Sign-sensitivity of metabolic networks: which structures determine the sign of the responses

Abstract

Perturbations are ubiquitous in metabolism. A central tool to understand their effect on metabolic networks is sensitivity analysis, which investigates how the network responds to external perturbations. We follow here a structural approach: the analysis is based on the network stoichiometry, only, and thus it is purely qualitative and does not require any quantitative knowledge of the reaction rates. We consider perturbations of reaction rates and metabolite concentrations, at equilibrium, and we investigate the responses of the reaction fluxes and the metabolite concentrations. In particular, for general metabolic systems, this paper focuses for the first time on the sign of such responses, i.e. whether a response is positive, negative or whether its sign depends on the parameters of the system. We identify and describe certain kernel vectors of the stoichiometric matrix, which are the main players in the sign description.