Molecular Structure and Permeability at the Interface between Phase

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B: Biomaterials and Membranes

Molecular Structure and Permeability at the Interface between Phase-Separated Membrane Domains Rodrigo Maghdissian Cordeiro J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b03406 • Publication Date (Web): 16 May 2018 Downloaded from http://pubs.acs.org on May 16, 2018

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The Journal of Physical Chemistry

Molecular Structure and Permeability at the Interface between Phase-Separated Membrane Domains Rodrigo M. Cordeiro*

Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Avenida dos Estados 5001, CEP 09210-580, Santo André (SP), Brazil

* Corresponding author. Tel.: +55 11 49960173. E-mail address: [email protected]

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ABSTRACT

Phase-separated membrane domains, also known as lipid rafts, are believed to play an important role in cell function. Although most rafts are sterol-enriched membrane regions, evidence suggests that living cells may also contain gel-like rafts. Interactions between gel and fluid domains have a large impact on membrane properties, as is the case with permeability. The membrane permeability may reach a peak at the main phase transition temperature, by far exceeding the values recorded at the fluid phase. It has been proposed that gel-fluid interfaces are leaky, but the effect has not yet been demonstrated at the molecular level. Here, we performed atomistic molecular dynamics simulations of phospholipid bilayers with coexisting gel-like and fluid domains. We found that the thickness mismatch between both phases, the membrane elasticity and the lipid packing acted together to promote the formation of a thickness minimum at the gel-fluid interface. Free energy calculations showed that pore-mediated ionic permeation was strongly facilitated at the constriction region, while water permeation by simple diffusion was only marginally affected. Long-lived, peristaltic undulations were recorded at the bulk fluid phase near the main transition temperature. They gave rise to thickness minima that, although shallower than the interface constrictions, could also enhance permeability. Finally, we demonstrated that an interface constriction was also formed at the boundaries of regular, cholesterol-enriched lipid rafts. Our simulation results will hopefully contribute to a better understanding of biological processes such as transport, signaling, and cellular damage promoted by low temperature and dehydration.


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1. INTRODUCTION

Fluidity has been traditionally considered as a pre-requisite for biomembrane function.1 Living cells are known to regulate their lipid composition in a way that their membranes are constantly kept at the fluid state. However, the fluid-to-gel phase transition often lies just bellow the physiological temperature. That proximity suggests that localized order-disorder transitions may serve useful biological functions.2 In fact, lipids are able to associate into highly ordered, phase-separated membrane nanodomains, also known as “lipid rafts”.3-5 These domains have been implicated in cellular trafficking and signaling events,5,6 as well as on the pathogenesis of neurodegenerative diseases.7,8 Lipid rafts are enriched in saturated lipids, which have higher fluid-to-gel transition temperatures. They are not strictly at the gel phase though, because rafts also contain large amounts of sterols, which keep membrane fluidity.9 However, there has been increasing evidence for the formation of sterol-independent, gel-like rafts in the plasma membrane of living cells.10,11 Molecular Biology is just beginning to appreciate the influence of (gel-like) lipid rafts on membrane structure and function. Permeability epitomizes the importance of gel-fluid domain interactions. In the absence of ion-specific channels, phospholipid bilayers are practically impermeable to ions. However, the ionic permeability sharply peaks when lipids are at their chain melting regime, reaching values that by far exceed the fluid-phase permeability.12 The effect is commonly referred to as the “permeability anomaly”. Interestingly, permeation events manifest themselves as quantized transmembrane current pulses, which are similar to those reported for protein ion channels.13,14 There are currently two competing explanations for the permeability anomaly.15 In the “leaky interface hypothesis”, permeation events are considered to be facilitated at the frontiers between coexisting gel and fluid domains.12 In the fluctuation model, near-critical density fluctuations are held accountable for a sharp increase in the area compressibility of the membrane, which is thought to facilitate pore formation.16 The 3 ACS Paragon Plus Environment


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controversy does not end there. While the existence of a permeability anomaly has been repeatedly confirmed for ionic species,17-21 the results for nonionic permeants have been largely divergent,20-25 most notably in the case of water.26-28 The detailed molecular mechanisms that link permeability to the membrane phase behavior still need to be set. One of the earliest microscopic models of the permeability anomaly was derived from Monte Carlo simulations.29 These simulations have shown that the gel-fluid interfacial area varied with temperature and reached a pronounced peak at the main transition. The permeability anomaly could be partially explained by postulating a higher permeation rate at the interface regions. However, the interfacial permeability has not been directly measured. Since then, molecular dynamics simulations have delivered a more detailed view of the thermotropic behavior of phospholipid bilayers.30-42 The transition dynamics has been investigated in membranes that were large enough for the coexistence of well-formed domains.43-48 However, the molecular structure at the domain boundaries has not been fully scrutinized, let alone their permeability properties. A few investigations have ventured on that issue, but they have mostly relied upon lower-resolution, coarse-grained lipid models, and considered water as the model permeant. Under this set of conditions, an almost continuous increase in permeability has been found during the transition from the gel to the fluid phase.49 In the case of lipid mixtures, a small permeability peak was recorded at the main transition, but it was easily surpassed by the permeability of the fluid phase a few degrees above the transition.50 Recently, it has been proposed that the line tension between different domains could assist permeation events that cause a reduction in the gel-fluid interface length. So far, that mechanism has been demonstrated for a very particular case, namely the permeation of a nanoparticle through a comparably small fluid pool, fully encircled by a rigid gel matrix.51,52 Here, we present atomistic molecular dynamics simulations of permeation events on phase-separated phospholipid bilayers at their main thermotropic transition. We undertook a computational effort that exceeded 20 µs of total simulation time. Our objective was to 4 ACS Paragon Plus Environment

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identify the physical basis of the permeability anomaly and to answer the following question: are gel-fluid interfaces really leaky? First, we present a short review of bilayer phase transitions and the simulation methods. In the results section, the structure of the gel-fluid interfaces and their permeability properties are carefully examined. Previous experimental investigations are reviewed and discussed under the lights of our simulation results, and a molecular-level model of the permeability anomaly is proposed. There are a number of applications and contemporary research topics that might benefit from a molecular-level understanding of the permeability anomaly. For instance, in the design of temperatureresponsive liposomes for drug delivery, the permeability anomaly could be cleverly explored to promote a temperature-triggered release of cargo.53,54 Our results could also help in the understanding of the structure and function of the mammalian skin barrier,55 as well as in the study of cellular damage promoted by low temperature,56 and dehydration.

57

Although it

might be contended that most biologically relevant rafts are not at the gel, but rather at the socalled liquid-ordered state, we shall demonstrate that both phases share similar structural features at their interface with a fluid phase. Thus, an analogous permeability enhancement might also take place in cholesterol-enriched, liquid-ordered rafts.

2. SCIENTIFIC BACKGROUND

Before we proceed, let us lay down some of the basic features of the thermotropic behavior of phosphatidylcholine (PC), one of the most common lipid types. At sufficiently low temperatures, PC bilayers exist at the gel phase (Lβ’), which is characterized by low molecular mobility and high molecular order.9 Lipid hydrocarbon tails are fully stretched and packed in a hexagonal array.58,59 However, lipids still exhibit in-plane orientational disorder.60 Due to the large headgroup-to-tail volume ratio of PC, lipid tails have to tilt in order to optimize molecular packing.61,62 The hydrocarbon chains are collectively and uniformly tilted along the 5 ACS Paragon Plus Environment


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direction of one of their nearest-neighbors.63 By heating the gel, the pre-transition temperature is reached, and the so-called “rippled gel” or “ripple phase” (Pβ’) is formed.64 As shown in Figure 1a, the membrane at the ripple phase has a static, out-of-plane sawtooth profile, with alternating regions of gel-like and fluid-like lipids.65 That feature probably stems from the packing frustration imposed by the large PC headgroups.66,67 In the gel-like regions, lipid tails are tilted along the ripple direction. Upon further heating, the main transition temperature (Tm) is eventually reached, and the membrane finally becomes fluid (Lα), with a large degree of lipid mobility and disorder. Figure 1b presents a conceptual view of the first-order transition between the ripple and the fluid phase. The formation and growth of a molten region within the ripple phase is consistent with atomic force microscopy (AFM) data.68 The melting of the ripples is strongly anisotropic and occurs faster in the longitudinal than in the transversal direction. Interfaces are formed between the gel-like domains and the fluid phase. Depending on the angle between the tilt direction and the interface plane, interfaces with different molecular configurations might arise. Interfaces that are perpendicular to the tilt direction probably predominate due to anisotropic melting. It must be kept in mind, however, that not all lipid types follow the same behavior. Phosphatidylethanolamine (PE), for instance, transitions directly from the gel to the fluid state, without the intervening ripple phase.69 That is probably related to the fact that PE headgroups are smaller than PC. In fact, PE exhibits almost no molecular tilt in the gel.61,62 For the sake of simplicity, we use the term “gel-fluid interfaces” to designate two different situations: i) in PC bilayers, the boundaries between the gel-like domains of the ripple phase and the fluid phase; and ii) in PE bilayers, the boundaries between regular gel and fluid phases.

3. COMPUTATIONAL METHODS


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3.1. Simulation Setup and Lipid Models. Molecular dynamics simulations70 were performed with the GROMACS 5.0.4 package.71,72 Newton’s equations of motion were integrated with a time step of 2 fs, with all chemical bonds constrained to their equilibrium values. The interatomic interactions of dipalmitoylphosphatidylcholine (DPPC) were described using the united-atom

force

field

of

Tieleman.73

The

parameters

for

dipalmitoylphosphatidylethanolamine (DPPE) were almost identical, except that the atom types, partial charges and bond lengths of the choline group were substituted by those of a terminal amine group, according to the GROMOS 53A6 force field.74 Parameters for Na+ and Cl- ions were also taken from GROMOS, and used in conjunction with SPC water.75 Standard protocols were adopted for the treatment of interatomic interactions, temperature and pressure. Further details are available as supporting information (Section S1), together with the force field data and molecular topology files of the simulated lipids.

3.2. Membrane Assembly and Equilibration. Phospholipid bilayers at either the gel or the fluid phase were generated in multiple steps, as described in Section S2. Each bilayer contained 120 lipids with 45 water molecules per lipid. A Cartesian system of coordinates was used with the membrane surface placed parallel to the xy-plane, and the membrane normal aligned with the z-axis. Periodic boundary conditions were employed. After 300 ns of equilibration at the isothermal-isobaric (NPT) ensemble, tensionless membranes were obtained at a pressure of 1 atm. The following systems were generated: i) PC-G, a gel-phase DPPC bilayer at 298 K, with lipid tails uniformly tilted along the x-axis; ii) PC-F, a fluidphase DPPC bilayer at 323 K; iii) PE-G, a gel-phase DPPE bilayer at 314.5 K, with lipid tails practically parallel to the membrane normal; and iv) PE-F, a fluid-phase DPPE bilayer at 367 K. The molecular structure files of the equilibrated bilayers are also available as supporting information. Based on the PC-G system, larger DPPC bilayers with phase-separated domains were built. A fully formed ripple-phase with multiple segments, as in Figure 1b, would be too 7 ACS Paragon Plus Environment


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large to simulate at atomic resolution. Therefore, we assembled systems that were smaller, but retained the most representative features of the interfaces between the ripple and the fluid phase. The simulated systems were: i) PC-GF-perp, a gel-like stripe embedded in a fluid matrix, with the gel-like chains tilted perpendicular to the gel-fluid interfaces; and ii) PC-GFpara, with chains tilted parallel to the interfaces. The interfaces represented by each of these systems are highlighted in Figure 1b. To assemble PC-GF-perp, the PC-G system was replicated three times along the x-axis. A 10 ns simulation was performed, in which lipids at the central replica were incubated at 298 K, while the rest of the membrane was annealed at 350 K. During 20 ns, both temperatures were gradually brought to 308.5 K, which is approximately the Tm of the DPPC model used here.45 Equilibration was performed for 300 ns at the NPT ensemble, whereby the membrane was constantly kept at the tensionless state by keeping a pressure of 1 atm along each Cartesian coordinate individually. The PC-GF-para system was formed according to the same procedure, except that the original PC-G system was rotated by 90° about the z-axis prior to replication. In the case of DPPE, due to the small degree of molecular tilt in the gel, only one boundary configuration was studied, here referred to as PE-GF. For comparison, larger all-fluid membranes were also equilibrated that were similar in size to the mixed-phase membranes. Average properties were extracted from the last 100 ns of simulations. The membrane thickness was calculated as the z-direction component of the interleaflet P-P distance. The number of gauche dihedrals per acyl chain was calculated for the region delimited by the C atoms 1 and 16. The lipid tilt was defined based on the angle between the membrane normal and the imaginary vector linking the C atoms 4 and 14 of the phospholipid acyl chains. In mixed-phase bilayers, local properties were calculated as function of the position along the x-axis. Systems were divided in thin slabs along the x-axis. Individual phospholipids were dynamically assigned to different slabs based on their instantaneous positions. Lipid properties were then computed at each slab. In strongly slanted membrane regions, the thickness was estimated as the z-component of the P8 ACS Paragon Plus Environment

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P distance, projected into the membrane normal direction. Graphical renderings of the simulated systems were produced using the VMD software.76

3.3. Free Energy Calculations. The free energy profiles associated to the translocation of water molecules and Na+ ions across phospholipid bilayers were calculated using the umbrella sampling method.77,78 Permeation was studied across both all-gel and all-fluid membranes individually, as well as across the gel-fluid interfaces of mixed-phase membranes. The starting structures for umbrella sampling were picked randomly from the last 100 ns of equilibrated trajectories. Evenly spaced umbrella positions were defined along the z-axis, forming complete permeation paths across the membranes. Permeants were attached to the umbrella positions by applying harmonic biases with force constants of 1000 kJ·mol-1·nm-2 along the z-axis. Their lateral motion was confined to ~1 nm cylindrical cross sections by the use of flat-bottomed cylindrical restraints. Umbrella positions were expressed in terms of the center-of-mass distances between permeants and bilayers. To minimize artifacts due to membrane undulation, only the bilayer atoms within a lateral distance of 1.2 nm to the permeants were considered for the computation of the centers-of-mass. Slightly different protocols were used for the simulations of water and Na+ permeation. In the case of water, adjacent umbrella windows were separated by 0.5 Å. In each individual umbrella simulation, four independent permeation paths were sampled simultaneously, and in each of them, four spatially separated windows. There were no close contacts between individual permeants. After an equilibration period of 500 ps, the collection of umbrella histograms took place for 2 ns in the NPT ensemble. In the case of small neutral solutes, these conditions have been demonstrated to lead to properly converged free energy profiles.79 In the case of Na+ ions, adjacent umbrella windows were spaced by 1 Å. In the smaller all-fluid and all-gel membranes, only one permeation path with a single permeating ion was considered in each umbrella simulation. In the larger, mixed-phase systems, two permeation paths were sampled 9 ACS Paragon Plus Environment


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simultaneously, one in each of the gel-fluid interfaces. To keep electroneutrality, enough Clcounterions were added at random positions at the aqueous phase. For Na+ ions placed within ~2.2 nm of the bilayer center, equilibration and sampling were run for 10 ns each. At the aqueous phase, 500 ps of equilibration and 2 ns of sampling were sufficient. For Na+, each complete set of umbrella simulations encompassed a total of ~1 µs of simulation time. To improve statistics, the umbrella simulations for Na+ were repeated one more time for selected systems (PC-F, PC-G, PC-GF-para, PC-GF-perp and PE-F). Free energy profiles were built by the weighted histogram analysis method (WHAM),80 as implemented in the g_wham tool.81 Histograms were reweighted according to an estimate of their integrated autocorrelation times. The periodicity of the free energy profile along the z-direction was considered. Statistical uncertainties were obtained by 50 repetitions of a Bayesian bootstrapping of complete histograms. Permeation free energy barriers were defined as the difference between maxima and minima in the profiles.

4. RESULTS AND DISCUSSION

4.1. Validation of Membrane Simulations. On the whole, simulations led to membrane properties that were consistent with experimental data. The main structural features of both gel and fluid-phase bilayers were satisfactorily described, as well as the phase equilibrium at the main transition. A detailed account on the validation of the lipid models and simulation conditions is presented in Section S3 (Figures S1 to S4 and Table S1).

4.2. The Structure of the Gel-Fluid Interface. Figure 2a and 2b shows images of equilibrated mixed-phase DPPC bilayers at their main transition. In all systems investigated, an ordered gel-like domain coexisted with a disordered fluid phase. At the molecular level, the spatial transition between both phases was smooth (Figure 2c) and the interface regions 10 ACS Paragon Plus Environment

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did not move, i.e. the gel-like domains did not grow nor melt during simulations. In spite of thermal fluctuations, the average membrane shape was almost planar in the PC-GF-para system. Conversely, in the PC-GF-perp system, the average shape was that of an undulated surface, with the entire gel-like domain bent with respect to the fluid region. In order to optimize lipid packing at the interface region, the gel-like and fluid regions spontaneously bent with respect to each other, giving rise to an undulated surface that resembled the distinctive sawtooth profile of the ripple phase.65 Perhaps the most striking feature of both the PC-GF-para and PC-GF-perp systems was the formation of a constriction region at the gelfluid interface. Figure 2d shows the spatial variations of thickness in these mixed-phase membranes. There was clearly a thickness mismatch between different phases, but the thickness decreased non-monotonically from the gel-like domain to the fluid phase, forming a minimum at the interface. Membranes were ~5 Å thinner at the interface regions, as compared to a bulk fluid phase above Tm. At the constriction regions, no significant lipid interdigitation was found, meaning that the bilayer structure was conserved (Figure 2e). Continuum elastic models82-84 may help to explain the formation of the interface constriction. Suppose that a small gel domain is suddenly embedded in an initially flat, fluid membrane at Tm. Due to the thickness mismatch, the fluid region will deform so that: i) the hydrophobic interior of the gel is hidden from the aqueous phase and ii) the total elastic energy of the membrane is minimized. At zero surface tension, the elastic energy contains a compression-expansion term, related to thickness deformations, and a splay-distortion term, related to the generation of curvature. Lipids surrounding the gel domain will stretch, becoming themselves gel-like. The restoring force that drives the membrane back to its equilibrium thickness will be counteracted by the bending force. Each bilayer leaflet will bend inwards, creating concavity. Away from the gel, lipids will become less stretched as the membrane narrows. A point will be reached where the thickness matches the equilibrium thickness of the fluid matrix. However, it will be forced to decrease even further due to the 11 ACS Paragon Plus Environment


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bending rigidity of the bilayer leaflets. Eventually, a thickness minimum will be formed. Both the thickness and the surface curvature will oscillate along the membrane, gradually converging to a flat profile. Overall, the transition region from the gel to the fluid phase will be characterized by exponentially decaying static undulations, until the equilibrium thickness of the fluid phase is finally reached. Similar findings have been reported in the case of hydrophobically mismatched protein inclusions.85-88 Specific aspects of lipid structure still need to be incorporated into that model. We found that the formation of the constriction was strongly dependent on the lipid type. Figure 3 shows the thickness variations in DPPC and DPPE planar bilayers, as represented by the PCGF-para and PE-GF systems, respectively. While a pronounced thickness minimum was formed in DPPC, the effect was almost negligible in DPPE. The static interface undulations were strong in DPPC and persisted far into the fluid phase. In DPPE, they flattened out at much shorter distances, and the interface constriction was barely recognizable. A possible explanation would be related to the larger stiffness of PE bilayers, which do not deform as easily as PC.89 Another key structural difference is that the PC headgroup is notably larger than PE. Fully stretched DPPC molecules have the shape of truncated cones, while DPPE molecules are almost cylindrical under the same conditions.90 As inferred from Figure 3d, the close-packing of stretched DPPC lipids at domain boundaries spontaneously leads to surface concavity. For that reason, a more pronounced curvature developed near the gel-like domain of DPPC, allowing for a steepest decrease in thickness. The prominent “undershooting” of the equilibrium thickness occurred because the surface had to turn from concave to convex before it could flatten out. Chain packing in the convex region required compression of DPPC tails (see also Figure 2e), further contributing to the formation of the constriction.

4.3. Permeation across the Gel-Fluid Interface. Figure 4 shows the free energy profiles associated to the permeation of water molecules and Na+ ions across phospholipid bilayers. 12 ACS Paragon Plus Environment

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Permeation was studied at: (i) fluid-phase DPPC above Tm (PC-F); (ii) gel-phase DPPC bellow Tm (PC-G) and; (iii) the gel-fluid interfaces of mixed-phase systems at Tm (PC-GFperp and PC-GF-para). For all the permeants investigated, permeation was invariably associated with a free energy barrier at the hydrophobic membrane interior. In the case of water at fluid-phase DPPC, the free energy profile was consistent with the solubility-diffusion model of permeation.91-92 The excess free energy steeply increased as water penetrated into the membrane, but remained almost constant as it moved within the hydrophobic membrane interior. The translocation of an individual water molecule did not disrupt the bilayer structure. The free energy barrier for Na+ permeation through fluid-phase DPPC was significantly larger, which is consistent with the fact that membranes are much less permeable to ions than to water. A shallow free energy minimum appeared at the headgroups region due to ionic adsorption.93 The free energy continuously increased as Na+ ions were brought from the membrane surface to its interior, reaching a peak at the membrane center. In that process, water molecules and lipid headgroups were dragged into the membrane interior by the ion. Permeation was accompanied by the formation of a narrow, transient pore, in line with previous simulations.94-97 For both water and Na+, barriers were consistently higher in the bulk gel than in the bulk fluid phase. In Section S4 (Figures S5 to S9), further details are provided about the permeation mechanisms, the validation of the free energy profiles against experimental data, and the convergence of the umbrella sampling simulations. Figure 4 also shows the free energy profiles at gel-fluid interfaces. They were recorded at the point of minimal membrane thickness, i.e. at the constriction regions of the PC-GF-perp and PC-GFpara systems. At these regions, both water and Na+ followed their regular permeation mechanisms, known for the bulk fluid phase. Water permeation across the constriction region had practically the same free energy barrier as in the bulk fluid phase above Tm. For Na+, however, the permeation barrier was ~15-20 kJ/mol smaller across the constriction than at the bulk fluid phase, depending on the interface type. Transition state theory relates the drop in 13 ACS Paragon Plus Environment


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free energy barrier to a local permeability enhancement (see eq S3). By neglecting the prefactor and considering only the dominating exponential term in eq S3, we found that the gelfluid interfaces in PC-GF-perp were somewhere between 2 and 4 orders of magnitude more permeable than the bulk fluid phase above Tm. To better understand this effect, we assembled a series of fluid-phase membranes using saturated PC lipids with different tail lengths, and calculated their permeation free energy barrier as function of the membrane thickness. As shown in Figure 5a, the energy barrier for ionic permeation significantly decreased as membranes were made thinner, implying that even small changes in thickness would lead to order-of-magnitude variations in the ionic permeability. On the other hand, the barrier for water permeation remained nearly constant. Water permeation can also be affected by the membrane thickness, but to a much smaller extent, mainly due to the variation of the intra-membrane diffusion length (eqs S1 and S2). These trends qualitatively agree with previous experimental98 and theoretical results.99,100 Remarkably, we found that, in the mixed-phase DPPC membranes (PC-GF-perp and PC-GFpara), the barriers recorded at the gel-fluid interfaces closely followed these trends too. It might be argued that the free energy minimum at the bilayer surface should not be accounted for in the calculation of the barrier height. After all, the attraction between the permeant and the membrane surface is cancelled out by the local enrichment of permeant molecules resulting from this attraction. However, Figure S10 demonstrates that the influence of membrane thickness on permeation remains valid even under a different definition of the free energy barrier. The local reduction in membrane thickness at the gel-fluid interface was apparently a major determinant of the decrease of the ionic permeation barrier. That notion was also corroborated by the absence of this effect in the mixed-phase DPPE membrane (PEGF), which lacked the constriction regions (Figure 5b). Taken together, the simulation results suggest that, when a constriction forms at the gel-fluid interface, this region becomes leaky to solutes whose main permeation mechanism involves the formation of transient pores. 14 ACS Paragon Plus Environment

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4.4. A Molecular Model for the Permeability Anomaly. Experiments have shown that Na+ self-diffusion rates through DPPC were up to three times higher near Tm, as compared to temperatures well above it.12 Based on our simulation results, we propose the following model to explain this effect. As the ripple phase melts, coexisting gel-like and fluid domains are formed. Depending on the lipid packing properties, a constriction may form at the gel-fluid interfaces, leading to lower free energy barriers for pore formation. Simulations support the leaky interface hypothesis by showing that the interface region was roughly 2-4 orders of magnitude more permeable to Na+ than the fluid phase. A more precise assessment of the permeability enhancement was precluded by the uncertainties inherent to the umbrella sampling method. Earlier studies have demonstrated that ionic permeation involves slow membrane reorganization events.101 Individual umbrella windows might require more than hundreds of nanoseconds to converge. Our results could be improved by extending the equilibration time of the umbrella windows, but it would come at an extremely large computational cost due to the large size of mixed-phase membranes. In fact, our mixed-phase membranes were about 6 times larger than those typically considered in previous ionic permeation studies.101 It is true that longer equilibration times would lead to more precise estimates of the individual free energy barriers. However, they would not change the most important qualitative outcome of this study, namely that gel-fluid interfaces were significantly more permeable to ions than the bulk fluid phase. The increase of the equilibration time seemed only to enhance the effect even further (Figure S11). By taking 2 orders of magnitude as an estimate of the permeability enhancement at the interface, one finds that the experimentally measured permeability peak at Tm could be elicited with rather few interfacial lipids, corresponding to a fractional surface area no higher than 3% (see eqs S4 and S5). In fact, AFM images have revealed that phase boundary regions only made up for a minor fraction of the total membrane area during the melting of a PC membrane.68 Moreover, that 15 ACS Paragon Plus Environment


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fractional area varied as internal stresses built up and caused domain rupture and coalescence. That could explain the dependence of the permeability anomaly on details of the vesicle preparation history, such as the use of manual agitation versus sonication.12 An alternative model has been proposed to explain the permeability anomaly. It has been suggested that, near the main transition, membranes might exist in a near-critical state with very large fluctuations in lipid density.16 Earlier Monte Carlo simulations have shown that, depending on the strength of intermolecular interactions, the lipid matrix could be microheterogeneous, becoming largely dominated by fluctuating interfaces near to the main transition,29,102 with transient pores spreading over the whole fluid matrix.103 Based on that, we also explored the possibility that the fluid matrix itself could contribute to the permeability anomaly. By incubating a sufficiently large, fluid-phase DPPC membrane at Tm, we witnessed the formation of rather strong peristaltic undulations, even in the absence of a well-formed gel-like phase. That is shown in Figure 6. We propose that, as Tm is approached, lipid tails tend to stretch out, and the packing frustration generated by the large PC headgroups manifests itself as undulations, which are likely the first stages of the ripple phase formation. The undulations were quite stable, meaning that they were either static, or fluctuated according to time scales that were much longer than 100 ns. The constriction regions thus formed were not as narrow as the interface constrictions, but were still more permeable to Na+ than a bulk fluid phase above Tm (Figure 5a). It is true that peristaltic undulations also produce thicker and less permeable regions, but they cannot counteract the permeability enhancement at the constrictions. The local permeability depends exponentially on the free energy barrier (eq S3), meaning that low-barrier regions dominate the total permeability. Hence, the enhancement of the ionic permeability, although stronger at the interface, would also take place farther away from it. As shown in Figure 3b, starting from the gel-fluid interface, not only one, but a series of successive constriction regions was discernible in a sufficiently large, mixed-phase DPPC membrane. 16 ACS Paragon Plus Environment

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Our simulations support the notion that the permeability anomaly is not a universal effect, as it was strongly dependent on the chemical nature of both the lipids and the permeants. Simulations showed that the formation of the interface constriction was favored as the lipid headgroups were made larger. So far, most of the experimental studies were based on PC diacyl lipids, which are known for their bulky headgroups.12,14,17-27 Single-tailed lipids, also known as lysolipids, tend to have an even greater headgroup-to-tail volume ratio. Experiments have shown that the permeability anomaly could be made stronger by adding PC lysolipids to membranes.104 Monopalmitoyl-glycerol, a lysolipid with a smaller headgroup, was unable to elicit the same effect. The influence of the headgroup-to-tail volume ratio has been also investigated using diacyl PCs with varying tail lengths. As the acyl chains were lengthened, the permeability anomaly became less pronounced, almost disappearing at a length of 20 carbons.105 It is revealing that, at about the same length, the pre- and main transitions merge together and the membrane passes directly from the gel to the fluid state, without the intervening ripple phase.64 The existence of a permeability peak at Tm has been established for a variety of ionic species, including alkali metal cations,12,18,19 anionic dyes,14,20 and zwitterions.21 However, results have been highly controversial in the case of nonionic permeants,20-25 especially water. The earliest investigations have shown only a continuous increase in water permeability during the transition from the gel to the fluid phase, with no evidence for a permeability peak at Tm.26,27 Our simulations did not show any significant drop in the permeation free energy barrier of water at the gel-fluid interface. The constriction region simply shortened the diffusion path, but the effect was not large enough to promote order-of-magnitude variations in permeability. Although we did not explicitly measure the transmembrane diffusion coefficients, we find unlikely that they would substantially increase at the constriction region. Besides that, while water permeability depends exponentially on the free energy barrier, it only depends linearly on the transmembrane diffusion coefficient (eqs S1 and S2). We rather 17 ACS Paragon Plus Environment


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take the view that, if any permeability anomaly should be expected for water, the effect would be far weaker than for ions. More recently, however, Jansen et al. found a water permeability maximum at the main transition of DPPC and even DPPE.28 From the ratio between the osmotic and diffusive water permeabilities, it was concluded that water permeation occurred mainly through small transient pores arising from density fluctuations in the membranes. That result has not been corroborated by other experimental98 and theoretical92 investigations, which pointed out to solubility-diffusion as the main mechanism of water permeation. That apparent contradiction would vanish if it could be demonstrated that, depending on the experimental conditions, mechanical stresses might develop at the main transition, forcing the opening of pores at gel-fluid interfaces and creating an alternative pathway for water permeation. There are key aspects of the permeability anomaly that might have been missed in previous theoretical studies. The formation of the interface constriction has been probably overlooked in atomistic molecular dynamics simulations of the gel-fluid equilibrium.45 Not to mention, the membrane size is always a critical issue in such simulations, since the spatial transition between the coexisting phases extends over a broad region of space (Figure 3c). Even more critical is the chemical nature of the permeant. Most simulation studies have been focused on water, for which only a weak effect would be expected anyway. Coarse-grained molecular dynamics simulations have revealed no signs of a water permeability peak at the main transition for DPPC, but a small effect has been witnessed upon addition of lysolipids.50 In another series of coarse-grained simulations, Yang et al. have even questioned the validity of the leaky interface hypothesis, showing that the frequency of water permeation events per lipid was higher at the fluid phase than at the gel-fluid interface.51 However, we call attention for the fact that specific coarse-grained lipid models might lack some of the structural features that are essential for the proper description of the gel-fluid interface. An earlier version of the widely used MARTINI force field has failed to reproduce the molecular tilt of gel-phase 18 ACS Paragon Plus Environment

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DPPC.43 As discussed by the authors, that limitation resulted from an underestimated headgroup-to-tail volume ratio, which turns out to be key for the formation of leaky interfaces. In that matter, our results could also guide the development of improved coarsegrained lipid models for the description of thermotropic phase transitions in membranes. More fundamentally, they reveal an interplay between the molecular tilt in the gel, the formation of the ripple phase and the manifestation of the permeability anomaly. All these phenomena are interconnected and can be traced back to one molecular feature: the packing frustration imposed by sufficiently large lipid headgroups.

4.5. Leaky Interfaces in Sterol-Enriched Lipid Rafts. It might be argued that most biologically relevant rafts are not at the gel, but rather at the liquid-ordered state. Liquidordered rafts are enriched in saturated phospholipids, sphingolipids and sterols. The flat sterol ring has a condensing and ordering effect upon phospholipids, but also acts as a membrane fluidizer. Consequently, the liquid-ordered phase exhibits a high degree of order that is typical of the gel, but lipids still retain a large degree of lateral mobility as in the fluid phase.9 To test whether sterol-enriched rafts might also have leaky interfaces, we assembled a simplified liquid-ordered raft domain containing DPPC and 30 % cholesterol. That domain was embedded in a liquid-disordered matrix composed of the unsaturated lipid 1-palmitoyl-2oleoyl-sn-glycero-3-phosphocholine (POPC). The protocol for membrane assembly and equilibration is outlined in Section S5. Using well-validated force fields,106-108 the membrane was equilibrated for 300 ns at 310 K, which is above Tm for the lipid composition studied. As shown in Figure 7, an interface constriction was also formed in this system, suggesting that a local permeability enhancement could also take place at the boundaries of regular lipid rafts. The formation of lipid rafts has been already investigated in previous coarse-grained simulations, but the permeability at domain boundaries has not been explored in detail.109,110 In that context, our results on cholesterol-enriched rafts should be taken as motivational for 19 ACS Paragon Plus Environment


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more detailed investigations. For instance, the issues of interleaflet domain coupling and composition need to be carefully addressed. Our assumed raft composition was representative of a nonequilibrium state, since lipids were not given enough time to reach their partition equilibrium between both phases through lateral diffusion. Nevertheless, our preliminary results strongly suggest that the boundaries of lipid rafts might be “hot spots” for pore formation and possibly even lipid flip-flop events, thereby interfering with the functional role of membrane domains in transport and signaling.

5. CONCLUSIONS

To explain why the permeability of biomembranes is highest at their chain melting regime, we performed molecular dynamics simulations of phospholipid bilayers with coexisting gel-like and fluid domains. Complex thickness deformations appeared at the gel-fluid interfaces. In DPPC, the membrane was substantially thinner at the interface region than at the bulk fluid phase. A constriction was formed from the combination of the following features: the hydrophobic mismatch between the coexisting domains, the large elasticity of the fluid phase, and the spontaneous curvature promoted by the large headgroup-to-tail volume ratio of lipid molecules. The headgroup size explained why a pronounced thickness minimum was formed in DPPC, while the effect was almost negligible in DPPE. Because of the smaller membrane thickness at the gel-fluid interface of DPPC, the free energy required for pore formation was locally reduced. Pore-mediated, ionic permeation events were facilitated at the gel-fluid interface, while the permeation of small neutral molecules by simple diffusion remained almost unaffected. That finding helped to reconcile some of the contradictory permeability data released during the last decades. We also investigated the structure of all-fluid DPPC membranes near the main transition. Even in the absence of well-formed gel-like domains, these membranes exhibited long-lived, peristaltic undulations and periodically spaced 20 ACS Paragon Plus Environment

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constriction regions that, although shallower than the interface constrictions, could also enhance the membrane permeability. Taken together, these data suggest that the permeability anomally originates both from leaky interfaces and from fluctuations in the fluid matrix. The simulation data also indicate that the lipid headgroup size, the molecular tilt in the gel, the formation of the ripple phase and the manifestation of the permeability anomaly are all interconnected. Finally, they strongly suggest that leaky interfaces may also form at the boundaries of cholesterol-enriched lipid rafts, adding up to their functional role in transport and signaling.

SUPPORTING INFORMATION

Treatment of interactions, temperature and pressure (Section S1). Preparation of all-gel and all-fluid membranes (Section S2). Validation of membrane simulations (Section S3, Figures S1 to S4, Table S1). Permeation mechanisms and validation of free energy calculations (Section S4, Figures S5 to S11). Simulation of a cholesterol-enriched lipid raft (Section S5). Suppolementary references. Molecular topology and structure files of the simulated lipids in GROMACS format.

ACKNOWLEDGEMENTS

We are grateful to Maurício S. Baptista for having inspired this work, and to Wendel A. Alves for helping us to improve the manuscript. We are also thankful for the financial support received from the São Paulo Research Foundation (FAPESP) (grant no. 2012/50680-5) and from the National Counsel of Technological and Scientific Development (CNPq) (grant no. 459270/2014-1). Computational resouces were provided by Universidade Federal do ABC.



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Figure 1. (a) Lateral schematic view of a phospholipid bilayer at the ripple phase, highlighting its sawtooth topography and its alternating fluid-like (light grey) and gel-like (white) regions. (b) Top view of a melting bilayer transitioning from the ripple to the fluid phase (dark grey). Arrows indicate the direction of molecular tilt within the gel-like regions. Dashed squares indicate the different interface types that were considered in simulations.


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Figure 2. Images of the simulated (a) PC-GF-para and (b) PC-GF-perp membranes after equilibration at Tm, as viewed along the x-axis (left) and along the y-axis, across the middle of the gel-like region (right). Atoms are represented according to the following code: cyan C, blue N, red O and brown P. Water molecules are omitted. Gel-fluid interfaces are numbered by roman numbers, as in Figure 1b. (c) Average number of gauche dihedrals per lipid acyl chain and (d) membrane thickness as function of the position along the x-axis. Depending on the membrane slant angle, either raw (full lines) or corrected (dashed) thickness data are presented (e) Close-up view of a gel-fluid interface in PC-GF-para. Lipids are colored differently in the two apposing bilayer leaflets and one interfacial lipid is highlighted.



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Figure 3. (a) Image of the simulated PE-GF membrane after equilibration at Tm, as viewed along the x-axis (left) and along the y-axis in the gel region (right). (b,c) Structure of the gelfluid interface in mixed-phase DPPC and DPPE membranes. Local membrane properties were symmetrized with respect to the middle of the gel region (x = 0). Data are presented for the systems PE-GF (red), PC-GF-para (black) and an extended version of PC-GF-para with a larger fluid region, equilibrated for 150 ns (grey). The horizontal dashed lines represent the fluid-phase thicknesses above Tm. (d) Schematic representation of the role of the headgroupto-tail volume ratio and the lipid packing in the formation of the interface constriction region.


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Figure 4. Free energy profiles related to the permeation of (a) water and (b) Na+ across DPPC bilayers. Results are presented for all-fluid bilayers above Tm (PC-F system), all-gel bilayers bellow Tm (PC-G system), and for permeation across the gel-fluid interfaces of mixed-phase bilayers at Tm (PC-GF-para and PC-GF-perp systems). Uncertainties are depicted as shaded regions in the profiles. Images of (c) a water molecule and (d) a Na+ ion permeating across the gel-fluid interface of PC-GF-para. Lipids are represented by lines, according to the same color code of Figure 2a, and with the P atoms highlighted as van der Waals spheres. Water molecules that make up the solvent are depicted in licorice representation, while permeants are represented as van der Waals spheres.



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Figure 5. (a) Free energy barriers associated to the permeation of water (empty symbols) and Na+ (filled symbols) across PC bilayers or bilayer regions with different thicknesses. Data are presented for: all-fluid bilayers with lipids of varying tail lengths and above their respective Tm (red circles); gel-fluid interface regions of mixed-phase bilayers at Tm (black circles); the region of maximal thickness within the fluid matrix of PC-GF-para, i.e. x ≈ 9 nm (grey diamond); the thickness minima that arise from undulations in all-fluid bilayers at Tm (grey triangle). The interface thickness was averaged over a region within ± 1.2 nm from the thickness minimum, which is equivalent to a typical pore diameter. Uncertainties (standard deviations) are nearly the same size as the symbols. (b) Free energy profiles for Na+ permeation across all-fluid DPPE above Tm (PE-F system), and across the gel-fluid interfaces of mixed-phase DPPE at Tm (PE-GF system). Uncertainties are depicted as shaded regions in the profiles.


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Figure 6. Peristaltic undulations in an all-fluid DPPC bilayer equilibrated at Tm, but in the absence of a well-formed gel-like domain. (a) Simulation snapshot. Regions of minimal thickness are indicated by grey arrows. (b,c) Comparison of local membrane properties. (d) Thickness profiles recorded during different intervals of the simulation.



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Figure 7. Thickness profile of a model membrane resembling a cholesterol-enriched lipid raft. The membrane contains a liquid-ordered domain composed of DPPC (blue) and 30% cholesterol (cyan), embedded in a liquid-disordered POPC matrix.


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TOC GRAPHIC



TOC 44x44mm (600 x 600 DPI)

ACS Paragon Plus Environment

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Fig 1 113x152mm (600 x 600 DPI)



Fig 2 194x213mm (300 x 300 DPI)


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Fig 3 149x126mm (300 x 300 DPI)



Fig 4a 83x83mm (300 x 300 DPI)


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Fig 4b 83x83mm (300 x 300 DPI)



Fig 4c 67x67mm (600 x 600 DPI)


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Fig 4d 67x67mm (600 x 600 DPI)



Fig 5a 83x83mm (300 x 300 DPI)


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Fig 5b 83x83mm (300 x 300 DPI)



Fig 6 179x269mm (300 x 300 DPI)


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Fig 7 59x29mm (600 x 600 DPI)


Molecular Structure and Permeability at the Interface between Phase

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