A new necessary condition on interaction graphs for multistationarity.
We consider a dynamical system, described by a system of ordinary differential equations, and the associated interaction graphs, which are defined using the matrix of signs of the Jacobian matrix. After stating a few conjectures about the role of circuits in these graphs, we prove two new results relating them to the dynamic behaviour of the system: a sufficient condition for qualitative unstability, and a necessary condition for the existence of several stationary states. These results are illustrated by examples of regulatory modules in two variables, such as those occurring in biological networks.
Kaufman
M
M
Unit of Theoretical and Computational Biology, Faculté des Sciences, Université Libre de Bruxelles (U.L.B.), Campus Plaine, C.P. 231, B-1050 Brussels, Belgium. Marcelle.Kaufman@ulb.ac.be
Soulé
C
C
Thomas
R
R
D000818:Animals; D002454:Cell Differentiation / Q000502:physiology; D005246:Feedback; D006706:Homeostasis; D008954:Models, Biological; D013598:Systems Theory