Continuous Petri nets for biochemical network analysis

Yield optimisation of a molecular species in a chemical reaction network is of interest in chemistry and biochemistry, especially in the study of metabolic networks. Chemical reaction networks find a natural computational analogue in Petri nets, with places modeling molecular species and transitions modeling the transformation of educts into products. Although molecules are discrete entities, the yield of a molecule from given sources can be semantically-equivalently abstracted by continuous Petri nets (CPNs). Additionally, CPNs benefit from lower computational complexity, reachability being polynomial. We implement the polynomial-time continuous Petri net coverability procedure of Fraca and Haddad and combine it with binary search to approximate the supremal yield of a designated product to a prescribed precision. As a contrasting formal strategy, we also encode the same objective in a mixed-integer linear framework, which trades provable complexity for broader expressiveness. We compare these two formulations on both synthetic examples and chemically inspired networks, alongside a case-study of the non-oxidative part of the pentose-phosphate pathway, highlighting chemically relevant results.