Molecular dynamics simulations of phase transition of lamellar lipid membrane in water under an electric field

Abstract

Molecular dynamics simulations were conducted to investigate phase behaviors of lamellar lipid membranes in water under a uniform external electric field. Poration, deformation and fusion of membranes were induced and water/membrane interfaces changed from perpendicular to parallel to the electric field. The hydration level of the lipids determined whether the final phase was the lamellar or inverted columnar structure. The simulations provide insights into phase transitions of amphiphile solutions in electric fields and mechanisms of cell electrofusion.

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1 Introduction

When dispersing in water, phospholipids, as typical amphiphiles, form different ordered mesophases by self-assembly, in which the lipid concentration plays an important role. For example, the “ideal” sequence of lyotropic liquid crystalline phases as a function of amphiphile concentration is micelles, normal hexagonal phase, lamellar phase, and inverted hexagonal phase, with different cubic phases as intermediates between adjacent ideal phases.¹Phospholipids are a major constituent of the composition of cell membranes. In living cells, membrane morphologic change appears in many cell activities, such as exocytosis, fertilization and virus infection.^2–4 Investigations on the phase transition of phospholipid membranes can provide insights into membrane morphologic change in cell activities. In addition, the understanding of mechanisms and the control of membrane phase transitions can provide guidance on how to use them in many biotechnology applications, such as in the development of novel drug delivery systems,⁵ and in the fabrication of microdomain structures in thin films composed of amphiphilic copolymers,⁶ which have similar physical properties as those of phospholipids in water.

One way to trigger membrane phase transition is the application of an external electric field, which has been observed experimentally in polystyrene-block-polyisoprene diblock copolymer solutions. Small-angle X-ray^7,8 and neutron⁹ scattering reveal that an external electric field, typically at the strength of 10–20 kV cm⁻¹, can induce lamellae reorientation from parallel to perpendicular to the electrodes and phase transition from cubic phase to hexagonal phase. A nucleation and growth mechanism and a rotation mechanism for lamellae reorientation are proposed based on dynamic self-consistent field theory¹⁰ and the Ginzburg–Landau approach.¹¹ However, phase transition dynamics is, as yet, unclear at the atomic level, which is where the mechanisms could be further illustrated.

In cells, vesicles and planar bilayer phospholipid membranes, external electric fields can induce membrane electroporation,¹²membrane electrofusion¹³ and vesicle deformation,¹⁴ in which vesicles elongate along the direction of an applied field. The electric field strengths are about 1–12 kV cm⁻¹ for electroporation and electrofusion¹⁵ and 0.2 kV cm⁻¹ for vesicle deformation.¹⁴ One question raised is; do the three phenomena relate to each other? For example, the main argument about the mechanism of electrofusion is whether electropores are involved in fusion pathways.^16,17 In the electropore-involved pathway model, electropores are formed first in membranes under external fields and then two approached membranes fuse around the site of the electropores. In the no-electropore-involved pathway model, point-defects are induced first on membranes by external electric fields, leading to protrusions of point-defects. Two approached membranes with protrusions of point-defects will contact each other at protrusions first and then fuse themselves. Clearly, more research is needed to clarify the mechanism of electrofusion. Investigations on membrane phase transitions will elucidate the mechanism of membrane fusion, because membrane phase transitions from lamellar phase to inverted phase, such as inverted hexagonal phase or inverted cubic phase, are considered to be involved in membrane fusion.^18–23

Besides experiments, molecular dynamics (MD) simulations have become an effective way to study membrane behaviors at the atomic level.²¹ The mechanism of electroporation has been extensively studied by MD simulations with different force fields^24–28 and at hydration levels of 26 waters per lipid (w/l),²⁹ 35 w/l,²⁵ 40 w/l²⁴ and 44 w/l.²⁷ The simulations reveal that electroporation occurs under applied electric fields ranging from 0.1 to 1 V nm⁻¹ in several or tens of nanoseconds. The MD simulations indicate that the electric field gradient at the water/membrane interfaces changes greatly under an external field due to rotation of water molecules^25,26 and provides the driving force to push water molecules into the membrane.^25,27 A hydrophobic pore in which water columns are in direct contact with lipid tails is first formed in electroporation. Then, lipids around the water pores rotate until their headgroups are oriented towards the water pore, thereby changing the pore from hydrophobic to hydrophilic. The mechanism of electroporation revealed by MD simulations remains basically the same when different force fields are used in the simulations.²⁹ The applied electric fields in MD simulations are apparently much higher than the field level used in experiments. Ziegler and Vernier²⁵ and Fernández et al.³⁰ gave some explanations about the difference in applied electric field observed in experiments and simulations. Interested readers may refer to their explanations.

If the main concern is electroporation, the MD simulations may be stopped at the stage of pore formation.^24–28 However, the configuration of a simulated system is not stable just after pore formation in membranes. For example, a strongly curved membrane was obtained just after 1–2 ns of the pore formation in the MD simulations on a large system under the applied electric field of 0.5 V nm⁻¹.²⁷ The author suggested that the curvature of membrane might facilitate membrane fusion. Long-time simulations to stabilize the configuration of a simulated system are necessary to fully illustrate the morphological change of membrane under an external electric field.

In the present work, all-atom MD simulations were performed on ion-free lamellar water/phospholipids system under a uniform external electric field. The simulations investigate phase transition of amphiphilic soft matter under an applied electric field, which will explain the mechanism of membrane electrofusion.

2 Methods

The employed ion-free water/membrane/water simulation system includes TIP3P water molecules³¹ and DOPE lipids. The simulation cell includes 125 DOPE molecules. For a given number of DOPE molecules, the number of water molecules determines the hydration level. Three hydration levels of 71 w/l, 44 w/l, and 24 w/l were employed in the present work. The simulation system was built up by using CHARMM-GUI Membrane Builder.³² MD simulations were performed with the NAMD V2.7b2 program.³³ The CHARMM27 force field was used for lipids.³⁴ The long range Coulomb interactions were evaluated by the Partical Mesh Ewald (PME) method³⁵ with tin-foil boundary conditions and the grid size was smaller than 1 Å. The van der Waals interactions and the real-space Ewald interactions were cut off at 12 Å with a switch function from 10 Å to 12 Å to smoothen the cut-off. The bond lengths of hydrogen atoms were constrained by the SHAKE algorithm.³⁶ The Langevin dynamics was used to maintain simulation temperature at 310 K. All simulations were performed with constant pressure of 1 atm and periodic boundary conditions. The Nosé-Hoover method³⁷ with piston fluctuations controlled by the Langevin dynamics³⁸ was used to perform the isobaric simulations. During simulations under an external electric field, a force F_i = q_iE was applied on atom i of partial charge q_i. A uniform electric field of E = 1.4 kcal (mol Å e)⁻¹ (1 kcal (mol Å e)⁻¹ ≈ 0.435 V nm⁻¹) was applied perpendicular to the original membrane/water interface, or along the z direction, in all simulations. The integration time step was 2 fs in all production simulations and the Visual Molecular Dynamics (VMD) program³⁹ was used to visualize and analyze results.

It has to be noted that the size of the representative cell plays a crucial role in MD simulations with the periodic boundary conditions. In the present study, the size of the representative cell was determined by choosing the number of lipids close to the widely used ones in the MD simulations on membrane electroporation. The number and type of lipids used in MD simulations on membrane electroporation are 64 DMPC lipids,²⁹ 128 POPC,^24–26DLPC, DPPC and DOPC²⁵lipids and 256 DOPC lipids.²⁷ The present representative cell contains 125 DOPE lipids, the size of which is about 64 Å × 64 Å × 106 Å for the 71 w/l system after relaxation.

Caution must be used in the simulations of a constant atom number system under constant pressure. For an isotropic simulated cell, the cell lengths should be allowed to change in the same way along the x, y, and z directions, which may be called the cubic boundary condition. For the presently simulated system, in which a membrane was initially sandwiched by water, the cell lengths in the normal and tangential directions to the original interfaces between the membrane and water should vary independently, while in the two tangential directions of the x and y axes, the cell lengths should be allowed to change in the same way, which was used in the present study. We examined the influence of how to control the change in lengths of the simulated cell on the simulation results with the 71 w/l system. We employed the cubic boundary condition and the orthorhombic boundary condition, under which three cell lengths are allowed to change independently along the x, y and z directions. The lamellae reorientations were all obtained in the simulations with the three types of boundary conditions, thereby indicating the following reported simulation results did not highly depend on the boundary condition. This conclusion holds for the present simulation system, in which the membrane is relatively rigid and the thermal fluctuation is relatively low, but might not be true for other simulation systems.

After set-up of the initial simulation system at the hydration level of 71 w/l, 2 0000 steps of energy minimization were performed with the conjugate gradient method. Then, the simulation system was heated up from 10 K to 310 K gradually for the period of 0.5 ns with a time step of 1 fs. At last, 1.0 ns relaxation with a time step of 2 fs was performed at 310 K. The surface area per lipid (APL) decreases from about 69 Ų to 65.5 Ų during the initial 0.6 ns and then fluctuates around 65.5 Ų, which is comparable with the experiment value 65 ± 5 Ų.⁴⁰ If 5.5 ns more relaxation was conducted, the APL only fluctuated between 63 and 67 Ų. This means that the simulated system reaches the equilibrium state after the 1.0 ns relaxation. Then, 7 250 000 steps simulation (14.5 ns) was performed under the external electric field based on the 1.0 ns relaxation configuration. To examine the convergence of simulation results, a 10 ns extended simulation was performed after the 7 250 000 steps simulation under the external electric field, while to examine the stability of the new phase structure, 10 ns extended simulation without any external electric field was also performed after the 7 250 000 steps simulation with the external electric field.

The 44 w/l system was set up by taking out a certain number of water molecules that were far away from the membrane at both sides in the 71 w/l system after the relaxation. After that, 5 000 steps of energy minimization and 0.5 ns relaxation at 310 K were conducted to let the 44 w/l system reach equilibrium. Then, the electric field was applied and 11 250 000 steps-simulation (22.5 ns) was conducted. Similarly, the 24 w/l system was set up based on the 44 w/l system just after the relaxation. After taking a certain number of water molecules out, 5 000 steps of energy minimization and 0.5 ns relaxation at 310 K were performed. Then, MD simulations on the 24 w/l system under the external electric field were conducted for 8 750 000 steps (17.5 ns). In addition, 5.0 ns relaxation was performed on the 24 w/l system after removing the external electric field.

3 Results and discussion

The MD simulations reveal a phase transition from a lamellar phase to a new lamellar phase in the 71 w/l system. Fig. 1 shows the transition details (Movie 3 in the ESI† shows the animation). The water/membrane interfaces in the parent lamellar phase are perpendicular to the direction of the external electric field, as indicated by the arrow in the snapshot of 0.0 ns in Fig. 1, while the water/membrane interfaces in the new lamellar phase are parallel to the direction of the external electric field. The first step of the structure transition is electroporation, as shown by the snapshot at 0.8 ns in Fig. 1. Hydrophobic pores are formed in the electroporation process and then converted into hydrophilic pores,^24,25,27 as described above. The mechanism of electroporation is confirmed by the present simulations. Once water pores were formed in the membrane, more and more water molecules move into the water pores and pore diameters expand quickly, as indicated by the snapshot at 2.2 ns in Fig. 1. At the same time, the membranes deform and elongate along the direction of the external electric field. The elongated membranes become longer so that they will contact adjacent neighbors. Finally, the membranes fuse themselves with neighbors, leading to a complex cubic structure, in which both water and membranes have 3-dimensional connections, as indicted by the snapshots at 3.0 ns and 6.0 ns in Fig. 1. The snapshots at 6.0 ns and 10.0 ns in Fig. 1 show the breaking of the membranes in their original in-plane direction and the initial formation of new lamellar membranes with the water/membrane interfaces roughly parallel to the direction of the external electric field. In the new membranes in the initial state, pores exist and the pore central axes are roughly perpendicular to the external electric field, as shown in the snapshot at 10.0 ns in Fig. 1. The pore size is gradually reduced and finally disappears, which is illustrated by the snapshot at 11.5 ns in Fig. 1. In the meantime, the interfaces between water and the new lamellar membranes become flat, thereby a new lamellar phase is formed at last with water/membrane interfaces parallel to the external electric field, as shown by the snapshot at 14.5 ns in Fig. 1.

Fig. 1 Snapshots of typical structures during membrane phase transition of the system with the hydration level of 71 water molecules per lipid. Lipid headgroups are shown in red and lipid tails in cyan. Lipids cross the periodic boundaries are not wrapped. Water molecules in the representative simulation cell and in images are shown in blue and ice-blue, respectively, to distinguish the representative cell. The snapshot at 0.8 ns is a close view of electroporation. Snapshots at 11.5 ns and 14.5 ns show only the representative simulation cell for clarity. Other snapshots are composed of 3 × 2 × 2 representative simulation cells to show membrane elongation, fusion and rotation. Water in the right images and lipids in the left images are removed for clarity of membranes and water, respectively. ↑E indicates the direction of the external electric field and ⊙E shows the electric field normally towards the outside direction of the paper.

The two 10 ns extended simulations with and without the external electric field exhibited the same results, in that the newly formed lamellar configuration remained the same as that just after the 14.5 ns simulation under the electric field, thereby indicating that the new lamellar configuration is stable regardless of the applied electric field. The APL of the membrane, however, decreased during the 10 ns extended simulations from about 78 Ų to about 72 Ų with the applied electric field or to 73.5 Ų without any applied electric field. As mentioned above, the APL might fluctuate with a magnitude of a few Ų. A large number of simulations with statistic analysis might be required to investigate the effect of applied electric field on the APL of the membrane, which is beyond the scope of the present study. Nevertheless, if the final morphology of the membrane is the main concern, we may approximately regard that the simulated system is converged to a steady state after the 7 250 000 steps simulation with the external electric field.

Fig. 2 shows snapshots of the initial and the final structures in the 44 w/l system. The phase transition dynamics is nearly the same as that in the 71 w/l system (animation of the phase transition dynamics can be found in Movie 2 in the ESI†). However, there are many defects in the new lamellar structure, which are tiny water pores in the center of the two leaflets in the newly formed membranes, as shown by the snapshot at 22.5 ns in Fig. 2. The water cylinder defects could connect to the bulk water sometimes at the edge of the simulation cell. The lamellar water/membrane interfaces and the water/membrane interfaces in the tiny water pores of the final phase are parallel to the external electric field.

Fig. 2 Snapshots of the initial and final structures for the system with the hydration level of 44 w/l. The representative scheme is the same as that used in Fig. 1. There are water cylinder defects in the center of two leaflets of the newly formed bilayer membrane.

Fig. 3 shows phase transition from a lamellar phase, the snapshot at 0.0 ns, to an inverted tetragonal phase, the snapshots at 17.5 ns and 22.5 ns (animation of the phase transition dynamics can be found in Movie 1 in the ESI†). The initial electroporation behavior of the 24 w/l is similar to that in the 71 w/l and 44 w/l systems. However, there is no disconnection of the membranes along any direction perpendicular to the external electric field after membrane fusion. The newly formed inverted tetragonal phase is a 2-dimensional ordered square lattice composed of water pillars on the plane perpendicular to the external electric field. Each water pillar has a parallelogram structure and lipid headgroups face the water pillars. The water/membrane interfaces are all parallel to the external electric field. After the 17.5 ns simulation, the external electric field was unloaded and the simulations continued. Comparing snapshots at 17.5 ns and 22.5 ns in Fig. 3 indicates that no reversible phase transition occurs and the water pillars evolve to a more regular parallelogram structure.

Fig. 3 Snapshots of typical structures for the system with the hydration level of 24 w/l. The representative scheme is the same as that used in Fig. 1 except that the color of lipid tails in the representative simulation cell is shown in violet to illustrate the representative simulation cell because water itself cannot indicate all boundaries any more. The initial system is the snapshot at 0.0 ns. The snapshot at 17.5 ns shows the structure after simulations under the external electric field, which was removed at 17.5 ns. The final structure of the simulated system after 5 ns relaxation without the external electric field is shown in the snapshot at 22.5 ns.

There are two factors playing significant roles in the observed phase transitions. The first factor is the phospholipid concentration, as stated for the ideal phase sequence in the Introduction. Another example is the experimental observations that suggest the hydration concentration of DOPE lipids must be lower than ∼20 w/l for the formation of the inverted columnar phase.⁴¹ The present simulation results are consistent with the experiment and the ideal phase sequence. The inverted columnar phase appeared only at the hydration level of 24 w/l. If the membrane phase transition from lamellar phase to inverted columnar phase is involved in membrane fusion,^21–23 low hydration level must be a necessary condition for membrane electrofusion. When two to-be-fused membranes are close to each other, which is the prerequisite in experiments to induce membrane electrofusion,⁴² the local hydration level must be very low, which will satisfy the requirement of low hydration level for the transition from lamellar phase to inverted columnar phase. The present simulations demonstrate that electroporation is the initial step of electrofusion. Membranes fuse themselves at the elongated points of membranes along the external electric field. Electropores form the final water columns after membrane fusion.

The second factor is obviously the application of external electric field. When an electric field is applied to a system of two dielectric media with an interface between them, the lowest free energy configuration is that the interface is parallel to the external electric field.⁴³ For example, when a solid plate inside water is under an electric field, the solid plate will rotate to make the plate surfaces parallel to the external electric field. The rotation behavior of hydrated nanoparticle plates in water under electric field has been studied by MD simulations.⁴⁴ The elongation of vesicles in the low frequency AC field might also be a result of dielectric interface orientation.¹⁴ An applied electric field provides a driving force to initiate the phase transition and plays a crucial role in the final phase structure and orientation. The present MD simulations illustrate typical reorientation dynamics of interfaces between amphiphilic soft matter and water at the atomic level. The reorientation dynamics of the water/membrane system include pore formation, deformation, fusion, fracture and pore- and crack-healing of membranes. Because membrane networks extensively exists in cells, the reorientation of water/membrane interfaces in electric fields might play important roles in biological activities.

The present results are consistent with experimental results in which lamellae reorientation and phase transition were observed in diblock copolymer solutions.^7–9 The lamellar membrane reorientation dynamics in MD simulations is similar to that described in the nucleation and growth mechanism proposed based on a self-consistent field theory.¹⁰ The reorientation dynamics is observed at the atomic level in the present MD simulations. Small domains of membrane (nuclei) form after electroporation. Via the expansion of water pores, these domains deform and elongate along the direction of the electric field, which can be seen as nuclei growth. Lastly, membrane domains recombine into lamellae parallel to the external electric field, as shown in Fig. 1 and Fig. 2.

4 Conclusions

In summary, MD simulations were performed on ion-free lamellar water/membrane systems to study the phase behavior under an external electric field. The simulation results show that the external electric field is an effective tool to induce membrane phase transition and to control the orientation of the final structure. The hydration level of membrane determines the final structure, whereas electroporation is the initial step of phase transition independent of the hydration level. Deformation, fusion, fracture and pore-resealing of the membranes were observed during the phase transitions. Complex cubic phases with 3-dimensional connections for both membrane and water appeared as the intermediate structures. The complex phase transition dynamics at the atomic level provides insights into the phase behaviors of block copolymer solutions under electric field, electroporation and electrofusion. The simulation results might inspire new experimental and theoretical work on the control of the microdomain structures of amphiphile solutions by external electric field.

Acknowledgements

The work was partially supported by a Research Project Competition Grant, RPC06/07.SC10, from the Hong Kong University of Science and Technology (HKUST) and S. Sun was partially supported by the Bioengineering Graduate Program of HKUST.

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Footnote

† Electronic supplementary information (ESI) available: Animations of phase transition at different hydration levels of lipids: Movie 1, Movie 2 and Movie 3. See DOI: 10.1039/c0sm00555j

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