Exequiel Jun Villejo, Dr. Aurelio de los Reyes V, and Dr. Bryan Hernandez of the UPD-CS Institute of Mathematics (IM) created CRITERIA, (Computing paRametrized posITive EquilibRIA), a computational tool that automates the analysis of biological systems. Instead of relying solely on numerical simulations, CRITERIA derives analytical expressions describing the possible steady states of these systems.

According to Dr. Hernandez, the team took a more general approach by deriving mathematical expressions that satisfy the equations describing a biological system at steady state, rather than fixing specific numerical values. These expressions describe possible steady states in terms of reaction parameters and a set of free variables, allowing the researchers to represent a range of possible system states without assigning specific numerical values to every variable.

“The expressions derived by CRITERIA give researchers a broader view of the system’s long-term behavior. They can help reveal properties such as whether multiple steady states are possible, how steady-state concentrations depend on reaction parameters, and which features of the system remain unchanged despite variations in those parameters,” Dr. Hernandez explained.

Before CRITERIA, the team developed COMPILES (COMPutIng anaLytic stEady States), an earlier framework for deriving analytical expressions for steady states. COMPILES can identify important biochemical properties, including bistability in a genetic toggle switch model and absolute concentration robustness in a complex insulin signaling pathway model. 

Although COMPILES worked for several biological systems, the team encountered limitations when applying it to more complex networks. Some of its computational steps could be expensive, some resulting expressions required additional mathematical manipulation, and its implementation was limited to a narrower class of reaction networks. These limitations motivated them to seek a more practical and flexible way to derive analytical descriptions of steady states in biochemical reaction networks.

“Like COMPILES, CRITERIA first breaks a biochemical reaction network into smaller pieces. This makes the system easier to analyze than treating the entire network all at once. Before the steady states can be computed, these smaller pieces need to satisfy certain mathematical conditions. CRITERIA uses a more efficient procedure to achieve these required conditions,” Dr. Hernandez said. 

In COMPILES, the steady states of smaller components are calculated first and then combined. However, this can sometimes produce formulas that depend on one another in a circular manner, requiring additional computation or algebraic manipulation. CRITERIA reverses this order: the transformed components are combined first, and the steady states of the resulting system are calculated afterward. This can help avoid some of the complications encountered with COMPILES.

“We tested this improvement using 26 benchmark biological models to compare the performance of the method,” Dr. Hernandez added. “COMPILES was unable to complete 11 of these models within one hour, while CRITERIA completed all 26, with most computations finishing within only a few seconds.”

Biological questions involve understanding how interacting molecules behave over time and what states they reach. CRITERIA can help researchers investigate the possible steady states of a biochemical system without having to assign specific values to every reaction parameter. This is useful because many biological parameters are difficult or expensive to measure experimentally.

CRITERIA could also be useful in studying disease-related processes. If a suitable model of a disease-related pathway is available, researchers could use the tool to examine whether the system can switch between different cellular states, which components maintain stable steady-state concentrations, and how changes in reaction parameters may affect its possible long-term behavior.

The study “CRITERIA: A network decomposition and elementary flux mode translation-based tool for computing equilibria of biochemical systems” is published in PLOS Computational Biology, a journal featuring works of exceptional significance that further our understanding of living systems at all scales through the application of computational methods. 

Reference:

Villejo, E. J., Los Reyes V, A. A., & Hernandez, B. S. (2026). Criteria: A network decomposition and elementary flux mode translation-based tool for computing equilibria of biochemical systems. PLOS Computational Biology, 22(8), e1014633. https://doi.org/10.1371/journal.pcbi.1014633