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Mathematical and numerical models of two asymmetric gene networks. / Golubyatnikov, Vladimir Petrovich; Kazantsev, Maxim Valer evich; Kirillova, Natalia Evgenievna et al.

In: Сибирские электронные математические известия, Vol. 15, 01.01.2018, p. 1271-1283.

Research output: Contribution to journal › Article › peer-review

Harvard

Golubyatnikov, VP, Kazantsev, MVE, Kirillova, NE, Bukharina, TAE & Furman, DP 2018, 'Mathematical and numerical models of two asymmetric gene networks', Сибирские электронные математические известия, vol. 15, pp. 1271-1283. https://doi.org/10.17377/semi.2018.15.103

APA

Golubyatnikov, V. P., Kazantsev, M. V. E., Kirillova, N. E., Bukharina, T. A. E., & Furman, D. P. (2018). Mathematical and numerical models of two asymmetric gene networks. Сибирские электронные математические известия, 15, 1271-1283. https://doi.org/10.17377/semi.2018.15.103

Vancouver

Golubyatnikov VP, Kazantsev MVE, Kirillova NE, Bukharina TAE, Furman DP. Mathematical and numerical models of two asymmetric gene networks. Сибирские электронные математические известия. 2018 Jan 1;15:1271-1283. doi: 10.17377/semi.2018.15.103

Author

Golubyatnikov, Vladimir Petrovich ; Kazantsev, Maxim Valer evich ; Kirillova, Natalia Evgenievna et al. / Mathematical and numerical models of two asymmetric gene networks. In: Сибирские электронные математические известия. 2018 ; Vol. 15. pp. 1271-1283.

BibTeX

@article{2627fbda7ecf4dc99be5fcca4ae6a4c4,
title = "Mathematical and numerical models of two asymmetric gene networks",
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 = "Brouwer fixed point theorem, Cycles, Gene networks models, Grobman-Hartman theorem, Hyperbolic equilibrium points, Nonlinear dynamical systems, Numerical analysis, Phase portraits",
author = "Golubyatnikov, {Vladimir Petrovich} and Kazantsev, {Maxim Valer evich} and Kirillova, {Natalia Evgenievna} and Bukharina, {Tatyana Anatol evna} and Furman, {Dagmara Pavlovna}",
year = "2018",
month = jan,
day = "1",
doi = "10.17377/semi.2018.15.103",
language = "English",
volume = "15",
pages = "1271--1283",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",

}

RIS

TY - JOUR

T1 - Mathematical and numerical models of two asymmetric gene networks

AU - Golubyatnikov, Vladimir Petrovich

AU - Kazantsev, Maxim Valer evich

AU - Kirillova, Natalia Evgenievna

AU - Bukharina, Tatyana Anatol evna

AU - Furman, Dagmara Pavlovna

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Brouwer fixed point theorem

KW - Cycles

KW - Gene networks models

KW - Grobman-Hartman theorem

KW - Hyperbolic equilibrium points

KW - Nonlinear dynamical systems

KW - Numerical analysis

KW - Phase portraits

UR - http://www.scopus.com/inward/record.url?scp=85071436589&partnerID=8YFLogxK

U2 - 10.17377/semi.2018.15.103

DO - 10.17377/semi.2018.15.103

M3 - Article

AN - SCOPUS:85071436589

VL - 15

SP - 1271

EP - 1283

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

ID: 22322625