Biopolym. Cell. 2014; 30(5):403-409.
http://dx.doi.org/10.7124/bc.0008B9
Discussions
Self-organization and chaos in the metabolism of a cell
1Grytsay V. I., 2Musatenko I. V.
  1. Bogolyubov Institute for Theoretical Physics, NAS of Ukraine
    14 b Metrologichna Str., Kyiv, Ukraine, 03680
  2. Taras Shevchenko National University of Kyiv
    64, Volodymyrska Str., Kyiv, Ukraine, 01601

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.
Keywords: metabolic process, mathematical model, self-organization, bifurcation, strange attractor, Lyapunov indices
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