Self-Organization and Fractality in the Metabolic Process of Glycolysis

Grytsay, V. I.

doi:10.15407/ujpe60.12.1251

Cited by 10 publications

(8 citation statements)

References 19 publications

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“…3,a demonstrates a change of the dynamics of the metabolic process. In works [22]- [23], this part of the phase-parametric characteristic was studied Fig. 3.…”

Section: Results Of Studiesmentioning

confidence: 99%

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

Grytsay

Musatenko

2013

Ukr. J. Phys.

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This work continues the study of the earlier constructed mathematical model of the metabolic process running in a cell.We will consider auto-oscillations arising on the level of enzymesubstrate interactions in the nutrient and respiratory chains, which leads to the self-organization in autocatalysis of the integral metabolic process in cells. The auto-oscillations organize themselves in the total metabolic process of cells at autocatalysis.The behavior of the phase-parametric characteristic under the high dissipation of a kinetic membrane potentialis analyzed. All possible oscillatory modes of the system and the scenario of formation and destruction of regular and strange attractors are studied. The bifurcations of the transitions "order-chaos", "chaos-order", "chaos-chaos" and "order-order" are calculated. The total spectra of Lyapunov indices and the divergences for all types of attractors on a part of the phase-parametric characteristic under consideration are determined. For various types of strange attractors, their Lyapunov dimensions, KS-entropies, and "predictability horizons" are calculated. Some conclusions about the structure of the chaos of strange attractors and its influence on the stability of the metabolic process in a cell are drawn.

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“…3,a demonstrates a change of the dynamics of the metabolic process. In works [22]- [23], this part of the phase-parametric characteristic was studied Fig. 3.…”

Section: Results Of Studiesmentioning

confidence: 99%

“…The spectrum of Lyapunov indices was calculated, by using Benettin's algorithm with orthogonalization of the perturbation vectors within the Gram-Schmidt method [23].…”

Section: Mathematical Model and Methods Of Its Studymentioning

confidence: 99%

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

Grytsay

Musatenko

2013

Ukr. J. Phys.

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“…A mathematical model of the process under flow conditions in a bioreactor was developed by the general scheme of metabolic processes in Arthrobacter globiformis cells at a transformation of steroids [8][9][10][11][12][13][14][15][16][17][18].…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Works [8][9][10][11][12][13][14][15][16][17][18] considered the mathematical model of a bioreactor transforming steroids [19] under flow conditions depending on a change of the dissipation, the kinetic membrane potential of cells, and the input flows of a substrate and oxygen. Various scenarios of the transition from stationary modes to selfoscillatory modes with different multiplicities were presented, and the regions of the formation of strange attractors were determined.…”

Section: Introductionmentioning

confidence: 99%

Structural Instability of a Biochemical Process

Grytsay

2017

Preprint

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By the example of a mathematical model of a biochemical process, the structural instability of dynamical systems is studied by calculating the full spectrum of Lyapunov indices with the use of the generalized Benettin algorithm. For the reliability of the results obtained, the higher Lyapunov index determined with the orthogonalization of perturbation vectors by the Gram-Schmidt method is compared with that determined with the overdetermination of only the norm of a perturbation vector. Specific features of these methods and the comparison of their efficiencies for a multidimensional phase space are presented. A scenario of the formation of strange attractors at a change of the dissipation parameter is studied. The main regularities and the mechanism of formation of a deterministic chaos due to the appearance of a fold or a funnel, which leads to the uncertainty of the evolution of a biosystem, are determined.

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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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Self-Organization and Fractality in the Metabolic Process of Glycolysis

Cited by 10 publications

References 19 publications

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

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

Structural Instability of a Biochemical Process

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

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