Mathematical model of transmembrane potential dynamics of loach early embryogenesis

Abstract

Heavy metals in the water environment are known to have a negative effect on the viability of fish in early development. We have discussed the influence of environmental factors on early embryo development from the viewpoint of the correlation adaptometry method. The analysis of time series with the subsequent construction of a mathematical model was used to determine the change in the greatest effect of certain types of ions on the values of the transmembrane potential for prognostic purposes. The membrane potential is accepted as an integral indicator of the state of the embryos. Structures of five elements of the same type were constructed for the time shifts from 0 to 180 minutes. Each element in the system characterizes the value of the transmembrane potential that was measured in a cell incubated in one of the five solutions during early embryo development. Mathematical models describing the cell membrane potential dynamics have been created and studied. It was noted that the transmembrane potential dynamics of embryo cells is dependent on a change in the value of the correlation coefficient between elements of the system. A decrease in the sum of the correlations between individual elements of the system with an increase in the magnitude of the time shift is established. The results of the numerical solutions of the system equations indicated the sequence of changes in the greatest effect of the incubation medium on the value of the membrane potential in cells. The study of the membrane potentials’ dynamics, using the total values of the strength of correlation, confirmed the influence of heavy metals in the incubation medium on the membrane potential of embryo cell in early development.