A note on the reverse Michaelis–Menten kinetics

We theoretically derived a general equation describing the enzyme kinetics that could be further simplified to the typical Michaelis–Menten (M–M) kinetics or the reverse M–M equation (RM–M) under the condition of S ≈ S1 >> E0 or S1 << E0, respectively, where E0 and S1 (= S + ES) are the concentrations of total enzyme and substrate including free substrate (S) and enzyme–substrate complex (ES). We showed that the related Schimel and Weintraub RM–M equation (RM–M–SW) can be derived from the Langmuir adsorption isotherm theory with S >> E0. Both the M–M and the RM-M-SW are appropriate to field soil conditions with S >> E0 given different values of specific reaction rate (k3) and half-saturation constant (Ks). In contrast to M–M and RM–M–SW models, the RM–M model is not applicable to field conditions because of its limited application to one substrate with a simple enzyme system. However, we demonstrate that the best formulation for the process of enzyme-mediated decomposition may vary depending on whether the process is limited by substrate or enzyme availability.