Effects of Cholesterol on the Thermodynamics and Kinetics of Passive

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Effects of Cholesterol on the Thermodynamics and Kinetics of Passive Transport of Water through Lipid Membranes Bilkiss B. Issack, and Gilles Herve Peslherbe J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp510497r • Publication Date (Web): 13 Feb 2015 Downloaded from http://pubs.acs.org on February 18, 2015

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The Journal of Physical Chemistry

Effects of Cholesterol on the Thermodynamics and Kinetics of Passive Transport of Water Through Lipid Membranes Bilkiss B. Issack†,‡ and Gilles H. Peslherbe∗,† Centre for Research in Molecular Modeling, and Department of Chemistry and Biochemistry, Concordia University, Montreal QC, Canada H4B 1R6 E-mail: [email protected] Phone: +1 (514) 848-2424. Fax: +1 (514) 848-2868

∗

To whom correspondence should be addressed Centre for Research in Molecular Modeling, and Department of Chemistry and Biochemistry, Concordia University, Montreal QC, Canada H4B 1R6 ‡ Current address: Département des sciences expérimentales, Université de Saint-Boniface, Winnipeg MB, Canada R2H 0H7 †

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Abstract

While it has long been known that cholesterol reduces the permeability of biological membranes to water, the exact mechanism by which cholesterol influences transmembrane permeation is still unclear. The thermodynamic and kinetic contributions to the transport of water across mixed DPPC/cholesterol bilayers of different composition are thus examined by molecular dynamics simulations. Our analyses show that cholesterol decreases transmembrane permeability to water mainly by altering the thermodynamics of water transport. In particular, the free energy barrier to permeation is magnified in the dense bilayer interior and the partitioning of water is significantly lowered. The changes are observed to correlate quantitatively well with the cholesteroldependent density and thickness of the bilayers. In contrast, diffusion coefficients are relatively insensitive to cholesterol concentration, except in the sparsely populated centre of the bilayer. Diffusion of water in cholesterol-containing bilayers appears to be related to changes in the free area in the middle of the bilayer and to the solute cross-sectional area in the denser hydrophobic regions. Overall, cholesterol is found to have an inhibitory effect on the permeation of water at all concentrations investigated although bilayers containing cholesterol concentrations up to 20 mol% display a more dramatic dependence on cholesterol content than at higher concentrations. Our results show that it is possible to quantitatively reproduce the relative effects of cholesterol


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on lipid bilayer permeability from molecular dynamics simulations.

Keywords Lipid Bilayer, Permeation, Free Energy, Diffusion, Molecular Dynamics

Introduction Cholesterol is a naturally occurring lipid in living cells and an important constituent of their plasma membranes. The distribution of cholesterol among eukaryotic membranes varies widely, ranging from negligible amounts in membranes of organelles to about 40 mol % of the lipid content in membranes of erythrocytes and myelin. 1 Cholesterol plays a major role in maintaining the morphology and integrity of cells by regulating various physical properties of lipid membranes, such as membrane fluidity, 2,3 lipid tail ordering 4–8 and molecular packing 6,9 among others. In addition, cholesterol also modulates transport processes across membranes. Its inhibitory effects on the permeability of membranes to small uncharged molecules are welldocumented. 10–21 For example, the rate of water permeation across model cholesterol-containing membranes has been measured using various experimental techniques. 10,16,17,21 Such investi-



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gations typically report permeation coefficients inferred by assuming a first-order transport process, and offer valuable insight into the overall permeation process. Several observations suggest that the decreased permeability of membranes originates from the altered structural properties of the cholesterol-containing membranes. 17,21,22 Xiang and Anderson concluded that the permeation and partitioning of acetic acid in cholesterol-containing lipid bilayers were governed by chain-ordering effects. 22,23 Other have speculated that the reduced permeabilities are the combined result of altered thermodynamic and dynamic effects. 24 Recently, Mathaiet al. showed that water permeability across mixed cholesterol/phospholipid bilayers correlated well with the area per lipid and the thickness of bilayers 21 and proposed that the rate-limiting step for water permeation occurs in the interfacial region 21 based on the observation that water permeability is correlated with the area per lipid and the thickness of bilayers. 21 Traditionally, experimentally observed permeation rates of small solutes have been explained in terms of the homogeneous slab model. 25 In this model, the permeation of solutes across a lipid bilayer is represented by a multistage process, consisting of the partitioning of solutes from the outer aqueous environment into the lipid interior, followed by their diffusion inside the bilayer and their subsequent partitioning into the aqueous medium on the other side of the bilayer. Despite its success, the model assumes that membranes consist of


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homogeneous regions separated by well-defined boundaries and thus has limited predictive power, as pointed out by several investigators. 12,16,21,22,26–28 Computer simulation represents an attractive alternative for exploring transport processes since they offer insight into molecular structure and dynamics at a level of atomic detail that is not directly accessible by conventional experiments. Computational studies have successfully employed the inhomogeneous solubility-diffusion model 29,30 to examine the permeation of a number of solutes including water, 30,31 oxygen and ammonia, 32 and several small organic molecules 31,33,34 as well as larger ones, 35 including buckyballed-sized molecules, 36 across lipid bilayers. The model takes into account the inherent heterogeneity of lipid bilayers by allowing the partition coefficients and diffusion coefficients to vary continuously through the bilayer. Permeation is then described as the combined local effects of thermodynamic and kinetic factors. 29,30 Solute partitioning to and from the lipid interior is a thermodynamic process governed by changes in free energy while solute diffusion inside the bilayer is governed by kinetics. Thus, the calculation of permeation coefficients requires the knowledge of the free energy of solute transfer across the bilayer and the local solute diffusion coefficients, both of which can be characterized by molecular dynamics (MD) simulations.More importantly, the relative ease with which numerous local solute properties can be calculated by MD simulation makes it a particularly suitable approach for probing po-



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tential correlations between transport properties and bilayer microstructure in the different regions of the bilayer for a better understanding of the molecular mechanisms underlying passive transport. Simulations of transmembrane permeation have traditionally focused on bilayers composed exclusively of phospholipids, such as dipalmitoylphosphatidylcholine (DPPC) 30–32,34,35 and dimyristoylphosphatidylcholine (DMPC), 33,37,38 and applications to cholesterol-containing lipid bilayers have been limited in comparison. 39–41 The individual aspect of solute partitioning into DMPC bilayers of varying cholesterol content has been explored by Monte Carlo techniques for a number of small-molecule solutes. 39 The free energy of transfer of water and other polar solutes was found to increase in the presence of cholesterol, while little effect was observed for slightly polar and apolar diatomic molecules. Similarly, cholesterol was recently reported to magnify the free energy barrier for the permeation of ammonia and carbon dioxide across cholesterol-containing phospholipid bilayers during MD simulations. 40 Permeation coefficients were also estimated by approximating the kinetic contribution with solute diffusion coefficients in aqueous solutions. The effects of bromination on the permeability of the larger hypericin molecule in cholesterol-containing membranes have also been investigated by MD simulations. 41 It is noteworthy that rapid developments in computer hardware and software have brought once intractable molecular dynamics simulations into the realms of


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feasibility, and that full transmembrane permeation processes have been observed in silico in cholesterol-free bilayers. 40 Saito and Shinoda 42 have reported that the reduced water permeability in simulations of cholesterol-containing DPPC bilayers and palmitoylsphingomyelin bilayers is mainly due to increases in the free energy barrier. Changes in the free energy of permeation were rationalized in terms of reduced cavity density inside the bilayers although no quantitative analysis was carried out. This work aims at providing quantitative insight into the effect of cholesterol on the molecular mechanism of water transport across lipid membranes from molecular dynamics simulations in terms of changes to their structural properties. For a thorough understanding of the role of cholesterol on the passive transport of water, the influence of cholesterol on the interplay between thermodynamic and kinetic contributions to transmembrane permeation needs to be assessed. Consequently, free energy profiles of water permeation and the associated diffusion coefficients are computed along the normal to binary lipid bilayers composed of DPPC and cholesterol at different concentrations. The correlation between the individual contributions to permeation and the altered structural properties of the bilayers is examined, in order to quantitatively understand the origin of cholesterol-induced modifications to transport processes.



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Methods Molecular dynamics simulations were performed for hydrated bilayers, consisting of 128 lipid (DPPC and cholesterol) molecules and 3655 water molecules, with the following lipid compositions: 0, 9, 20, 30 and 41 mol % cholesterol. The initial structure of the pure DPPC bilayer was obtained from http://moose.bio.ucalgary.ca/index.php?page=Structures_ and_Topologies. The binary lipid mixtures were prepared by randomly substituting equal numbers of DPPC molecules by cholesterol molecules in each leaflet. As for intermolecular interactions, the DPPC and cholesterol molecules were described by the force fields of Bergeret al. 43 and Höltjeet al., 44 respectively and water molecules were represented by the simple point charge (SPC) model. 45 Lennard-Jones and electrostatic interactions were cut off at 1.0 nm and long range electrostatics were evaluated by the smooth particle mesh Ewald method. 46 The equations of motion were integrated every 2 fs, with bond constraints enforced for lipid and water molecules with the LINCS 47 and SETTLE 48 algorithms, respectively. Cholesterol molecules were inserted randomly into the bilayer, one at a time, in replacement of a DPPC molecule, while making sure that the same concentration was present in each leaflet. Following each insertion, a steepest-descent minimization was performed to relieve bad contacts between the DPPC and cholesterol molecules while restraining the sterol 8 ACS Paragon Plus Environment

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oxygen atom to the head-group region. Energy minimization was followed by heating and gradual cooling from 423 K to 323 K over 1 ns at constant volume, using the weak coupling algorithm 49 with a time constant of 40 fs, to ensure randomization of the lipid tails. The Berendsen barostat 49 was then applied by semi-isotropically coupling the pressure with a time constant of 1 ps over 2 ns. The strength of the temperature coupling was subsequently weakened, with a time constant of 100 fs, and the simulations were continued for 50 ns in the NPT ensemble. Structural properties were computed from the second half of the simulations. Free energy changes associated with the motion of water molecules along the normal to the membrane were computed from the potential of mean force (PMF) experienced by the solute as a function of its distance from the centre of the bilayer, z. The technique of umbrella sampling 50 was applied to ensure adequate conformational sampling along the selected coordinate. The large majority of MD studies employ the particle insertion method or its variants to compute free energy changes associated with transmembrane permeation. 30–32,35,41,42 We have determined that umbrella sampling provides superior sampling and hence more reliable results than the aforementioned method for computing free energies. 51 A total of 32 simulations was required to generate a single PMF in pure DPPC. Each simulation box contained two harmonically-restrained water molecules, located at least 1.3 nm apart in different leaflets of the bilayer. We employed the distribution of umbrella windows previously used for



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hexane in a phospholipid bilayer. 52 In the relatively dense head-group region of the bilayer, the centres of the biasing potentials were spaced by 0.1 nm and their force constants were 3200 kJ mol−1 nm−2 . In less dense regions (near bulk water and the centre of the bilayer), the spacing was increased to 0.25 nm and the force constant was decreased to 500 kJ mol−1 nm−2 . A similar distribution was employed for mixed bilayers containing 9 and 20 mol % cholesterol. At higher cholesterol concentrations, more windows were required (36) along the reaction coordinate as a result of the characteristic thickening experienced by the bilayers. Each umbrella sampling simulation was performed for 30 ns and the first nanosecond was discarded as equilibration. The PMFs of water inside the bilayers were constructed by unbiasing the distribution of solutes with the weighted histogram analysis method (WHAM), 53 as implemented by Alan Grossfield. 54 The accurate computation of the free energy of permeation requires proper sampling of the bilayer by the solute along the xy-plane. Small solutes inside the mixed DPPC/cholesterol bilayers are especially sensitive to sampling problems, owing to the increased lateral heterogeneity that accompanies the introduction of cholesterol molecules into lipid bilayers. The non-uniform distribution of cholesterol molecules across the right leaflet of an equilibrated bilayer containing 20 mol % cholesterol is shown in Figure S1 of the Supporting Information. The partial exploration of the xy-plane by water molecules in the same bilayer over three 30


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ns trajectories, also shown in Figure S1, highlights the potentially inadequate sampling of the bilayer by a single simulation. Consequently, for every umbrella window, 3 trajectories starting from different solute coordinates in the lateral plane were propagated for 30 ns in each leaflet, resulting in 6 PMFs per bilayer (3 per leaflet). In all, 402 simulations were performed on a cluster of Intel Xeon dual Quad-Core processors and data was collected over a total of 11 µs. Each simulation was performed in parallel with 8 processors, using version 4.0.4 of the GROMACS software package. 55 The final PMF was averaged over both leaflets and the error bars were estimated from the asymmetry between the mean PMF in each leaflet. The convergence of the umbrella sampling calculations was verified by comparing the mean PMFs for increasing simulation timescales. For all bilayers investigated, the final PMFs appeared to converge within the timescale of the simulations. Despite our efforts to minimize artifacts due to sampling, however, we cannot completely rule out the influence of systematic sampling errors due to slow bilayer reorganization or other rare events, as recently uncovered in simulations of amino acid side-chain analogs in lipid bilayers. 56 Local diffusion coefficients for water molecules inside the bilayers were estimated from umbrella sampling trajectories according to a simplified form of the Woolf and Roux equation: 57,58 D(z = hzi) =

var(z) . τz


(1)


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hzi is the average position of the harmonically restrained water molecule along the normal to the membrane, var(z) = hz 2 i − hzi2 is its variance and τz is its correlation time, formally defined as: R∞ τz =

0

hδz(t)δz(0)idt , hδz 2 i

(2)

where δz(t) = z(t) − hzi. Values of τz were estimated by integration up to 10 ps and error bars associated with the diffusion coefficients were determined from the procedure described earlier for free energy profiles.

Results and discussion

Atomic density It is well documented that cholesterol induces molecular rearrangements in phospholipid bilayers, and subsequently alters their structural properties. Modifications to DPPC bilayers include the increased ordering of the acyl tails, 8,9,59–66 bilayer widening (or thickening), 61,63,66–69 and compression of the lateral dimensions (i.e, reduction of the area of the bilayer), better known as the condensing effect. 6,8,9,61–64,66,69,70 Since these effects have already been extensively studied both experimentally and using simulations, we show only the influence of cholesterol on molecular packing inside DPPC bilayers in Figure 1. Other


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structural changes are presented in the Supporting Information (see Figures S2 and S3). In all cases, our results agree reasonably well with the existing reports.

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Total atomic density (kg m )

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-2

-1

0 z (nm)

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Figure 1: Total atomic density profiles across the bilayer at various distances z from the bilayer centre for different cholesterol concentrations. The centre of the bilayer is located at z = 0. Statistical uncertainties estimated from 10 individual profiles determined over 2.5 ns each amount to less than 0.02 kg m−3 and are omitted for clarity.

Traditionally, the four-region model, proposed by Marrink and Berendsen, 30 has been used to analyse data from simulated bilayers. In the present work, the definition of common frontiers for regions of the bilayer is less straightforward due to the varying thickness of the bilayers as a function of cholesterol content. Although regions overlap, it is possible to define three main regions, namely a first region characterized by |z| > 2.8 nm which corresponds 13 ACS Paragon Plus Environment


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to the bilayer exterior and is mostly occupied by water molecules; the second region roughly spans |z| = 1.4 − 2.8 nm and contains the majority of head groups; finally, in the third region, hydrocarbon tails (and cholesterol rings) extend from about 1.4 nm to the centre of the bilayers where z = 0. The total density profiles of binary mixtures of DPPC and cholesterol shown in Figure 1 exhibit a slight outward shift in the density maximum upon cholesterol enrichment, indicative of the characteristic thickening of cholesterol-containing DPPC bilayers, observed in X-ray diffraction experiments 21,69 as well as in computer simulations. 8,62,71 The gradual formation of a shoulder around 0.5-1.25 nm from the centre of the bilayer reveals a progressive crowding among hydrophobic tails, and can be related to the condensing and ordering effects of cholesterol. The calculated density profiles are in excellent agreement with those of cholesterol-containing dioleylphosphatidylcholine (DOPC) bilayers determined from diffuse X-ray scattering. 21 They are also comparable to density profiles of cholesterol-containing DPPC bilayers from previous simulations, 8,9,24,62 except in the centre of the bilayer, where cholesterol has been reported to slightly decrease the local density, 8,9,62 whereas little influence from cholesterol is found in this region according to Fig. 1. The slight discrepancy at the centre of the bilayer between the simulated density profiles may result from differences in force fields and/or simulation protocols.


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Free energies The free energy ∆G(z) profiles of water in lipid bilayers of varying cholesterol content are presented in Figure 2. We observe that the overall shape of the free energy profiles is preserved at all cholesterol concentrations investigated in the present work. The profiles are characterized by a gradual increase in the free energy of water permeation as the solute penetrates the bilayer interior until a maximum is reached, followed by a reduction in the free energy as the solute approches the centre of the bilayer. The free energy profile for water inside pure DPPC bilayers has been reported in the literature 30,31 and compares reasonably well with the corresponding profile in Figure 2 considering the differences in the force field and temperature of the simulations. The initial gain in free energy associated with the motion of a water molecule as it exits bulk water and crosses the head group and lipid regions is due to the increase in density and the loss of stabilizing electrostatic interactions. The centre of the bilayer, on the other hand, is characterized by lipid tail endings and intermolecular voids and is typically less dense than other parts of the bilayer, as evidenced by the atomic density profiles (see Figure 1). As a result, there are fewer unfavourable interactions, and a dip is observed in the free energy profiles in this region. Since all profiles display the same general trend, it is reasonable to conclude that changes in molecular interactions as a result of water permeation are similar



in nature for all cholesterol concentrations of lipid bilayers investigated in this work.

0% 9% 20 % 30 % 41 %

30

-1

∆G (kJ mol )

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20

10

0 -4

-3

-2

-1

0 z (nm)

1

2

3

4

Figure 2: Free energy profiles of water inside bilayers of different cholesterol concentrations. The maximum statistical uncertainty associated with the profiles are 1.45, 1.06, 1.95, 0.94 and 0.96 kJ mol−1 at 0, 9, 20, 30 and 41% bilayer cholesterol content, respectively.

Quantitatively, however, cholesterol concentration can have a marked effect on the free energy of permeation. In general, the presence of cholesterol amplifies the free energy of transfer of water into the bilayer relative to the lipid/water interface. The effect is most pronounced in the hydrophobic core of the lipid bilayer, where increasing concentrations of cholesterol gradually raise the hydrophobic barrier. The observations are in agreement with the literature, although the absolute values of the free energy maxima are higher than


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reported previously. 42 We have observed differences of a similar magnitude between free energy profiles computed from umbrella sampling and from the particle insertion method. 51 Umbrella sampling was preferred in this work since it allowed for better sampling of the bilayer and more reliable results (smaller error bars). Compared to a pure DPPC bilayer, the free energy barrier1 for transferring a water molecule to the centre of the bilayer is 6 kJ mol−1 larger for the bilayer with 41 mol % cholesterol. Since the major contribution to the free energy in the nonpolar lipid tail region comes from Lennard-Jones interactions, it is reasonable to expect that this increase in the free energy barrier reflects increasingly unfavorable interactions as a result of tighter packing. In fact, the increase in the free energy of transfer of water from bulk water to the hydrophobic core at 1 nm from the bilayer centre (around the free energy maximum) is found to correlate well with the corresponding local density of bilayers of varying cholesterol content (Figure 3), in support of a direct relationship between the enhanced hydrophobic character of the lipid core and the formation of the shoulder in the density profiles. These results provide a quantitative rationale for the reduced cavity density around cholesterol molecules as a possible explanation for the larger free energy barrier in cholesterol-containing bilayers, proposed by Saito and Shinoda. 42 In addition to the increased hydrophobicity, the presence of cholesterol causes an outward 1

The expression free energy barrier describes the barrier in the free energy profile and should not be confused with an activation barrier which is typically encountered during kinetic processes.



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shift of the free energy barrier. This leads to a widening of the dip in the free energy profiles, consistent with the broadening of the trough in Figure 1, and the characteristic thickening of the bilayers. The relationship between the position of the free energy barrier and the thickness of the hydrophobic region is shown in Figure 4. The shift in the free energy barrier is observed to correlate well with the growth in bilayer thickness, and this may provide an explanation for the dependence of the permeability coefficients of water on the thickness of DOPC/cholesterol bilayers reported by Mathai et al.. 21 Although free energy barriers to the permeation of water inside lipid bilayers are modulated by their cholesterol content, the free energy of transfer of a water molecule from the lipid/water interface to the centre of the bilayers is unaffected by cholesterol within the precision of our calculations. This observation suggests that the partitioning of water, and hence its solubility, is reduced only in the dense regions of the cholesterol-containing bilayers. Recent simulations show that cholesterol has a similar effect on the potential of mean force of ammonia permeation across mixed bilayers of palmitoyloleoylphosphatidylethanolamine (POPE), palmitoyloleoylphosphatidylcholine (POPC) and cholesterol. 40 For water, Jedlovszky and Mezei 39 also reported an increase in the magnitude of the net free energy barrier inside cholesterol-containing DMPC bilayers. The larger barrier, however, was attributed to a lowering of the free energy in the region occupied by the hydroxyl group of cholesterol


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molecules at 1-2 nm from the centre of the bilayers. This behavior is not observed for mixed DPPC/cholesterol bilayers in our simulations.

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∆G (kJ mol )

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25 20

0% 9% 20 % 30 % 41 %

15 10

0.900

0.925

0.950

0.975

1.000

-3

Density (kg m ) Figure 3: Free energies of water transfer to the hydrophobic core vs total atomic densities calculated at 1.0 nm from the bilayer centre at different cholesterol concentrations.

Experimental investigations have attributed the decreased permeability of phospholipid/cholesterol mixtures to their reduced area per lipid 21 and to the ordering effects of cholesterol. 23 In Figure 5, we examine the dependence of these structural properties on the free energy barrier to the permeation of water. The effect of ordering is investigated by averaging over the order parameters for methylene carbon atoms 6-10 in sn-1 and sn-2 chains, which correspond to an



1.6

max

(nm)

1.4

d∆G

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1.2 0% 9% 20 % 30 % 41 %

1 0.8 0.6 2.9

3

3.1

3.2

3.3

dHC (nm) Figure 4: Distance between the free energy maxima d∆Gmax vs hydrocarbon thickness of the bilayer dHC , defined as the average distance between the carbon atoms lying at the interface of the hydrocarbon and head group region of the lipids in each leaflet for different cholesterol concentrations. approximate distance of 1.0 nm from the bilayer center based on the findings of Smondyrev and Berkowitz. 9 Both the area per lipid and the order parameters show modest correlation with the permeability as a function of cholesterol concentration.

Diffusion coefficients Local diffusion coefficients of water molecules inside the bilayer were estimated from Eq. 1 after integration of the position autocorrelation functions in Eq. 2. Diffusion coefficients 20 ACS Paragon Plus Environment

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0% 9% 20 % 30 % 41 %

30 -1

∆G (kJ mol )

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25 20 15 10

0.45

0.5

0.55

0.6

0.65

2

Area per lipid molecule (nm ) Figure 5: Free energy of transfer of water to the hydrophobic core at 1.0 nm from the bilayer centre vs area per lipid molecule of bilayers at different cholesterol concentrations. Statistical uncertainties of the area per lipid in the pure DPPC bilayer are smaller than the markers. were found to be sensitive to the time range used to estimate the characteristic correlation times, as previously noted by Hummer. 58 However, the relative effects of cholesterol on the local diffusion coefficients were observed to be similar regardless of the integration time. The diffusion profiles of water in bilayers of varying cholesterol content are shown in Figure 7. At all cholesterol concentrations investigated, estimated diffusion coefficients decrease as water enters the bilayer, reaching a plateau in the range |z| = 0.5 − 2.2 nm corresponding to the dense head group and hydrocarbon core regions. The profiles all peak in the centre



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∆G (kJ mol )

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0.35

0.4

< |SCD | > Figure 6: Free energy of transfer of water to the hydrophobic core at 1.0 nm from the bilayer centre vs average order parameters of the acyl chain at different cholesterol concentrations. of the bilayers, where local densities are at their lowest. The diffusion profile of water inside the pure DPPC bilayer compares well with those previously reported. 30,31 Similar to the free energy profiles, cholesterol appears to have little effect on the shape of the diffusion profiles since the general trend is also unaltered in cholesterol-containing bilayers. The height of the peaks however exhibits a clear dependence on the cholesterol content of the bilayers: increasing molar concentrations of cholesterol are observed to hinder the diffusion of water in the centre of the bilayers. The effects of cholesterol are generally restricted to the low-density


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lipid interior, as estimated local diffusion coefficients are virtually unaltered by cholesterol elsewhere inside the bilayers.

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8

6

-5

2 -1

D(z) (10 cm s )

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4

2

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-3

-2

-1

0 z (nm)

1

2

3

4

Figure 7: Diffusion profiles of water inside cholesterol-containing DPPC bilayers at different cholesterol concentrations

The effects of temperature, 72 solute size 12 and cholesterol 73,74 on diffusion coefficients have been rationalized in terms of free-volume 75 theory. According to the theory, diffusion occurs through a series of jumps when cavities or voids of a certain critical size open up next to a solute. In the dense regions of the lipid bilayer, the proposed mechanism of diffusion involves solute molecules rattling around voids for a relatively long period of time



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between jumps to neighboring voids. 26,27,37 In the middle of the bilayer where atomic density is markedly lower, diffusion is thought to be related to the frequency and size of jumps. 37 Falck et al. 76 investigated the influence of cholesterol on the distribution of the free area per molecule along the normal to mixed cholesterol/DPPC bilayers at concentrations comparable to those used in this work. All distributions feature a decrease in free area at the interfacial region relative to the exterior, a minimum in the denser parts of the bilayer interior and a sharp increase in the middle of the bilayer, not unlike the diffusion profiles shown in Figure 7. In the denser parts of the bilayer, however, the wide trough between |z| = 1.0 − 2.0 nm is narrower in the free area profiles. Increasing cholesterol content was observed to reduce the free area per molecule throughout the bilayer. While the reduction in free area per molecule accounts for the increasingly impaired diffusional motion in the bilayer centre, it does not account for the behaviour in the denser lipid interior where estimated diffusion coefficients are largely unaffected by cholesterol. This suggests that solute diffusion in the denser parts of the bilayer is not limited by the free area per molecule. In support, no strong correlation was observed between the free volume distribution and diffusion coefficients of small solutes (including water) inside a pure DPPC bilayer. 77 It has been suggested that the displacement of solutes inside a lipid bilayer is related to the redistribution of free volumes during lipid chain gauche-trans isomerization. 78 The hypothe-


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sis is supported by the observation that torsional isomerization of hydrocarbon chains affects jumps of benzene inside DMPC bilayers by modifying the connectivity between cavities. 38 We have analyzed the torsional motion of the lipid tails from the frequency of interconversion, defined as the average number of gauche-trans or trans-gauche interconversion per unit time during the simulation. The results are plotted in Figure 8. It is evident that increasing cholesterol content leads to less frequent isomerization which corresponds to a stiffening of the hydrocarbon tails consistent with the increased ordering of the lipid tails (see Figure S3 of the Supporting Information). The effects of cholesterol on the rate of torsional isomerization is analogous to the documented effect of cooling 38 a pure lipid bilayer. The effects are more prominent in the dense regions of the hydrophobic core (carbon atoms 2 to 8) which coincide with the position of cholesterol rings inside DPPC bilayers. 9 Accordingly, slower reorganization of the lipid tails is expected to increasingly hinder diffusional motion in the dense regions of the bilayer when cholesterol content is increased. This is in contrast with our observations, thus suggesting that, for a small solute such as water, diffusion in mixed DPPC/cholesterol bilayers is not limited by the torsional motion of the lipids. Similarly, Bemporad et al. concluded that diffusion of several small molecular solutes in a pure DPPC bilayer was not correlated to the lipid chain internal dynamics. 77 Xiang has proposed a model in which diffusion in a lipid bilayer is related to the solute



0.04

-1

-1

Interconversion rate (ps molecule )

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0.035 0.03 0.025 0.02

0% 9% 20 % 30 % 41 %

0.015 0.01 0

2

4

8 10 6 Carbon atom

12

14

Figure 8: Rate of gauche-trans or trans-gauche interconversion vs carbon atom along the lipid tails averaged over the sn1 and sn2 chains. The trans conformer is defined by torsional angles |φ| larger than 60o . Statistical uncertainties on the values are determined from 10 independent data sets generated from trajectory segments of 2.5 ns. At concentrations of 0, 9 and 20 %, they are smaller or comparable to the size of the symbols and are omitted for clarity. cross-sectional area. 78 Diffusive motion is described by the displacement of a solute upon formation of a void whose cross-sectional area (free area) is greater or equal to the area of the solute molecule itself. In support of this model, permeability has been reported to correlate better with the cross-sectional area than with solute volume or radius. 79 Local diffusion coefficients obtained from MD simulations for several small solutes in pure DPPC bilayer also displayed a dependence on the solute cross-sectional area. 77 Falck et al. 76 showed,


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using MD simulations, that the distribution of free volume fractions accessible to a solute in DPPC bilayers containing cholesterol is heavily dependent on the size of the penetrant. For a penetrant of the size of a water molecule, practically no free volume was accessible in the denser parts of a bilayer containing 20 % cholesterol. It is therefore reasonable to expect any free volume-reducing effect of cholesterol to be nearly imperceptible at even higher concentrations. This would account for the observation that estimated diffusion coefficients are consistently small and hardly affected by cholesterol concentration (see Figure 7) in the dense bilayer interior. Thus it appears that diffusive motion is modulated by solute size (or cross-sectional area) in the region occupied by the head groups and cholesterol rings in bilayers.

Local resistances and permeation coefficients The resistance to the permeation of water across the bilayers, R was calculated from the corresponding free energy and diffusion profiles according to

Z R=

lz

Z

lz

R(z) dz = 0

0

exp(∆G(z)/RT ) dz . D(z)

(3)

by assuming the inhomogeneous solubility-diffusion mechanism. 29,30 R(z) is the local resistance defined as the resistance to permeation felt by a water molecule at given distances 27 ACS Paragon Plus Environment


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from the centre of the bilayers and lz denotes the distance between the extremities of the bilayers and their centre. The effect of cholesterol on the local resistance profiles of water is shown in Fig. 9. The barrier to permeation inside the lipid bilayers arises within their dense hydrophobic core region, where both water partitioning and diffusion are least favorable compared to the bulk water phase. The barriers in the resistance profiles are raised in the presence of cholesterol. Because the diffusion coefficients are unaltered by cholesterol in this region, the increased resistance to permeation originates essentially from cholesterol-induced changes in the free energies. In other words, the resulting lowered permeability of DPPC bilayers to water is mainly a thermodynamic effect. Figure 10 illustrates the permeation coefficients of water inside DPPC bilayers of varying cholesterol content, defined as P = 1/R. Our results reproduce the experimentally-observed decrease in water permeation with increasing concentrations of cholesterol (see Table 1). The reduction in the rate of transport is more pronounced at low cholesterol mole fractions than at high cholesterol content. For instance, the permeation coefficient of water decreases by about 25 % upon insertion of 9 mol % cholesterol and by over 80 % with 20 mol % cholesterol. At higher concentrations, the change in bilayer permeability is less sensitive to increasing cholesterol concentrations inside DPPC bilayers. The permeation coefficient for the passage of water across the pure DPPC bilayer is deter-


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7

0% 9% 20 % 30 % 41 %

6 5 4

10

-2

R(z) (10 s cm )

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


3 2 1 0 -4

-3

-2

-1

0 z (nm)

1

2

3

4

Figure 9: Local resistance of water inside cholesterol-containing DPPC bilayers for different cholesterol concentrations. mined to be 1.14(±0.047) × 10−2 cm s−1 , in good agreement with the value of 1.33(±0.28) × 10−2 cm s−1 reported from MD simulations of water permeation inside pure DPPC bilayers at 323 K. 31 Marrink and Berendsen obtained a slightly higher value of 7(±3) × 10−2 cm s−1 at 350 K. 32 Our value is also within the range of 10−4 to 10−2 cm s−1 for experimentallydetermined permeation coefficients of water in pure DPPC 10,12,15,16,42,80–82 reported in the literature (see Table 1). In comparison with permeability measurements in pure DPPC bilayers, fewer experimen-


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30

b

a

at 40 mol % at 4 mol %

egg lecithin at 298 K 81 egg lecithin at 309 K 10 egg lecithin at 310 K 80 DPPC at Tm + 10 K 16 egg lecithin at 298 K 12 egg lecithin at 298 K 15 DPPC at 310 K 80 egg lecithin at Tm + 10 K 16 DPPC at 303 K 82

this work (323 K) DPPC at 323 K 31 DPPC at 323 K 32 DPPC at 323 K 42 Experiments

MD simulations

System

0.22 0.43 0.55 (±0.013) 0.0632 (±0.0018) 0.34 0.19 (±0.09) 0.315 (±0.0011) 0.0205 (±0.0013) 2.40

1.14 (±0.047) 1.33 ± (0.28) 7(±3) 26

0 mol %

0.05730b

12

0.85 (±0.06)

9 mol %

8.8

0.19 (±0.03)

0.46

0.10 (±0.01)

P (×10−2 cm s−1 ) 20 mol % 30 mol %

0.15a

0.08 (±0.05)

41 mol %

≈ 0.25 0.25 (±0.015) 0.00716 (±0.00032)

0.037

50 mol %

Table 1: Computed and measured permeation coefficients of water through cholesterol-containing DPPC bilayers at different cholesterol concentrations

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tal measurements have been performed for water across cholesterol-containing bilayers, as shown in Table 1. Again, we note that the measured permeabilities span a wide range of values ranging from 10−3 to 10−5 cm s−1 at 50 mol % cholesterol. From our simulations, we obtained a value of 8 × 10−4 cm s−1 , well within the experimental range, at 40 mol % cholesterol (the highest concentration investigated in this work). Based on the trend depicted in Figure 10, it is reasonable to expect that computed water permeation coefficients will be comparable in magnitude across DPPC bilayers containing 40 mol % or 50 mol % cholesterol. Relative to pure DPPC, the computed permeability to water in the presence of 40 mol % cholesterol is reduced by 92 %, in very good agreement with the 88 % decrease observed in a spectrophotometric experiment by Carruthers and Melchior 16 for water permeation coefficients in DPPC bilayers containing 50 mol % cholesterol. Much earlier investigations by Graziani and by Finkelstein had shown a less pronounced drop of 50% in the transmembrane permeability of egg lecithin containing 50 mol % cholesterol relative to the cholesterol-free membrane. 10,80 At higher cholesterol concentrations, Finkelstein reported a decrease in water permeation from 4.3 × 10−3 cm s−1 in egg lecithin films without cholesterol to 0.75 × 10−3 cm s−1 in an 8:1 cholesterol:phospholipid membrane. 10 The evolution of permeation coefficients with cholesterol concentration, displayed in Figure 10, is qualitatively similar to plots reported by Xiang and Anderson for the permeation



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of acetic acid inside bilayers of binary mixtures of cholesterol and DPPC above the melting temperature. 22 The osmotic permeability measurements of Mathai et al. 21 also indicate a similar, albeit milder effect in DOPC bilayers where the addition of 40 mol % cholesterol resulted in a reduction of about 56 % in the permeation coefficients at 303 K. It is noteworthy that the relative effects of cholesterol on water permeation are very well reproduced in this work. The permeation coefficents are also in reasonable agreement with experimental measurements considering the wide range of values that have been reported. Past MD investigations 42 of transport across cholesterol-containing membranes using different techniques for calculating the free energy of permeation and the diffusion coefficients produced water permeation coefficients which differed from their experimental counterparts by at least an order of magnitude (see Table 1).

Conclusion The present work brings some insight into understanding the reduced permeability of cholesterolcontaining bilayers in terms of their molecular and structural properties. The local thermodynamic and kinetic contributions to the passive transport of water inside mixed DPPC/cholesterol bilayers were determined and the results rationalized in terms of cholesterol-induced structural changes. The effects of cholesterol on the thermodynamics of water transport are 32 ACS Paragon Plus Environment

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12.5 10.0 -1

P (10 cm s )

7.5

-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 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5.0 2.5 0.0 0

10

20 30 mol % cholesterol

40

Figure 10: Permeation coefficients of water inside cholesterol-containing DPPC bilayers vs cholesterol concentration. two-fold. First, the free energy of transfer of a water molecule from the interface into the dense hydrophobic regions of the bilayer is magnified i.e. water partitioning is lowered, with increasing cholesterol content. Second, the location of the free energy barrier to water permeation is shifted outwards. Quantitative comparison with various structural properties show that these observations correlate well with molecular crowding in the bilayer interior and with the signature thickening of cholesterol-containing bilayers. Diffusion coefficients on the other hand are less sensitive to the effects of cholesterol except in the relatively sparsely populated centre of the bilayer where increasing cholesterol concentration slows down wa-



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ter diffusion in parallel with the reduction in free area. In the denser hydrophobic regions, diffusion appears to be limited by the solute cross-sectional area. Our analysis shows that the increasingly unfavorable thermodynamics are the main reason for the observed impaired water permeability in the presence of cholesterol. In other words, cholesterol decreases permeability by lowering the solubility of water in the dense hydrophobic region of the bilayer. Overall, permeation coefficients are found to be highly sensitive to the cholesterol content of DPPC bilayers at low concentrations, up to 20 mol %, an effect that becomes less and less pronounced at higher cholesterol concentrations. To the best of our knowledge, our work presents the first attempt to quantitatively compare the thermodynamic and kinetic contributions to water transport with cholesterol-induced changes to the bilayer structure. This information is valuable since it can help guide the design of further experiments and simulations to better understand the influence of cholesterol on transmembrane transport. Our calculated permeation coefficients fall within the wide range of experimental measurements for water permeability. In addition, the results indicate a 90% decrease in transmembrane permeability with the addition of 40-50 mol% cholesterol, reproducing, almost quantitatively, the relative decrease found in the latest experiments. 16 This gives us confidence in the simulation protocols, models and approximations employed in this investigation for further application to permeation events in cholesterol-containing bilayers. Ongoing work


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involves investigating the mechanism of action of cholesterol on the transport of other small solutes across lipid bilayers and determining whether the altered thermodynamics is always the dominant effect.

Acknowledgement The authors would like to thank Bulent Mutus (University of Windsor, Canada) for stimulating discussions that led to this work, Peter Tieleman (University of Calgary, Canada) for helpful discussions in the course of this work and an anonymous Reviewer for insightful comments. Computational resources were provided by Calcul Québec and the Centre for Research in Molecular Modeling (CERMM). This work was funded by the Canadian Institutes of Health Research (CIHR), Concordia University and the Natural Sciences and Engineering Research Council (NSERC) of Canada. GHP is a Concordia University Research Fellow.

Supporting Information Available 1. Lateral heterogeneity in mixed DPPC/cholesterol bilayers and implications for phase space sampling.

2. Evidence for the condensing and ordering effects of cholesterol in the lipid bilayers.

This material is available free of charge via the Internet at http://pubs.acs.org/. 35 ACS Paragon Plus Environment


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Graphical TOC Entry Permeation rate of water through bilayers

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10

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30

mol % cholesterol

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Effects of Cholesterol on the Thermodynamics and Kinetics of Passive

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