Stochastic model for electric field-induced membrane pores. Electroporation.

Abstract

Electric impulses (1-20 kV cm-1, 1-5 microseconds) cause transient structural changes in biological membranes and lipid bilayers, leading to apparently reversible pore formation ( electroporation ) with cross-membrane material flow and, if two membranes are in contact, to irreversible membrane fusion ( electrofusion ). The fundamental process operative in electroporation and electrofusion is treated in terms of a periodic lipid block model, a block being a nearest-neighbour pair of lipid molecules in either of two states: (i) the polar head group in the bilayer plane or (ii) facing the centre of a pore (or defect site). The number of blocks in the pore wall is the stochastic variable of the model describing pore size and stability. The Helmholtz free energy function characterizing the transition probabilities of the various pore states contains the surface energies of the pore wall and the planar bilayer and, if an electric field is present, also a dielectric polarization term (dominated by the polarization of the water layer adjacent to the pore wall). Assuming a Poisson process the average number of blocks in a pore wall is given by the solution of a non-linear differential equation. At subcritical electric fields the average pore size is stationary and very small. At supercritical field strengths the pore radius increases and, reaching a critical pore size, the membrane ruptures (dielectric breakdown). If, however, the electric field is switched off, before the critical pore radius is reached, the pore apparently completely reseals to the closed bilayer configuration (reversible electroporation ).