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Networks and Heterogeneous Media

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

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  • 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.


  • This article has been cited by:

    1. Murat Arcak, Eduardo D. Sontag, 2007, A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks, 978-1-4244-1497-0, 4477, 10.1109/CDC.2007.4434115
    2. Ismail Belgacem, Jean-Luc Gouzé, Global Stability of Enzymatic Chains of Full Reversible Michaelis-Menten Reactions, 2013, 61, 0001-5342, 425, 10.1007/s10441-013-9195-3
    3. Somnath Tagore, Rajat K. De, Dipshikha Chakravortty, Simulating an Infection Growth Model in Certain Healthy Metabolic Pathways of Homo sapiens for Highlighting Their Role in Type I Diabetes mellitus Using Fire-Spread Strategy, Feedbacks and Sensitivities, 2013, 8, 1932-6203, e69724, 10.1371/journal.pone.0069724
    4. David Angeli, Eduardo D. Sontag, Oscillations in I/O Monotone Systems Under Negative Feedback, 2008, 53, 0018-9286, 166, 10.1109/TAC.2007.911320
    5. Eduardo D. Sontag, Murat Arcak, 2008, Chapter 14, 978-1-84800-154-1, 195, 10.1007/978-1-84800-155-8_14
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  • © 2006 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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