Equilibria and stability analysis of a branched metabolic network with feedback inhibition

Frédéric Grognard (1) , Yacine Chitour (2) , Georges Bastin (3)

1 COMORE - Modeling and control of renewable resources
2 L2S - Laboratoire des signaux et systèmes
3 CESAME - Centre for systems engineering and applied mechanics [Louvain]

This paper deals with the analysis of a metabolic network with feedback inhibition. The considered system is an acyclic network of mono-molecular enzymatic reactions in which metabolites can act as feedback regulators on "preceding" enzymes of their own pathway, and in which one metabolite is the root of the whole network. We show, under mild assumptions, the uniqueness of the equilibrium. In the simplified case where inhibition only acts on the reactions having the root of the network as substrate, we show that the equilibrium is globally attractive. This requires that we impose conditions on the kinetic parameters of the metabolic reactions.

Mots clés: Metabolic network; small gain; stability; limit cycle

Domaines: Automatique; Sciences de l'ingénieur [physics]; Sciences du Vivant [q-bio]

Frédéric Grognard, Yacine Chitour, Georges Bastin. Equilibria and stability analysis of a branched metabolic network with feedback inhibition. Networks and Heterogeneous Media, 2006, 1 (1), pp.219-239. ⟨10.3934/nhm.2006.1.219⟩. ⟨hal-01090325⟩