Eq. 9.8 implies that for each metabolite at least one enzyme exerts negative control. For example, in the two-step pathway of Eq. 9.2 the CCC C2 will normally be negative because cx will decrease when the activity of E2 is increased .
The control coefficients are systemic properties of the overall metabolic system. Local properties of individual enzymes in the metabolic network can be described by elasticity coefficients such as the sensitivities of reaction rates with respect to metabolite concentrations. The elasticity of the ith reaction rate with respect to the concentration of metabolite Xj is the ratio of the relative change in the reaction rate caused by an infinitesimal change in the metabolite concentration, assuming that none of the other system variables changed from their steady state values:
Elasticity coefficients may also be defined for other compounds that influence a reaction rate that may not be pathway intermediates.
The relationship between FCCs and elasticity coefficients is expressed by the flux-control connectivity theorem that indicates how local enzyme kinetics affect flux control [267, 565]:
For the two-step pathway of Eq. 9.2, the connectivity theorem gives indicating that large elasticities are associated with small FCCs. For example, reactions operating close to thermodynamic equilibrium are normally very sensitive to variations in metabolite concentrations; their elasticities are large indicating that flux control for such reactions would be small . Connectivity theorems have also been developed for CCCs.
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