Mathematical and numerical models of two asymmetric gene networks

Vladimir Petrovich Golubyatnikov, Maxim Valer evich Kazantsev, Natalia Evgenievna Kirillova, Tatyana Anatol evna Bukharina, Dagmara Pavlovna Furman

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1271-1283
Number of pages13
JournalСибирские электронные математические известия
Volume15
DOIs
Publication statusPublished - 1 Jan 2018

Keywords

  • Brouwer fixed point theorem
  • Cycles
  • Gene networks models
  • Grobman-Hartman theorem
  • Hyperbolic equilibrium points
  • Nonlinear dynamical systems
  • Numerical analysis
  • Phase portraits

OECD FOS+WOS

  • 1.01 MATHEMATICS

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