Improved energy model for membrane electroporation in biological cells subjected to electrical pulses.

A self-consistent model analysis of electroporation in biological cells has been carried out based on an improved energy model. The simple energy model used in the literature is somewhat incorrect and unphysical for a variety of reasons. Our model for the pore formation energy E(r) includes a dependence on pore population and density. It also allows for variable surface tension, incorporates the effects of finite conductivity on the electrostatic correction term, and is dynamic in nature. Self-consistent calculations, based on a coupled scheme involving the Smoluchowski equation and the improved energy model, are presented. It is shown that E(r) becomes self-adjusting with variations in its magnitude and profile, in response to pore population, and inhibits uncontrolled pore growth and expansion. This theory can be augmented to include pore-pore interactions to move beyond the independent pore picture.

Theoretical predictions of electromechanical deformation of cells subjected to high voltages for membrane electroporation.

An electromechanical analysis based on thin-shell theory is presented to analyze cell shape changes in response to external electric fields. This approach can be extended to include osmotic-pressure changes. Our calculations demonstrate that at large fields, the spherical cell geometry can be significantly modified, and even ellipsoidal forms would be inappropriate to account for the deformation. Values of the surface forces obtained from our calculations are in very good agreement with the 1--10 mN/m range for membrane rupture reported in the literature. The results, in keeping with reports in the literature, demonstrate that the final shape depends on membrane thickness. This has direct implications for tissues in which significant molecular restructuring can occur. It is also shown that, at least for the smaller electric fields, both the cellular surface area and volume change roughly in a quadratic manner with the electric field. Finally, it is shown that the bending moments are generally quite small and can be neglected for a simpler analysis.

Self-consistent simulations of electroporation dynamics in biological cells subjected to ultrashort electrical pulses.

The temporal dynamics of electroporation of cells subjected to ultrashort voltage pulses are studied based on a coupled scheme involving the Laplace, Nernst-Plank, and Smoluchowski equations. A pore radius dependent energy barrier for ionic transport, accounts for cellular variations. 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) s delay, followed by a much slower closing at a time constant of about 10(-1) s. This establishes a time-window during which the pores are mostly open, and hence, the system is most vulnerable to destruction by a second electric pulse. The existence of such a time window for effective killing by a second pulse is amply supported by our experimental data for E. coli cells. The time constant for the longer process also matches experiments. The study suggests that controlled manipulation of the pore "open times" can be achieved through multiple, ultrashort pulses.