Sensitivity of Contending Cellular Objectives in the Central Carbon Metabolism of Escherichia Coli

To ensure homeostasis as well as proliferation, cellular systems usually adapt to changes in environmental and intracellular conditions at the level of the flux phenotype. The latter is characterized by the biochemical reaction rates in the underlying metabolic network and depends on the concentration of individual metabolites. As a result, concentrations of metabolites with large effect on the flux phenotype are expected to be tightly controlled. We examine the sensitivity of the flux phenotype upon changes in metabolite concentrations via the shadow prices in a flux balance analysis using multiple contending objectives of the central carbon metabolism of E. coli. The shadow prices of the metabolites are determined individually for sampled solutions of the Pareto front and objective functions. Utilization of 13C flux measurements for different environmental conditions enables us to draw conclusions about the relation of shadow prices and physiological cellular states. We find that E. coli operates in the vicinity of an area of the Pareto front which exhibits low variation of shadow prices compared to the whole front, which enables to react to changing conditions without large changes in the reguatory machinery. In addition, the determined shadow prices under different conditions suggest an increased requirement for regulation of concentrations of metabolites from the pentose phosphate pathway under carbon-limiting conditions compared to aerobe conditions. Our study extends the applicability of concepts from classical constraint-based modelling in a multi-objective settings to obtain predictions about regulation of metabolite levels based solely on stoichiometry.