Abstract
Enzymatic inhibition is one of the key regulatory mechanisms in cellular metabolism, especially the enzymatic competitive inhibition by product. This inhibition process helps the cell regulate enzymatic activities. In this paper, we derive a mathematical model describing the enzymatic 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. Integrating the model numerically, the effects of the model parameters on the model output are also investigated. Finally, a potential application of the model to realistic enzymes is briefly discussed.
Highlights
IntroductionEnzymes are capable of increasing the rates of the chemical reactions by reducing the activation energy of reactions [1, 2]
Enzymes are biocatalysts naturally present in living organisms
The formula for the product formation rate is already available in the literature [8, 9, 10], we shall derive it in a transparent manner by non-dimensionalising the equations and making rational approximations
Summary
Enzymes are capable of increasing the rates of the chemical reactions by reducing the activation energy of reactions [1, 2]. Enzymatic inhibition processes are very common mechanisms in cellular metabolism [3, 4]. In the competitive inhibition process, the enzyme molecule has one binding site for the substrate and inhibitor. Inhibitor molecules compete with substrate molecules for the binding sites of enzyme molecules. The enzyme molecule has one binding site that can accommodate both the substrate and the product. A minimal set of chemical reactions representing competitive product inhibition is given by.
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