*3.2. Modeling Results*

The rate of the planar lipid bilayer capacitance change at *tbr* was calculated for all three lipid compositions. The results are presented in Figure 3 (left side). Planar lipid breakdowns that occur at slower transmembrane voltage build-up are accompanied by very small rates of the planar lipid bilayer capacitance change (10−<sup>12</sup> <sup>≤</sup> *dC dt* <sup>≤</sup> <sup>10</sup>−<sup>10</sup> F/s). They do not follow any specific pattern. While the changes in the planar lipid bilayer capacitance for POPC planar lipid bilayer occur in the 0.11–0.32 V interval and for POPS planar lipid bilayer in 0.33–0.45 V interval, the changes in the planar lipid bilayer capacitance for POPC:POPS mixture are present also at higher voltages (≤0.65 V). The rates of the planar lipid bilayer capacitance change, which accompany fast transmembrane voltage rise, are considerably greater (10−<sup>7</sup> <sup>≤</sup> *dC dt* <sup>≤</sup> <sup>10</sup>−<sup>5</sup> F/s). As reflected in Figure 3 (right side), the rates of change of the planar lipid bilayer capacitance, in all specific compositions, are exponentially dependent on *Ubr*: ln( *dC dt* ) = *m* · *Ubr* + *n*. Referring to the kinetic model for membrane failure at fast loading rates, mentioned by Evans et al. [24], the parameter *m* is related to the pore radius *r*, in accordance with the equation *m* = *<sup>π</sup><sup>r</sup>* 2 *kBT* , where *k<sup>B</sup>* is Boltzmann constant and *T* is an absolute temperature. Estimated pore radii at the breakdown moments at room temperature (*T* = 298 K), following fast rise of transmembrane voltage were 0.101 nm, 0.110 nm, and 0.106 nm, for planar lipid bilayers composed of POPC, POPS, and POPC:POPS, respectively. Parameter exp(*n*) can be considered as a spontaneous rate of the capacitance change or a spontaneous rate of water pores formation [24]. Its calculated value is 9.1 · <sup>10</sup>−<sup>9</sup> F/s, 1.5 · <sup>10</sup>−<sup>9</sup> F/s, and 4.6 · <sup>10</sup>−<sup>9</sup> F/s for planar lipid bilayers composed of POPC, POPS, and POPC:POPS, respectively.

**Figure 3. Left** side of the figure presents the rate of the planar lipid bilayer capacitance change at *tbr* as a function of breakdown voltage *Ubr*. Results regarding fast rise of transmembrane voltage are enlarged on the **right** side. Slope *m* of the linear relation between ln( *dC dt* ) and *Ubr* is related to pore radius. See text for details.

In Figure 4, the fraction of the planar lipid bilayer area that is occupied by water pores is presented as a function of *Ubr*. In the case of slow transmembrane voltage rise, which results in low values of *Ubr*, the area of the planar lipid bilayer that is occupied by water pores is in the range of 10−6%.The fraction increases to a couple of percent in case of fast transmembrane voltage rise, which results in higher values of *Ubr* (see also data in Tables 2–4).

**Figure 4.** The fraction of the planar lipid bilayer area that is occupied by water pores as a function of *Ubr*.
