No abstract

In this paper, we develop a comprehensive mathematical model to describe the phosphorylation of glucose by the enzyme hexokinase I. Glucose phosphorylation is the first step of the glycolytic pathway, and as such, it is carefully regulated in cells. Hexokinase I phosphorylates glucose to produce glucose-6-phosphate, and the cell regulates the phosphorylation rate by inhibiting the action of this enzyme. The cell uses three inhibitory processes to regulate the enzyme: an allosteric product inhibitory process, a competitive product inhibitory process, and a competitive inhibitory process. Surprisingly, the cellular regulation of hexokinase I is not yet fully resolved, and so, in this study, we developed a detailed mathematical model to help unpack the behaviour. Numerical simulations of the model produced results that were consistent with the experimentally determined behaviour of hexokinase I. In addition, the simulations provided biological insights into the abstruse enzymatic behaviour, such as the dependence of the phosphorylation rate on the concentration of inorganic phosphate or the concentration of the product glucose-6-phosphate. A global sensitivity analysis of the model was implemented to help identify the key mechanisms of hexokinase I regulation. The sensitivity analysis also enabled the development of a simpler model that produced an output that was very close to that of the full model. Finally, the potential utility of the model in assisting experimental studies is briefly indicated.

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 dierential 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 eects of the model parameters on the model output are also investigated. Finally, a potential application of the model to realistic enzymes is briey discussed.