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

A biological cell’s membrane can be electroporated to temporarily increase its permeability in a pulsed electric field (PEF) with certain parameters. This method is practical, versatile, and ubiquitous. The PEF’s heterogeneous biological structure, which includes both native pores of different sizes and different protein inclusions, has a significant impact on the process and outcome of the membrane interaction with the PEF. Heterogeneity in the electrophysical characteristics results from this. All of this ultimately has an impact on the PEF’s cellular conduction, which is both a sign of and a key element in the electroporation of the membrane as a whole. The physical characteristics of the membrane and the cells as pulsed current conductors can be modelled in order to simulate this process. It is impossible to represent all of the characteristics of the native membrane pore structure, including freshly created electropores brought about by interaction with the external PEF. However, it becomes possible to create a suitable model of electroporation if we take a probabilistic approach to the production of electropores. The mathematical model of cell conductivity is established in this chapter and is based on the likelihood that electropores will form in a membrane under the action of PEF. The concept is predicated on the idea that electropores of various sizes originate in membranes, and that their distribution obeys the standard Gauss’s law. Using an integral equation for the entire current flowing through the electropore membrane and an equation for its conductivity, which includes the creation of the electropore probability function, an integral for the total conductivity of the electroporated membrane is generated. The Fokker-Planck differential equation can be solved to obtain the broad perspective of the electropore production probability function. The overall perspective of the conductivity function relating it with electropore calibre was obtained by substituting the answer to this equation’s conductivity integral. The main reason for the exponential increase in cell conductivity with increasing electrical field strength is similar nature of conductivity increase with increasing electropore calibre up to membrane breakdown, according to a comparison of the probability electroporation model constructed with experimental data on mice oocyte conductivity. The created probability model of cell conductivity during membrane electroporation with increasing PEF agrees with the experimental results.

Author(s) Details:

V. A. Shigimaga,
State Biotechnological University, Alchevskih str. 44, Kharkov, 61002, Ukraine.

N. G. Kosulina,
State Biotechnological University, Alchevskih str. 44, Kharkov, 61002, Ukraine.

M. A. Chorna,
State Biotechnological University, Alchevskih str. 44, Kharkov, 61002, Ukraine.

S. V. Kosulin,
Department of Oncology, Kharkiv Emergency Hospital and Teaching and Research Activities, Radiotherapy and Palliative Care, Amosova str. 58, Kharkov, 61176, Ukraine.