Section: New Results

A Stronger Necessary Condition for the Multistationarity of Chemical Reaction Networks

Participant : Sylvain Soliman.

In the last thirty years, the conjecture of Thomas on the necessary presence of a positive circuit for the occurrence of multistationarity has opened a whole field of research, allowing better modeling and understanding of biochemical networks, especially in the emerging field of systems biology. However, if that aspect is striking in the field of discrete modeling of gene regulatory networks, it did not have the same impact in the Ordinary Differential Equations (ODE) based modeling community. This is mostly due to the fact that this necessary condition, the existence of a positive loop in the Jacobian of the ODE system, is almost always satisfied.

In [5] we improve on the ten years old proof by Soulé, using the structural information from the stoichiometric matrix of a biochemical reaction system. This allows us to state a more strict version of the famous Thomas’ necessary condition for multistationarity. In particular, the obvious cases where Thomas’ condition was trivially satisfied, mutual inhibition due to a multimolecular reaction and mutual activation due to a reversible reaction, can now easily be ruled out. The new condition makes it possible to use circuit analysis as an useful tool in the arsenal of the computational biologist, together with other structural methods.