DISCUSSION
This study is aimed at investigating electroporation of lipid bilayer models using MD simulations. In agreement with experimental speculations, we witnessed formation of water wires and water channels in the hydrophobic domain of lipid bilayers when these are subject to an electrical field in the range 0.5–1.0 V.nm–1. Permeation of the lipid core is initiated by formation of water wires that span the membrane. Those ‘defects’ grow in size, reaching the nanometer length scale, and drive the translocation of a few lipid headgroups toward the interior of the bilayer. The whole process takes place within a few nanoseconds and is more rapid for the highest field applied.
The configuration of the large pores indicates a rather nonuniform pathway with both hydrophilic and hydrophobic walls (cf. Fig. 1 e), formed by participating lipid headgroups and acyl chains. Such pores are large enough to serve as a conduit for ions and small molecules.
Under an electric field, reorientation of the solvent molecules at the bilayer-water interface is rather fast (a few picoseconds). This is followed by the slow reorientation of lipid headgroup dipoles, which appears to be the limiting step for complete reorganization of the bilayer, resulting in translocation of some lipid headgroups inside the hydrophobic membrane domain. Tieleman (2004)
has recently observed a similar behavior. The simulations here presented show furthermore that switching off the applied field for a few nanoseconds is enough to allow complete resealing and reconstitution of the membrane bilayer. The limiting step in this reverse process is now the dissociation of lipid headgroup-headgroup located in the membrane core. At the final stage of the resealing process, all are expelled toward the interface. Interestingly enough, as expected, this reorganization is random, i.e., leads to repartition of the lipid molecules independent of their initial location. The resealing of the pores in this study was achieved within a few nanoseconds. It is however important to note that the studied system did not contain ions that, if present in the pores, would stabilize the latter for a much longer time. The very short time necessary for complete resealing of the model membrane seems, though, within orders of magnitude of estimates from experiments. These range from 100 ms (Melikov et al., 2001) to 100 s (Koronkiewicz et al., 2002). In both cases, the results of the data are interpreted in terms of a memory effect, in which, before resealing, the conductive pores, after turning off the electric pulse, transform to a nonconductive metastable state with long relaxation time. It is not clear whether the disagreement between our results and those inferred from experimental data is inherent to the samples used (salt solution, complex buffers, ...) or is due to size effects. Further simulations considering larger pores and salt are necessary to shed light on the kinetics of the resealing process.
To further quantify the effect of the electric field on the membranes, we analyzed their surface tension. It is well established that pore formation in membranes may also be induced by mechanical stress. Biomembranes have been shown to rupture at surface tensions in a range from 
1 to 25 mN.m–1 depending on the lipid composition (Bloom et al., 1991; Evans and Needham, 1987; Hallett et al., 1993; Mui et al., 1993; Needham et al., 1988; Olbrich et al., 2000). On the other hand, it has been recently argued (Lewis, 2003) that the electric field causes a lateral stress in the membrane that directly influences the interfacial tension and therefore has a dominant role in determining headgroup packing and pore formation. Here it is possible to make use of computer simulation to estimate the lateral pressure exerted on a membrane when subject to a transverse electric field. In the MD simulations presented so far, the calculations were carried out at constant temperature and constant total pressure. In such a case, the system is allowed to relax and to adjust its size from the initial configuration, which permits an estimate of A, the area per lipid and hydrocarbon thickness, without imposing an external stress or a given value for A. Doing so, however, we impose that the surface tension of the system, given by 
where 
and 
are, respectively, the lateral pressure and the pressure normal to the water-lipid interface, is essentially null. To verify that application of an electric field induces a surface tension and to roughly estimate the latter, a different scheme for the simulation must be used. One possibility is to use the well-equilibrated systems as a starting point and perform MD simulations under an electric field at constant volume, i.e., without allowing relaxation of the lateral pressure. We accordingly performed such calculations on the DMPC bilayer subject to transmembrane voltages of 0.5 V.nm–1 and 1.0 V.nm–1 where a single large pore was created in the system. These calculations reveal that electroporation of the bilayer in both cases occurs within the same timescales as for previous calculations. At equilibration, the surface tension of the system 
after breakdown of the bilayer amounts to, respectively, 1 and 2 mN.m–1.
At this stage, we did not investigate the effect of the asymmetry of the bilayer induced by the field. One expects indeed that the torques on the interfacial lipid dipoles are not the same on both sides of the bilayer due to their orientations with respect to the applied field. This should contribute to the change in surface tension, and further careful investigations of pressure profiles across the bilayer are underway to quantify such effects. Such profiles would be very helpful in determining the interplay between asymmetry of the effect on the headgroups and the probability of water penetration through either interface into the hydrophobic core. We also point out that the surface tension calculated as above in the small system is likely to vary with system size and hole size and should therefore be interpreted with caution.
It is interesting, however, to note that the herein calculated strength of the surface tension induced by the electroporation is within the range of values known to produce pore formation in membrane systems. More calculations are underway to refine the data and to investigate on one hand the case of multiple pores formation, where the importance of coupling between pores formation is to be considered (Neu and Krassowska, 2003; Smith et al., 2004) and, on the other hand, how the results vary with the lipid characteristics such as headgroup charges and the nature of the lipid tails that govern, respectively, the hydrophilic and hydrophobic interactions within the membrane. It is clear, however, that our results support the model proposed by Lewis (2003) that stresses the role played by a rather significant lateral component to the stress vector generated by the transverse electric field. It may be at the origin of the differences in rupture kinetics recorded between membranes composed of lipids with difference tail compositions, such as those found between diphytanoyl-DPh and palmitoyl-oleoyl-PO membranes (Diederich et al., 1998).
One remaining crucial question is how the induced lateral stress relaxes in a macroscopic system when a voltage pulse is applied. Regardless of the topology of the bilayer, i.e., in planar lipid membranes or in a liposome, one expects that such relaxation will depend on 1), on the size of the defect created, i.e., the voltage applied; 2), the density of pores; and 3), the composition of the membrane. One may speculate that short bursts would create hydrophobic pores that may vanish and close rapidly as the stress relaxes and would correspond to the occurrence of the so-called prepore (Melikov et al., 2001) and that in the case of formation of rather hydrophilic pores stabilized by participating lipid headgroups, relaxation of the stress alone is unlikely to trigger coalescence of the pore.
We investigated the possible origins of stabilization of a membrane by integral proteins observed experimentally (Troiano et al., 1999) by studying a system consisting of an ion channel embedded in a lipid bilayer. In this case, we observed that no large pores are created in the immediate vicinity of the channel. We attributed this to the stabilizing effect of the anchoring of the lipid headgroups to the channel's side chains. Other calculations, performed on different samples, are necessary to confirm such a hypothesis.
For the DNA/lipid system, we considered a small fragment of a realistic DNA strand. In in vitro applications, the use of such plasmids concerns rather long molecules, for which our results may be viewed as investigating the behavior of one extremity. The overall process of DNA translocation thought to take place agrees with our finding, as it shows that the plasmid is stabilized in the membrane core after electroporation. DNA migration from one side of the cell to another is beyond this study, and no calculation was carried out to follow the resealing process. Electroporation-mediated DNA delivery concerns much larger plasmids than the 12 basepairs construct considered here. Transfer of such plasmids is certainly a complex process for which all aspects may not be addressed by our simulations. For instance, our data do not rule out the existence of multiple noncontinuous contacts, i.e., the occluding interaction of DNA with many small electropores (Smith et al., 2004). Similarly, the results here obtained may be envisioned as an initial step to a sliding process that is initiated from one end of the strand and that occurs at much longer timescales (De Gennes, 1999).
In comparing two systems, we have shown that, under a high electric field, the DNA strand considered diffused toward the interior of the bilayer when a pore was created beneath it, and within the same timescale, it remained at the interfacial region when no pore was present. Diffusion of the strand toward the interior of the membrane leads to a complex DNA/lipid in which the lipid headgroups encapsulate the strand. The partial charges carried by the zwitterionic phosphatidylcholine groups of the lipids are known to be efficient for neutralizing the charges carried by the DNA (Bandyopadhyay et al., 1999). Such interactions between the plasmid and the lipid contribute to the effective screening of DNA charges and therefore to the stabilization of the complex. The process herein described provides support to the gene delivery model by Teissié and collaborators (Golzio et al., 2002), in which it is proposed that only localized parts of the cell membrane brought to the permeabilized state is competent for transfer and that the proper transfer of DNA—that does not require that the electric pulse is maintained—is preceded by an "anchoring step" connecting the plasmid to the permeabilized membrane that takes place during the pulse.
It is important to note that most of the systems under study are mimics of real membranes but do not explicitly contain ion populations (except for the DNA systems, to ensure electrical neutrality). In cells, the presence of ions on both sides of the membrane may lead to a somewhat different process, as they participate in the collapse of the electrostatic potential. In such a case indeed, application of electrical fields of magnitudes similar to those applied here would lead to repartition of ions and charged species that ultimately contribute to the overall potential across the membrane. Furthermore, due to the use of periodic boundary conditions, the systems under study are, in fact, multilamellar stacks of lipid bilayers. To a certain extent, these results are more pertinent to the discussion of electroporation in the outermost Stratum Corneum skin tissues (Michaels et al., 1975).
The overall results here presented are believed to capture the essence of the several aspects of the electroporation phenomena in bilayers' membranes. It is noteworthy that electrical fields applied here, despite the fact that they are one magnitude higher than those applied experimentally for electroporation, do not lead to significant distortion of either the ion channel formed by hydrogen bonded stacks of peptide rings or the DNA fragment, which rationalizes the use of such techniques for a wide range of applications.
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