Master Thesis MONOMOLECULAR REACTION NETWORKS: A NEW PROOF OF FLUX TRANSITIVITY

In the case of monomolecular reaction networks, we study the network response to perturbations of a reaction rate j∗. Specifically, we describe which other reaction rates j′ respond by nonzero reaction flux, at steady state. Nonzero responses of j′ to j∗ are called flux-influence of j∗ on j′. Mochizuki and Fiedler established transitivity of flux-influence for monomolecular reaction networks. We give a new, independent and conceptually simplified proof of that intriguing fact. Our proof uses standard connectivity concepts from graph theory, and Menger’s Theorem. Based on the network structure only, this also leads to a simplified characterization of all flux-influenced sets.