Self-organization and chaos in the metabolism of a cell

arXiv: Adaptation and Self-Organizing Systems Pub Date : 2014-09-28 DOI:10.7124/bc.0008B9

V. Grytsay, I. V. Musatenko

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引用次数: 10

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.

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细胞新陈代谢中的自组织和混乱

的目标。研究细胞内酶-底物相互作用水平上产生的自振荡动力学，寻找代谢过程中自组织和混沌形成的条件。方法。球形关节杆菌类固醇转化代谢过程的数学模型。非线性动力学的数学仪器。结果。确定了代谢过程中引起奇异吸引子出现的分岔。对所选模式，构造了吸引子相图的投影。计算了李雅普诺夫指数的总谱。研究了所得吸引子的结构稳定性。通过规律吸引子和奇异吸引子形成的一般场景，发现了细胞代谢过程中的结构-功能联系。研究了它们的物理性质。结论。该模型解释了在球形拟南草细胞中观察到的自振荡的形成机制，并证明了代谢过程的数学建模对细胞自组织及其重要活动的物理解释的可能性。

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arXiv: Adaptation and Self-Organizing Systems

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