Lyapunov Indices and the Poincar\'e Mapping in a Study of the Stability of the Krebs Cycle

TL;DR

This study uses mathematical modeling to analyze the stability and chaotic behavior of the Krebs cycle, revealing how mitochondrial potential dissipation influences cellular respiration dynamics and stability.

Contribution

It introduces a detailed analysis of the Krebs cycle's stability using Lyapunov indices and Poincaré mappings, highlighting the role of mitochondrial potential in cycle synchronization.

Findings

Identification of multiple autoperiodic and chaotic modes.

Calculation of Lyapunov spectra and fractal dimensions.

Insights into the synchronization of cellular respiration processes.

Abstract

On the basis of a mathematical model, we continue the study of the metabolic Krebs cycle (or the tricarboxilic 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. Poincar\'{e} 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 tricarboxilic acid cycle and the electron transport chain are presented.