Georgia Institute of Technology College of Sciences

Reaction networks are commonly used to model a variety of physical systems ranging from the microscopic world like cell biology and chemistry, to the macroscopic world like epidemiology and evolution biology. A biologically relevant property that reaction networks can have is absolute concentration robustness (ACR), which refers to when a steady-state species concentration is maintained even when initial conditions are changed. Networks with ACR have been observed experimentally, for example, in E. coli EnvZ-OmpR and IDHKP-IDH systems. Another reaction network property that might be desirable is multistationarity-the capacity for two or more steady states, since it is often associated with the capability for cellular signaling and decision-making.

While the two properties seem to be opposite, having both properties might be favorable as a biochemical network may require robustness in its internal operation while maintaining flexibility as a signal-response mechanism. As such, our driving motivation is to explore what network structures can produce ACR and multistationarity. We show that it is highly atypical for both properties to coexist in very small and very large reaction networks without special structures. However, it is possible for them to coexist in certain classes of reaction networks. I will discuss in detail one such class of networks, which consists of multisite phosphorylation-dephosphorylation cycles with a ``paradoxical enzyme".