Cell Conductivity in Pulsed Electric Field as a Probabilistic Process of Membrane Electroporation

Abstract

The membrane electroporation of a biological cell has been well known as a convenient, multipurpose and universal way of temporarily increasing its permeability in a pulsed electric field (PEF) with certain parameters. The process and result of the membrane interaction with the PEF is greatly influenced by its heterogeneous biological structure, which has both native pores of various sizes and various protein inclusions. This leads to heterogeneity of the electrophysical properties. All this ultimately affects the cellular conduction in the PEF, which are both an indicator and an integral characteristic of the electroporation process of the membrane as a whole. This process can be modelled, taking into account the physical properties of the membrane and the cells, as conductors of the pulsed current. However, to take into account in modelling all the features of the native structure of the membrane pores, as well as newly formed electropores as a result of interaction with the external PEF is impossible. But if we apply a probabilistic approach to the formation of electropores, it becomes possible to construct an adequate model of electroporation.
In this chapter is developed the mathematical model of cell conductivity, constructed on the basis of electropores formation probability in a membrane under the influence of PEF. The model is based on the assumption that in membrane are formed electropores of different calibers, the distribution of which is submits to normal Gauss's law. An integral for the total conductivity of the electroporated membrane is obtained using an integral equation for the total current through the electropore membrane and an equation for its conductivity, including the formation of the electropore probability function. The general view of electropore formation probability function is received by solution of Fokker-Planck's differential equation. Substitution of the solution of this equation to conductivity integral gave the general view of conductivity function connecting it with electropore caliber. Comparison of the constructed probability electroporation model with experimental data on mice oocyte conductivity showed that the main reason for exponential increase of cell conductivity in increasing electrical field strength is similar nature of conductivity increase with increasing electropore caliber up to membrane breakdown. The constructed probability model of cell conductivity at membrane electroporation in increasing PEF is in agreement with the experimental data.