qBio Seminar Series (Wisconsin Institute for Discovery)

Chemical reaction networks are mathematical models for studying the time evolution of systems undergoing biochemical transformations. When many molecules are present in the system, then the dynamics are modelled deterministically by means of ordinary differential equations. If few molecules are present, then the dynamics are essentially stochastic and continuous Markov chains are used to describe them. It is natural to wonder what are the relationships between the two models, and whether they predict different dynamical features.

Some link between the stochastic and deterministic models are known, and I will show them. However, some discrepancies concerning the long term behaviour are also present. I will show some examples, with particular focus on the case of “absolute concentration robust” systems, which are deterministic models where a chemical species exhibits always the same value at any positive equilibrium. If the same system is stochastically modelled then something very different occurs: some chemical species are completely degraded and go extinct with probability one. However, we can show that this happens after a long time, partially resolving the conflict between the deterministically and the stochastic models, but also suggesting new questions.

The Wisconsin Institute for Discovery, Madison, WI, USA

Madison, WI, USA