A kinetic model of the hydrocortisone-to-prednisolone transformation by Arthrobacter globiformis is constructed using the experimental data obtained in studies of this process. Besides adequately describing experimental data, the model allows one to determine the relation between hydrocortisone oxidation and the level of endogenous substrates in bacterial cells, and the relation between the saturating concentration of hydrocortisone in the enzymic system of bacteria and the content of endogenous substrates in their cells, as well as the regulation of the transmembrane potential and the activation by the uncouplers.

Within a mathematical model, the process of interaction of the metabolic processes such as glycolysis and gluconeogenesis is studied. As a result of the running of two opposite processes in a cell, the conditions for their interaction and the self-organization in a single dissipative system are created. The reasons for the appearance of autocatalysis in the given system and autocatalytic oscillations are studied. With the help of a phase-parametric diagram, the scenario of their appearance is analyzed. The bifurcations of the doubling of a period and the transition to chaotic oscillations according to the Feigenbaum scenario and the intermittence are determined. The obtained strange attractors are created as a result of the formation of a mixing funnel. Their complete spectra of Lyapunov indices, KS-entropies, "horizons of predictability," and the Lyapunov dimensions of strange attractors are calculated. The conclusions about the reasons for variations of the cyclicity in the given metabolic process, its stability, and the physiological state of a cell are made.

This work continues the study of the earlier constructed mathematical model of the metabolic process running in a cell.We will consider auto-oscillations arising on the level of enzymesubstrate interactions in the nutrient and respiratory chains, which leads to the self-organization in autocatalysis of the integral metabolic process in cells. The auto-oscillations organize themselves in the total metabolic process of cells at autocatalysis.The behavior of the phase-parametric characteristic under the high dissipation of a kinetic membrane potentialis analyzed. All possible oscillatory modes of the system and the scenario of formation and destruction of regular and strange attractors are studied. The bifurcations of the transitions "order-chaos", "chaos-order", "chaos-chaos" and "order-order" are calculated. The total spectra of Lyapunov indices and the divergences for all types of attractors on a part of the phase-parametric characteristic under consideration are determined. For various types of strange attractors, their Lyapunov dimensions, KS-entropies, and "predictability horizons" are calculated. Some conclusions about the structure of the chaos of strange attractors and its influence on the stability of the metabolic process in a cell are drawn.

I n the present work with the help of a mathe matical modeling, we continue the study of a prostacyclinthromboxane system of blood. We will investigate how low density lipoproteins (LDL) influence the dynamics of this metabolic process. In the construction of equations (Eqs.) of our model and the determination of its parameters, we used the re sults obtained by Prof. S.D. Varfolomeev and Prof. A. T. Mevkh. Their book and the fruitful collabo ration with them [13] allow Prof. V.P. Gachok and the author to obtain calculation results similar to the experimental ones in the case where the system is in a stable state of hemostasis [49], which state charac terizes a healthy blood vessel. It is the ideal state, which is attained by synchronization of the systems of thrombosis and antithrombosis. The dynamical stationary equilibrium arises. The desynchroniza tion of these systems results in the appearance of autooscillatory modes in the metabolic process of a prostacyclinthromboxane system. If the stationary kinetics is broken so that the level of thromboxane increases, then the coagulability of blood grows as well, and the appearance of thrombosis becomes possible in the circulatory system. On the contrary, if the level of prostacyclin increases, then the coagu lability of blood decreases, and hemophilia occurs. If the autooscillatory mode arises, then the appearance of a thrombus as a result of increased coagulabil ity on some time interval and its abruption under a decrease of the coagulability in the following time interval are possible. The actions of external and in ternal factors induce various modes in the system.The metabolic process of coagulability of blood is considered by the author of the article as an open nonlinear system. The study was conducted using methods of nonlinear dynamics.The kinetic model [49] allowed us to trace the effect of various levels of activities of phospholipases and concentrations of prostacyclin and thromboxane on properties of a biosystem, to determine the role of the arachidonic acid exchange between thrombo cytes and endothelium, to analyze the influence of parallel processes running with the participation of arachidonic acid on kinetics of changes and on sta tionary levels of prostanoids, and to find the struc turalfunctional connections of selforganization in the biosystem.

Aim. To study the dynamics of auto-oscillations arising at the level of enzyme-substrate interaction in a celland to find the conditions for the self-organization and the formation of chaos in the metabolic process. Methods. A mathematical model of the metabolic process of steroids transformation in Arthrobacter globiformis. The mathematical apparatus of nonlinear dynamics. Results. The bifurcations resulting in the appearance of strange attractors in the metabolic process are determined. The projections of the phase portraits of attractors are constructed for some chosen modes. The total spectra of Lyapunov's indices are calculated. The structural stability of the attractors obtained is studied. By the general scenario of formation of regular and strange attractors, the structural-functional connections in the metabolic process in the cell are found. Their physical nature is investigated. Conclusions. The presented model explains the mechanism of formation of auto-oscillations observed in the A. globiformis cells and demonstrates a possibility of the mathematical modeling of metabolic processes for the physical explanation of the self-organization of a cell and its vital activity.