Uniqueness and multiplicity of steady states in monocyclic enzyme cascades: a graph-theoretic analysis

Monocyclic enzyme cascades are important regulators of biochemical reactions in living cells. The reaction network may have either one steady state or many, depending on its structure. The occurrence of multiple steady states has important biological implications. A simple graph-theoretic method has been applied to five reaction mechanisms—which together cover many common monocyclic cascades—to determine which mechanisms generate just one steady state and which ones allow more than one state. It is shown that an unstable steady state in a multiplicity region can be usefully exploited and that in some cases transitions may occur between uniqueness and multiplicity regions. The possible effects of such transitions are discussed.