Self-Organization and Fractality in the Metabolic Process of Glycolysis

TL;DR

This paper models glycolysis as a self-organizing, fractal process using dynamical systems theory, revealing conditions for chaos, bifurcations, and stability in cellular metabolism.

Contribution

It introduces a mathematical framework applying dissipative structures theory to glycolysis, exploring self-organization, chaos, and bifurcation phenomena in metabolic dynamics.

Findings

Identification of conditions for self-organization in glycolysis

Demonstration of chaotic modes and bifurcation cascades

Quantitative analysis of strange attractors and predictability

Abstract

Within a mathematical model, the metabolic process of glycolysis is studied. The general scheme of glycolysis is considered as a natural result of the biochemical evolution. By using the theory of dissipative structures, the conditions of self-organization of the given process are sought. The autocatalytic processes resulting in the conservation of cyclicity in the dynamics of the process are determined. The conditions of breaking of the synchronization of the process, increase in the multiplicity of a cyclicity, and appearance of chaotic modes are studied. The phase-parametric diagrams of a cascade of bifurcations, which characterize the transition to chaotic modes according to the Feigenbaum scenario and the intermittence, are constructed. The strange attractors formed as a result of the funnel effect are found. The complete spectra of Lyapunov indices and divergences for the obtained modes are calculated. The values of KS-entropy, horizons of predictability, and Lyapunov dimensions of strange attractors are determined. Some conclusions concerning the structural-functional connections in glycolysis and their influence on the stability of the metabolic process in a cell are presented.