Applied Mathematics Colloquium: Dr. Casian Pantea

Title: Inheritance of bistability in biochemical reaction networks

The study of biochemical reaction network behaviors that are a function of their structure (broadly termed Chemical Reaction Network Theory) has seen a surge of interest in the last decade. This is partly due to its increasing relevance to systems biology, but also to its ramifications to other areas of mathematics. This talk focuses on the question of bistability, or existence of multiple (stable) positive equilibria, a dynamical property that underlies important cellular processes, and a recurring theme in Chemical Reaction Network Theory. Namely, we consider the question: "when can we conclude that a network admits multiple stable positive equilibria based on analysis of its subnetworks?”

We identify a number of operations on reaction networks that preserve bistability as we build up the network, and we illustrate the power of this approach on the much-studied Huang-Ferrell MAPK cascade. Work in this direction is an essential step towards a rigorous theory of “motifs”, a central theme in systems biology.