The molecular basis of electroporation
© Tieleman; licensee BioMed Central Ltd. 2004
Received: 01 February 2004
Accepted: 19 July 2004
Published: 19 July 2004
Electroporation is a common method to introduce foreign molecules into cells, but its molecular basis is poorly understood. Here I investigate the mechanism of pore formation by direct molecular dynamics simulations of phospholipid bilayers of a size of 256 and of more than 2000 lipids as well as simulations of simpler interface systems with applied electric fields of different strengths.
In a bilayer of 26 × 29 nm multiple pores form independently with sizes of up to 10 nm on a time scale of nanoseconds with an applied field of 0.5 V/nm. Pore formation is accompanied by curving of the bilayer. In smaller bilayers of ca. 6 × 6 nm, a single pore forms on a nanosecond time scale in lipid bilayers with applied fields of at least 0.4 V/nm, corresponding to transmembrane voltages of ca. 3 V. The presence of 1 M salt does not seem to change the mechanism. In an even simpler system, consisting of a 3 nm thick octane layer, pores also form, despite the fact that there are no charged headgroups and no salt in this system. In all cases pore formation begins with the formation of single-file like water defects penetrating into the bilayer or octane.
The simulations suggest that pore formation is driven by local electric field gradients at the water/lipid interface. Water molecules move in these field gradients, which increases the probability of water defects penetrating into the bilayer interior. Such water defects cause a further increase in the local electric field, accelerating the process of pore formation. The likelihood of pore formation appears to be increased by local membrane defects involving lipid headgroups. Simulations with and without salt show little difference in the observed pore formation process. The resulting pores are hydrophilic, lined by phospholipid headgroups.
Electric fields can induce pore formation and other structural defects in lipid membranes, including cell membranes and skin [1, 2]. Electroporation is widely used in the laboratory for gene transfection, introduction of polar and charged molecules such as dyes, drugs, proteins and peptides and also has applications in drug delivery in cancer treatment [3–8]. Electropermeabilized vesicles are more prone to fuse with cells and can be loaded with a wide range of (drug) molecules . Most of our experimental understanding of electroporation is derived from experiments on black lipid membranes [10, 11], and it is generally assumed that aqueous pores lined with phospholipid headgroups are created in the membrane [1, 12]. Although several models are available that predict aspects of the size and spatial distributions of pores, the molecular basis of pore formation remains poorly understood. We have recently shown that pore formation by mechanical stress and by electric fields can be studied by detailed computer simulations . Here I propose a mechanism for the molecular basis of electroporation based on extensive computer simulations of dioleoylphosphatidyl-choline (DOPC) bilayers in which the formation of water-filled pores can be followed at atomic resolution, and of a simpler system that allows detailed numerical analyses of the interactions of water with the electric field. Such simulations use a realistic description of the interactions between lipid and water atoms and have become a very powerful technique to study lipids and membrane proteins . The results show, surprisingly, that the initial steps of pore formation do not seem to depend on the nature of the lipid headgroups but are determined by the increased likelihood of water defects in the membrane interior with increasing applied electric field.
The main result of the simulations are the motions of all molecules involved during pore formation in phospholipid bilayers and in a water/octane system. In this section these primary results are described, while a more detailed numerical analysis of the same process is presented in the discussion.
This bilayer is an excellent model for a membrane due to its size, which allows substantial curvature and multiple pores. It consists of over 420,000 atoms, however, and is too large for extensive simulations under different conditions because of current computational limitations. I therefore turned to a smaller bilayer (45,000 atoms) and a water/octane system (ca. 7,000 atoms) to investigate the mechanism of pore formation in more detail.
The simulations give a graphical view of the pore formation process, but why do pores form in the first place?
This gradient depends on the strength of the applied field and on the left side increases as the applied field becomes stronger.
Without applied field the local field rapidly changes direction at the interface with approximately equal magnitudes. In the presence of an applied external field, as in electroporation experiments, the local field gradient is no longer symmetric for both interfaces. On one side, the field gradient increases with a higher external potential, on the other side it decreases. To amplify the effect of the increased gradient at the positive potential side, water molecules become strongly oriented in the presence of an external field so that both the projected dipole moment in the Z-direction and the field gradient forcing these dipoles into the membrane become larger (Figure 5B), and depending on the exact location the average force due to the gradient of the field acting on water dipoles (Figure 5C). For orientation, the density profiles, showing the density of different parts in the system as a function of Z, are also shown (Figure 5D).
Local fluctuations and hydrogen bonding facilitate the process of insertion; hydrogen bonding in a hydrophobic interior is stronger than in water, so that the probability of a defect growing is substantially larger than the probability of the initial formation of a defect. If the field gradient is the driving force for water defect formation it should be expected that defect formation from both sides is not equally likely because the field gradients are not symmetric.
Indeed the formation of pores in the simple water/octane system has a much higher chance of initiating from the positive side. In 100 simulations of water/octane with an applied field of 0.8 V/nm, pore formation occurred over 90 times from positive side, while in the remaining cases substantial defects from both sides combined to form the initial single file water defect spanning the octane phase. This is consistent with the small force at the right side (high Z) of the 0.5 V/nm octane/water simulation.
For the lipid bilayers the forces are more symmetric, and indeed in the small number of pore formation events observed water defects from both sides play a role. The effect of the external field on water orientation is similar in the bilayers compared to octane. On the positive side, the field causes a significant increase in water ordering, with the same direction as in water/octane despite the 'extra' negative peak at ca. 3 nm. On the negative side, the external field orders water molecules in the opposite direction than the interface does, and the average degree of orientation decreases. In fact, in the region with a water density of less than 10% of the bulk density, the orientation of water is reversed at higher fields compared to zero field.
Although the main focus of this paper is to address the question why pores form, the simulations give interesting suggestions about several experimental observations and hypotheses.
First, DNA can be transported into cells by electroporating their membranes. The molecular basis of this process is controversial; there currently appear to be two major hypotheses, without critical experiments to decide between them. In the first, DNA is transported through large stable pores that form without significant interaction with DNA and then reseal. A recent theoretical model supports this idea . The second, more widely supported, hypothesis suggests that DNA is transported into cells by direct interaction with lipids and intermediates that involve a complex of lipid components and DNA. In this case, permeabilization by an electric field might cause a number of smaller pores that by themselves are not large enough to allow DNA transport but make the membrane amenable to structural modifications that allow translocation of DNA [4, 18, 19]. The simulation of the large bilayer gives holes that have a diameter of up to 10 nm, which would be sufficiently large to allow the transport of double-stranded DNA. This is not a definitive answer, however, because the electric field in the presence of pores might be higher than can be achieved in real cell experiments (see below), and it remains to be shown that pores of this size are reversible and will reseal when the electric field is removed. A recent molecular dynamics study by Leontiadou et al. investigated the stability of small pores in bilayers and established a minimum radius at which hydrophilic pores in dipalmitoylphosphatidylcholine bilayers could be stable , but the maximum radius to my knowledge is not known, although a recent model suggests it can be quite large .
The simulations also suggest an explanation of the experimental observations that lipid headgroup charge and ionic strength of the solution appear to have little effect on electroporation but that lipid tails, cholesterol and hydrophobic polymers do have a significant effect [21–23]. First, the simulations suggest that there is almost no salt effect because the contributions of these charges to the local field gradients at the interface practically cancel. Although no electroporation in bilayers with lipids with charged headgroups was simulated, this would be an interesting extension. The important contribution appears to be the added effect of the external field at the interface, regardless of the exact composition of the interface. Second, it can be expected that changes in the hydrophobic part of the membrane (e.g. changing lipid tails from palmitoyl-oleoyl to diphytanoyl or adding cholesterol) have a significant effect because the force required to move water into the hydrophobic interior will change. For lipids that are more densely packed the formation of water defects is likely to be less favourable. For longer lipids one might also expect that the formation of water defects spanning the bilayer is less likely. For lipid bilayers with structural defects, such as those caused by surfactants, electroporation would be expected to be easier because it is more favourable for water to penetrate. These hypotheses could be tested both experimentally and in further simulations. The simulations also suggest why coating the outside of bilayers with polymers can increase the resistance to pore formation: water defects would still form but the next stages in which lipid headgroups move in to form more stable headgroup lined pores is frustrated .
An interesting and experimentally useful observation is that electropermeabilized vesicles and cells are more prone to fusion . The present simulations suggest a number of possible explanations for this, including higher curvature of these vesicles (analogous to the large bilayer), the metastable nature of the fusion pores, and increased hydrophobic surface area of electropermeabilized vesicles which would facilitate fusion. Fusion is difficult to study directly in full atomistic detail, but recently developed coarse-grained models of phospholipids have been used to investigate fusion between vesicles and could also be used to test these hypotheses [25, 26].
Although the simulations presented here give unprecedented atomistic detail of the pore-formation process, they suffer from several limitations. These include both relatively obvious limits on the size of the simulation system and the length of the simulations, but also more subtle questions on the comparison to experimental data.
The largest bilayer simulated is initially ca. 25 × 29 nm in the plane of the membrane, but the z-dimension is much shorter, initially only 8 nm. As pores form, the bilayer deforms and 'folds' (Fig. 1). This folding is influenced by the periodic boundary conditions, because these allow independent changes in x and y, the plane of the membrane. While this is the most realistic choice of boundary conditions, both the magnitude and shape of structural fluctuations is affected by the requirement that the curvature at the boundaries is continuous on each side of the box. It is also possible to scale x and y together. This would maintain the shape of the bilayer, and would make the extreme curving observed in the present simulation impossible, although it would allow curvature in the form of a 'dimple'.
An important question is to what type of experiments the simulations correspond to in terms of the incorporation of an electric field. The voltage in the simulations is maintained at a constant value of the box length times the applied field, regardless of whether a pore is present or not. The simulations assume that the potential everywhere in the system due to the applied constant field is the same as the potential caused by electrodes at a large distance from the membrane in a black lipid membrane experiment. Figure 4 shows that this is reasonable for the case without pores, but the potential distribution inside the pores is too noisy to calculate accurately from the simulation for a detailed comparison with a continuum electrostatics model. Nonetheless, experiments under voltage clamp conditions measure the current as a function of time and show a jump in conductance as pores form, but are able to maintain the original voltage in the presence of pores until the membrane ruptures. Alternatively, measurements can be done under conditions of constant current, monitoring the voltage fluctuations. An interesting question that is outside the scope of this study is how planar lipid bilayer experiments relate to electroporation experiments on whole cells. A study by Hibino et al. showed that the membrane potential has a maximum value, presumably because large pores dissipate the transmembrane potential in whole-cell solutions .
Experimentally, the critical voltage that induces pore formation in a black lipid membrane is of the order of 0.25 – 0.50 V. In the case of an applied field of 0.4 V/nm the total potential difference across the membrane is approximately 3 V, or 5–10 times as much. However, pore formation can be induced by much higher fields in the simulations, while still showing the same characteristics, although at a faster time scale. Experimentally, the lifetime of a black lipid membrane is shorter when a stronger voltage is applied, but individual pore properties do not depend on the applied voltage . It is likely pore formation in the simulations at lower potential differences would be slower but would still occur. A critical voltage cannot be determined from this type of simulations.
Exact correspondence in time scales between simulation and experiment cannot be expected because of the small size of the simulation membrane compared to experiment and the experimental time scales involved due to membrane capacitance and time resolution of the measurements . It is also not possible to predict the distribution of pore sizes or their spatial distribution in a large membrane, although the simulation of the large bilayer shows that pores can be quite close to each other without affecting each other much, at least on a nanosecond time scale. Much more extensive simulations would be required to address the important issue of pore coalescence. The system would have to be so large and the simulations so long that this is probably not practical at the moment at this level of atomistic detail, although coarser lipid models could be used . I am currently exploring this.
Detailed computer simulations of lipid bilayers in the presence of an external electric field have given an atomistic description of the process of electroporation. Pore formation is promoted by an increased likelihood of transmembrane water defects in the presence of an external electric field. Pores form even in octane layers, suggesting the primary role of water dipoles. Water defects are caused by the interaction of water dipoles with the electric field gradient at the water/lipid or water/octane interface. The presence or absence of salt has little effect on the process of pore formation. Pores in the lipid bilayers are lined by phospholipid headgroups. These results provide a better understanding of this fundamental process and form a basis for future work to investigate conditions that experimentally change electroporation phenomenology and to study transport through bilayer pores.
A bilayer of 256 DOPC lipids and 11228 water molecules was simulated without salt with applied fields of 0 V/nm (20 ns), 0.33 V/nm (50 ns), 0.4 V/nm (20 ns, pore formation at 12–14 ns) and 0.5 V/nm (pore formation at ca. 3 ns). The same bilayer with 1 M NaCl (ions replacing water molecules, resulting in 10828 water molecules, 200 Na+ ions, and 200 Cl- ions) was simulated at 0 V/nm and 0.5 V/nm (pore formation after ca. 5 ns). In addition, a bilayer consisting of 2304 lipids and 101052 water molecules was simulated with an applied field of 0.5 V/nm (multiple pores form after ca. 2.5 ns).
Water/octane simulations used a system of 182 octane and 1802 water molecules, in a box with a flexible height (ca. 6.6 nm) and an interface kept fixed at 4 × 4 nm. Simulations were 50 ns each with applied fields of 0 V/nm, 0.33 V/nm, and 0.5 V/nm (no pore formation), and 100 simulations with a field of 0.8 V/nm each until pore formation occurred, typically somewhere between 50 ps and 2 ns. The final equilibrium structure of the water/octane systems is one in which the octane slab is rotated 90 degrees, with its normal now along either the x or the y axis; this arrangement is a consequence of trying to minimize both the water/octane interface perpendicular to the applied field and minimizing the water/octane interfacial area and depends on the geometry of the box. For the present purpose of investigating the structure of the interface before pore formation and the early events of pore formation, up to the point where phospholipid headgroups would move in to line the pore, only the initial part of the water/octane simulations are relevant.
Phospholipid parameters were taken from the OPLS-based force field of Berger et al.  combined with GROMOS87 bonded parameters and parameters for the CH1 atoms in the double bonds. Parameter files are available from http://moose.bio.ucalgary.ca. Octane parameters were taken from the GROMOS96 force field 45a3 . In both cases, methyl and methylene groups are treated as united atom, so that an octane molecule has 8 atoms and a DOPC lipid 54. In all simulations the temperature was set to 300 K using the weak coupling algorithm  with τT = 0.1 ps, and pressure to 1 bar independently in each dimension with τp = 1 ps (in z only for water/octane). This allows the dimensions of the system to change in normal fluctuations but also as a response to the applied electric field or pore formation. A 1 nm Coulomb cutoff combined with Particle-Mesh-Ewald was used for electrostatic interactions  with a 1 nm cutoff for Lennard-Jones interactions. In the case of a non-zero applied field the system has a net dipole moment, which results in a surface charge on the replicated systems. In vacuum this would require a correction, but because this surface charge is exactly balanced by the tin-foil boundaries used in the PME implementation this effect is zero. The time step was 2 fs except in the last 30 ns of the DOPC bilayer with no salt and a field of 0.33 V/nm, where it was 5 fs. This larger time step has no effect on the structure of a similar dipalmitoylphosphatidylcholine bilayer as determined by 150 ns simulations in which only the time step was varied . The water model used was the Simple Point Charge model . All simulations were performed using the GROMACS set of programs [35, 36].
The charge density shown in Figure 4A and used to calculate the force on a dipole at the interface can be calculated directly from the simulation and is related to the potential through Poisson's equation which, averaged over the x, y plane, is: where the second integration constant ψ(0) is chosen as 0 V in the middle of the water phase on the left side of the box at z = 0 and the first integration constant, the electric field E(0), is taken as 0 V/nm in the middle of water layer. Because of the applied field, the actual field in the middle of the water phase is not zero and the value E(0) could be taken as Ez divided by the experimental dielectric constant of water or the dielectric constant of the SPC water model under the conditions simulated. This choice makes no difference for the field gradient and has an effect of only ca. 7 mV in the case of the strongest applied field of 0.8 V/nm in water/octane, within the accuracy of the quoted values for the transmembrane potentials. The average field is shown in Figure 4B. The calculated potential drop across each system is the applied field times the length of the simulation box in the z-dimension, validating this simple approach (Figure 4C). In the bilayers, an applied field of 0.33 V/nm corresponds to a transmembrane potential of ca. 2.6 V. In octane, a field of 0.33 V/nm corresponds to a "transmembrane" potential of ca. 2 V. This potential difference remains the same in the presence of pores. I make the assumption that the potential distribution in the system in this case is still realistic, although I have only shown this explicitly for the case without pores (figure 4).
All systems use periodic boundary conditions in three dimensions, so that effectively a multilamellar stack of bilayers (or octane slabs) with infinite dimensions in the x, y plane is simulated.
DPT is a Scholar of the Alberta Heritage Foundation for Medical Research. This work was supported by the Natural Sciences and Engineering Research Council of Canada. I thank the reviewers for their comments, as well as my group members and other colleagues for comments during the Biophysical Society annual meeting in 2004.
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