Piecewise Linear Dynamical System Modeling Gene Network with Variable Feedback

Golubyatnikov, V. P.; Kazantsev, M. V.

doi:10.1007/s10958-018-3725-0

Cited by 3 publications

(2 citation statements)

References 9 publications

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“…In the Sobolev Institute of Mathematics SB RAS is studied the qualitative theory of dynamical systems describing various gene networks that are regulated by feedbacks. Golubyatnikov and his colleagues have studied in their works (Gaidov, Golubyatnikov, 2007;Golubyatnikov et al, 2010;Akinshin, Golubyatnikov, 2012;Golubyatnikov, Kazantsev, 2016; Golu-…”

Section: Application Of Gene Network In the Modeling Of Oscillatory Systemsmentioning

confidence: 99%

The finding and researching algorithm for potentially oscillating enzymatic systems

et al. 2021

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Many processes in living organisms are subject to periodic oscillations at different hierarchical levels of their organization: from molecular-genetic to population and ecological. Oscillatory processes are responsible for cell cycles in both prokaryotes and eukaryotes, for circadian rhythms, for synchronous coupling of respiration with cardiac contractions, etc. Fluctuations in the numbers of organisms in natural populations can be caused by the populations’ own properties, their age structure, and ecological relationships with other species. Along with experimental approaches, mathematical and computer modeling is widely used to study oscillating biological systems. This paper presents classical mathematical models that describe oscillatory behavior in biological systems. Methods for the search for oscillatory molecular-genetic systems are presented by the example of their special case – oscillatory enzymatic systems. Factors influencing the cyclic dynamics in living systems, typical not only of the molecular-genetic level, but of higher levels of organization as well, are considered. Application of different ways to describe gene networks for modeling oscillatory molecular-genetic systems is considered, where the most important factor for the emergence of cyclic behavior is the presence of feedback. Techniques for finding potentially oscillatory enzymatic systems are presented. Using the method described in the article, we present and analyze, in a step-by-step manner, first the structural models (graphs) of gene networks and then the reconstruction of the mathematical models and computational experiments with them. Structural models are ideally suited for the tasks of an automatic search for potential oscillating contours (linked subgraphs), whose structure can correspond to the mathematical model of the molecular-genetic system that demonstrates oscillatory behavior in dynamics. At the same time, it is the numerical study of mathematical models for the selected contours that makes it possible to confirm the presence of stable limit cycles in them. As an example of application of the technology, a network of 300 metabolic reactions of the bacterium Escherichia coli was analyzed using mathematical and computer modeling tools. In particular, oscillatory behavior was shown for a loop whose reactions are part of the tryptophan biosynthesis pathway.

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Section: Application Of Gene Network In the Modeling Of Oscillatory Systemsmentioning

confidence: 99%

The finding and researching algorithm for potentially oscillating enzymatic systems

et al. 2021

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“…The problem is mainly caused by the presence of clearances, dead-zone characteristics, dry friction, and switching among subsystems in the system structure, thereby leading to different nonlinear characteristics of the system in divergent motion stages. 1–4 For instance, the piecewise problem in mechanical systems may lead to system clearances because of the existence of processing error, installation error, and subsequent wear. The system clearances will change the system movement behavior and will cause repeated shocks between the components and even lead to jumping, bifurcation, and chaos.…”

Section: Introductionmentioning

confidence: 99%

Periodic response characteristics on a piecewise hysteresis nonlinear system

Wang

Chen

Liu

et al. 2019

Journal of Low Frequency Noise, Vibration and Active Control

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A piecewise hysteresis nonlinear dynamic model with nonlinear stiffness and damping is established for a system with alternating elastic constraints and hysteresis nonlinearity. First, the amplitude-frequency response equation of the system is solved by using the averaging method under periodic excitation. Two frequency regions with multiple solutions are then identified in the system, and the amplitude-frequency response characteristics under different system parameters are obtained. Thus, the influence law of different piecewise nonlinear factors on system stability is explored. Second, the bifurcation behavior of the system under different external disturbances is analyzed. Given the change of perturbation parameters, the system is found to be a complex dynamic system with alternating periodic, double periodic, and chaotic motions, and many other forms of movement. Moreover, lower buffer damping leads to the complex and unpredictable chaotic state of the system's dynamic behavior.

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Non-Uniqueness of Cycles in Piecewise-Linear Models of Circular Gene Networks

Golubyatnikov

Gradov

2021

Sib. Adv. Math.

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Piecewise Linear Dynamical System Modeling Gene Network with Variable Feedback

Cited by 3 publications

References 9 publications

The finding and researching algorithm for potentially oscillating enzymatic systems

The finding and researching algorithm for potentially oscillating enzymatic systems

Periodic response characteristics on a piecewise hysteresis nonlinear system

Non-Uniqueness of Cycles in Piecewise-Linear Models of Circular Gene Networks

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