Membrane electroporation: chemical thermodynamics and flux kinetics revisited and refined.

The chemical thermodynamic concept for membrane electroporation is critically revisited. The hysteresis in the electric field dependence of the rapid in-field electroporation events (on the in-field hysteresis branch) and the slower post-field pore resealing process (zero-field hysteresis branch) is a typical ensemble property involving rapid single-pore opening-closing events that are temporally and spatially distributed. In the case of spherical membrane shells in homogeneous external fields, the acting local field is dependent on the polar-angular position. Hence, the experimental state distribution constant and the ensemble rate coefficients are statistical position averages; they are cosine square averages of the polar angle. Advanced flux analysis uses the concept of time-dependent flux coefficients reflecting the kinetics of the rate-limiting structural processes of electroporation and membrane resealing. The explicit integral flux equations rationalize the sigmoid onset of the in-field kinetics and quantify the post-field-stretched exponentials as exponentials of exponentials. Finally, the new analytical proposal for the evaluation of the electric field strength dependence of global cell electroporation data starts with the low-field range and continues with iterative parameter optimisation over the entire field strength range.