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Stability analysis of a reduced transcription-translation model of RNA polymerase

Ismail Belgacem 1 Edith Grac 2 Delphine Ropers 2 Jean-Luc Gouzé 1 
1 BIOCORE - Biological control of artificial ecosystems
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique
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 analyse the dynamicalbehaviour of models of gene transcription-translation for thesynthesis of RNA polymerase in a cell, with a closed loopfrom the produced RNA polymerase (end-product) to thetranscription step (RNA polymerase is needed to transcribe itsown gene). Using monotone system theory we study a reducedversion of this model with two variables (mRNA and protein),and show that it has either a single globally stable trivialequilibrium in (0, 0), or has an unstable zero equilibrium anda globally stable positive one. This dynamical behaviour can berelated to biological observations on the bacterium Escherichiacoli.
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Contributor : Jean-Luc Gouzé Connect in order to contact the contributor
Submitted on : Friday, December 5, 2014 - 5:49:01 PM
Last modification on : Monday, July 25, 2022 - 3:44:36 AM


  • HAL Id : hal-01091674, version 1


Ismail Belgacem, Edith Grac, Delphine Ropers, Jean-Luc Gouzé. Stability analysis of a reduced transcription-translation model of RNA polymerase. Proceedings of the 53rd IEEE Conference on Decision and Control, Dec 2014, Los Angeles, CA, United States. ⟨hal-01091674⟩



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