*2.6. Calculation of a Fraction of the Planar Lipid Bilayer That Is Occupied By Pores*

In the short interval before *tbr* we can assume that non-conductive water pores are already present in the planar lipid bilayer [14,15,32]. Therefore, *Cbr* can be represented as

$$\mathbf{C}\_{br} = \sum\_{i=1}^{n} \mathbf{C}\_{pi} + \sum\_{j=1}^{m} \mathbf{C}\_{lj\prime} \tag{8}$$

where *Cpi* = *ε <sup>p</sup>ε*<sup>0</sup> *Api D* is the capacitance of the *i*th water pore and *Clj* = *ε<sup>l</sup> ε*0 *Alj D* capacitance of *j*th patch of the still intact planar lipid bilayer. *ε <sup>p</sup>* is a dielectric constant of water pores (*ε <sup>p</sup>* = 80), *ε<sup>l</sup>* is a dielectric constant of planar lipid bilayer (*ε<sup>l</sup>* = 2), and *ε*<sup>0</sup> is vacuum permittivity (*ε*<sup>0</sup> = 8.854 <sup>×</sup> <sup>10</sup>−<sup>12</sup> Fm−<sup>1</sup> ). The thickness *D* of the planar lipid bilayer was considered to be37.5 nm and 43.2 nm for POPC and POPS, respectively, obtained from MD simulation as the head to head distance between two electron density profiles [33]. Due to lack of data considering *D* of POPC:POPS mixtures in scientific literature, we determined it according to MD simulation studies which deal with structure, dynamics and hydration dynamics of the mixed lipids [34,35]. Kastel et al. showed presence of domains of POPC and POPS lipids in planar lipid bilayers formed from POPC:POPS (4:1) mixtures [35]. The value 40.0 nm was assumed for the POPC:POPS mixture. Area of the planar lipid bilayer *A* is

$$\sum\_{i=1}^{n} A\_{pi} + \sum\_{j=1}^{m} A\_{lj} = A. \tag{9}$$

Therefore, Equation (8) can be rewritten as

$$\mathcal{C}\_{br} = \frac{\varepsilon\_0}{D} (\varepsilon\_l A + \sum\_{i=1}^n A\_{pi} (\varepsilon\_p - \varepsilon\_l)). \tag{10}$$

Change in planar lipid bilayer capacitance ∆*C* due to the pore formation is

$$
\Delta \mathcal{C} = \mathcal{C}\_{br} - \mathcal{C} = -\frac{\varepsilon\_0}{D} \sum\_{i=1}^{n} A\_{pi} \cdot (\varepsilon\_p - \varepsilon\_l) \,, \tag{11}
$$

if we assume that capacitance of planar lipid bilayer *C* at the beginning of the experiment is *C* = *ε<sup>l</sup> ε*0 *A D* . To obtain the fraction of the planar lipid bilayer that is occupied by pores (*Awat*/*A*), ∑ *n <sup>i</sup>*=<sup>1</sup> *Api* is calculated from ∆*C* and normalized on the whole area of planar lipid bilayer *A*.

We calculated ∆*C* from *<sup>d</sup>*(*C*(*t*)) *dt* |*tbr*. It was multiplied by the planar lipid bilayer time constant *tc*, which was calculated from experimental data in accordance with Equation (2).
