Oberwolfach workshop: Reaction Networks and Population Dynamics

Node balanced graphs and subgraphs of deterministic and stochastic reaction networks

Chemical reaction networks can be modelled either deterministically, by means of a system of ordinary differential equations, or stochastically, by means of a continuous time Markov chain. In both cases, a graph (called the “reaction graph”) can be associated with the model. In the deterministic setting, the relationship between dynamical features of the model and structural properties of the graph have been intensively studied, with a special focus on detailed balanced and complex balanced equilibria. Similar results concerning the stationary distribution of the stochastic model hold. I will explore further the concept of graphical equilibria, by considering subgraphs of the network. The connection between graphical equilibria in the deterministic and in the stochastic models will be shown. As a result, a new relationship between the detailed balanced equilibria of the deterministic model and the detailed balanced distribution of the corresponding stochastic model is unveiled. This presentation covers works done in collaboration with Elisenda Feliu, Badal Joshi and Carsten Wiuf.