Sensitivity of chemical reaction networks: A structural approach. 1. Examples and the carbon metabolic network

In biological cells, chemical reaction pathways lead to complex network systems like metabolic networks. One experimental approach to the dynamics of such systems examines their “sensitivity”: each enzyme mediating a reaction in the system is increased/decreased or knocked out separately, and the responses in the concentrations of chemicals or their fluxes are observed. In this study, we present a mathematical method, named structural sensitivity analysis, to determine the sensitivity of reaction systems from information on the network alone. We investigate how the sensitivity responses of chemicals in a reaction network depend on the structure of the network, and on the position of the perturbed reaction in the network. We establish and prove some general rules which relate the sensitivity response to the structure of the underlying network. We describe a hierarchical pattern in the flux response which is governed by branchings in the network. We apply our method to several hypothetical and real life chemical reaction networks, including the metabolic network of the Escherichia coli TCA cycle.