Multi-objective shadow prices point at principles of metabolic regulation

Perturbations in environmental and intracellular conditions often lead to changes across all cellular layers, from transcription to metabolism. Regulatory mechanisms are key to mediating these changes to maintain homeostasis and to ensure viability. Since changes in metabolic reaction rates are partly due to perturbations in metabolite concentrations, it is expected that metabolites with large effect on those reaction rates which govern metabolic functionality are tightly regulated. The extent of metabolic regulation has been quantified by the sensitivity of an individual metabolic function to changes in metabolite concentrations, in particular by shadow prices in the constraint-based modeling framework. However, the system-wide characterization of the extent to which metabolite concentrations are regulated in the more realistic scenario of multiple contending tasks remains elusive. Here we examine multi-objective shadow prices for the central carbon metabolism of Escherichia coli whose reaction rates are shaped by several contending metabolic functions. We determine shadow prices for sampled solutions of the Pareto front, which characterizes the space of multi-objective optima, for three contending metabolic functions that provide the best agreement with 13C-labeling experiments. By analyzing the parts of the Pareto front closest to the experimentally determined flux phenotypes, we show that E. coli operates in the vicinity of an area of the Pareto front which facilitates robust and efficient regulation. In addition, we find significant associations between features of the transcriptional regulatory network and the sensitivity of E. coli's metabolic functionality to changes in metabolite concentrations. We demonstrate that the structural constraints of the metabolic network together with data on condition-specific flux phenotypes can be effectively used to dissect metabolic regulation on a system-wide level.