The Smallest Multistationary Mass-Preserving Chemical Reaction Network

Authors:
Anne Shiu
Affiliations:
Dept. of Mathematics, University of California, Berkeley, USA CA 94720-3840
Venue:
AB '08 Proceedings of the 3rd international conference on Algebraic Biology
Year:
2008

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Abstract

Biochemical models that exhibit bistability are of interest to biologists and mathematicians alike. Chemical reaction network theory can provide sufficient conditions for the existence of bistability, and on the other hand can rule out the possibility of multiple steady states. Understanding small networks is important because the existence of multiple steady states in a subnetwork of a biochemical model can sometimes be lifted to establish multistationarity in the larger network. This paper establishes the smallest reversible, mass-preserving network that admits bistability and determines the semi-algebraic set of parameters for which more than one steady state exists.