The Structure of a Chaos of Strange Attractors within a Mathematical Model of the Metabolism of a Cell

Grytsay, V. I.; Musatenko, I. V.

doi:10.15407/ujpe58.07.0677

Cited by 10 publications

(7 citation statements)

References 16 publications

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“…While studying the phase-parametric diagram of the system under study, we have got the scenario of adaptation modes of the metabolic process in a cell at a decrease in the dissipation of the kinetic membrane potential 𝛼 [17]. The calculated plots of the kinetics of modes manifest a stationary behavior and autoperiodic or chaotic oscillations.…”

Section: Results Of Studiesmentioning

confidence: 99%

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Spectral Analysis and Invariant Measure in the Study of a Nonlinear Dynamics of the Metabolic Process in Cells

Grytsay

2017

Ukr. J. Phys.

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The metabolic process in a cell is modeled with the use of the Fourier transformation. The histograms of the invariant measures of chaotic attractors are constructed. In particular, a scenario of adaptation of the metabolic process under a change in the dissipation of a kinetic membrane potential and the sequence of the modes of self-organization and deterministic chaos are determined. Respectively, the spectral mapping of the attractors of these modes is considered. The structural-functional connections of the metabolic process in a cell as an integral dissipative system are analyzed.K e y w o r d s: mathematical model, metabolic process, self-organization, deterministic chaos, Fourier series, strange attractor, invariant measure, bifurcation.

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Section: Results Of Studiesmentioning

confidence: 99%

“…In what follows, we will study the earlier constructed mathematical model of the metabolic process in a cell [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. The model is based on the experimental data concerning bacteria Arthrobacter globiformis at a transformation of steroids [20].…”

Section: Introductionmentioning

confidence: 99%

Spectral Analysis and Invariant Measure in the Study of a Nonlinear Dynamics of the Metabolic Process in Cells

Grytsay

2017

Ukr. J. Phys.

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“…The study of solutions of the given mathematical model (1)- (19) was performed with the help of the theory of nonlinear differential equations [28,29] and the methods of mathematical modeling of biochemical systems applied and developed in [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47].…”

Section: Mathematical Modelmentioning

confidence: 99%

Lyapunov Indices and the Poincare Mapping in a Study of the Stability of the Krebs Cycle

Grytsay

2015

Ukr. J. Phys.

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On the basis of a mathematical model, we continue the study of the metabolic Krebs cycle (or the tricarboxylic acid cycle). For the first time, we consider its consistency and stability, which depend on the dissipation of a transmembrane potential formed by the respiratory chain in the plasmatic membrane of a cell. The phase-parametric characteristic of the dynamics of the ATP level depending on a given parameter is constructed. The scenario of formation of multiple autoperiodic and chaotic modes is presented. Poincaré sections and mappings are constructed. The stability of modes and the fractality of the obtained bifurcations are studied. The full spectra of Lyapunov indices, divergences, KS-entropies, horizons of predictability, and Lyapunov dimensionalities of strange attractors are calculated. Some conclusions about the structural-functional connections determining the dependence of the cell respiration cyclicity on the synchronization of the functioning of the tricarboxylic acid cycle and the electron transport chain are presented. K e y w o r d s: Krebs cycle, metabolic process, self-organization, strange attractor, bifurcation, Feigenbaum scenario.

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“…The study of solutions of the given mathematical model (1)- (19) was performed with the help of the theory of nonlinear differential equations [25,26] and the methods of mathematical modeling of biochemical systems applied and developed by the authors in [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43].…”

Section: Mathematical Modelmentioning

confidence: 99%

“…In our studies, we used the classical tools of nonlinear dynamics [28,29] and some methods of simulation of biochemical processes developed by the authors in [30][31][32][33][34][35].…”

Section: Mathematical Modelmentioning

confidence: 99%

Self-organization and fractality in a metabolic processes of the Krebs cycle

Musatenko

2013

Ukr.Biochem.J.

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The present work continues studies of the mathematical model of a metabolic process of the Krebs cycle. We study the dependence of its cyclicity on the cell respiration intensity determined by the formation level of carbon dioxide. We constructed the phase-parametric characteristic of the consumption of a substrate by a cell depending on the intensity of the metabolic process of formation of the final product of the oxidation. The scenarios of all possible oscillatory modes of the system are constructed and studied. The bifurcations with period doubling and with formation of chaotic modes are found. Their attractors are constructed. The full spectra of indices and divergencies for the obtained modes, the values of KS-entropies, horizons of predictability, and Lyapunov dimensions of strange attractors are calculated. Some conclusions about the structural-functional connections of the cycle of tricarboxylic acids and their influence on the stability of the metabolic process in a cell are presented. K e y w o r d s : Krebs cycle, metabolic process, self-organization, strange attractor, bifurcation, Feigenbaum scenario.One of the possible problems of synergetics is the study of the internal dynamics of metabolic processes in cells. Its solution allows one to find the structural-functional connections defining the self-organization of these processes and to answer the question how the catalyzed enzymatic reactions create the internal space-time ordering of the cell life.The most general metabolic process in cells is the cycle of tricarboxylic acids [1]. This is the key stage of the respiration of all cells. In its course, the di-and tricarbon compounds, which are formed as intermediate products in the transformation of carbohydrates, fats, and proteins, are transformed up to CO 2 . In this case, the released hydrogen is oxidized further up to water, by taking the direct participation in the synthesis of ATP, being the universal energy source.Studies of the functioning of the Krebs cycle were carried out both experimentally and theretically in [2][3][4][5][6][7][8][9][10].In the study of the given process, we use the mathematical model of the growh of cells Candida utilis on ethanol, which was developed by Professor V.P. Gachok [11,12]. The analogous modeling of a growth of cells was performed independently by J. Monod, V.S. Podgorskii, L.N. Drozdov-Tikhomirov, N.T. Rakhimova, G.Yu. Riznichenko, and other researchers [13][14][15][16][17].With the help of this model, the unstable modes in the cultivation of cells observed in experiments were considered. The kinetic curves of the chaotic dynamics obtained with the help of computational experiments were in agreement with experimental data [18]. Then the given model was modified and refined in [19] due to the account for the influence of the CO 2 level on the respiration intensity. With the help of the model, the structural-functional connections of the metabolic process in a cell, which cause the appearance of complicated oscillations in the metabolic process, were invest...

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The Structure of a Chaos of Strange Attractors within a Mathematical Model of the Metabolism of a Cell

Cited by 10 publications

References 16 publications

Spectral Analysis and Invariant Measure in the Study of a Nonlinear Dynamics of the Metabolic Process in Cells

Spectral Analysis and Invariant Measure in the Study of a Nonlinear Dynamics of the Metabolic Process in Cells

Lyapunov Indices and the Poincare Mapping in a Study of the Stability of the Krebs Cycle

Self-organization and fractality in a metabolic processes of the Krebs cycle

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