A mathematical model of the metabolism of a cell. Self-organization and chaos

TL;DR

This paper models cellular metabolism using nonlinear dynamics to explore self-organization and chaos, revealing bifurcations, attractors, and transitions in metabolic processes with detailed mathematical analysis.

Contribution

It introduces a mathematical model of cell metabolism that demonstrates how chaos and self-organization emerge through bifurcations and attractor transitions.

Findings

Identification of bifurcations leading to chaos and order

Construction of phase portraits and Poincaré sections

Calculation of Lyapunov spectra confirming attractor stability

Abstract

Using the classical tools of nonlinear dynamics, we study the process of self-organization and the appearance of the chaos in the metabolic process in a cell with the help of a mathematical model of the transformation of steroids by a cell Arthrobacter globiformis. We constructed the phase-parametric diagrams obtained under a variation of the dissipation of the kinetic membrane potential. The oscillatory modes obtained are classified as regular and strange attractors. We calculated the bifurcations, by which the self-organization and the chaos occur in the system, and the transitions "chaos-order", "order-chaos", "order-order", and "chaos-chaos" arise. Feigenbaum's scenarios and the intermittences are found. For some selected modes, the projections of the phase portraits of attractors, Poincar\'e sections, and Poincar\'e maps are constructed. The total spectra of Lyapunov indices for the modes under study are calculated. The structural stability of the attractors is demonstrated. A general scenario of the formation of regular and strange attractors in the given metabolic process in a cell is found. The physical nature of their appearance in the metabolic process is studied.