Electroporation: A unified, quantitative theory of reversible electrical breakdown and mechanical rupture in artificial planar bilayer membranes

Abstract

We present a quantitative theory of electroporation of artificial planar lipid bilayer membranes. Assuming that aqueous pores are involved in electroporation, we describe the pore population of the membrane by the density function n ( r, t), where n ( r, t) d r is the number of pores with radius between r and r + d r at time t. We further assume that there is a minimum pore size r min, that pores of radius r min are created and destroyed by thermal fluctuations, and that the pore creation rate is proportional to exp( aΔφ m 2/ kT, where a is a constant, Δφ m is the membrane voltage, k is Boltzmann's constant, and T is the absolute temperature. We use a simple formula for the conductance of a pore as a function of radius, the expression for the pore energy previously derived by Pastushenko and Chizmadzhev, and a simple model of the external circuit. We solve the equations numerically and compare the solutions to the results of charge pulse experiments. In a charge-pulse experiment a membrane suffers one of four possible fates: (1) a slight increase in electrical conductance, (2) mechanical rupture, (3) incomplete reversible electrical breakdown, resulting in incomplete discharge of the membrane, or (4) reversible electrical breakdown (REB), resulting in complete discharge of the membrane. In agreement with experiment, this theory describes these four fates and predicts that the fate in any particular experiment is determined by the properties of the membrane and the duration and amplitude of the charging pulse.