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 Model. Anal. Inform. Sist., 2019, Volume 26, Number 3, Pages 365–404 (Mi mais686)

Computer system organization

New approach to gene network modeling

S. D. Glyzina, A. Yu. Kolesova, N. Kh. Rozovb

a P.G. Demidov Yaroslavl State University, 14 Sovetskaya str., Yaroslavl 150003, Russia
b M.V. Lomonosov Moscow State University, Leninskie Gory, Moscow, 119991, Russia

Abstract: The article is devoted to the mathematical modeling of artificial genetic networks. A phenomenological model of the simplest genetic network called repressilator is considered. This network contains three elements unidirectionally coupled into a ring. More specifically, the first of them inhibits the synthesis of the second, the second inhibits the synthesis of the third, and the third, which closes the cycle, inhibits the synthesis of the first one. The interaction of the protein concentrations and of mRNA (message RNA) concentration is surprisingly similar to the interaction of six ecological populations — three predators and three preys. This allows us to propose a new phenomenological model, which is represented by a system of unidirectionally coupled ordinary differential equations. We study the existence and stability problem of a relaxation periodic solution that is invariant with respect to cyclic permutations of coordinates. To find the asymptotics of this solution, a special relay system is constructed. It is proved in the paper that the periodic solution of the relay system gives the asymptotic approximation of the orbitally asymptotically stable relaxation cycle of the problem under consideration.

Keywords: artificial gene network, repressilator, self-symmetric cycle, asymptotics, stability.

 Funding Agency Grant Number Russian Foundation for Basic Research 18-29-10055_ìê The reported study was funded by RFBR according to the research project № 18-29-10055.

DOI: https://doi.org/10.18255/1818-1015-365-404

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UDC: 517.926
Revised: 09.09.2019
Accepted:11.09.2019

Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “New approach to gene network modeling”, Model. Anal. Inform. Sist., 26:3 (2019), 365–404

Citation in format AMSBIB
\Bibitem{GlyKolRoz19} \by S.~D.~Glyzin, A.~Yu.~Kolesov, N.~Kh.~Rozov \paper New approach to gene network modeling \jour Model. Anal. Inform. Sist. \yr 2019 \vol 26 \issue 3 \pages 365--404 \mathnet{http://mi.mathnet.ru/mais686} \crossref{https://doi.org/10.18255/1818-1015-365-404}