Perturbation Theory in the Catalytic Rate Constant of the Henri-Michaelis-Menten Enzymatic Reaction

The Henry-Michaelis-Menten (HMM) mechanism of enzymatic reaction is studied by means of perturbation theory in the reaction rate constant k2 of product formation. We present analytical solutions that provide the concentrations of the enzyme (E), the substrate (S), as well as those of the enzyme-substrate complex (C), and the product (P) as functions of time. For k2 small compared to k-1, we properly describe the entire enzymatic activity from the beginning of the reaction up to longer times without imposing extra conditions on the initial concentrations Eo and So, which can be comparable or much different. © 2012 Society for Mathematical Biology.