Transition probabilities for piecewise affine models of genetic networks

Madalena Chaves 1 Etienne Farcot 2, 3 Jean-Luc Gouzé 1
1 COMORE - Modeling and control of renewable resources
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée
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
Abstract : In the piecewise affine framework, trajectories evolve among hyperrectangles in the state space. A qualitative description of the dynamics - useful for models of genetic networks - can be obtained by viewing each hyperrectangle as a node in a discrete system, so that trajectories follow a path in a transition graph. In this paper, a probabilistic interpretation is given for the transition between two nodes A and B, based on the volume of the initial conditions on hyperrectangle A whose trajectories cross to B. In an example consisting of two intertwinned negative loops, this probabilistic interpretation is used to predict the most likely periodic orbit given a set of parameters, or to find parameters such that the system yields a desired periodic orbit with a high probability.
Type de document :
Communication dans un congrès
Proc. Int. Symp. Mathematical Theory of Networks and Systems (MTNS 10), Budapest, Hungary, Jul. 2010., 2010, Budapest, Hungary. 2010
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Madalena Chaves, Etienne Farcot, Jean-Luc Gouzé. Transition probabilities for piecewise affine models of genetic networks. Proc. Int. Symp. Mathematical Theory of Networks and Systems (MTNS 10), Budapest, Hungary, Jul. 2010., 2010, Budapest, Hungary. 2010. 〈hal-00831793〉

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