Cholesterol Bilayer

Article Cite This: J. Phys. Chem. B 2018, 122, 2556−2563

pubs.acs.org/JPCB

Stretch-Induced Interdigitation of a Phospholipid/Cholesterol Bilayer Taiki Shigematsu,*,† Kenichiro Koshiyama,‡ and Shigeo Wada‡ †

Global Center for Medical Engineering and Informatics, Osaka University, 2-2 Yamadaoka, Suita, Osaka 565-0871, Japan Department of Mechanical Science & Bioengineering, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan

‡

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S Supporting Information *

ABSTRACT: The interdigitated gel (LβI) phase is one of the membrane phases of phospholipid molecules in which the hydrophobic tails of the phospholipid molecules penetrate the opposite leaflet of the bilayer. Recent molecular dynamics (MD) simulations have shown that interdigitation can take place as a phase transition from the liquid-ordered (Lo) phase to the LβI phase under stretching. However, there is still no conclusive experimental evidence for this process, so its existence remains controversial. In this study, to explain the transition from energy balance, we propose a free-energy model. The model consists of three energy components: the elastic deformation energy, surface energy at the bilayer− water interface, and interphase boundary energy. To determine the parameters of the model, we perform MD simulations of a stretched 1,2dipalmitoyl-sn-glycero-3-phosphocholine/cholesterol bilayer. The phase diagrams from our model are in good agreement with those obtained from MD simulations. The energy balance among the components in the stretched bilayer quantitatively explains the stretchinduced transition. In the model, increasing the system size to that used in experiments shows that interdigitation is favorable for rigid bilayers under stretching or in alcohol solutions. These results suggest that the stretch-induced interdigitation might be observed in microscopic experiments.

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INTRODUCTION The interdigitated gel (LβI) phase is one of the membrane phases of phospholipid molecules.1,2 In the LβI phase, the hydrophobic tails of the phospholipid molecules interdigitate as they penetrate the opposite leaflet of the bilayer, and the tips of the tails locate at the bilayer−water interface. According to experimental studies, the phase transition to the LβI phase occurs when the gel (Lβ)-phase bilayers are placed at high hydrostatic pressure3,4 or exposed to small amphiphilic molecules, such as alcohols.5,6 In addition to pressure-induced and chemically induced interdigitation, recent numerical simulation studies have reported that mechanical stretching can induce interdigitation in phospholipid bilayers.7−10 Previously, we have demonstrated numerically that stretch-induced interdigitation occurs in a 1,2dipalmitoyl-sn-glycero-3-phosphocholine (DPPC)/cholesterol bilayer in the liquid-ordered (Lo) phase.9,10 However, the detailed mechanism of stretch-induced interdigitation is still not well understood. Furthermore, to the best of our knowledge, there has been no direct experimental observation of stretchinduced interdigitation. Mechanical stresses are ubiquitous in biological membranes, and are known to be essential for various cell activities, including growth, division, migration, and signal transduction.11−13 However, excessive mechanical stresses can induce irreversible rupture of the membrane, and avoiding this rupture is important for the implementation of several © 2018 American Chemical Society

experimental and medical techniques, such as sonoporation,14,15 and the use of extracorporeal lithotripters16 or ventricular-assisted devices.17 The transition to the LβI phase involves a significant decrease in bilayer thickness and a significant increase in the apparent bilayer area. These might influence the activities of the membrane proteins,18 or the mechanical toughness of the bilayer.9 Thus, understanding the mechanism of stretch-induced interdigitation is an important goal. In this paper, to understand the mechanism of stretchinduced interdigitation, we propose a free-energy model and perform molecular dynamics (MD) simulations of stretched DPPC/cholesterol bilayers. To the best of our knowledge, there exists no model to explain the energy balance underlying the stretch-induced interdigitation quantitatively, although there are several speculations on the energy balance underlying chemically induced interdigitation.19−21 Accordingly, we develop a free-energy model of the stretched bilayer in the Lo and LβI phase coexistence state. The results of the MD simulations of these stretched DPPC/cholesterol bilayers are used to determine the parameters of the free-energy model. We present the phase diagrams and tension versus areal strain plots obtained from both the MD simulations and the free-energy Received: October 27, 2017 Revised: January 12, 2018 Published: February 8, 2018 2556

DOI: 10.1021/acs.jpcb.7b10633 J. Phys. Chem. B 2018, 122, 2556−2563

Article

The Journal of Physical Chemistry B

tension is positive, which is common for phase boundaries of phospholipid bilayers,22 the boundary length should be minimized to minimize Ub. To minimize the boundary length under periodic boundary conditions, the shape of the phase boundary must be a circle, stripe, or inverted circle, depending on the range of α (see Figure 2G−I(circle),J−L(stripe),M(inverted circle)). At equilibrium, U must be minimized. Here, αmodel(εA) and βmodel(εA) are defined as the optimal values of α and β that minimize U(εA, α, β), and can be found by varying α and β. A phase transition is considered to have started when αmodel(εA) changes from zero to nonzero. We define the areal strain, at which the phase transition starts, as the areal strain εC. Additionally, because U is the energy stored in the bilayer under stretching, the tension of the bilayer γS can be calculated as γS = (∂U(εA, αmodel(εA), βmodel(εA))/∂εA)(∂εA/∂A∥).

model and clarify the energy competitions underlying the stretch-induced interdigitation. Using the free-energy model, we clarify the effects of system size, area compressibility modulus of bilayers, and the surface tension at the bilayer− water interface on the phase behavior.

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THEORY Let us first consider the stretched bilayer in the Lo and LβI phase coexistence state, which consists of N membrane molecules. The bilayer is assumed to be flat and maintains its integrity even under stretching. The LβI and Lo phases are continuous under periodic boundary conditions. The area of the whole bilayer is A∥ and that of the unstretched bilayer portion is A0. The areal strain of the entire bilayer is defined as εA = A∥/A0 − 1. In the stretched bilayer in the Lo and LβI phase coexistence state, the bilayer areas in the LβI phase or the Lo phase are, respectively, defined as αA∥ and (1 − α)A∥, where α is a fraction parameter in the range of 0−1. In addition, using a fraction parameter β, the number of membrane molecules in the LβI phase or the Lo phase is given by βN or (1 − β)N, respectively. Here, we consider the total free energy U of the stretched bilayer in the Lo and LβI phase coexistence state to be U = Ue + Uh + Ub. Ue is the elastic deformation energy in each phase, Uh is the surface energy at the bilayer−water interface of each phase, and Ub is an interphase boundary energy between the LβI and Lo phases. The elastic deformation energy Ue is proportional to square of the areal strain, and hence can be expressed as Ue(εA , α , β) = +

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METHODS Bilayer System. The initial configuration of the DPPC/ cholesterol bilayer was obtained from our previous study.10 The bilayer system consisted of 128 DPPC, 86 cholesterol, and 13 842 water molecules and was well equilibrated at 323 K and 0.1 MPa. The cholesterol concentration of the DPPC/cholesterol bilayer was about 40 mol %, which is within the physiological range of animal cell membranes (20−50 mol %).11 The DPPC23 and cholesterol molecules24 were represented by united atom models, and the water molecules were represented by the simple point charge model.25 The bilayer was placed on the x−y plane of the rectangular simulation box, and the basic structural characteristics of the bilayer indicated that it was in the Lo phase. Here, the bilayer system was replicated twice in both the x- and y-directions and was consequently composed of 512 DPPC, 344 cholesterol, and 55 368 water molecules. The replicated bilayer system equilibrated in the MD simulation under constant temperature (323 K) and pressure (0.1 MPa) conditions for 800 ns. The temperatures of the DPPC, cholesterol, and water molecules were separately maintained by the velocity rescaling method26 with a 0.2 ps time constant, and the pressure was maintained semi-isotropically using the Berendsen weak coupling method27 with a 0.5 ps time constant. As a result of equilibration, the system box size was 12.8 × 12.8 × 12.0 nm3 at equilibrium. Details of the MD simulation parameters are summarized in the Supporting Information. All of the MD calculations were carried out using GROMACS 4.6,28,29 and all of the snapshots of the bilayer system were rendered using visual molecular dynamics.30 MD Simulation of Stretched Bilayers. The stretched bilayer was expressed by a constant NPzA∥T simulation with various fixed areas A∥. To obtain the starting configurations, an unsteady stretching (US) simulation10,31 of the equilibrated bilayer system was performed. In the US simulation, the temperature and pressure in the z-direction were maintained by a thermostat and barostat, respectively. For the x- and ydirections, the box lengths were elongated at a constant rate of c = 0.1 nm/ns. Simultaneously, the atom positions were proportionally scaled to follow the changes in the box dimensions. From the trajectories of the US simulation, the stretched bilayers, where A∥ satisfies the areal strain values εA = 0.013, 0.027, 0.038, 0.055, 0.074, 0.101, 0.127, 0.173, 0.279, 0.423, 0.535, and 0.638, were extracted as the starting configurations. Using these stretched bilayers, the constant NPzA∥T simulations were performed for at least 400 ns. As with the areal strain in the free-energy model, the value of εA for the stretched bilayer in the MD simulations was also defined as εA

⎞2 βNa Li 1 Li⎛ α(1 + εA )A 0 0 ⎟ KA ⎜ − 1 2 ⎝ βNa0Li /2 2 ⎠

⎞2 (1 − β)Na Lo 1 Lo⎛ (1 − α)(1 + εA )A 0 0 ⎟ KA ⎜ − 1 L 2 2 ⎝ (1 − β)Na0 o /2 ⎠ (1)

where KALi, KALo, a0Li, and a0Lo are area compressibility modulus and area per molecule for the unstretched membrane in the LβI and Lo phases, respectively. The area per molecule for each phase is defined as the surface membrane area divided by the total number of membrane molecules composed of the phase. The surface energy Uh is proportional to the surface area Uh(εA , α) = 2α(1 + εA )A 0σ Li + 2(1 − α)(1 + εA )A 0σ Lo (2)

where σ and σ are surface tensions at the bilayer−water interfaces of the LβI and Lo phases, respectively. The interphase boundary energy Ub is proportional to the boundary length, and can be expressed as Li

Lo

⎧ 2γ ⎪ L ⎪ ⎪ ⎪ ⎪ 2γ Ub(εA , α) = ⎨ L ⎪ ⎪ ⎪ 2γ ⎪ L ⎪ ⎩

πα(1 + εA )A 0 (circle, 0 ≤ α < 1/π ) (1 + εA )A 0 (stripe, 1/π ≤ α < 1 − 1/π ) π(1 − α)(1 + εA )A 0 (inverted circle, 1 − 1/π ≤ α ≤ 1)

(3)

where γL is a line tension (energy per unit length of boundary) on the boundary between the LβI and Lo phases. When the line 2557


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Figure 1. Representative sliced snapshots of DPPC/cholesterol bilayers for εA = 0.000 (A) and 0.173 (B). The hydrophilic headgroups of the DPPC molecules are shown in red, hydrophobic tails in orange, cholesterol molecules in green, and water molecules in blue. The vertical black lines indicate the outline of the simulation box.

Figure 2. Representative Voronoi diagrams of the stretched bilayers. The color of the Voronoi cell indicates the occupied area of the cell. The slices enclosed by the dashed lines in (A) and (I) correspond to the sliced side views of the bilayers in Figure 1A,B, respectively.

= A∥/A0 − 1, where A0 is the averaged bilayer area during the equilibrium simulation. The tension γS of the stretched bilayer was calculated by γS = (2Pzz − Pxx − Pyy)lz/2, where Pii is a component of the pressure tensor and li is the length of the simulation box in the i-direction (i = x, y, z). The line tension γL of the phase boundary was calculated by γL = (Pyy − Pxx)lylz/ 2, when the boundaries were stripelike and oriented along the x-direction across the periodic images.32 The simulation times for each of the stretched bilayers are listed in Table S1 of the Supporting Information. The trajectories during the final 200 ns were used in the analyses. The equilibrium simulation was used as the εA = 0.000 case. The MD simulation parameters in the US and NPzA∥T simulations were the same as those for the equilibrium simulations, except for the scaling of the box lengths in the x-and y-directions. Phase Transition in the MD Simulation. To quantify the phase transitions between the Lo and LβI phases in the MD simulations, we used a two-dimensional Voronoi tessellation analysis.33,34 The centers of mass of the sn-1 and sn-2 tails of the DPPC molecules, and the hydrophobic parts of cholesterol molecules, were considered the seed points. For a twodimensional tessellation, these seed points were projected on the xy-plane. The Voronoi tessellation was conducted on the bilayer, which means that the seed points in the upper and lower layers of the bilayer were used without distinction. This

particular choice of the Voronoi tessellation here was useful to analyze the phase transition between the LβI and Lo phases, although the Voronoi tessellation analysis is often conducted for the upper and lower leaflets of the bilayer separately. A detailed explanation for this is given in the Supporting Information. The DPPC and cholesterol in the LβI phase were arranged in a single plane, unlike those in the Lo phase that were arranged in two planes (a bilayer). Thus, the area of the Voronoi cell in the LβI phase is expected to be larger than that in the Lo phase. When the area of the Voronoi cell is larger than a threshold value, it is defined to be in the LβI phase. On the other hand, when the area is smaller than this value, the cell is considered to be in the Lo phase. The ratio of the total Voronoi cell area belonging to the LβI phase to the entire bilayer area A∥ was defined to be αMD. The Voronoi tessellation analysis was conducted on the snapshots for the final 200 ns (10 snapshot/ns) for each areal strain condition. Isolated Voronoi cells belonging to the same phase were analyzed without distinction. The threshold value was defined using Otsu’s threshold selection method.35 Relationship to Free-Energy Model. Among the material parameters in eqs 1−3, a0Lo and KALo were obtained from the MD simulations. a0Lo is defined as the area per molecule for εA = 0.000. KALo is defined as the slope of the γS − εA plot in the Lo phase, which was calculated using a standard least-squares 2558


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The Journal of Physical Chemistry B method with the assumption of a proportional relationship between γS and εA. Additionally, σLo is considered to be 0 mN/ m. The other parameters were tuned to minimize an evaluation function, which is defined here as the root-mean-square difference between αmodel and αMD. The optimal parameter set was found using the simulated annealing method.36 Parameter sensitivities of the optimal parameter set on the evaluation function are shown in the Supporting Information.

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RESULTS AND DISCUSSION Phase Transitions in the MD Simulation. Representative snapshots of the bilayers for εA = 0.000 and 0.173 are shown in Figure 1. The periodic images are also shown, in which the vertical black lines indicate the outline of the simulation box. Figure 1A shows the Lo phase bilayer for εA = 0.000. The DPPC and cholesterol molecules were ordered, and the lateral molecular distribution and the bilayer thickness were uniform. For εA = 0.173 (Figure 1B), some DPPC and cholesterol molecules were interdigitated, and the tips of the DPPC tails and the cholesterol molecules were exposed to water. The structural characteristics of such bilayers corresponded to those in the LβI phase.1,2 The bilayer structure of the other region seemed to be still in the Lo phase. During equilibration for each areal strain condition, multiple LβI phase regions were not formed in the patch membrane. To visualize and quantify the progress of the phase transition, two-dimensional Voronoi tessellation analyses were conducted on the stretched bilayers. Figure 2 shows representative Voronoi diagrams of the stretched bilayers, in which the color of each Voronoi cell indicates the area of the cell. For εA ≤ 0.074 (Figure 2A−F), there was no significant inhomogeneity in the Voronoi diagrams. On the other hand, for εA = 0.101 (Figure 2G), the Voronoi cells that had relatively large areas, shown in orange, appeared locally. The area of the largecell region increased with increasing εA. The shape of the largecell region was circular for εA = 0.101, 0.127, and 0.173 (Figure 2G−I); stripelike for εA = 0.279, 0.423, and 0.535 (Figure 2J− L); and inverted circular for εA = 0.638 (Figure 2M). The slices enclosed by the dashed lines in Figure 2A,I correspond to the sliced side views of the bilayers in Figure 1A,B, respectively. Both the side-view snapshot (Figure 1B) and the top-view Voronoi diagram (Figure 2I) clearly showed the location of the LβI phase region. Figure 3 shows the probability distributions of the Voronoi cell areas for the sn-2 tails. For εA ≤ 0.074 (solid lines), the profiles show Gaussian-like distributions. The mode is about 0.12 nm2 for εA = 0.000, and increases slightly with increasing εA. For εA ≥ 0.101 (dashed lines), the profiles are bimodal, with the first and second modes around 0.12 and 0.22 nm2, respectively. The second peak increases with increasing εA. At the same time, the first peak diminishes. From the semilog plots (inset of Figure 3), it can be seen that the second peak appears when the areal strain εA is in the range of 0.074−0.101. The first and second modes around 0.12 and 0.22 nm2 correspond to the blue and orange regions in the Voronoi diagrams (Figure 2), respectively. The probability distributions of the Voronoi cell areas of the sn-1 tails and cholesterol molecules are shown in Figure S2 in the Supporting Information. They are essentially the same as those of the sn-2 tails. To distinguish between the LβI and Lo phase regions quantitatively, we defined the threshold values for the Voronoi cell area of sn-1, sn-2, and cholesterol at 0.175, 0.174, and 0.189 nm2, respectively, as shown in vertical dash-dotted lines in

Figure 3. Probability distributions of the Voronoi cell areas of the sn-2 tails of DPPC molecules. The vertical dash-dotted line indicates a threshold value, which distinguishes the cells in the LβI and Lo phase regions. The inset is a semilog plot of figure.

Figures 3 and S2. The relationship between the ratio αMD of the total area of the Voronoi cells, whose areas are larger than the threshold value, to the entire bilayer area A∥ with the areal strain εA is shown in Figure 4. For εA ≤ 0.074, αMD is around 0. For εA ≥ 0.101, αMD monotonically increases with increasing εA.

Figure 4. Relationship between αMD and εA (circles), and between αmodel and εA (black line).

These results (Figures 1−4) show that in the MD simulation here the DPPC/cholesterol bilayer was in the Lo phase for εA ≤ 0.074 and in the LβI and Lo phase coexistence state for εA ≥ 0.101. Thus, the critical areal strain εC, at which the phase transition starts, is expected to be in the range of 0.074−0.101. Mechanical Properties. Figure 5 shows the relationship between the areal strain εA and the tension of the stretched bilayer γS. For εA ≤ 0.074, γS monotonically increases with increasing εA and reaches a maximum at εA = 0.074. On the other hand, γS decreases for εA ≥ 0.074. Using the relationship between γS and εA for εA ≤ 0.074, where the bilayer is in the Lo phase, KALo was calculated to be 1949 mN/m. This value is larger than those for bilayers composed of similar lipids. For example, it is 1281.2 ± 140.8 mN/m for DPPC with 40 mol % cholesterol37 and 1718 ± 484 mN/m for sphingomyelin with 50 mol % cholesterol.38 We consider that this is an acceptable difference because of the large variations seen both in experiments37,38 and MD simulations.39 2559


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Figure 6. Total free energy and its components as a function of εA. The inset provides finer resolution around the critical areal strain εC.

Figure 5. Relationship between γS and εA in the MD simulations (circle) and the free-energy model (black line).

in the Lo phase and the losses at the phase boundary, along with the surface energy. In fact, the surface energy loss is the dominant factor. Effect of System Size on Interdigitation. In the MD simulations, the phase transition to the LβI phase occurs locally when the applied areal strain exceeds the critical value εC, which is expected to be in the range of 0.074−0.101. One may think that areal strains near 0.1 are too large to use in experiments. In micropipette aspiration experiments using giant unilamellar vesicles (GUVs), bilayer rupture occurs under smaller areal strains (0.01−0.05).38 In a patch membrane system with periodic boundary conditions, the wavelengths of all phenomena in the simulation are limited to the system box length. For example, because of this limitation, the phase transition between the Lβ and liquid-disordered (Ld) phases,40 pore formation by stretching,41 and undulation of the bilayer42 are known to be suppressed. In this subsection, we discuss the effects of the system size, that is, the number of membrane molecules N on the critical areal strain εC using the free-energy model. Figure 7 shows the relationship between N and εC estimated from the free-energy model. The value of εC decreases with

Because the shape of the phase boundaries of the bilayers for εA = 0.279, 0.423, and 0.535 are stripes oriented in the xdirection (Figure 2J−L), the line tension γL of the phase boundary can be calculated using γL = (Pyy − Pxx)lylz/2. The γLs of the bilayers for εA = 0.279, 0.423, and 0.535 are 0.4, 33.4, and 30.2 pN, respectively. There are large differences in γL for εA = 0.279 compared to the others. We do not suggest here any physical reasons for the difference, although it might be related to the large fluctuations in the pressure tensors and the phase boundaries. As for uncertainty, the value of γL estimated from the MD simulations is not used in the free-energy model. Instead, it is considered a tuning parameter in the model. Free-Energy Model. The unknown parameters used in the free-energy model in eqs 1−3 are a0Li, a0Lo, KALi, KALo, σLi and γL. From a series of MD simulations of the stretched bilayers, KALo (Figure 5) and a0Lo were directly obtained. Using the simulated annealing method, the other four parameters were defined. In the optimal parameter set, a0Li, KALi, σLi, and γL were 0.738 nm2, 684 mN/m, 19.0 mN/m, and 29.2 pN, respectively. The values of these parameters were consistent with typical values for the phospholipid bilayers or estimates of the structural characteristics of the LβI phase bilayer. A detailed discussion is presented in the Supporting Information. Hereafter, the parameters used for the model are the same as those estimated using the MD simulation results, unless otherwise stated. The relationship between εA and αmodel is shown in Figure 4 (solid line). The value of αmodel is in good agreement with αMD. In the model, the critical areal strain εC was estimated to be 0.09. Additionally, γS in the free-energy model is shown in Figure 5 (solid line). The trend of the relationship between γS and εA, obtained in the free-energy model, agrees with that in the MD simulations. Therefore, all of the parameters estimated using the simulated annealing method may be considered reasonable, and the freeenergy model implemented with these parameters successfully reproduced the characteristics of the stretch-induced phase transition to the LβI phase observed in the MD simulations. Figure 6 shows the relationship between the components of the free energies and εA. For εA < εC, the total energy U is composed only of the elastic deformation energy in the Lo phase. When εA exceeds εC, the elastic energy decreases and, simultaneously, both the phase boundary energy Ub and the surface energy Uh increase. After that, Uh strongly increases with increasing εA. This indicates that the stretch-induced phase transition to the LβI phase can be explained by the balance between the energy gained from the elastic deformation energy

Figure 7. Relationship between the number of lipid molecules N and critical areal strain εC.

increasing N, and is about 0.04 at N = 6.55 × 109, which corresponds to GUVs with diameters about 20 μm. In this situation (N = 6.55 × 109 and εA = 0.04), αmodel is 5.0 × 10−4 and the domain diameter is estimated to be about 0.9 μm, if a single domain is formed in the GUVs. The phase transition can 2560


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KALo, εC decreases for N = 128, 856, and 6.55 × 109. When KALo is 250 mN/m, which corresponds to the value of a pure DPPC bilayer,49 εC is estimated to be 0.65 for N = 128. In the model, the bilayer is assumed to keep its integrity, without pore formation or rupture, even under stretching. Thus, depending on the material properties, the critical areal strain for the phase transition in the model can exceed the areal strain that leads to pore formation. Indeed, in our previous MD simulation studies,10 in which a pure DPPC bilayer composed of 128 molecules was used, pore formation occurs for εA = 0.6− 0.8. This range for the areal strain is comparable to the critical areal strain of the stretch-induced interdigitation estimated from the model (0.65). This might be a reason why stretchinduced interdigitation does not occur in the pure DPPC bilayer in the MD simulations, that is, pore formation occurs before interdigitation. For GUVs, a higher-area compressibility modulus is also required for the stretch-induced interdigitation to occur before bilayer rupture. On the basis of this argument, the higher-area compressibility modulus of the cholesterolcontaining bilayer is conducive to the realization of stretchinduced interdigitation. Li and co-workers conducted impulsive stretching experiments on red blood cells (RBCs) using laserinduced cavitation.50,51 They reported that the RBCs can withstand areal strains of 0.3 without bilayer rupture or significant leakage of preloaded fluorescent molecules from the RBCs.50,51 The RBC membranes are known to contain a large fraction of cholesterol (40−50 mol %), as does the bilayer used in this study. The stretch-induced interdigitation, which significantly increases apparent bilayer area, might help maintain the integrity of the stretched RBC membranes and prevent the leakage of intracellular molecules. Effects of Surface Tension on Interdigitation. A dominant free-energy component that hampers stretch-induced interdigitation is the surface energy Uh (Figure 6). This surface energy is due to the exposure of the tips of the hydrophobic tails to the water in the LβI phase. The relationship between the surface tension in the LβI phase σLi and εC for N = 6.55 × 109 is shown in Figure 9. With a decrease in σLi, εC decreases linearly,

be explained on the basis of the balance among Ue, Ub, and Uh (Figure 6). The latter two values are energy losses that accompany the phase transition. Because Ue and Uh are proportional to N and Ub is proportional to √N (eqs 1−3), the contribution of Ub to U becomes relatively small for large values of N. Thus, the phase transition is expected to occur under smaller areal strains in larger bilayers. Micropipette aspiration experiments38 on GUVs have shown that some cholesterol-containing bilayers can withstand areal strains up to 0.05. In such stressed GUVs, the stretch-induced phase transition to the LβI phase would occur before the bilayer rupture. Additionally, the LβI phase domain is expected to be large enough to be observed under microscope if successfully labeled with fluorescent dyes. For example, we suspected that the dyes to label the difference of hydrophobic thickness between the LβI and Lo phases (Figure 1) might be useful. We must note that, in the free-energy model proposed here, we considered that only a single LβI phase domain exists in the patch membrane. However, many experimental studies reported the formations of single or multiple domains in phase-separated lipid membranes.22,43−46 To express both the single- and multiple-domain formation by the free-energy model, the energetic terms, related with the domain coalescence, e.g., entropic penalty and electrical repulsion,43,46,47 might be included into the model. Nevertheless, our model presented here facilitates the experimental challenges to observe the stretch-induced interdigitation and further investigations of its mechanisms. Cholesterol Effects on Interdigitation. In previous studies,9,10 we showed that cholesterol is required for stretchinduced interdigitation so that interdigitation does not occur in pure DPPC bilayers. Cholesterol is known to increase the ordering of the coexisting phospholipids,48 which is thought to alter the mechanical properties of the bilayer, such as the area compressibility modulus KA. Figure 8 shows the relationships

Figure 8. Relationship between area compressibility modulus KALo (KALi = 0.35KALo) and critical areal strain εC.

between the area compressibility moduli and εC estimated from the free-energy model. It should be noted that the change in the bilayer composition is expected to affect both the area compressibilities of the bilayers before and after the phase transition. Thus, in Figure 8, both KALo and KALi changed under a constant ratio of KALi to KALo (KALi/KALo = 0.35). The dashed black, solid black, and solid red lines show the results for N = 128, 856, and 6.55 × 109, which correspond to the bilayer in our previous MD simulation,10 the bilayer in the current study, and GUVs with diameters of about 20 μm. With the increase in

Figure 9. Relationship between the effective surface tension in the LβI phase σLi and critical areal strain εC.

and is about 1.2 × 10−3 for σLi = 0 mN/m. This implies that bilayers become more favorable in the LβI phase when the surface tension decreases. Alcohol molecules can act as surfactants and decrease the surface tension at oil−water interfaces. At the LβI-phase bilayer−water interface, small alcohols are absorbed and are expected to decrease the surface 2561


The Journal of Physical Chemistry B tension by covering the tips of the hydrophobic tails of the phospholipid molecules in the LβI phase.52 Thus, small alcohols are not only required for chemically induced interdigitation, but they might also help induce stretch-induced interdigitation. This scenario is supported by the experimental findings reported by Tierney and co-workers,37 in which ethanolinduced interdigitation might occur in the DPPC/sterol bilayers under stretching, even when the ethanol concentration is below the threshold value required for interdigitation without stretching.

ACKNOWLEDGMENTS

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REFERENCES

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CONCLUSIONS To understand the stretch-induced phase transition from the Lo phase to the LβI phase, i.e., interdigitation, we proposed a freeenergy model of the stretched bilayer in the Lo and LβI phase coexistence state. The model included the elastic deformation energy of the bilayer, the surface energy at the bilayer−water interface, and the interphase boundary energy between the LβI and Lo phases. The material parameters used in the model were estimated from a series of MD simulations of the stretched bilayers in the Lo and LβI phase coexistence state. The model successfully reproduced the phase diagram and the relationship between the tension and areal strain obtained in the MD simulation. From the free-energy composition, the stretchinduced interdigitation was quantitatively explained by the balance between the energy gain in the elastic deformation energy in the Lo phase and the losses in the phase boundary and the hydrophobic exposure at the LβI phase bilayer−water interface. Additionally, the model predicted that the critical areal strain, at which the interdigitation starts, decreases with increases in the area of the bilayer. The same is true for increases in the area compressibility modulus of the bilayer or decreases in the surface tension in the LβI phase. This implies that when the system size increases to that used in experiments, the stretch-induced interdigitation might be favorable to a bilayer containing cholesterol molecules or in alcohol solution. These results suggest that the phase transition from the Lo phase to the LβI phase can be observed in microscopic experiments. ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b10633. Details of MD simulation parameters; simulation time for NPzA∥T MD simulations; Voronoi tessellation analysis; probability distributions of Voronoi cell area for sn-1 tails of DPPC molecules and cholesterol molecules; parameters of the free-energy model; and simulated annealing procedure (PDF)

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This work was supported by JSPS KAKENHI Grants 17K13033 and 15K01284.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +81 6 6850 6275. Fax: +81 6 6850 6173. ORCID

Taiki Shigematsu: 0000-0001-8881-4516 Notes

The authors declare no competing financial interest. 2562


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