Second Italian Meeting on Probability and Mathematical Statistics

Stationary distributions for biochemical reaction networks

Chemical reaction networks are mathematical models ubiquitously used in biochemistry. Typically, if few molecules are present in the system, the time evolution of the molecule counts are modeled through a continuous time Markov chain. In this setting, information on the form or even on the existence of a stationary distribution is important to perform model simplifications, to infer qualitative properties of the model, and to design synthetic biochemical circuits. However, such information is typically not available, except for restricted scenarios. I will give a brief overview of the known results. I will then present a novel and fast convex programming technique that checks if sufficient conditions for the existence of a piece-wise linear Foster-Lyapunov function hold. If this is the case, the existence of a stationary distribution follows the seminal work of Meyn and Tweedie.