Determining Elasticities from Multiple Measurements of Steady-state Flux Rates and Metabolite Concentrations: Theory

A method to determine elasticities of individual enzymes within a metabolic pathway is developed. The method is based on measurements of steady-state metabolite pools and flux rates rather than the usual kinetic in vitro measurements on isolated enzymes. In this respect, it is an extension of the "double modulation method" by Kacser & Burns (1979, Biochem. Soc. Trans. 7, 1149-1160). The approach requires the use of effectors to modulate specifically the activities of individual enzymes. The number of specific effectors necessary to determine all elasticities depends upon the number of metabolites influencing the enzyme reaction rates. Two sets of implicit equations for the enzyme elasticities are derived. These equations hold for any pathway of any complexity but are, because of their complexity, studied in detail only for the simple case of a metabolic chain. For this case, enzyme elasticities can be calculated from measured metabolite concentrations and flux rates provided that certain conditions are met for the relative positions within the pathway of the modulated enzymes. For a metabolic chain in which the rate law of each enzyme is affected only by the reaction substrate(s) and product(s), the existence of two effectors specific for different enzymes allows determination of the kinetic laws of all enzymes positioned between the two target enzymes.