Article Contents

2006, Volume 1, Issue 1: 219-239. Doi: 10.3934/nhm.2006.1.219

This issue Previous Article Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue Next Article

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: June 2005

Revised: September 2005

Published: March 2006

Abstract / Introduction Related Papers Cited by

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.

Keywords:

Mathematics Subject Classification: 93B05, 93B60, 35P20.

Citation:

Article Metrics

HTML views() PDF downloads(127) Cited by(0)

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

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

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

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content