Theory of electroporation of planar bilayer membranes: predictions of the aqueous area, change in capacitance, and pore-pore separation

Abstract

A large increase in the transmembrane voltage, U(t), of a fluid bilayer membrane is believed to result in the occurrence of temporary aqueous pathways ("pores") across the membrane. The number, size, and evolution dynamics of these pores are expected to be crucial to the transport of water-soluble species ranging from small ions to macromolecules such as proteins and nucleic acids. In this paper we use a transient aqueous pore theory to estimate the fraction of the membrane area, Fw(t), which is temporarily occupied by water-filled pores for short square, exponential, and bipolar square pulses. For short pulses, "reversible electrical breakdown" occurs when the transmembrane voltage reaches about 1 V, and Fw(t) is predicted to rise rapidly, but always to be less than 10(-3). The conductance of a large number of pores causes reversible electrical breakdown and prevents a significantly larger U from being reached. Despite the large dielectric constant of water, for reversible electroporation the associated change in membrane capacitance, delta C, due to the pores is predicted to be small. Moreover, for a flat membrane the minimum value of the mean pore-pore separation is large, about 60 times the minimum pore radius. In flat membranes, pores are predicted to repel, but the opposite is expected for curved cell membranes, allowing the possibility of coalescence in cell membranes. For some moderate values of U, rupture (irreversible electrical breakdown) occurs, as one or more supracritical pores expand to the membrane boundary and the entire membrane area becomes aqueous. In all cases it is found that a quantitative description of electroporation requires that a pore size distribution, rather than a single size pore.