Reduction and stability analysis of a transcription-translation model of RNA polymerase

Ismail Belgacem 1 Stefano Casagranda 1 Edith Grac 2 Delphine Ropers 2 Jean-Luc Gouzé 1, 3
1 BIOCORE - Biological control of artificial ecosystems
CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique, LOV - Laboratoire d'océanographie de Villefranche
2 IBIS - Modeling, simulation, measurement, and control of bacterial regulatory networks
LAPM - Laboratoire Adaptation et pathogénie des micro-organismes [Grenoble], Inria Grenoble - Rhône-Alpes, Institut Jean Roget
Abstract : The aim of this paper is to analyze the dynamical behavior of biological models of gene transcription and translation. We focus on a particular positive feedback loop governing the synthesis of RNA polymerase, needed for transcribing its own gene. We write a high-dimension model based on mass-action laws and reduce it to a two-variable model (RNA polymerase and its mRNA) by means of monotone system theory and timescale arguments. We show that the reduced model has either a single globally stable trivial equilibrium in (0, 0), or an unstable zero equilibrium and a globally stable positive one. We give generalizations of this model, notably with a variable growth rate. The dynamical behavior of this system can be related to biological observations on the bacterium Escherichia coli.
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Bulletin of Mathematical Biology, Springer Verlag, 2018, 80 (2), pp.294-318. 〈10.1007/s11538-017-0372-4〉
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Ismail Belgacem, Stefano Casagranda, Edith Grac, Delphine Ropers, Jean-Luc Gouzé. Reduction and stability analysis of a transcription-translation model of RNA polymerase. Bulletin of Mathematical Biology, Springer Verlag, 2018, 80 (2), pp.294-318. 〈10.1007/s11538-017-0372-4〉. 〈hal-01655367〉

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