Facilitated and Non-Gaussian Diffusion of Cholesterol in Liquid

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Biophysical Chemistry, Biomolecules, and Biomaterials; Surfactants and Membranes

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 J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b02982 • Publication Date (Web): 22 Oct 2018 Downloaded from http://pubs.acs.org on October 23, 2018

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The Journal of Physical Chemistry Letters

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 E-mail: [email protected]

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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 microseconds for lipid bilayers with various concentrations of cholesterol. We find that the cholesterol diffusion in 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 an upright orientation diffuses relatively slowly. Such position-dependent dynamics of cholesterol leads to the facilitated and non-Gaussian diffusion.

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Cholesterol is an essential component of biological membranes and plays critical roles in various processes such as cholesterol-enriched domain formation 1–13 and signal transduction. 14–23 Because the transport of cholesterol affects the rate of the processes, the 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 flip-flop: when a cholesterol molecule underwent a flip-flop at least once, the cholesterol traveled 2.6 times longer distance during 500 ns than cholesterol that never flip-flopped. This indicates that the 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 solid (gel) phase, where both lipids and cholesterol diffuse hardly. As T increases, liquid disordered (Ld ) phase develops such that both lipids and cholesterol are quite mobile. As more cholesterol is introduced to the lipid bilayers at a given T , liquid ordered (Lo ) phase may appear. In the Lo phase, cholesterol were often found 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

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reported that small molecules such as methanol diffused faster at the lipid bilayer center than 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 to 360K) and compositions (xchol = 0.1 to 0.5). We perform coarse-grained molecular dynamics simulations using Martini force fields 50 and 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 virtual site, 52 wet Martini with virtual site, and wet Martini without 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 different models (the comparison is provided in 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 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 insane python script provided by Marrink group. 55 About 720 molecules are inserted into the simulation cell. The lateral dimension of the simulation cell varies from 11 nm to 15 nm depending on T and xchol . Figure 1(A) depicts a representative simulation snapshot for T = 330K and xchol = 0.5. Molecular structures of a lipid and a cholesterol are shown in Figures 1(B). We equilibrate simulation systems during several hundreds of nanoseconds

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until the potential energy converges. We use Berendsen barostat 56 during equilibration but employ Parrinello-Rahman barostat 57 during 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.

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Figure 1: (A) A representative simulation snapshot for xchol = 0.5 and T =330K. Grey and orange molecules represent DPPC and cholesterol, respectively. Only head groups are represented with spherical beads. (B) The structures of Martini model DPPC and cholesterol. (C) The definition of θ, an angle between the vector from C1 bead to ROH bead and the vector normal to the membrane surface. 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 (Figures 2(A) and (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 cholesterol to the ROH bead and the unit vector along the z-axis (Figures 1(C)). θ = 0◦ and 180◦ correspond to cholesterol with canonical upright orientation, whereas θ ≈ 90◦ for cholesterol staying 5



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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 2(C) 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 Rπ temperature of lipid bilayers. We estimate the free energy profile (F (z) = −kB T ln[ θ=0 P (z, θ)dθ]) for the cholesterol as a function of z. Here, kB denotes the Boltzmann constant. As shown in Figure 2(D), when xchol < 0.3 at T = 330K, 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 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 fo xchol ≥ 0.3. ∆F ‡ (a free energy barrier that cholesterol needs to overcome in order to move from z = 0 to z = ±1.8 nm) is increased as either xchol increases or T decreases (Figure 2(E)). An increase in ∆F ‡ indicates that the state of cholesterol being 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 leaflet 2 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 the flux of cholesterol molecules from the leaflet to the center and a local minimum at the membrane center. The presence of the local minimum in the free energy may also depend on the saturation level 43,59,61 and the length of lipids. 42

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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 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 x-y plane (membrane surface). We calculate the lateral mean-square displacement (h(∆r(t))2 i ≡ h[~ri (t) − ~ri (0)]2 i) and the self-part of the van Hove correlation function (Gs (r, t) ≡ hδ{r − |~r(t) − ~r(t = 0)|}i). Here, ~r(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. h· · · i denotes an ensemble average. According to the Einstein relation, h(∆r(t))2 i ∼ t1 in the Fickian regime. Figures 3(A) and (B) depict h(∆r(t))2 i’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 T = 300K and xchol = 0.1, the lateral diffusion is very slow and never reaches a Fickian regime in our simulations until 100 µs. h(∆r(t))2 i 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 = 330K, both lipids and cholesterol exhibit subdiffusion at relatively short time scales, but reach Fickian regime after tens of nanoseconds. As xchol is increased at T = 330K and a phase transition occurs from Ld to Lo phase, the lateral diffusion becomes slower with a decrease in the lateral diffusion coefficient D, which is obtained from the Einstein relation. Interesting is that in the Lo phase, D of cholesterol is decreased with an increase in xchol not as much as that of lipids is decreased (Figure 3(C)). In the inset of the figure are the ratios (Dchol /Dlipid ) of diffusion coefficients of cholesterol and lipids. Dchol /Dlipid stays constant as a function of xchol for xchol ≤ 0.3. However, in case of xchol > 0.3, Dchol /Dlipid increases rapidly, which indicates that the 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

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to stay constant in simple liquids. Such a facilitated lateral diffusion of cholesterol (and an increase in Dchol /Dlipid ) indicates that the Stokes-Einstein relation breaks down for cholesterol in Lo phase and the transport mechanism for cholesterol might be complicated.

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Figure 3: The mean-square displacements (h(∆r(t))2 i) of (A) lipids and (B) cholesterol for different values of xchol . The lateral diffusion coefficient (D) of lipids and cholesterol at T = 330K. In the inset is the ratio of the values of D of lipids and cholesterol. The lateral diffusion of lipids at liquid (ordered and disordered) phases exhibit 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 h(∆r(t))2 i 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 (Gs (r, t) ∝

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from h(∆r(t))2 i. Gs (r, t)’s of lipids are described quantitatively well by Gaussian functions. The non-Gaussian parameter (α2 (t) ≡

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ure 4(E)). 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 = 330K), Gs (r, t) is non-Gaussian even up to t = 1.2 µs (Figure 4(D)). As shown in Figure 3(B), however, h(∆r(t))2 i ∼ t1 at t = 1.2 µs, and the cholesterol already enters 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 cat-

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egorize 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 being in the bilayer center when rz ≤ 0.3 nm and 70◦ ≤ θ ≤ 110◦ .

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Figure 5: (A) 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) The 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 = 12ns) obtained from all cholesterol molecules in the lipid bilayers. We investigate trajectories of single cholesterol molecules and find that cholesterol at the bilayer center diffuses more quickly than cholesterol within leaflets. Figures 5(A) and (B) depict a representative trajectory of the center of mass of a single cholesterol molecule that undergoes a flip-flop. Figure 5(A) exhibits the z values of the trajectory as a function of time, whereas Figure 5(B) shows its trajectory projected on the x-y plane. As shown in Figure 5(A), 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). 11



Interesting is that as shown in Figure 5(B), the cholesterol travels much farther at the bilayer center (black) than the cholesterol within leaflets (blue and red). h(∆r(t))2 i 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 studies 48,49 showed that the number density around the bilayer center was smaller than within leaflets, for which cholesterol can have larger free volume and diffuse faster at the bilayer center. We calculate Gs (r, t)’s for cholesterol at the bilayer center and within leaflets separately (Figure 5(C)). Gs (r, t)’s of cholesterol at the bilayer center (red) and within leaflets (blue) are all Gaussian. Interesting is that overall Gs (r, t) obtained from all cholesterol molecules (solid line in Figure 5(C)) 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 diffuse much longer distance at the bilayer center. This indicates that the non-Gaussian 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 non-Gaussian. 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 ≥ 330K, 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

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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: small one for the leaflets and large one for the bilayer center. Therefore, when cholesterol may stay 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 the domain formation.

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

Supporting Information Available Details on (1) the phase behavior of binary component lipid membranes, and (2) the structure and dynamics of wet Martini membranes. This material is available free of charge.

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(3) Pantelopulos, G. A.; Nagai, T.; Bandara, A.; Panahi, A.; Straub, J. E. Critical Size Dependence of Domain Formation Observed in Coarse-Grained Simulations of Bilayers Composed of Ternary Lipid Mixtures. J. Chem. Phys. 2017, 147, 095101. (4) Lingwood, D.; Lingwood, D.; Simons, K.; Simons, K. Lipid Rafts as a MembraneOrganizing Principle. Science 2010, 327, 46–50. (5) Alwarawrah, M.; Dai, J.; Huang, J. A Molecular View of the Cholesterol Condensing Effect in DOPC Lipid Bilayers. J. Phys. Chem. B 2010, 114, 7516–7523. (6) Donaldson, S. H.; de Aguiar, H. B. Molecular Imaging of Cholesterol and Lipid Distributions in Model Membranes. J. Phys. Chem. Lett. 2018, 9, 1528–1533. (7) Martinez-Seara, H.; Róg, T.; Karttunen, M.; Vattulainen, I.; Reigada, R. Cholesterol Induces Specific Spatial and Orientational Order in Cholesterol/Phospholipid Membranes. PLoS ONE 2010, 5, e11162. (8) de Meyer, F.; Smit, B. Effect of Cholesterol on the Structure of A Phospholipid Bilayer. Proc. Natl. Acad. Sci. U. S. A. 2009, 106, 3654–3658. (9) Arnarez, C.; Webb, A.; Rouvière, E.; Lyman, E. Hysteresis and the Cholesterol Dependent Phase Transition in Binary Lipid Mixtures with the Martini Model. J. Phys. Chem. B 2016, 120, 13086–13093. (10) Róg, T.; Pasenkiewicz-Gierula, M.; Vattulainen, I.; Karttunen, M. Ordering Effects of Cholesterol and its Analogues. Biochim. Biophys. Acta-Biomembr. 2009, 1788, 97–121. (11) Jacobson, K.; Mouritsen, O. G.; Mouritsen, O. G.; Anderson, R. G. W. Lipid Rafts: At a Crossroad Between Cell Biology and Physics. Nat. Cell Biol. 2007, 9, 7–14. (12) Loverde, S. M. Molecular Simulation of the Transport of Drugs Across Model Membranes. J. Phys. Chem. Lett. 2014, 5, 1659–1665.

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(39) Bennett, W. F. D.; MacCallum, J. L.; Hinner, M. J.; Marrink, S. J.; Tieleman, D. P. Molecular View of Cholesterol Flip-Flop and Chemical Potential in Different Membrane Environments. J. Am. Chem. Soc. 2009, 131, 12714–12720. (40) Jo, S.; Rui, H.; Lim, J. B.; Klauda, J. B.; Im, W. Cholesterol Flip-Flop: Insights from Free Energy Simulation Studies. J. Phys. Chem. B 2010, 114, 13342–13348. (41) Marquardt, D.; Kučerka, N.; Wassall, S. R.; Harroun, T. A.; Bach, D.; Katsaras, J. Cholesterol’s Location in Lipid Bilayers. Chem. Phys. Lipids 2016, 199, 17–25. (42) Marquardt, D.; Heberle, F. A.; Greathouse, D. V.; Koeppe, R. E.; Standaert, R. F.; Van Oosten, B. J.; Harroun, T. A.; Kinnun, J. J.; Williams, J. A.; Wassall, S. R. et al. Lipid Bilayer Thickness Determines Cholesterol’s Location in Model Membranes. Soft Matter 2016, 12, 9417–9428. (43) Harroun, T. A.; Katsaras, J.; Wassall, S. R. Cholesterol Is Found To Reside in the Center of a Polyunsaturated Lipid Membrane. Biochemistry 2008, 47, 7090–7096. (44) Kučerka, N.; Perlmutter, J. D.; Pan, J.; Tristram-Nagle, S.; Katsaras, J.; Sachs, J. N. The Effect of Cholesterol on Short- and Long-Chain Monounsaturated Lipid Bilayers as Determined by Molecular Dynamics Simulations and X-Ray Scattering. Biophysical Journal 2008, 95, 2792–2805. (45) Kučerka, N.; Marquardt, D.; Harroun, T. A.; Nieh, M.-P.; Wassall, S. R.; Katsaras, J. The Functional Significance of Lipid Diversity: Orientation of Cholesterol in Bilayers Is Determined by Lipid Species. J. Am. Chem. Soc. 2009, 131, 16358–16359. (46) Weiner, M. D.; Feigenson, G. W. Presence and Role of Midplane Cholesterol in Lipid Bilayers Containing Registered or Antiregistered Phase Domains. J. Phys. Chem. B 2018, 122, 8193–8200.

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(A) z y x

(B) C2A

(C)

ROH R2 C2B

R3

ROH

z

θ

C1 C1

Lipid (DPPC)

Cholesterol ACS Paragon Plus Environment

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(A)

(B)

(C)

10

(E)

xchol ΔF

0.5 0.4 0.3 0.2 0.1

‡

2

300K 330K 360K

1

‡

5

ΔF (kBT)

(D) F (kBT)

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


0

0

-5 -2

-1

0

z (nm)

1

2 ACS Paragon Plus Environment

0.1

0.2

0.3

xchol

0.4

0.5

10

0

10

-1

10

-2

10

-3

10

Lipid

-4

10

0.1, 330K 0.2, 330K 0.3, 330K 0.4, 330K 0.5, 330K 0.1, 300K

2

10

1

10

0

10

-1

10

-2

10 10

Cholesterol

-4

10

10 -5

10

-3

10

-1

10

1

10

t (ns)

3

10

5

10

-4

10

-5

10

-5

10

-3

10

-1

10

1

10

t (ns)


3

10

5

10

4

2

0.1 0.2 0.3 0.4 0.5

xchol

-6

10

-3

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Dchol / Dlipid

1

(C)

xchol, T

3

D (nm /ns)

10

2

2

(nm )

0.1, 330K 0.2, 330K 0.3, 330K 0.4, 330K 0.5, 330K 0.1, 300K

4

10

2

10

(Δr(t))

(Δr(t))

(B)

xchol, T

3

2

2

(nm )

(A)

2

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

4

10


Cholesterol Lipid 0.1

0.2

0.3

xchol

0.4

0.5

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(A) 10

0

10

-3

10

10


10

1.2 ns 12 ns 120 ns

-2

Gs(r,t)

10

0

-1

1.2 ns 12 ns 120 ns

-2

Gs(r,t)

(B)

Lipid (xchol = 0.1)

-1

-4

10

-5

10

-3

10

-4

10

-5

10

10

-6

-6

10

10 0

4

8

12

0

4

r (nm)

(C) 10

0

10

(D) 10

0

10

-3

10

12 ns 120 ns 1.2 µs

-2

Gs(r,t)

10

-4

10

-5

10

-3

10

-4

10

-5

10

10

-6

-6

10

10 0

4

8

12

0

4

r (nm) 10 8 6 4 2 0

(F)

xchol

Lipid

0.5 0.4 0.3 0.2 0.1 -2

10

0

10

2

10

t (ns)

8

12

r (nm)

α2(t)

α2(t)

(E)

12


-1

120 ns 1.2 µs 12 µs

-2

8

r (nm)

Lipid (xchol = 0.5)

-1

Gs(r,t)

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


4

10


10 8 6 4 2 0

Cholesterol 0.5 0.4 0.3 -2

10

0

10

2

10

t (ns)

4

10


(B)

2

2

(C) 10

1

0

0

10

-2 -2 200 300 400 500 600

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10

t (ns) z (nm) 2 6 0 4

Cholesterol Center Leaflet

0

Gs(r,t)

z (nm)

(A)

y (nm)

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

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-2

10

-3

10

-4

-2

10

-5

10

2 t = 200 ns

-6

10

t = 600 ns

0 0

2

4

x (nm)

0

6 ACS Paragon Plus Environment

1

2

r (nm)

3

4

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1

Probability of Displacement

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


10

0

10

-1

10

-2

10

Center Leaflet

-3

10

-4

10

-5

10

0

1

2

3

4

Displacement of Cholesterol (nm) ACS Paragon Plus Environment

Facilitated and Non-Gaussian Diffusion of Cholesterol in Liquid

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