Modular metabolic control analysis of large responses in branched systems--application to aspartate metabolism

Organisms subject to changing environmental conditions or experimental protocols show complex patterns of responses. The design principles behind these patterns are still poorly understood. Here, modular metabolic control analysis is developed to deal with large changes in branched pathways. Modular aggregation of the system dramatically reduces the number of explicit variables and modulation sites. Thus, the resulting number of control coefficients, which describe system responses, is small. Three properties determine the pattern for large changes in the variables: the values of infinitesimal control coefficients, the effect of large rate changes on the control coefficients and the range of rate changes preserving feasible intermediate concentrations. Importantly, this pattern gives information about the possibility of obtaining large variable changes by changing parameters inside the module, without the need to perform any parameter modulations. The framework is applied to a detailed model of Asp metabolism. The system is aggregated in one supply module, producing Thr from Asp (SM1), and two demand modules, incorporating Thr (DM2) and Ile (DM3) into protein. Their fluxes are: J(1), J(2), and J(3), respectively. The analysis shows similar high infinitesimal control coefficients of J(2) by the rates of SM1 and DM2 (C(v1)(J2) = 0.6 and C(v2)(J2) = 0.7, respectively). In addition, these coefficients present only moderate decreases when the rates of the corresponding modules are increased. However, the range of feasible rate changes in SM1 is narrow. Therefore, for large increases in J(2) to be obtained, DM2 must be modulated. Of the rich network of allosteric interactions present, only two groups of inhibitions generate the control pattern for large responses.