Mathematical modeling and analysis for Michaelis–Menten kinetics

IF 2 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2025-07-11 DOI:10.1007/s10910-025-01739-4

Gülnihal Meral, Derya Altıntan

引用次数: 0

Abstract

In this paper, the Michaelis–Menten dynamics are studied by reducing the original system to a new set of two nonlinear ordinary differential equations obtained via conservation relations and variable transformations. A stability analysis of the reduced system reveals the existence of a stable equilibrium point. The properties of boundedness, positivity, existence, and uniqueness of the solutions are established by constructing two sequences, which are subsequently proven to be Cauchy sequences. Finally, numerical simulations are performed to validate the theoretical results and illustrate the expected behavior of the model.

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Michaelis-Menten动力学的数学建模与分析

本文研究了Michaelis-Menten动力学，将原系统简化为由守恒关系和变量变换得到的两个非线性常微分方程的新集合。对简化后的系统进行了稳定性分析，揭示了稳定平衡点的存在。通过构造两个序列，得到了解的有界性、正性、存在性和唯一性，并证明了它们是柯西序列。最后，进行了数值模拟，验证了理论结果，并说明了模型的预期行为。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Chemistry 化学-化学综合

CiteScore

3.70

自引率

17.60%

发文量

105

审稿时长

6 months

期刊介绍： The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches. Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.