Evaluation of thermodynamic consistency of kinetic parameters in cyclic enzyme-catalyzed reaction networks

It is shown by analysis of a cyclic enzymatic network that the presence of zero net flux/current cycles impose strong thermodynamic constraints on the values of the kinetic parameters. Thermodynamic analysis is carried out for the four-node pyramidal reaction network involving the conversion of 7,8-­dihydrofolate (H₂F) and NADPH in the presence of H⁺ to 5,6,7,8-­tetrahydrofolate (H₄F) and NADP⁺ catalyzed by the universal enzyme dihydrofolate reductase (DHFR). The complete set of empty reaction routes in the DHFR pathway is identified, equations for the thermodynamic constraints imposed on the rate constants of the various elementary steps are written down, and the thermodynamic consistency of the experimentally determined rate constants is evaluated. The visual approach based on the theory of graphs can be employed to test the thermodynamic consistency of kinetic parameters of general cyclic enzyme-catalyzed reaction networks.