Molecular Structure and Permeability at the Interface between Phase-Separated Membrane Domains

SUPPORTING INFORMATION Molecular Structure and Permeability at the Interface between Phase-Separated Membrane Domains Rodrigo M. Cordeiro Universidade Federal do ABC, Avenida dos Estados 5001, CEP 09210-580, Santo André (SP), Brazil rodrigo.cordeiro@ufabc.edu.br S1

Contents S1. Treatment of Interactions, Temperature and Pressure. S3 S2. Preparation of All-Gel and All-Fluid Membranes. S3 S3. Validation of Membrane Simulations......... S4 Figure S1.... S5 Figure S2.... S6 Table S1...... S7 Figure S3.... S8 Figure S4.... S9 S4. Permeation Mechanisms and Validation of Free Energy Calculations... S10 Figure S5... S12 Figure S6... S13 Figure S7....... S14 Figure S8... S15 Figure S9... S16 Figure S10. S17 Figure S11. S18 S5. Simulation of a Cholesterol-Enriched Lipid Raft.. S18 Supporting References....... S19 S2

S1. Treatment of Interactions, Temperature and Pressure. Lennard-Jones interactions were truncated at 1 nm and electrostatic interactions were treated by the particle-mesh-ewald (PME) method S1,S2 with a real space cutoff of 1 nm. Long-range dispersion corrections were applied to both energy and pressure. Temperature was controlled by a Nosé-Hoover thermostat S3,S4 with a coupling time constant of 0.5 ps. The thermostat was applied independently to the bilayer and to the aqueous phase. Pressure was controlled by a Parrinello-Rahman barostat S5,S6 with a coupling time constant of 2.0 ps and a compressibility of 4.5 10-5 bar -1. For fluid-phase bilayers, a semiisotropic coupling scheme was applied to allow for independent variation of the system length in the z-direction and the membrane area at the xy-plane. For gel- and mixed-phase bilayers, an anisotropic coupling scheme was employed, allowing for independent pressure control along all Cartesian directions. S2. Preparation of All-Gel and All-Fluid Membranes. The DPPC bilayer at the gel phase (PC-G) was assembled in three steps, here referred to as packing, tilting, and equilibration. In the packing step, a single phospholipid was created with all-trans hydrocarbon chains. Following a previous work, 47 a Monte Carlo simulation was set up to replicate that lipid in a hexagonal lattice, with random rotations about the z-axis, so as to reflect the in-plane orientational disorder characteristic of the gel phase. 60 When we equilibrated this system, hydrocarbon chains spontaneously tilted with respect to the membrane normal. Within the same bilayer, all chains tilted uniformly in the direction of one of their nearest neighbors, in line with experimental data. 63 However, we noted that the tilt directions were not necessarily alligned in both leaflets, and varied among individual simulation runs. In fact, previous simulations of the DPPC gel reported on the formation of both tilted (i.e. opposite tilt directions at both leaflets) and cross-tilted (i.e. same tilt direction) configurations. 36,39,41 The canonical picture of the DPPC gel is reminiscent of the crystal structure of phosphatidylcholine lipids, in which the tilt directions at both leaflets are opposite to each other. S7 We speculate that other tilt configurations might be metastable. To ensure the formation of the canonical tilted configuration, we decided to employ the tilting step. A short (100 ps) simulation was performed in which the tail ends were kept fixed, and the headgroups were collectively pulled along the x-axis. Headgroups at the upper and the lower bilayer leaflets were pulled in opposite directions, giving rise to a moderate tilt angle of ~20. Water molecules were then added and the equilibration step was performed for 20 ns with all hydrocarbon chain dihedrals restricted to trans. Finally, the restrictions were released, and a longer NPT equilibration was performed for 300 ns at 298 K and 1 atm. A DPPE bilayer at the gel phase (PE-G) was created by taking the DPPC structure after the packing step, substituting the choline by amine groups and equilibrating at 314.5 K. A DPPC bilayer at the fluid phase (PC-F) was assembled by annealing the equilibrated PC-G system at 353 K for 10 ns, and cooling to 323 K at a rate of 1.5 K/ns. A NPT equilibration was then performed for 300 ns at 323 K and 1 atm. During that process, the barostat was switched from anisotropic to semiisotropic. Following a similar protocol, a DPPE bilayer at the fluid phase (PE-F) was generated from the PE-G system. S3

S3. Validation of Membrane Simulations. The simulation conditions led to well-converged membrane properties (Figure S1). Although the DPPC force field was originally developed to describe the fluid phase, 73 the fundamental structure of the DPPC gel was satisfactorily reproduced. That includes, for instance, the electron density profile along the bilayer normal (Figure S2a). The profile obtained from simulations was very structured due to the low atomic mobility and the use of atom-centered point charges. A better agreement with experimental data S8 was achieved after smoothing the profile with an interval of 0.35 nm, which is roughly the size of an atomic diameter. Simulations slightly underestimated the bilayer thickness, as inferred from the position of the electron density maximum. However, they reproduced other features of the DPPC gel, such as the hexagonal packing of lipid acyl chains, with in-plane orientational disorder (Figure S2b), and the uniform tilt of lipid tails in the nearestneighbor direction (Figure S2c and S2d). Properties such as the area per lipid, the bilayer thickness, and the number of gauche dihedrals per hydrocarbon chain were reasonably close to reference experimental data for both DPPC and DPPE, at either the gel or the fluid phase (Table S1). The largest deviations were found for the tilt angle. The average molecular tilt angle in the simulated DPPC gel was ~30% higher than in experiments. That behavior has also been witnessed in previous simulations. 39,45 Here, we did not spend further efforts to improve the force field, as it was considered of acceptable quality for our main purposes. At the qualitative level, the force filed successfully accounted for the fact that the DPPC gel is strongly tilted, while the DPPE gel has almost no tilt. Basic features of the main transition were also well represented. Figure S3a to S3c shows the temporal evolution of the lipid tail order in mixed-phase systems. When phase-separated DPPC membranes were equilibrated at 308.5 K, the degree of tail order, as averaged over the whole membrane, converged during simulation time and remained constant over the last 100 ns. The gel-like domain remained stable, without melting nor growing. Only 1.5 K above that temperature, melting of the gellike domain took place, as indicated by the steady increase in the overall membrane disorder. The temperature of 308.5 K was considered as a reasonable approximation for the T m of the DPPC model. 45 This value lies only 6 K bellow the experimentally measured value. 64 For the DPPE model, a T m of ~352.5 K was found, which lies 15 K above reference experimental data. S15 In the PC-GF-para system, the membrane was practically planar, while in PC-GF-perp, an undulated membrane contour formed early and persisted throughout the whole simulation (Figure S3d). In these mixed-phase membranes, the gel-like domains preserved some of the basic structural features of the gel phase, such as the hexagonal packing and the molecular tilt in the nearest-neighbor direction (Figure S4a and S4b). Earlier X-ray diffraction studies of the ripple phase revealed that the gel-like chains were oriented towards their next-nearest-neighbors, rather than towards their nearest-neighbors. 65 However, the effect might have originated from the incomplete hydration of the studied membranes. In fact, a similar change in the tilt direction has been demonstrated upon partial dehydration of a fully hydrated gel phase. S16 Our simulations also revealed that the molecular tilt with respect to the membrane normal was ~10 lower, and the membrane thickness was ~5 Å higher in the gel-like domains at T m, as compared to the all-gel bilayer simulated bellow T m (Figure S4c and S4d). To the extent that gel-like lipids can be considered as rigid rods, it is expected that the membrane thickness should increase as lipids become less tilted. In the same X-ray study mentioned before, the molecular tilt was found to be S4

~14 lower in the gel-like ripples than in the gel, with no change in thickness. 65 But once again, a direct comparison between simulations and experiments is probably limited due to the different hydration levels considered in both. Simulations suggest that, during melting of DPPC, the ordered domain retains some of the characteristics of the gel phase, but does not have exactly the same structure as a canonical gel phase. That is consistent with the notion that the main transition in DPPC is a phase equilibrium between the ripple and the fluid phase. Therefore, we refer to this domain as gel-like. In DPPE (PE- GF), the ordered domain kept a structure much more similar to the gel (Figure S4c), as the melting transition did not involve a ripple phase. Figure S1. Temporal evolution of the (a) area per lipid, (b) membrane thickness and (c) lipid tilt angle of the simulated all-fluid and all-gel phospholipid bilayers. S5

Figure S2. Structure of the all-gel DPPC bilayer equilibrated bellow T m (PC-G system). (a) Electron density profiles, including raw simulation data, simulation data smoothed with a 0.35 nm interval, and experimental data based on the 1G and 2G models of Wiener et al. S8 (b) Top view (xy-plane) of the bilayer, showing the average positions of lipid acyl chains (spheres). Average positions were determined from the coordinates of the methylene units located in a region between 0.6 and 0.9 nm above the bilayer center. The connectivity of individual double-tailed lipids is represented by arrows that point from the sn-1 to the sn-2 chains. The grey arrow points to the lipid tilt direction. Dashed lines mark the positions of the periodic boundaries. Images of the lateral (c) yz- and (d) xz-planes of the bilayer with atomic detail. Water was omitted for clarity. S6

Table S1. Biophysical Properties of Simulated Single-Phase Phospholipid Bilayers a. System Area per lipid (nm 2 ) Thickness b (nm) Gauche/chain Tilt angle ( ) PC-F 0.63(1) / 0.63 c 3.72(6) / 3.80 c 3.0(1) / ~3.8 d PC-G 0.528(6) / 0.47 e 4.02(4) / 4.28 e 0.76(8) / <1 f 43.0(8) / 31.6 e PE-F 0.55(1) / 0.52 gh 4.09(6) / 3.8 g 3.0(1) PE-G 0.397(2) / 0.41 i 5.01(2) 0.43(7) 8(2) / ~0 j a Data are presented following the pattern simulation result (standard deviation in the last digit) / experimental result. b From the interleaflet P-P distance (simulations) or from the distance between electron density maxima (experimental). c Reference S9. d Reference S10. e Reference 63. f Reference S11. g Reference S12, for fluid-phase DPPE at 348 K. h Significantly higher values of 0.60 and 0.64 nm 2 were reported in reference S13 for fluid-phase DPPE at 342 and 358 K, respectively. i Reference S14, for the shorter DLPE lipid at 293 K. j Reference 62. S7

Figure S3. Temporal evolution of the overall lipid tail order during simulation of the (a) PC-GF-para, (b) PC-GF-perp, and (c) PE-GF systems at different temperatures. Starting from all-gel membranes, the simulation protocol began with the annealing of the yet-to-become fluid region (phase I), followed by equilibration (phase II) and sampling (phase III). (d) Images of the PC-GF-perp system at various time instants. S8

Figure S4. Lipid packing in the gel-like domains of the (a) PC-GF-para and (b) PC-GF-perp systems. The average positions of lipid acyl chains (spheres) are depicted along with the lipid tails (lines). (c) Average lipid tilt in the ordered domains of mixed-phase membranes, as compared to regular gel phases. (d) Electron density profiles sampled across the gel-like domains, along the direction of the membrane normal. S9

S4. Permeation Mechanisms and Validation of Free Energy Calculations. Water permeation is thought to occur according to the solubility-diffusion model. 91,92 In this model, water molecules first penetrate into the membrane, at the cost of losing hydration, and then diffuse in a nearly flat energy landscape across the membrane interior. That permeation mechanism was successfully reproduced by simulations (Figure S5a). As shown in Figure 4a, the excess free energy steeply increased as water penetrated into fluid-phase DPPC (PC-F), reaching 26.1 ± 0.6 kj/mol, and remained nearly constant in the membrane interior. The barrier closely matched the water-to-hexadecane transfer free energy of 25 kj/mol recorded for water. S17 According to the solubility-diffusion model, the permeability coefficient (P) is given by: exp G( z) / RT D( z) 1 2 P dz, (S1) z1 z where ΔG(z) is the position-dependent excess free energy, R is the ideal gas constant, T is the temperature and D(z) is the local diffusion coefficient along the membrane normal. The integration limits are set near to the membrane surfaces. Although we did not explicitly calculate D(z), a few assumptions can be made to obtain an order-of-magnitude estimate of P from our free energy profiles. From previous simulations, 92 we took the intra-membrane diffusion coefficient as 1.4 10-4 cm 2 /s, and neglected its spatial variations. With these approximations, eq S1 led to a permeability of 6 10-2 cm/s for water through fluid phase DPPC, which is consistent with experimental data in the range of 10-3 10-2 cm/s. 98,S18 In fluid-phase bilayers, the integral in eq S1 is dominated by the free energy plateau in the membrane interior. Hence, eq S1 can be simplified to: D exp Gb / RT P, (S2) where ΔG b is the barrier height and is the thickness of the water-depleted membrane interior. Eq S2 shows that P is much more sensitive to variations in ΔG b than to variations in D. As for the gel phase (PC-G), water permeation followed the solubility-diffusion mechanism too (Figure S5b). The free energy profile had a double-peak shape, with pronounced free energy maxima located halfway through each bilayer leaflet (Figure 4 a). From eq S1, we estimated P to be at least 4 orders of magnitude lower than at the fluid phase. By comparison, experimental data point to a ratio of 3 orders of magnitude. We speculate that in real, macroscopically sized membranes, the presence of packing defects and grain boundaries might increase the permeability of the gel. These structural features were absent in the small gel patch simulated. The permeation of Na + through fluid-phase DPPC did not follow the same mechanism as water. The translocation of individual Na + ions was accompanied by the formation of transient, water-filled pore defects (Figure S6a), in line with experimental 98 and theoretical 94-97 evidence. The convergence of the free energy profile is shown in Figure 7a. The profile had a nearly triangular shape and reached its maximum at the bilayer center (Figure 4b), in qualitative agreement with previous simulations. 94-97,S19 S10

The permeation free energy barrier was 80 ± 3 kj/mol, not very far from the 98 ± 3 kj/mol measured for phosphatidylserine membranes. S20 We also note that the barrier was significantly lower than the energy required for complete ionic dehydration, S21 showing that Na + ions retained at least some of their hydration waters. In analogy to transition state theory, the ionic permeability can be written as: P f T) exp G / RT, (S3) ( b where f(t) is a temperature-dependent pre-factor. The permeation barrier posed by the gel was ~100 kj/mol larger than that of the fluid phase (Figure S7b). Application of eq S3 showed that the gel-phase permeability was practically null in comparison to the fluid phase. However, experimental measurements have revealed a low residual permeability in the gel. 12 Once again, the absence of defects and grain-boundaries in the simulated gel might have led to the underestimation of its permeability. Simulations showed that, at low immersion depths, Na + ions still managed to drag hydration waters to the interior of gel-phase DPPC, much like they did in fluid-phase DPPC. However, pores did not form when ions were deeper into the membrane interior (Figure S6b). It is possible that even longer equilibration and sampling times would be required for complete pore formation. Otherwise, it is also conceivable that the lowest-energy permeation mechanism switches from pore-mediated to solubilitydiffusion when membranes become excessively thick and rigid. 98,104 As depicted in Figure S8, the ion-induced pore formation was different in DPPC and DPPE. A complete pore spanning the whole membrane thickness was formed in fluid-phase DPPC, while a much smaller hemipore was formed in fluid-phase DPPE. Figure S9 shows that, in mixed-phase membranes, the ionic permeation at the interface regions conserved these same characteristics. We recall that each umbrella window was produced by inserting the ion at the desired position and letting the pore to form spontaneously, not by pulling the ion from the aqueous phase to the desired position. In DPPC, stable membrane-spanning pores were formed after 10 ns of equilibration in cases where the Na + was placed at the very membrane center (z = 0). At positions away from the membrane center, only a hemipore was formed. Following a previous work, 29 we write down the total membrane permeability as the average between the local permeabilities of the coexisting gel-like (g), fluid (f) and interfacial (i) regions. Taking their respective fractional areas (a) as weighting factors, we have that: P( T) a P. (S4) g ( T) Pg af ( T) Pf ai ( T) i In eq S4, the regional permeabilities are assumed to be constant, and the temperature-dependence of the fractional areas accounts solely for the variation of the total membrane permeability with temperature. P f is simply taken as the fluid-phase permeability well above the main transition temperature. Although these are rather crude approximations, they allow for an order-of-magnitude quantification of the interface effect. By neglecting the individual contributions of the gel-like and the fluid phases, we end up with a lower bound estimate of the relative permeability enhancement at T m : S11

P( T P f m ) P i ai ( Tm ). (S5) Pf In eq S5, permeabilities are conveniently expressed as relative to the bulk fluid-phase permeability. Now, the P i /P f ratio can be inferred from the free energy barriers using eq S3. Figure S5. Images from umbrella sampling simulations of water permeation across (a) an all-fluid DPPC bilayer above T m (PC-F) and (b) an all-gel DPPC bilayer bellow T m (PC-G). Panels show the permeants at the positions z = 0.6 nm (left), z = 0 (center) and z = -0.6 nm (right) with respect to the bilayer center. S12

Figure S6. Images from umbrella sampling simulations of Na + permeation across (a) an all-fluid DPPC bilayer above T m (PC-F) and (b) an all-gel DPPC bilayer bellow T m (PC-G). Panels show the permeants at the positions z = 0.6 nm (left), z = 0 (center) and z = -0.6 nm (right) with respect to the bilayer center. S13

Figure S7. (a) Influence of the simulation time length on the free energy profiles of Na + permeation across all-fluid DPPC above T m (PC-F). Values refer to the total time length adopted for umbrella windows at the membrane region (i.e. between -2.2 and 2.2 nm), equally divided between equilibration and sampling. Outside this region, at the aqueous phase, simulations were shorter, with only 0.5 ns of equilibration and 2 ns of sampling. An additional test simulation was performed with an extended, 20 ns simulation time in the aqueous phase as well, as indicated by the (+) symbol. (b) Full free energy profile of Na + permeation across all-gel DPPC bellow T m (PC-G) (see also Figure 4b). Uncertainties are depicted as the shaded region. S14

Figure S8. Temporal evolution of the ion-induced pore defect in all-fluid (a) DPPC (PC-F) and (b) DPPE (PE-F) above T m. Images show the umbrella windows corresponding to Na + ions at the bilayer center (z = 0) at 12.5 ns (left), 15 ns (center) and 20 ns (right). S15

Figure S9. Images from umbrella sampling simulations of Na + permeation across the interface regions of the (a) PC-GF-para, (b) PC-GF-perp and (c) PE-GF membranes at their respective T m. Bilayers are viewed along the x-axis (left) and along the y-axis at the interface region (right). S16

Figure S10. Free energy profiles of (a) water and (b) Na + permeation across a series of all-fluid PC bilayers made of unsaturated lipids with varying tail lengths. (c) Bootstrapped free energy profiles of Na + permeation across the all-fluid DPPC bilayer above T m (PC-F system) and the gel-fluid interfaces of mixed-phase DPPC at T m (PC-GF-perp system). Bootstrapped profiles were used to estimate the uncertainties in the free energy barriers. The definition of G b is shown, along with the transfer free energies from the bulk aqueous phase to the bilayer center (G max ) and to the point of minimal energy at bilayer surface (G min ). (d) Energetics of Na + permeation across PC bilayers and bilayer regions with different thicknesses. Symbols are coded as in Figure 5. S17

Figure S11. Convergence of the free energy barrier for ionic permeation across different membranes. Sampling time was 10 ns in all cases. S5. Simulation of a Cholesterol-Enriched Lipid Raft. The simulation of a phase-separated raft bilayer was carried out using GROMOS-type force field parameters for phospholipids 106,107 and cholesterol. 108 We used the same setup as for the gel-fluid simulations, except that a double-range cutoff at 0.8 and 1.1 nm was employed for Lennard-Jones interactions and a real space cutoff of 0.8 nm was employed for PME electrostatics. A membrane at the liquid-ordered state was assembled by adding 54 cholesterol molecules to a pre-equilibrated DPPC bilayer containing 128 lipids. Cholesterol molecules were equally distributed among both leaflets and were placed at random lateral positions. They were oriented parallel to the membrane normal, with their polar hydroxyl groups pointing to the aqueous phase. After 100 ns of equilibration at 323 K, the temperature was lowered to 310 K, and equilibration was continued for 300 ns. That system was then replicated three times along the x-axis. In all but the central replica, cholesterol was removed and DPPC was gradually converted to POPC by lengthening the sn-2 chain and adding a cis double bond at the correct position. Equilibration was performed for 300 ns at 310 K, which is well-above the T m of POPC. 64 The membrane thus formed contained a liquid-ordered raft domain composed of DPPC and 30 % cholesterol, embedded in a liquid-disordered, pure POPC matrix (Figure 7). S18

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