Motivation: The robustness of a biochemical network is defined as the tolerance of variations in kinetic parameters with respect to the maintenance of steady state. Robustness also plays an important role in the fail-safe mechanism in the evolutionary process of biochemical networks. The purposes of this paper are to use the synergism and saturation system (S-system) representation to describe a biochemical network and to develop a robustness measure of a biochemical network subject to variations in kinetic parameters. Since most biochemical networks in nature operate close to the steady state, we consider only the robustness measurement of a biochemical network at the steady state.
Results: We show that the upper bound of the tolerated parameter variations is related to the system matrix of a biochemical network at the steady state. Using this upper bound, we can calculate the tolerance (robustness) of a biochemical network without testing many parametric perturbations. We find that a biochemical network with a large tolerance can also better attenuate the effects of variations in rate parameters and environments. Compensatory parameter variations and network redundancy are found to be important mechanisms for the robustness of biochemical networks. Finally, four biochemical networks, such as a cascaded biochemical network, the glycolytic-glycogenolytic pathway in a perfused rat liver, the tricarboxylic acid cycle in Dictyostelium discoideum and the cAMP oscillation network in bacterial chemotaxis, are used to illustrate the usefulness of the proposed robustness measure.