Sensitivity of monomolecular reaction networks: Signed flux-response to reaction rate perturbations

Sensitivity studies the network response to the perturbation of a reaction, at steady state. Ishii et al., among others, performed biological experiments, which study the response of metabolic networks to the knock-out of certain targeted reactions. The response is given as the increase, or decrease, or zero response, for each experimentally accessible concentrations of chemicals or fluxes in the system. In previous work, Brehm, Fiedler, and Mochizuki were able to present systematic criteria which distinguish zero response from nonzero response. Their results were based on the network structure, only, and neither depend on numerical models of the reactions, nor on numerical values of their parameters. With a focus on monomolecular reaction networks, our present paper extends these results to provide for the first time a criterion for predicting the sign of any nonzero response, without requiring any additional input information.