**4. Discussion**

In this study, planar lipid bilayers were exposed to linearly rising voltage and current signals of various slopes to examine *Ubr*, the change in *C* at *tbr* and the fraction of the planar lipid bilayer occupied by water pores close to the membrane rupture. Three planar lipid bilayer compositions were used; non-charged zwitterionic POPC with mostly zero spontaneous curvature, negatively charged POPS with negative spontaneous curvature, and a mixture of both lipids at 1:1 ratio.

According to the fact that special attention should be given to *C* of each planar lipid bilayer, which is included in experimental studies [8], we measured *C* by two different measuring methods. Using a widely established discharge method and voltage to period conversion method, we proved that both methods give the same results and their reproducibility is comparable.

We found that within the experimental error, the specific capacitance of the POPC planar lipid bilayer was quite similar (Table 1) to that obtained for POPC bilayers reported previously (*cBLM* <sup>≈</sup> 0.6 <sup>µ</sup>F/cm<sup>2</sup> ) [36–38], although much lower values (*cBLM* = 0.28 µF/cm<sup>2</sup> ) have also been reported [39]. In addition, the specific capacitance measured for POPS planar lipid bilayers was slightly lower than values reported in the literature for lipids of similar type (*cBLM* = 0.624 µF/cm<sup>2</sup> ) [40]. The measured specific capacitance for planar lipid bilayers formed from a POPC:POPS mixture was considerably lower than previously reported values (*cBLM* = 0.6 µF/cm<sup>2</sup> ) [41]. For all three lipid compositions, we measured lower values of the specific capacitance. The most likely due to the use of a small diameter hole (*d* = 117 µm), where the torus is not negligible and therefore the true planar lipid bilayer area is smaller than the geometric area associated with the hole diameter. Micelli et al. [42] studied the capacitance dependence on the hole radius and gave a simple relation for the width of the torus evaluation. If we consider *cBLM* = 0.6 µF/cm<sup>2</sup> as an appropriate value for the specific capacitance of POPC:POPS planar lipid bilayers, the width of the torus is 16.3 µm, which is reasonable. We think that the width of the torus can be dependent also on the planar lipid bilayer composition due to lipid molecules packing differences.

From *Ubr* measurements presented in Figure 2, it is clear that *Ubr* depends on dynamics of transmembrane voltage build-up. Application of slow slopes of linearly rising stimulus (*k<sup>i</sup>* ≤ 10 µA/s) caused high variability of *Ubr*. The mean values of *Ubr* for specific lipid composition, calculated from all measurements obtained by slow slopes of linearly rising stimulus, were not statistically different. It seems that at slow slopes of linearly rising stimulus, the planar lipid bilayer rupture process, which occurs in the range of seconds, is stochastic to a great extent. At constant voltage applied on the planar lipid bilayer, fluctuations of conductance spikes were noticed [19] and associated with defects in planar lipid bilayer that appear and vanish spontaneously. Similarly, we noticed small voltage drops during constant or slowly linearly rising stimulus and reported about them in our previous studies [22,43,44]. Such conductive defects that appear and due to slowly rising stimulus are able also to vanish, locally discharge the planar lipid bilayer and can be the reason for the high variability of *Ubr* in slow slopes of linearly rising stimulus conditions. MD simulations support the occurrence of a hydrophilic pore in planar lipid bilayers made from POPC [22] while POPS planar lipid bilayers exhibited only hydrophobic pores [44]. Although the appearance of a pore in POPS planar lipid bilayers was hydrophobic, ions were driven through the pore and discharged the planar lipid bilayer. Full recovery of the planar lipid bilayer in the case of hydrophilic pores is according to MD simulations tens of times longer as in the case of hydrophobic pores, whose lifetime is only a few nanoseconds. This is consistent with experimentally noticed voltage drops in POPS planar lipid bilayers being observed less frequently [44]. Similar observations were reported also on droplet interface planar lipid bilayers, where a population of pores of various sizes were visualized at constant voltage applied [45]. It was also reported that bilayer rupture takes place via a single electropore which grows while other pores shrink and close [45]. The lowest values of *Ubr* were obtained for POPC planar lipid bilayers. In some cases of slowly increasing transmembrane voltage, planar lipid bilayers ruptured at transmembrane voltages close to 100 mV, which is in the range of the electric potential difference across a range of biological membranes [46]. Biological membranes, however, are not homogeneous single-component bilayers, but heterogeneous media with a complex organization of lipids and proteins. If we consider planar lipid bilayers of a POPC:POPS (1:1) mixture as a very simple model of a multicomponent bilayer, the experimental results showed that *Ubr* is always higher than 200 mV, which can be an approximation of the upper value of the resting potential of biological membranes [47].

Application of fast slopes of linearly rising stimulus (4.8 kV/s ≤ *k<sup>u</sup>* ≤ 48.1 kV/s) resulted in typical "strength-duration" behavior of *Ubr*. The steeper the slope of the linearly rising stimulus, the higher the transmembrane voltage that is needed for planar lipid bilayer rupture. We fitted the strength–duration curve proposed by Dimitrov [30] to (*tbr*, *Ubr*) points measured for all three lipid compositions. The chosen strength–duration curve

considers the planar lipid bilayer as a thin viscoelastic film with fluctuating surfaces and was originally used to predict the critical voltage and critical time needed to breakdown the planar lipid bilayer at applied constant voltage. Planar lipid bilayers composed of POPS ruptured at higher voltages than planar lipid bilayers composed of POPC or the POPC:POPS mixture. According to the study on POPS/POPC (1:20) vesicles [48] and according to the study on solid-supported membranes of POPC:POPS (4:1) [35], irregularly shaped domains are formed in bilayers of POPC-POPS lipid mixtures. The formation of anionic lipid domains is mediated by the presence of cations in the environment; experiments and MD have shown that Ca2<sup>+</sup> ions force the formation of larger PS domains [49] and it is also known that monovalent ions are able to induce domain formation [50]. However, charged lipids themselves also form segregated zones in membranes [51]. Moreover, the phase transition temperatures of PS lipids are always higher than those of its PC counterparts with the same acyl chains (e.g., that of POPC is −2 °C and that of POPS is +14 °C [52]), so incomplete lateral mixing of POPC and POPS is expected.

Measurements based on 2H nuclear magnetic resonance [48,53] have shown that the lipid hydrocarbon chains in pure PC and PS membranes have different order parameters at room temperatures. Namely, although both were in a lamellar liquid crystalline phase, PS was more ordered than PC. This difference is also reflected in differences in the lipid–lipid interaction at the lipid–water interface; namely, in the presence of an electric field, the incorporation of water into the hydrophobic region of the planar lipid bilayer is significantly enhanced in the disordered domains and almost unchanged in the ordered domains [54]. From molecular dynamics simulation studies, two regions in bilayers consisting of different domains are suggested for pore formation in the presence of an electric field: lipid regions with greater disorder [54,55] and thinned regions at domain boundaries [56]. According to Reigada et al. [54], pores are formed in lipid regions with greater disorder, and the smaller the disordered domains, the faster they are electroporated.. Our results are in line with these observations. Indeed, *Ubrmin* were 0.42 ± 0.01 V and 0.54 ± 0.02 V for POPC and POPS planar lipid bilayers, respectively, implying that pores form more easily in more disordered POPC planar lipid bilayers. Moreover, for POPC planar lipid bilayers, the estimated spontaneous rate of water pore formation is six times higher than in the case of POPS planar lipid bilayers. *Ubrmin* obtained for POPC:POPS mixture was even lower, 0.38 ± 0.01 V, which is consitent with the fact that smaller disordered domains are more susceptible for pore formation. On the other hand, the formation of pores could also be expected at the domain boundaries, where near the phase transition of single-component DPPC planar lipid bilayer, pore formation induced by an external electric field was obtained in thinned regions at the liquid and gel-domain interfaces [56]. Although our experiments were performed far from the transition temperature (at least 10 °C), thinner regions with reduced stability [57] can also be attributed to boundaries between disordered POPC and more ordered POPS lipid domains.

The rate of capacitance change of the planar lipid bilayer can be related to the rate of water pores formation [14,16,18]. Ruptures of planar lipid bilayer that occur as a consequence of a slow build-up of transmembrane voltage are accompanied by very small rates of the capacitance change, which do not exhibit any specific pattern. However, the rates of capacitance change which appear at fast build-up of transmembrane voltage are exponentially dependent on *Ubr*. Similarly, Evans et al. [24] reported that the size and frequency of initial defect formation of fluid membrane vesicles depend on the loading rate of micro-pipette suction. Estimated radii of pores that govern ruptures of a planar lipid bilayer are 0.101 nm, 0.110 nm, and 0.106 nm for planar lipid bilayers composed of POPC, POPS, and POPC:POPS, respectively. The values are in the range of radii for hydrophobic pores predicted by Akimov's model [15]. The model also predicts a slightly larger radius of hydrophobic pores for planar lipid bilayers composed of lipids with negative spontaneous curvature while compared with planar lipid bilayers composed of lipids with zero spontaneous curvature, which is in agreement with our experiments and modeling.

Estimation of the area fraction that is occupied with water pores at the moment of planar lipid bilayer rupture reveals that the number of water pores is considerably lower in the case of slow build-up of transmembrane voltage. It is probably due to the fact that during slow rise of the transmembrane voltage, conducting pores are already present in planar lipid bilayer [19,45], which also changes the electrical resistance of planar lipid bilayer. It should be noted that this change was not taken into account in our calculations. Aqueous fractional area in the planar lipid bilayer due to an exponential pulse, bipolar square pulse, or a square pulse was theoretically evaluated by Freeman et al. in 1994 [14]. According to their calculations, only 0.1% of the membrane is occupied by pores, which is in good agreement with our results obtained for a fast build-up of transmembrane voltage. Moreover, recently, Anosov et al. [18] presented a computational model which predicts the number of hydrophobic pores in planar lipid bilayer using the variance of the membrane current. Their calculations showed that the area of hydrophobic pores at the phase transition (absence of a stimulus) does not exceed 4.5% of the planar lipid bilayer area, which is also in agreement with our observations.

The area fraction that is occupied with water pores is similar in the case of planar lipid bilayers formed of POPC and POPC:POPS mixture, while POPS planar lipid bilayers exhibited lower values. Lipid molecules in POPS planar lipid bilayers are more ordered than in POPC planar lipid bilayers [58] and according to MD simulations in POPS planar lipid bilayers mostly hydrophobic pores are formed where lifetime is only a few nanoseconds [44], allowing quick planar lipid bilayer discharge. As a result that pores are harder to form in ordered planar lipid bilayer, also our results show a six times lower spontaneous rate of water pore formation in comparison with POPC lipids. Therefore, it is possible that the area fraction that is occupied with water pores at the moment of planar lipid bilayer rupture in POPS planar lipid bilayers is indeed noticeably smaller in comparison with POPC and POPC:POPS planar lipid bilayers. The area fraction occupied with water pores at the moment of the planar lipid bilayers rupture is similar in the case of POPC and POPC:POPS planar lipid bilayers. Although it seems that in the planar lipid bilayers made of POPC:POPS mixture, pores are predominantly formed in more disordered POPC domains, additional experimental and theoretical studies are needed to confirm this guess.

Estimation of the radius of a water pore that governs planar lipid bilayer rupture and the fraction of planar lipid bilayer area that is occupied by water pores at the moment of rupture is based on prediction that small water pores are present in the planar lipid bilayer. Therefore, the difference in the dielectric permittivity of planar lipid bilayer (*ε* = 2) and water (*ε* = 80) is the only reason for the change in capacitance. This assumption is a considerable simplification of all phenomena that are involved in water pore creation and existence. Close to the charged surface, for example, strong orientational water dipole ordering may result in a local decrease of permittivity [59,60]. The relative permittivity of the electrolyte solution decreases with the increasing magnitude of the electric field strength. In narrow tubes, like in water pores, the water dipoles are partially oriented also close to the axis of the tube, which decreases the relative water permittivity [61]. To obtain more reliable results, at least orientational ordering of water molecules in pores and close to the membrane should be taken into account.
