an increase in xchol (Figure 3C). In the inset of the figure are the ratios of diffusion coefficients of cholesterol and lipids (Dchol/Dlipid). Dchol/Dlipid stays constant as a function of xchol for 6532


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We calculate Gs(r,t)’s for cholesterol at the bilayer center and within leaflets separately (Figure 5C). Gs(r,t)’s of cholesterol at the bilayer center (red) and within leaflets (blue) are all Gaussian. Interesting is that the overall Gs(r,t) obtained from all cholesterol molecules (solid line in Figure 5C) can be described by a linear combination of Gs(r,t)’s of cholesterol at the bilayer center (red) and within leaflets (blue). The overall Gs(r,t) at r ≤ 1 nm is dominated by the cholesterol within leaflets. On the other hand, the overall Gs(r,t) at r ≥ 1 nm is dominated by the cholesterol at the bilayer center because the cholesterol diffuses a much longer distance at the bilayer center. This indicates that the nonGaussian diffusion of cholesterol in the Lo phase results from the position-dependent dynamics. When the bilayer center becomes a metastable state for a cholesterol and the cholesterol can reside at the bilayer center for a while, the lateral diffusion of cholesterol is facilitated and becomes nonGaussian. In summary, we investigate the lateral diffusion and spatial distribution of cholesterol molecules in the binary component lipid membranes of saturated lipids and cholesterol. We perform coarse-grained molecular dynamics simulations up to 100 μs. The spatial distribution of cholesterol depends on the composition (xchol) of the bilayers. In the Ld phase of xchol < 0.3 at T ≥ 330 K, cholesterol is hardly observed at the bilayer center because cholesterol is unstable at the bilayer center. As xchol is increased beyond 0.3, cholesterol is more likely to stay at the bilayer center while the cholesterol flip-flops between two leaflets. We also find that the cholesterol at the bilayer center diffuses much faster than cholesterol within leaflets. In other words, cholesterol in the binary component lipid bilayers diffuses with two different diffusion coefficients: a small one for the leaflets and a large one for the bilayer center. Therefore, when cholesterol stays at the bilayer center for a sufficiently long time, the lateral diffusion of cholesterol is facilitated significantly compared to that of lipids. The dual diffusion coefficients of cholesterol leads to the non-Gaussian diffusion of cholesterol even at very long times. In the future, we plan to investigate how the saturation level and the length of lipids would affect the free energy of cholesterol and how the fast diffusion of cholesterol at the bilayer center would relate to the kinetics of domain formation.

to stay constant in simple liquids. Such facilitated lateral diffusion of cholesterol (and an increase in Dchol/Dlipid) indicates that the Stokes−Einstein relation breaks down for cholesterol in the Lo phase and the transport mechanism for cholesterol might be complicated. The lateral diffusion of lipids at liquid (ordered and disordered) phases exhibits Gaussian statistics regardless of xchol, as expected from the central limit theorem. On the other hand, the lateral diffusion of cholesterol shows non-Gaussian behavior in the Lo phase even when ⟨(Δr(t))2⟩ of cholesterol enters the Fickian regime. Figure 4 depicts Gs(r,t) for lipids and cholesterol at various times from t = 1.2 ns to 12 μs. Symbols are simulation results, and solid lines are Gaussian fits exp(−r 2 / 4D)

(Gs(r , t ) ∝ ), with diffusion coefficients obtained 4π D from ⟨(Δr(t))2⟩. Gs(r,t)’s of lipids are described quantitatively well by Gaussian functions. The non-Gaussian parameter (α2(t) ≡

⟨(Δ r )⃗ 4 (t )⟩ 2⟨(Δ r )⃗ 2 (t )⟩2

− 1) is also quite negligible for lipids

(Figure 4E). Similarly, in the Ld phase, Gs(r,t) of cholesterol is also Gaussian. On the other hand, in the Lo phase (at xchol ≥ 0.3 and T = 330 K), Gs(r,t) is non-Gaussian even up to t = 1.2 μs (Figure 4D). As shown in Figure 3B, however, ⟨(Δr(t))2⟩ ≈ t1 at t = 1.2 μs, and the cholesterol already enters the Fickian regime. Such a seemingly Fickian but non-Gaussian diffusion, which was also observed for colloids in actin suspensions and glasses, has been an issue of significance.66−71 In order to understand the facilitated and non-Gaussian diffusion of cholesterol, we categorize cholesterol molecules into (a) cholesterol within leaflets and (b) cholesterol at the bilayer center. We determine a cholesterol molecule to be within leaflets if the distance (rz) between the bilayer center and the cholesterol head group is larger than 1.5 nm and the angle θ of the cholesterol molecule is smaller than 15° or larger than 165°. On the other hand, a cholesterol molecule is considered to be in the bilayer center when rz ≤ 0.3 nm and 70 ≤ θ ≤ 110°. We investigate trajectories of single cholesterol molecules and find that cholesterol at the bilayer center diffuses more quickly than cholesterol within leaflets. Figure 5A,B depicts a representative trajectory of the center of mass of a single cholesterol molecule that undergoes a flip-flop. Figure 5A exhibits the z values of the trajectory as a function of time, whereas Figure 5B shows its trajectory projected on the x−y plane. As shown in Figure 5A, from t = 200 to 360 ns, the cholesterol stays within a lower leaflet (blue). Then, the cholesterol begins to flip-flop and stays at the bilayer center (black) until t = 420 ns. After t = 420 ns, the cholesterol completes the flip-flop and stays in the upper leaflet (red). Interesting is that, as shown in Figure 5B, the cholesterol travels much farther at the bilayer center (black) than the cholesterol within leaflets (blue and red). ⟨(Δr(t))2⟩ of cholesterol at the bilayer center is also much larger than that of cholesterol within leaflets (not shown), which indicates that cholesterol diffuses much faster at the bilayer center. Therefore, cholesterol diffuses in the binary component lipid bilayers with two different diffusion coefficients: a relatively small diffusion coefficient for cholesterol within leaflets and a larger diffusion coefficient for cholesterol at the bilayer center. Recent simulation studies48,49 showed that the number density around the bilayer center was smaller than that within leaflets, for which cholesterol can have larger free volume and diffuse faster at the bilayer center.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.8b02982. Details on (1) the phase behavior of binary component lipid membranes and (2) the structure and dynamics of wet Martini membranes (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Younghoon Oh: 0000-0003-2454-1701 Bong June Sung: 0000-0002-7717-1559 Notes

The authors declare no competing financial interest. 6533


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ACKNOWLEDGMENTS This work was supported by Samsung Science and Technology Foundation under Project No. SSTF-BA1502-07.

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