Equilibria and stability analysis of a branched metabolic network with feedback inhibition
-
1.
Laboratoire des systèmes et signaux, Université Paris-Sud, CNRS, Supélec, 91192, Gif-sur-Yvette
-
2.
INRIA Sophia-Antipolis, COMORE Project-team, 2004 route des lucioles, BP 93, 06902 Sophia-Antipolis Cedex
-
3.
Centre for Systems Engineering and Applied Mechanics (CESAME), Université Catholique de Louvain, Bâtiment Euler, 4-6, avenue G.Lemaitre,, 1348 Louvain la Neuve
-
Received:
01 June 2005
Revised:
01 September 2005
-
-
93B05, 93B60, 35P20.
-
-
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 enzymes located "at the beginning" 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. We then show that this equilibrium is globally attractive if we impose conditions on the kinetic parameters
of the metabolic reactions. Finally, when these conditions are not satisfied, we
show, with a specific fourth-order example, that the equilibrium may become
unstable with an attracting limit cycle.
Citation: Yacine Chitour, Frédéric Grognard, Georges Bastin. Equilibria and stability analysis of a branched metabolic network with feedback inhibition[J]. Networks and Heterogeneous Media, 2006, 1(1): 219-239. doi: 10.3934/nhm.2006.1.219
-
Abstract
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 enzymes located "at the beginning" 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. We then show that this equilibrium is globally attractive if we impose conditions on the kinetic parameters
of the metabolic reactions. Finally, when these conditions are not satisfied, we
show, with a specific fourth-order example, that the equilibrium may become
unstable with an attracting limit cycle.
-
-
-
-
DownLoad: