Limit cycles in models of circular gene networks regulated by negative feedback loops
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RESEARCH
Open Access
Limit cycles in models of circular gene networks regulated by negative feedback loops Vitaly A. Likhoshvai1 ˆ, Vladimir P. Golubyatnikov2,3* and Tamara M. Khlebodarova1,3 From 11th International Young Scientists School “Systems Biology and Bioinformatics” - SBB-2019 Novosibirsk, Russia. 24-28 June 2019 *Correspondence: vladimir.golubyatnikov1@fulbright mail.org ˆDeceased 2 Laboratory of Inverse Problems of Mathematical Physics, Sobolev Institute of Mathematics Siberian Branch RAS, Novosibirsk, Russia 3 Novosibirsk State University, Novosibirsk, Russia Full list of author information is available at the end of the article
Abstract Background: The regulatory feedback loops that present in structural and functional organization of molecular-genetic systems and the phenomenon of the regulatory signal delay, a time period between the moment of signal reception and its implementation, provide natural conditions for complicated dynamic regimes in these systems. The delay phenomenon at the intracellular level is a consequence of the matrix principle of data transmission, implemented through the rather complex processes of transcription and translation. However, the rules of the influence of system structure on system dynamics are not clearly understood. Knowledge of these rules is particularly important for construction of synthetic gene networks with predetermined properties. Results: We study dynamical properties of models of simplest circular gene networks regulated by negative feedback mechanisms. We have shown existence and stability of oscillating trajectories (cycles) in these models. Two algorithms of construction and localization of these cycles have been proposed. For one of these models, we have solved an inverse problem of parameters identification. Conclusions: The modeling results demonstrate that non-stationary dynamics in the models of circular gene networks with negative feedback loops is achieved by a high degree of non-linearity of the mechanism of the autorepressor influence on its own expression, by the presence of regulatory signal delay, the value of which must exceed a certain critical value, and transcription/translation should be initiated from a (Continued on next page)
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