Exact Fluid Lumpability for Chemical Reaction Networks

Abstract. We present a technique for the automatic reduction of chemical re-action networks (CRNs). We study exact fluid lumpability, a partition of species satisfying the dynamical property that species in the same block have the same output at all times if initialized equally. Inspired by analogous approaches in tradi-tional models of computation such as labelled transition systems, we characterize this property as a behavioral equivalence over species which can be checked only using CRN structural information. We give an algorithm to construct a quotient CRN induced by exact fluid lumpability. Further, we provide an algorithm that computes the coarsest partition in polynomial time. As an application, we find significant, lossless reductions in a number of models of biological processes available in the literature. In two cases we allow the analysis of benchmark mod-els which would be otherwise intractable due to their memory requirements.