Analytical solution of coupled non-linear second order differential equations in enzyme kinetics

Govindhan Varadharajan,Lakshmanan Rajendran

doi:10.4236/ns.2011.36063

Abstract

The coupled system of non-linear second-order reaction differential equation in basic enzyme reaction is formulated and closed analytical ex-pressions for substrate and product concentra-tions are presented. Approximate analytical me-thod (He’s Homotopy perturbation method) is used to solve the coupled non-linear differential equations containing a non-linear term related to enzymatic reaction. Closed analytical expres-sions for substrate concentration, enzyme sub-strate concentration and product concentration have been derived in terms of dimensionless reaction diffusion parameters k, and us-ing perturbation method. These results are compared with simulation results and are found to be in good agreement. The obtained results are valid for the whole solution domain.

Highlights

INTRODUCTIONThe reaction rate is measured and the effects of varying the conditions of the reaction investigated
Enzyme kinetics is the study of the chemical reaction that are catalysed by enzymes
The functionbvp4c in Scilab software which is a function of solving two-point boundary value problems (BVPs) for ordinary differential equations is used to solve this equation

Summary

INTRODUCTION

The reaction rate is measured and the effects of varying the conditions of the reaction investigated. Enzymes are usually protein molecules that manipulate other molecules the enzymes substrate These target molecules bind to an enzyme’s active site and are transformed into products through a series of steps known as the enzymatic mechanism. These mechanisms can be divided into single-substrate and multiple-substrate mechanisms. To understand the role of enzyme kinetics, the researcher has to study the rates of reaction, the temporal behaviours of the various reactants and the conditions which influence the enzyme kinetics. Varadharajan et al / Natural Science 3 (2011) 459-465 analytical expressions for substrate concentration, enzyme substrate concentration and product concentration interms of dimensionless reaction diffusion parameters k, and using Homotopy perturbation method (HPM) and compartive study of the same with Numerical simulation

MATHEMATICAL FORMULATION OF THE PROBLEM

NUMERICAL SIMULATION

AND DISCUSSION

Findings

CONCLUSIONS