Seminari di Statistica, Probabilita' e Ottimizzazione (Politecnico di Torino)

Stochastic reaction networks are mathematical models used to describe a biological system with low molecule counts. If few molecules are present, then the dynamics of the system is strongly affected by stochastic noise, and the changes of the molecules counts are described by means of a continuous time Markov chain.

I will introduce stochastic reaction networks and give an overview of the main results concerning them. In particular, I will show the connections between stochastic reaction networks and deterministic reaction networks, which can be regarded as fluid limits of the stochastic models.

Finally, I will outline some results pertaining stationary distributions of stochastic reaction networks. I will further present some recent investigation on the potentiality of stochastic reaction networks. The possibility of physically implement a given reaction network by means of DNA strands opened new questions and new challenges in the field. Specifically, I will show that it is possible to design chemical reaction networks whose stationary distribution approximate a given probability distribution with arbitrary precision.

Politecnico di Torino, Torino, Italy

Torino, Italy