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

Abstract

With the help of a mathematical model, the metabolic process of the Krebs cycle is studied. 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 a 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 metabolic process 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 the metabolism of a cell.