Identifying Phenotype-Indicative Molecules from the Structure of Biochemical Reaction Networks

Multistability in chemical reaction networks (CRNs) is a key mechanism underlying the diversity in cellular phenotypes. Identifying the steady state a cell occupies requires measuring molecular concentrations. This in turn raises a fundamental question: which chemical species should be selected to reliably distinguish among multiple steady states? We introduce a network-structural approach for identifying indicator species--a subset of species whose concentrations alone suffice to identify which steady state the system occupies. By decomposing a CRN into subnetworks based on structural criteria and applying topological degree theory, we show that the concentrations within certain subnetworks uniquely determine those of all remaining species. These subnetworks thus provide indicator species that distinguish all possible steady states. Crucially, our method relies only on stoichiometric and regulatory information, without requiring kinetic parameters. Implemented via a computational algorithm, the framework is validated through numerical simulations and applied to biochemical networks. This work provides a principled strategy for steady-state identification in high-dimensional biochemical networks from partial observations, with potential applications in single-cell data analysis and biomarker discovery.