Periodic Solutions of Piecewise Affine Gene Network Models with Non Uniform Decay Rates: The Case of a Negative Feedback Loop

Etienne Farcot 1, 2 Jean-Luc Gouzé 3
2 VIRTUAL PLANTS - Modeling plant morphogenesis at different scales, from genes to phenotype
CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique, Centre de coopération internationale en recherche agronomique pour le développement [CIRAD] : UMR51
3 COMORE - Modeling and control of renewable resources
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This paper concerns periodic solutions of a class of equations that model gene regulatory networks. Unlike the vast majority of previous studies, it is not assumed that all decay rates are identical. To handle this more general situation, we rely on monotonicity properties of these systems. Under an alternative assumption, it is shown that a classical fixed point theorem for monotone, concave operators can be applied to these systems. The required assumption is expressed in geometrical terms as an alignment condition on so-called focal points. As an application, we show the existence and uniqueness of a stable periodic orbit for negative feedback loop systems in dimension 3 or more, and of a unique stable equilibrium point in dimension 2. This extends a theorem of Snoussi, which showed the existence of these orbits only.
Type de document :
Article dans une revue
Acta Biotheoretica, Springer Verlag, 2009, 57 (4), pp.429-455. 〈10.1007/s10441-009-9086-9〉
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Soumis le : mercredi 20 novembre 2013 - 09:46:00
Dernière modification le : mercredi 19 septembre 2018 - 01:28:02

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Etienne Farcot, Jean-Luc Gouzé. Periodic Solutions of Piecewise Affine Gene Network Models with Non Uniform Decay Rates: The Case of a Negative Feedback Loop. Acta Biotheoretica, Springer Verlag, 2009, 57 (4), pp.429-455. 〈10.1007/s10441-009-9086-9〉. 〈hal-00831799〉

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