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 approximate to S-1 >> E-0 or S-1 << E-0, respectively, where E-0 and S-1 (= 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 >> Eo. Both the M M and the RM-M-SW are appropriate to field soil conditions with S >> E-0 given different values of specific reaction rate (k(3)) and half-saturation constant (K-s). 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. Published by Elsevier Ltd.