Modeling Electroporation in a Single Cell. I. Effects of Field Strength and Rest Potential

Abstract

This study develops a model for a single cell electroporated by an external electric field and uses it to investigate the effects of shock strength and rest potential on the transmembrane potential V(m) and pore density N around the cell. As compared to the induced potential predicted by resistive-capacitive theory, the model of electroporation predicts a smaller magnitude of V(m) throughout the cell. Both V(m) and N are symmetric about the equator with the same value at both poles of the cell. Larger shocks do not increase the maximum magnitude of V(m) because more pores form to shunt the excess stimulus current across the membrane. In addition, the value of the rest potential does not affect V(m) around the cell because the electroporation current is several orders of magnitude larger than the ionic current that supports the rest potential. Once the field is removed, the shock-induced V(m) discharges within 2 micros, but the pores persist in the membrane for several seconds. Complete resealing to preshock conditions requires approximately 20 s. These results agree qualitatively and quantitatively with the experimental data reported by Kinosita and coworkers for unfertilized sea urchin eggs exposed to large electric fields.

The current-voltage relation for electropores with conductivity gradients

“…The value for the pore size corresponds to that of an equilibrium hydrophilic pore used in standard electroporation theories; 39,40 the value for the extracellular conductivity is taken from sea urchin egg electroporation experiments, 13 which has been studied by various groups. 11,20,24 The good agreement between the analytical solution and the DNS for V m = 0.05 V is primarily attributed to a small degree of charge separation, shown in Fig. 4͑a͒.…”

“…12,18 This model was further more rigorously developed by Barnett,19 and has been widely used by various groups pursuing electroporation modeling research. [20][21][22][23][24][25][26][27][28] A salient feature of this model is the inclusion of the effects due to membrane polarization ͑the Born energy͒ and steric hindrance. The most complete formula following this approach is that by Vasilkoski et al, 26 in which the authors also take into account the spreading resistance in a manner similar to Krassowska and co-workers.…”

Probing Lipid Bilayers under Ionic Imbalance

“…Both theoretical modeling (20,21) and experiments (4) have revealed that the TMP varies at different locations of cell membranes when the cells are placed in an external electric field, as occurs in electroporation. Under these conditions, one polar end of the cell develops a large positive TMP and the other polar end develops a large negative TMP.…”

“…The threshold potential is an intrinsic property of the membrane that is related to the composition of lipids and proteins in the membrane. Several theoretical models that estimate the probability of pore formation as a function of TMP have been proposed (20,24,25), but these models employ several approximations, in particular that the structure of the membrane or the pore is not affected by an ionic imbalance.…”

Influence of Cellular Properties on the Electric Field Distribution Around a Single Cell

“…Later studies added more complexity to the modeled cell and provided insight into the factors affecting the induced transmembrane potential. This included both the electrical [5,[9][10][11][12] and geometrical properties of the cell, such as its shape [13,14] and orientation to the field [15,16]. These works stressed the importance of cellular properties in the build-up of the transmembrane potential.…”