Study the Dynamic Behavior of the Enzyme-Substrate Reaction using Mathematical Modeling

Kaushal Patel*, Jyoti Kumawat
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Abstract

ABSTRACT: Physiological reaction plays a vital role in the human body. These reactions are analysed through Enzyme kinetics using a Mathematical model which helps to predict how enzymes behave in living organisms. However, many factors affect the working mechanism of biocatalysts (Enzymes). Chemical denaturant creates high disruption to the structure of enzyme with time. The determination of enzyme activities with time delivers information on enzyme parameters. Here the analysis aims to mathematical study for the development of Enzyme - substrates reaction for product formation based on time. So we formulate the model as a system of nonlinear differential equations which predicts the behaviour of product formation based on Enzyme- Substrate reaction parameters. Compute the threshold value for studying the enzyme effectiveness, complexity, and other parameters for the substrate product. Study the stability analysis for the ideal product formation and hence derive asymptotically stable solutions for the Enzyme- Substrate model with numerical simulation.
用数学模型研究酶-底物反应的动态行为
摘要:生理反应在人体中起着至关重要的作用。这些反应是通过酶动力学使用数学模型来分析的,该模型有助于预测酶在生物体中的行为。然而,许多因素影响着生物催化剂(酶)的工作机制。随着时间的推移,化学变性剂对酶的结构造成高度破坏。测定酶的活性随时间的变化可提供有关酶参数的信息。本文的分析目的是对酶-底物反应的发展进行基于时间的产物生成的数学研究。因此,我们将该模型表述为一个非线性微分方程组,该方程组根据酶-底物反应参数预测产物形成的行为。计算研究底物产物的酶效、复杂性和其他参数的阈值。研究了理想产物形成的稳定性分析,从而用数值模拟方法推导出酶-底物模型的渐近稳定解。
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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