Mathematics

Stochastically modeled reaction network

Jinsu Kim (University of California Irvine)

Abstract: A reaction network is a graphical configuration that describes an interaction between species (molecules). If the abundances of the network system are small, then the randomness inherent in the molecular interactions is important to the system dynamics, and the abundances are modeled stochastically as a jump by jump fashion continuous-time Markov chain. One of the challenging issues facing researchers who study biological systems is the often extraordinarily complicated structure of their interaction networks. Thus, how to characterize network structures that induce characteristic behaviors of the system dynamics is one of the major open questions in this literature. In this talk, I will provide a class of reaction networks whose associated stochastic process is stable. I will also provide how this stability can be used in system biology and control theory.