DOI: https://doi.org/10.15588/1607-3274-2017-4-7

MODELLING AND ANALYSIS OF ELECTROPORATION PARAMETERS OF THE MEMBRANE OF A BIOLOGICAL CELL IN A VARIED INTENSITY PULSED ELECTRIC FIELD

V. A. Shigimaga, Yu. Ye. Megel, S. V. Kovalenko, S. M. Kovalenko

Abstract


Context. The problem of constructing electroporation models for membranes of biological cells by the methods of nonlinear approximation using the experimental dependences of their specific electric conductivity on intensity pulsed electric field was solved in the paper.

Objective is a construction of models, which adequately describe the experimentally obtained nonlinear effects of the conductivity of the cell, including reversible electroporation, irreversible electrical breakdown or local reversible electrical breakdown of membranes at the fusion of two contacting cells.

Method. Polynomials of 8–10 degrees are chosen as the functions that modelling the experimental ones and the criteria for estimating the parameters of electroporation are the coordinates of the local extrema of their curvature and inflexion points that characterize the specified state of the cell membrane at current field intensity. The approximation problem was solved by the least squares method. The calculation of the estimate of the polynomials coefficients was carried out by the Gaussian elimination – the forward and reverse moves were realized. It is possible to search for extrema of the obtained polynomials of high degrees by specifying a calculation error. The root-mean-square error of the approximation is used for finding the degree of the polynomial. The current curvature of the polynomial is counted by calculating the first and second order derivatives of conductivity. The values of the curvature, which obtained via these methods, make possible to determine the inflexion points of the curve for purpose to determine breakdown of a cell membrane.

Results. Applied software was developed, polynomial models of the conductivity of a biological cell in a varied intensity pulsed electric field were constructed and their quantitative mathematical analysis was carried out by using this software. All these calculations are proved by graphs, some of which can be viewed on an enlarged scale.

Conclusions. The parameters of electroporation of a biological cell membrane obtained by analysing the curvature function of polynomial models are calculated. The developed analytical methods and software for determining the parameters of electroporation allow us to recommend them for use in practice in calculating the numerical values of the field intensity and conductivity at which specific electroporation regimes of the biological cell membrane are provided.

Keywords


Pulse electric field, intensity; electroporation; membrane; biological cell; modeling; algorithm; approximation; polynomial.

References


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