Constraints on reciprocal flux sensitivities in biochemical reaction networks

We identify a connection between the structural features of mass-action networks and the robustness of their steady-state fluxes against rate constant variations. We find that in all positive steady states of so-called injective networks-networks that arise, for example, in metabolic and gene regulation contexts-there are certain firm bounds on the flux control coefficients. In particular, the control coefficient of the flux of a reaction, with respect to variation in its own rate constant, is delimited in a precise way. Moreover, for each pair of reactions, the flux of at least one of them must have a precisely delimited control coefficient with respect to variation in the rate constant of the other. The derived bounds can, however, be violated in noninjective networks, so for them a more pronounced lack of robustness could be exhibited. These results, which indicate a mechanism by which some degree of robustness is induced in the injective setting, also shed light on how robustness might evolve.