Development of transmembrane potential in concentric spherical, confocal spheroidal, and bispherical vesicles subjected to nanosecond-pulse electric field.

Electroporation of concentric compound spherical and confocal spheroidal as well as eccentric compound spherical vesicles, considered to be good models for corresponding nucleate cells, are investigated with an emphasis on their response to nanosecond pulse electric field (nsPEF). Analytical models are developed for the estimation of the transmembrane potential (TMP) across the bilayers of the inner and the outer vesicles and finite-element simulations are also carried out for the eccentric case. Our calculations show that with an increase in the aspect ratio, while the TMP decreases when nsPEF is used, it increases for confocal spheroids when the pulse width is greater than the membrane charging time, leading to fully charged vesicles. Bipolar pulses are shown to effectively control the TMP for a desired time period in the nsPEF regime, and a fast decay of the TMP to zero can be achieved by judicious use of pulse polarity. The external conductivity is found to significantly influence the TMP in nsPEF, unlike millisecond pulses where its effect is insignificant. Additionally the critical electric field required to induce a TMP of 1 V at the inner vesicle is presented for different pulse widths, rise time, as well as membrane capacitance, and the TMP of the outer vesicle is found to be within limits of reversible poration. It is found that the maximum TMP has a roughly linear dependence on the outer aspect ratio of the vesicle. We also introduce a new method to obtain the particular solution to the Laplace equation for bispherical system, and it is validated with finite-element simulations. Our study on nsPEF electroporation of bispherical vesicles shows that the north pole TMP is typically greater than the south pole, thereby suggesting the typical pathway a charged species might take inside an eccentric nucleate cell under electroporation.