(A) PM transmembrane voltage for the exponential pulse (E⁰_app = 1 kV/cm, τ_pulse = 40 μs) anodic and cathodic poles of the cell model. Δψ_{PM, anode} is displayed here as –Δψ_{PM, anode} for better comparison with the behavior of the cathodic pole. Starting at the resting potential, both Δψ_PM rise to their respective peaks, followed by a drop and a voltage-regulated plateau value of ∼0.5 V. Notably, Δψ_PM does not follow the time-dependence of the exponential pulse. After the pulse Δψ_PM remains at approximately zero voltage (depolarized PM) for the lifetime of the pores. (B) Pore energy W (relative to the minimum pore size energy W(r_{p, min} = 0.8 nm), see Supporting Material) as function of pore radius for three transmembrane potentials. For Δψ_PM = 0.5 V, the plateau value typical for conventional EP, an energy maximum at pore radius of 2.1 nm causes the part of the pore distribution (sketched by blue profile) with pore sizes smaller than 2.1 nm to shift to smaller pore sizes, and simultaneously the other part with pore sizes larger than 2.1 nm to shift to larger pore sizes. In contrast, lower (e.g., 0.4 V) and larger (e.g., 0.6 V) values of Δψ_PM lead exclusively to either pore shrinkage or pore expansion, respectively. As the postpulse transmembrane voltage is essentially zero for EP, all pores eventually shrink to minimum size in this model (reversible EP).

(Left panels) Distributed electrical response of the cell model to exponential pulse (E⁰_app = 1 kV/cm, τ_pulse = 40 μs, 1 μs rise time); color bar shows the potential scale. White dots are local membrane sites with ≥50 pores (corresponding to a pore density of N_p = 10¹³m⁻²). (Right panels) Pore histograms for the anodic and cathodic membrane side give the total number of pores and their size within intervals of 0.1 nm. (A) EP starts at t = 0.9 μs on the anodic side, followed at t = 1.0 μs on the cathodic side in panel B. Pore expansion also starts initially at the anodic side. (C) Significant pore expansion at t = 1.3 μs at both the anodic and cathodic side; the presence of intracellular equipotential lines reveal the emergence of electric fields in the cell interior. (D) At t = 31 μs, the pore histograms regain maxima at r_{p, min}, but simultaneously show nonequilibrium tails toward larger pores. Pore histograms are similar on both cell sides, anodic and cathodic side mean pore sizes, and pore number differ only slightly (see text). Note that the organelles do not show intraorganelle electric fields, as there is no organelle EP here.

Intracellular electric fields in response to the exponential pulse of Fig. 2. (A) The intracellular field E_int, at the cell center without any organelle present: a passive PM yields essentially zero E_int except during the brief pulse rise time (black). The asymptotic EP model without pore expansion leads to E_int values of ∼25% of E_app (blue). The SE EP model (based on Eq. S1 and Eq. S2 in the Supporting Material) leads to ∼50% of the applied field due to pore expansion and therefore further membrane conductance increase (red). (B–E) Local organelle transmembrane voltages change at the ERM, NOM, MIM, and MOM from their respective resting potentials by several tens of millivolts, whereby a larger size of the organelle leads to a larger change in the organelle transmembrane voltage. These deviations from organelle resting potentials (hyper- and depolarized) provide the possibility of stimulating voltage-dependent organelle channels. (F–I) Distributed electric response of the cell system model to the exponential pulse of Fig. 2 (τ_pulse = 40 μs) but for different field strengths at a time point of t = 20 μs. EP is highlighted by white dots that correspond to local sites with at least 50 pores (corresponding to a pore density of N_p = 10¹³ m⁻²). With increasing field strength, the distance of the intracellular equipotential lines decreases compared to the distance of the extracellular potentials, demonstrating increased values of the intracellular electric fields. Organelle EP emerges at larger field strengths, in particular for 2 kV/cm at the ERM (G), for 4 kV/cm at the NOM and NIM (H), and for at 7 kV/cm at the MOM (I). The boundary between the electroporated and nonelectroporated region along the PM circumference also depends on the field strength and expands toward the equatorial region for larger field strengths (also seen for the NOM) (41). Compare the progressively increased organelle EP shown here to the smaller magnitude conventional EP pulse of Fig. 2, for which there is no intracellular EP.

(A) Distributed electrical response to a 2 ms trapezoidal pulse with E⁰_app = 0.7 kV/cm at t = 0.3 ms (long after the high conductance state is achieved at the PM). EP occurs in a smaller PM region than compared to Figs. 1 and 2 due to the smaller field strength E⁰, but still sufficient to yield significant intracellular electric fields E_int, as shown by the presence of equipotential lines inside the cell. (B) Transients of resulting transmembrane voltages changes, Δψ_ERM(t), at various local sites of the ERM in panel A. Δψ_ERM(t) starts off at the ERM resting potential of 0.09 V and returns to this value postpulse. During the pulse, significant values of Δψ_ERM(t) in duration and magnitude for channel activation are shown.