Self-organization and chaos in the metabolism of a cell

TL;DR

This paper models cellular metabolism to understand how auto-oscillations and chaos emerge, revealing the conditions and mechanisms behind self-organization in cell metabolic processes using nonlinear dynamics.

Contribution

It introduces a mathematical model of steroid metabolism in bacteria that explains the formation of auto-oscillations and chaos through bifurcations and attractors.

Findings

Bifurcations lead to strange attractors in metabolism.

Phase portraits of attractors are constructed and analyzed.

Lyapunov spectra confirm the stability and chaos in the model.

Abstract

Aim. To study the dynamics of auto-oscillations arising at the level of enzyme-substrate interaction in a cell and to find the conditions for the self-organization and the formation of chaos in the metabolic process. Methods. A mathematical model of the metabolic process of steroids transformation in Arthrobacter globiformis. The mathematical apparatus of nonlinear dynamics. Results. The bifurcations resulting in the appearance of strange attractors in the metabolic process are determined. The projections of the phase portraits of attractors are constructed for some chosen modes. The total spectra of Lyapunov's indices are calculated. The structural stability of the attractors obtained is studied. By the general scenario of formation of regular and strange attractors, the structural-functional connections in the metabolic process in the cell are found. Their physical nature is investigated. Conclusions. The presented model explains the mechanism of formation of auto-oscillations observed in the A. globiformis cells and demonstrates a possibility of the mathematical modeling of metabolic processes for the physical explanation of the self-organization of a cell and its vital activity.