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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 1271–1283 (Mi semr994)  

Differentical equations, dynamical systems and optimal control

Mathematical and numerical models of two asymmetric gene networks

V. P. Golubyatnikova, M. V. Kazantsevb, N. E. Kirillovac, T. A. Bukharinad

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Polzunov Altai State Technical University, Lenin avenue, 46, 656038, Barnaul, Russia
c Novosibirsk State University, Pirogova street, 1, 630090, Novosibirsk, Russia
d The Federal reaearch center Institute of Cytology and Genetics SB RAS, Lavrent'ev avenue, 10, 630090, Novosibirsk, Russia

Abstract: We construct and study mathematical models of two gene networks: a circular gene network of molecular repressilator, and a natural gene network which does not have circular structure. For the first model, we consider discretization of phase portrait of corresponding nonlinear dynamical system and find conditions of existence of an oscillating trajectory (cycle) in this phase portrait. The second model describes the central regulatory circuit of one gene network which acts on early stage of the fruit fly Drosophila melanogaster mechanoreceptors morphogenesis. For both models we give biological interpretations of our numerical simulations and give a short description of software elaborated specially for these experiments.

Keywords: nonlinear dynamical systems, cycles, phase portraits, gene networks models, hyperbolic equilibrium points, Grobman-Hartman theorem, Brouwer fixed point theorem, numerical analysis.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00057_a
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0324-2018-0017
0314-2018-0011
0324-2018-0021
Supported by RFBR (grant 18-01-00057); by FASE program project N 0324-2018-0017; and by complex program of SBRAS, projects 0314-2018-0011 and 0324-2018-0021.


DOI: https://doi.org/10.17377/semi.2018.15.103

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Document Type: Article
UDC: 517.93
MSC: 37N25
Received March 26, 2018, published October 25, 2018
Language: English

Citation: V. P. Golubyatnikov, M. V. Kazantsev, N. E. Kirillova, T. A. Bukharina, “Mathematical and numerical models of two asymmetric gene networks”, Sib. Èlektron. Mat. Izv., 15 (2018), 1271–1283

Citation in format AMSBIB
\Bibitem{GolKazKir18}
\by V.~P.~Golubyatnikov, M.~V.~Kazantsev, N.~E.~Kirillova, T.~A.~Bukharina
\paper Mathematical and numerical models of two asymmetric gene networks
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1271--1283
\mathnet{http://mi.mathnet.ru/semr994}
\crossref{https://doi.org/10.17377/semi.2018.15.103}


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