Instability and invariant measure in the mathematical model for oxidative phosphorylation and ATP synthesis in the cell

Abstract

The aim of this work was to analyze the process of oxidative phosphorylation and ATP synthesis in a cell using a mathematical model. The scenario of occurrence of the autoperiodic and chaotic modes depending on the ATP dissipation values was determined. The invariant measure of the strange attractor was calculated, and histograms of its projections on the phase plane were plotted. Some recommendations were made on how to eliminate biochemically the chaotic mode and restore the stability of the self-organization of the cell biosystem. Keywords: ATP, Feigenbaum scenario, invariant measure, Krebs cycle, mathematical model, oxidative phosphorylation, self-organization, strange attractor