Necessary conditions for multistationarity in discrete dynamical systems

Authors:
Adrien Richard;Jean-Paul Comet
Affiliations:
Laboratoire IBISC, CNRS & Universitéé d'Evry, Boulevard François Mitterrand, 91000 Evry, France and INRIA Rhône-Alpes, 655 avenue de l'Europe, Montbonnot, 38334 Saint Ismier, F ...;Laboratoire IBISC, CNRS & Universitéé d'Evry, Boulevard François Mitterrand, 91000 Evry, France and Programme Epigénomique, 523 place des terrasses de l'Agora, 91000 Evry, Fran ...
Venue:
Discrete Applied Mathematics
Year:
2007

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Abstract

R. Thomas conjectured, 20 years ago, that the presence of a positive circuit in the interaction graph of a dynamical system is a necessary condition for the presence of several stable states. Recently, E. Remy et al. stated and proved the conjecture for Boolean dynamical systems. Using a similar approach, we generalize the result to discrete dynamical systems, and by focusing on the asynchronous dynamics that R. Thomas used in the course of his analysis of genetic networks, we obtain a more general variant of R. Thomas' conjecture. In this way, we get a necessary condition for genetic networks to lead to differentiation.