Simulations of electroporation dynamics and shape deformations in biological cells subjected to high voltage pulses

The temporal dynamics of electroporation of cells subjected to ultrashort voltage pulses are studied based on a coupled scheme involving the Laplace, Nernst-Planck, and Smoluchowski equations. It is shown that a finite time delay exists in pore formation, and leads to a transient overshoot of the transmembrane potential V_mem beyond 1.0 V. Pore resealing is shown to consist of an initial fast process, a 10^-4 second delay, followed by a much slower closing at a time constant of about 10^-1 s. This establishes a time window for effective killing by a second pulse. The results are amply supported by our experimental data for E.-coli cells, and the time constant also matches experiments. An electromechanical analysis for analyzing cell shape changes is also presented. Our calculations show that at large fields, the spherical cell geometry can be significantly modified, and even ellipsoidal forms would be inappropriate to describe the deformation. Values of surface forces obtained are in very good agreement with the 1-10-nN/m range reported for membrane rupture. It is also demonstrated that, at least for the smaller electric fields, both the cellular surface area and volume change roughly in a quadratic manner with electric field. Finally, it is shown that the bending moments are generally quite small and can be neglected for a simpler analysis.