**1. Introduction**

Biological membranes, the barriers that envelope the cell and its inner organelles, play an important role in the physiology and functionality of cells. Although biological membranes are composed of lipids, proteins, and small amounts of carbohydrates, the barrier function is assured by the thin lipid bilayer. Basic understanding of barrier properties of biological membranes can be obtained by investigating model systems, such as artificial liposomes or vesicles, which mimic the geometry and size of the cell membrane but are devoid of ion channels and the multitude of other embedded components, commonly present in the cell membrane. The simplest model of a cell membrane patch is a planar lipid bilayer. The chemical composition of the planar lipid bilayer can be chosen in advance and is therefore well defined. However, to mimic a non-curved fragment of the cell membrane, the planar lipid bilayer should separate two electrolytes. Therefore, the planar lipid bilayer is usually vertically formed across a small aperture in a hydrophobic partition that separates two compartments filled with electrolytes [1]. Visual observation of the planar lipid bilayer in such an experimental system is limited. However, electrodes immersed in the electrolyte permit measurements of electric parameters of the planar lipid bilayer. As a planar lipid bilayer can be electrically considered as a non-perfect capacitor, the capacitance *C* of an ideal capacitor and the resistance *R* of a resistor in parallel both describe planar lipid bilayer's characteristic [2,3]. Voltage-controlled and current-controlled

**Citation:** Maˇcek Lebar, A.; Miklavˇciˇc, D.; Kotulska, M.; Kramar, P. Water Pores in Planar Lipid Bilayers at Fast and Slow Rise of Transmembrane Voltage. *Membranes* **2021**, *11*, 263. https://doi.org/10.3390/ membranes11040263

Academic Editors: Francisco Monroy and Monika Naumowicz

Received: 7 March 2021 Accepted: 29 March 2021 Published: 5 April 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

methods enable observing electrical properties of the planar lipid bilayer and its structural changes that are reflected in the electrical characteristics [4–7].

The capacitance *C* is the parameter considered as the best tool for probing the stability and proper formation of planar lipid bilayer and for this reason, it is measured for each planar lipid bilayer studied with electrical methods, even when other properties are in the focus of investigation. For comparison between different studies, the measured value of the capacitance is normalized by the area of planar lipid bilayer to determine the specific capacitance *c* [8].

An exposure of planar lipid bilayer to external electrical stimulus and formation of transmembrane voltage alter both electrical parameters of planar lipid bilayer model, *R* and *C*. Molecular dynamics (MD) simulations have shown that small so-called water fingers are formed on both sides of the planar lipid bilayer in the presence of transmembrane voltage and create water or hydrophobic pores [9,10]. The lipids adjacent to the water molecules inside the pores start reorienting their polar headgroups toward water molecules and stabilizing the pores into hydrophilic state, which allows more water and ions to enter the pores. These conductive paths reduce *R* of the planar lipid bilayer. At low transmembrane voltages, when pores are not created yet, a capacitance increase can be observed. An electrostrictive thinning of the planar lipid bilayer has been suggested as the mechanism responsible for this phenomenon [11,12]. The capacitance of the planar lipid bilayer depends on applied voltage *U* according to the equation

$$\mathcal{C}(\mathcal{U}) = \mathcal{C}\_0[1 + a\mathcal{U}^2].\tag{1}$$

where *C*<sup>0</sup> is the planar lipid bilayer capacitance at zero transmembrane voltage, and *α* is the proportionality coefficient. Experiments revealed that its value is around 0.02 *V* −2 [11], while using numerical models it was assessed to be in the range of 0.053–0.082 *V* −2 [13]. However, at higher transmembrane voltages, appearance of water and hydrophilic pores leads to reduction of the planar lipid bilayer capacitance, due to significant difference in dielectric constant values of lipid bilayer and water [14,15]. A long-lasting exposure to strong electric stimulus causes irreversible damage to a planar lipid bilayer. Electrical measurements permit determination of the breakdown voltage value *Ubr*.

Hydrophobic pores formed in planar lipid bilayer were first hypothesized decades ago in Abidor's theory of electroporation [16] and as water pores successfully modeled by molecular dynamic simulation [17]. Since such water pores are very small transient structures, they cannot be directly observed. As far as we know, the only study that associated experimental data with the existence of hydrophobic pores in the planar lipid bilayers were reported by Anosov et al. [18]. The experimentally observed increase in the variance of membrane current, that was attributed to small current fluctuations due to membrane capacitance changes, was connected to the number of hydrophobic pores in the membrane during the phase transition. Even experimental information about conducting hydrophilic pores and their characteristics comes only from indirect measurements, like current fluctuations measurements [19], voltage fluctuations measurements [20,21], or observing voltage drops [22]. Recently, Akimov et al. [15,23] introduced an improved theory on the pore formation, which allows modeling continuous trajectories of pore formation, both in the absence and presence of stress conditions. The theory nicely explains the complex behavior of pores during their formation under lateral tension, even in various loading rates regimes that were studied in giant unilamellar vesicles (GUV) aspiration experiments [24]. Namely, at low loading rates, GUV membrane ruptured at small tensions and, according to theory, membrane breakdown is governed by the pore expansion. On the other hand, at high loading rates, GUV membrane rupture occurs at high values of tensions and is theoretically limited by water pore formation, which is lipid type (curvature) dependent. Akimov's theory predicts that the planar lipid bilayer, exposed to the electric field, behaves similarly as in the presence of lateral tension.

To explore if different membrane rupture mechanisms can be predicted also from experiments in which transmembrane voltage is raised at various rates, we exposed pla-

nar lipid bilayers to linearly rising voltage or current signals of different slopes. Planar lipid bilayers were formed using two types of lipid molecules: 1-pamitoyl 2-oleoyl phosphatidylcholine (POPC), lipid molecules with a zwitterionic head group and almost zero spontaneous curvature, negatively charged 1-pamitoyl 2-oleoyl phosphatidylserine (POPS) molecules with negative spontaneous curvature, as well as mixture of both lipid types in a 1:1 ratio. For each planar lipid bilayer composition, *C* was measured using two different methods—discharge pulse [4,25] and voltage to period converter [26,27]. Changing rates of transmembrane voltage rise and measuring *Ubr* and time at which planar lipid bilayer rupture occurs *tbr*, we evaluated changes in *C* that correspond to water pores, estimated water pore radius at the rupture moment, and calculated the fraction of planar lipid bilayer area that is occupied by water pores.
