de Mathématiques de Luminy
Remy Elisabeth, Ruet Paul, Thieffry Denis.
Positive or negative regulatory circuit inference from multilevel dynamics
In the course of his work on the analysis of genetic regulatory networks represented by signed directed graphs, R. Thomas has proposed that the occurrence of a positive regulatory circuit is a necessary condition for the occurrence of multiple stable states, whereas a negative circuit is necessary to generate stable oscillations. Here, we enunciate and demonstrate one theorem establishing these rules in a multilevel discrete framework.