Electric field-induced breakdown of lipid bilayers and cell membranes: A thin viscoelastic film model

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Abstract
A simple viscoelastic film model is presented, which predicts a breakdown electric potential having a dependence on the electric pulse length which approximates the available experimental data for the electric breakdown of lipid bilayers and cell membranes (summarized in the reviews of U. Zimmermann and J. Vienken, 1982,J. Membrane Biol. 67:165 and U. Zimmermann, 1982,Biochim. Biophys. Acta 694:227). The basic result is a formula for the time τ of membrane breakdown (up to the formation of pores): τ=α(μ/C)/(ε m 2 ε 0 2 U 4/24σGh 3+T 2/σGh−1), where α is a proportionality coefficient approximately equal to ln(h/2ζ0),h being the membrane thickness and ζ0 the amplitude of the initial membrane surface shape fluctuation (α is usually of the order of unity), μ represents the membrane shear viscosity,G the membranes shear elasticity modules, ε m the membrane relative permittivity, ε0=8.85×10−12 Fm,U the electric potential across the membrane, σ the membrane surface tension andT the membrane tension. This formula predicts a critical potentialU c ;U c =(24σGh 3/ε m 2 ε 0 2 )1/4 (for τ=∞ andT=0). It is proposed that the time course of the electric field-induced membrane breakdown can be divided into three stages: (i) growth of the membrane surface fluctuations, (ii) molecular rearrangements leading to membrane discontinuities, and (iii) expansion of the pores, resulting in the mechanical breakdown of the membrane.