Geodesic
Mathematical and numerical models of two asymmetric gene networks
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1271-1283

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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, gene networks models, hyperbolic equilibrium points, Grobman-Hartman theorem, Brouwer fixed point theorem, numerical analysis.
Mots-clés : cycles, phase portraits 
@article{SEMR_2018_15_a103,
     author = {V. P. Golubyatnikov and M. V. Kazantsev and N. E. Kirillova and T. A. Bukharina},
     title = {Mathematical and numerical models  of two asymmetric gene networks},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1271--1283},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a103/}
}
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V. P. Golubyatnikov; M. V. Kazantsev; N. E. Kirillova; T. A. Bukharina. Mathematical and numerical models  of two asymmetric gene networks. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1271-1283. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a103/