A mathematical model of enzymatic non-competitive inhibition by product and its applications

Enzymes are biological catalysts naturally present in living organisms, and they are capable of accelerating biochemical reactions in the metabolism process. Cells use many regulatory mechanisms to regulate the concentrations of cellular metabolites at physiological levels. Enzymatic inhibition is one of the key regulatory mechanisms naturally occurring in cellular metabolism, especially the enzymatic non-competitive inhibition by product. This inhibition process helps the cell regulate enzymatic activities. In this paper, we develop a novel mathematical model describing the enzymatic non-competitive inhibition by product. The model consists of a coupled system of nonlinear ordinary differential equations for the species of interest. Using nondimensionalization analysis, a formula for product formation rate for this mechanism is obtained in a transparent manner. Further analysis for this formula yields qualitative insights into the maximal reaction velocity and apparent Michaelis-Menten constant. Asymptotic solutions of the model are carefully given by using the homotopy perturbation analysis. A good agreement between the asymptotic solutions and numerical solutions are found. In addition, a Sobol global sensitivity analysis is implemented to help identify the key mechanisms of the enzyme activities. The results of this analysis show that the rate of product formation is relatively sensitive to the following factors: the catalytic rate of the enzyme, the rates of binding/unbinding of the product to/from the enzyme/enzyme complex. The numerical simulations provide insights into how variations in the model parameters affect the model output. Finally, an application of the model to the phosphorylation of glucose by mutant-hexokinase I enzyme is briefly discussed.