Séminaire de Mathématique-Biologie

Multistationarity of biochemical reaction networks as continuous systems, beyond Thomas’ condition


Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois-Marie 35, route de Chartres 91440 Bures-sur-Yvette
Thomas' conjecture about the necessity of a positive circuit for the multistationarity has been proved both in the discrete and continuous setting. Nevertheless it has mostly been used in the discrete case since, as we will demonstrate, it is almost always satisfied by biochemical reaction networks. In order to work around this shortcoming, we will go back to the decomposition of the Jacobian matrix determinant and notice that, for dynamical systems corresponding to biochemical reactions, certain patterns allow the statement of a stronger necessary condition. We will illustrate how that new condition rules out the cases that trivially satisfied the classical condition of Thomas on a simple example of enzymatic reaction.
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