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.

Germ cells of aquatic organisms are complex systems whose growth and development depends on many factors, one of which is the composition of the aquatic environment. We used parameters in our analysis from aggregate data available from published literature. They are data of the transmembrane potential of the germinal cells of Misgurnus fossilis (Linnaeus, 1758) at the development stage from 180th to 360th minutes. Embryos were incubated in an environment with nickel, cobalt, tin, and zinc ions and without them. Plotted lines of the transmembrane potential were digitized and calibrated at intervals of 10 minutes. Rows of numerical values of the transmembrane potentials were obtained. These rows were used for calculation of autocorrelation and cross-cross-correlation functions. It was established that the transmembrane potential describes nonperiodic and quasi-periodic oscillations. The higher statistically significant values of the autocorrelation coefficients were observed in the first lags. Autocorrelation analysis indicates that the periods of oscillations of the transmembrane potential increase with the action of nickel, cobalt, tin and zinc on the germ. The phenomena and processes that occur in the germ cell are well reflected at the initial stages of the auto-correction and are lost when the magnitude of the lag increases. The degree of similarity of transmembrane potentials with the help of cross-correlation analysis is quantitatively characterized. The distribution of fluctuations of cross-correlation functions with complex dynamics, which arise with time shifts both in the forward and reverse directions, were established. It is established that for large values of time shifts, the cross-correlation coefficient is a low-informative indicator, since information about the influence of the factor on the living system is lost. A graph for a given time shift was constructed. The connection between the nodes is the magnitude of the cross-correlation coefficients between the vapor of the transmembrane potentials, which indicate the degree of similarity of the bioelectric processes. Graphs will be used for qualitative and quantitative study of system dynamics. The obtained results confirm the existence of a close relationship between environmental nickel, cobalt, tin, and zinc and the oscillation of transmembrane potential during early embryogenesis.