Exact Fluid Lumpability for Chemical Reaction Networks

We present a technique for the automatic reduction of chemical reaction 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 traditional 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 models which would be otherwise intractable due to their memory requirements.