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

Kaushal Patel^* and Jyoti Kumawat

Department of Mathematics, Veer Narmad South Gujarat University, Surat, India.

Corresponding Author E-mail:kbpatel@vnsgu.ac.in

DOI : http://dx.doi.org/10.13005/bbra/3155

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.

KEYWORDS: Asymptotic Behaviour; Kinesiology of Enzymes; Next Generation Matrix Technique(R₀); System of Non-linear equations for reaction; Stability Analysis; Sensitive Analysis

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