CRITERIA: A network decomposition and elementary flux mode translation-based tool for computing equilibria of...

Analytically deriving equilibria, which often govern the long-term behavior of biochemical reaction networks, is essential for understanding cellular decision-making and robustness, yet remains computationally challenging for large and complex systems. The COMPILES framework of Hernandez et al. addresses this problem via network decomposition but is limited by a computationally intensive translation step and by its restriction to networks with zero kinetic deficiency. We introduce CRITERIA (Computing paRametrized posITive EquilibRIA), a new framework that overcomes these limitations through two key advances. First, it replaces the translation mechanism of COMPILES with a more efficient graph-theoretic formulation based on the work of Johnston and Burton, which generates a reaction-to-reaction graph from elementary flux modes and identifies directed cycles of the constructed graph via a binary linear program. Second, CRITERIA computes equilibria on a single unified translated network rather than solving subnetworks independently, thereby eliminating interdependencies that previously required extensive symbolic manipulation. Across a benchmark set of 26 biochemical models, CRITERIA achieves consistent and often substantial speed improvements while expanding applicability beyond the restricted class of zero kinetic deficiency systems. We demonstrate the biological utility of the framework by analyzing multistationarity, which underlies cellular decision-making, and absolute concentration robustness, a key mechanism for maintaining stable biochemical outputs, in the EnvZ-OmpR signaling pathway and a large-scale CRISPRi toggle switch, respectively. By improving both scalability and applicability, CRITERIA enables a systematic equilibrium analysis in biochemical networks of realistic size and complexity, providing a practical tool for studying long-term dynamical behavior in systems biology.