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.

中文翻译：

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模拟人己糖激酶 I 对葡萄糖的磷酸化

在本文中，我们开发了一个综合数学模型来描述己糖激酶 I对葡萄糖的磷酸化。葡萄糖磷酸化是糖酵解途径的第一步，因此，它在细胞中受到仔细调节。己糖激酶 I磷酸化葡萄糖以产生 6-磷酸葡萄糖，细胞通过抑制该酶的作用来调节磷酸化速率。细胞使用三个抑制过程来调节酶：变构产物抑制过程、竞争产物抑制过程和竞争性抑制过程。令人惊讶的是，己糖激酶 I的细胞调节尚未完全解决，因此，在本研究中，我们开发了一个详细的数学模型来帮助解开该行为。模型的数值模拟产生的结果与实验确定的己糖激酶 I 的行为一致。此外，模拟提供了对深奥酶促行为的生物学见解，例如磷酸化速率对无机磷酸盐浓度或产物 6-磷酸葡萄糖浓度的依赖性。对该模型进行了全局敏感性分析，以帮助确定己糖激酶 I的关键机制规定。敏感性分析还支持开发更简单的模型，该模型产生的输出非常接近完整模型的输出。最后，简要指出了该模型在辅助实验研究中的潜在效用。