Multistability in Biochemical Reaction Systems: Structural Approach

In living cells, biochemical reactions form intricate networks that can exhibit multistability, allowing a single system to maintain multiple stable states under identical conditions. However, determining theoretically whether a given reaction system can exhibit multistability is challenging because detailed kinetic parameters are often unknown.

In this presentation, we introduce a structural framework that decomposes biochemical networks into subnetworks based solely on network topology. For each subnetwork, we define a scalar quantity, and an index-theoretic argument shows that the sign of this quantity determines whether the subnetwork can contribute to multistability. Our method identifies indicator species whose concentrations distinguish all steady states without detailed kinetic information, thereby enabling efficient measurement design in large networks.