Pore Formation in a Membrane Submitted to High Voltages. Influence of the Membrane Vicosity

Abstract

We present here a new model of pore formation based on physical considerations of membrane energy. The idea is to revisit the pore expansion theory, as described by Weaver, Chizmadzhev et al. [4] in the 90's. We first recover the curvature-driven closure of the pore as obtain by Kroeger et al. [2], thanks to Langevin equation written on the pore area instead of the pore raldius. Then we consider the influence of the membrane viscosity around the region where pores have already appeared. This changes in membrane viscosity have been reported in the experiments of Tsai et al. [3] Around the pore region, the mobility of the lipids is constraint, which makes the membrane viscosity decrease locally. Then, once a critical pore radius is reached, it costs more to enlarge the pore, than to create another pore elsewhere. This has also an influence on the number of pores, which are hardly created in the high viscocity regions. Our model avoids an important drawback of the previsous models: the pore radius and the pore density cannot grow infinitely unlike the model of Krassowska, Neu et al [1]. After the derivation of the equations, we will present numerical simulations that corroborate quantitatively the experimental data obtained by patch-clamp experiments.[1] K. DeBruin et al. Modelling electroporation in a single cell. Biophysical Journal, 77, 1999.[2] Jens H Kroeger, et al.Curvature-driven pore growth in charged membranes during charge-pulse and voltage-clamp experiments. Biophysical journal, 96(3), 2009.[3] J. Tsai, et al. Non-brownian diffusion of membrane molecules in nanopatterned supported lipid bilayers. Nano Letters, 8(2), 2008.[4] J.C. Weaver and Y.A. Chimazdzhev. Theory of electroporation: A review. Bioelectrochemistry and Bioenergetics, 41, 1996.