Robust Perfect Adaptation of Reaction Fluxes Ensured by Network Topology

Maintaining stability in an uncertain environment is essential for proper functioning of living systems. Robust perfect adaptation (RPA) is a property of a system that generates an output at a fixed level even after fluctuations in input stimulus without fine-tuning parameters, and it is important to understand how this feature is implemented through biochemical networks. The existing literature has mainly focused on RPA of the concentration of a chosen chemical species, and no generic analysis has been made on RPA of reaction fluxes, that play an equally important role. Here, we identify structural conditions on reaction networks under which all the reaction fluxes exhibit RPA against the perturbation of the parameters inside a subnetwork. Based on this understanding, we give a recipe for obtaining a simpler reaction network, from which we can fully recover the steady-state reaction fluxes of the original system. This helps us identify key parameters that determine the fluxes and study the properties of complex reaction networks using a smaller one without losing any information about steady-state reaction fluxes.