Joint talk with B. Joshi, N Kaihnsa and A. Shiu (California State University, San Marcos, University of Copenhagen, Texas A&M University).
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 the 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 first show that it is highly atypical for both properties to coexist in reaction networks without special structures. Next, we establish the minimum conditions for the coexistence of both properties; and provide necessary and sufficient conditions for ACR (and multistationarity) for a class of reaction networks: multisite phosphorylation cycles with a bifunctional enzyme.
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