A mathematical model of the metabolic process of atherosclerosis.

A mathematical model of the metabolic process of atherosclerosis is constructed. The functioning of the polyenzymatic prostacyclin-thromboxane system of blood and the influence of a level of "bad cholesterol", namely low density lipoproteins (LDL), on it are studied. With the help of the numerical experiment, we analyze the influence of the concentration of molecules of fat on hemostasis of blood in blood vessels. The kinetic curves for components of the system, phase-periodic bifurcation diagrams, attractors for various modes, and Poincaré cross-section and image of a strange attractor are constructed. The complete spectra of Lyapunov's exponents, divergencies, KS-entropies, predictability horizons, and Lyapunov dimensions of the fractality of strange attractors are calculated. Conclusions about the structural-functional connections, which determine the dependence of hemostasis of a circulatory system on the level of cholesterol in blood are drawn.

Self-oscillatory dynamics of the metabolic process in a cell.

In this work, a mathematical model of self-oscillatory dynamics of the metabolism in a cell is studied. The full phase-parametric characteristics of variations of the form of attractors depending on the dissipation of a kinetic membrane potential are calculated. The bifurcations and the scenarios of the transitions "order-chaos", "chaos-order" and "order-order" are found. We constructed the projections of the multidimensional phase portraits of attractors, Poincaré sections, and Poincaré maps. The process of self-organization of regular attractors through the formation torus was investigated. The total spectra of Lyapunov exponents and the divergences characterizing a structural stability of the determined attractors are calculated. The results obtained demonstrate the possibility of the application of classical tools of nonlinear dynamics to the study of the self-organization and the appearance of a chaos in the metabolic process in a cells.

Self-organization and fractality in a metabolic processes of the Krebs cycle.

The metabolic processes of the Krebs cycle is studied with the help of a mathematical model. The autocatalytic processes resulting in both the formation of the self-organization in the Krebs cycle and the appearance of a cyclicity of its dynamics are determined. Some structural-functional connections creating the synchronism of an autoperiodic functioning at the transport in the respiratory chain and the oxidative phosphorylation are investigated. The conditions for breaking the synchronization of processes, increasing the multiplicity of cyclicity, and for the appearance of chaotic modes are analyzed. The phase-parametric diagram of a cascade of bifurcations showing the transition to a chaotic mode by the Feigenbaum scenario is obtained. The fractal nature of the revealed cascade of bifurcations is demonstrated. The strange attractors formed as a result of the folding are obtained. The results obtained give the idea of structural-functional connections, due to which the self-organization appears in the metabolism running in a cell. The constructed mathematical model can be applied to the study of the toxic and allergic effects of drugs and various substances on cell metabolism.

Kinetic model of hydrocortisone 1-en-dehydrogenation by Arthrobacter globiformis.

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.

Kinetic model for the regulation of redox reaction in steroid transformation by Arthrobacter globiformis cells.

A kinetic model of hydrocortisone transformation was developed in studies of the kinetics of biochemical systems. The regulatory bases of the model are the biosynthesis of steroid-transforming enzymes and their activity, the level of endogenous substrates, the respiratory chain activity, and the initial concentrations of reagents. When compared, the experimental data completely coincide with the results of the computer modeling, the coincidence being not only qualitative but also quantitative. It indicates that the model suggested can be used for further studies of other transformations of steroid compounds, as well as for transformation of steroid compounds under close-to-biotechnological conditions. The results obtained by means of this model permit one to trace in dynamics the behavior of a number of parameters characterizing the process which is very difficult or not feasible to do in a biochemical experiment. The following was shown: (1) the behavior of the respiratory chain (the reversible transition of its oxidized and reduced forms); (2) the change of the transmembrane potential of hydrogen ions within a far larger stretch of time than is feasible to register in a biochemical experiment; (3) the regulation of the activity of 20beta-hydroxysteroid dehydrogenase and 1, 2-reductase not only by the change in the level of endogenous substrates, but also by means of their biosynthesis; and (4) the regulatory role of 3-ketosteroid-1-en-dehydrogenase.