Global stability of reversible enzymatic metabolic chains

Ibrahima Ndiaye 1 Jean-Luc Gouzé 1, *
* Corresponding author
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
Abstract : We consider metabolic networks with reversible enzymatic reactions. The model is written as a system of ordinary differential equations, possibly with inputs and outputs. We prove the global stability of the equilibrium (if it exists), using techniques of monotone systems and compartmental matrices. We show that the equilibrium does not always exist. Finally, we consider a metabolic system coupled with a genetic network, and we study the dependence of the metabolic equilibrium (if it exists) with respect to concentrations of enzymes. We give some conclusions concerning the dynamical behavior of coupled genetic/metabolic systems.
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Ibrahima Ndiaye, Jean-Luc Gouzé. Global stability of reversible enzymatic metabolic chains. Acta Biotheoretica, Springer Verlag, 2012, 61 (1), pp.41-57. ⟨10.1007/s10441-013-9171-y⟩. ⟨hal-00848438⟩

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