Lyapunov Indices and the Poincare Mapping in a Study of the Stability of the Krebs Cycle

Abstract

On the basis of a mathematical model, we continue the study of the metabolic Krebs cycle (or the tricarboxylic acid cycle). For the first time, we consider its consistency and stability, which depend on the dissipation of a transmembrane potential formed by the respiratory chain in the plasmatic membrane of a cell. The phase-parametric characteristic of the dynamics of the ATP level depending on a given parameter is constructed. The scenario of formation of multiple autoperiodic and chaotic modes is presented. Poincaré sections and mappings are constructed. The stability of modes and the fractality of the obtained bifurcations are studied. The full spectra of Lyapunov indices, divergences, KS-entropies, horizons of predictability, and Lyapunov dimensionalities of strange attractors are calculated. Some conclusions about the structural-functional connections determining the dependence of the cell respiration cyclicity on the synchronization of the functioning of the tricarboxylic acid cycle and the electron transport chain are presented. K e y w o r d s: Krebs cycle, metabolic process, self-organization, strange attractor, bifurcation, Feigenbaum scenario.

Self-Organization and Fractality in the Metabolic Process of Glycolysis

“…Then the product of glycolysis can be used in three ways: the complete oxidac ○ V.I. GRYTSAY, 2015 tion to CO 2 and water under aerobic conditions and the fermentation to lactate or ethanol under anaerobic ones. Glycolysis includes 10 successive reactions, which are running under the action of enzymes in the cytoplasm of cells and are not connected with membrane systems.…”