The relative values of the turnover number and the dissociation rate constant determine the definition of the Michaelis-constant

Abstract. In this work, we attempt to determine the assumptions of each case of the QSSA. We came to the conclusion that for an enzyme with average kinetics parameters the REA is a good approximation to derive the rate equation and the Km value tends to equal the dissociation constant K d . The active site classifies the population of the substrate into two energy states, the ground state, and the transition state. The ratio K m /K d is equal to the partition function of the assumed two-state-system. For the average enzyme, the partition function of the transition tends to equal 1 thus the majority of the substrate molecules are in the ground state and the assumption kcat << k −1 is valid hence Km ≈ Kd. In contrast, when the enzyme is diffusion controlled, the Km value is equal to the productive dissociation rate k cat /k 1 . We have also redefined the Km value as the equivalence point of the reaction rates, namely, the effective diffusion rate and the maximal catalytic rate, which reflects more clearly the transition from the bimolecular reaction to the unimolecular reaction in the saturation curve.