Mathematical Model for Bio-directional Diffusion of Reactants and Products in the Enzymatic Reaction of Glucose in a Spherical Matrix

K Saranya

doi:10.11648/j.acm.20170602.16

Abstract

In this paper the theoretical model of glucose–oxidaise loaded in chitosan-aliginate microsphere and hydrogen peroxide production is discussed. The glucose and oxygen in the medium diffuse into the microsphere and react, as a catalyst by glucose oxidase, to produce gluconic acid and hydrogen peroxide. The model involves the system of nonlinear nonsteady-state reaction-diffusion equations. Analytical expressions for the concentrations of glucose, oxygen, gluconic acid and hydrogen peroxide are derived from these equations using homotopy perturbation and the reduction of order method. A comparison of the analytical approximation and numerical simulation is also presented. An agreement between analytical expressions and numerical results is observed. The effect of various parameters (glucose concentration in the external solution, particle size, enzyme loading and Michaelis constant etc.) on the concentration of gluconic acid and hydrogen peroxide release is discussed. Sensitivity analysis of parameters is also discussed.

Highlights

Reactive oxygen species (ROS) are chemically reactive molecules containing oxygen
[2] [3] discuss the theoretical and experimental model of glucose sensitive membrane. [2] have developed a mathematical model to describe a dynamic process of diffusion of reactants, coupled with an enzymatic reaction inside a glucose composite membrane containing an ionic nano particles, glucose oxidase and catalase embedded in a hydrophobic polymer. [4] analyzed the theoretical model describing the process of reaction and diffusion in glucoseresponsive composite membranes
The analytical expression of concentration of glucose, oxygen, gluconic acid and hydrogen peroxide versus radius of microsphere is compared with simulation results in Fig. 3, for steady state condition

Summary

Introduction

Reactive oxygen species (ROS) are chemically reactive molecules containing oxygen. Examples include peroxides, superoxide, hydroxyl radical and singlet oxygen. [2] have developed a mathematical model to describe a dynamic process of diffusion of reactants, coupled with an enzymatic reaction inside a glucose composite membrane containing an ionic nano particles, glucose oxidase and catalase embedded in a hydrophobic polymer. To the best of author’s knowledge, no general analytical expressions for the concentrations glucose, oxygen, gluconic acid and hydrogen peroxide for all values of reaction/diffusion parameters. The purpose of the present study is to derive simple approximate analytical expression for concentrations profiles of various species inside the GOX-MS for steady and non-steady state conditions. This model can be used to predict the system performance and determine the appropriate combination of material and geometries that can yield useful devices

Objectives

Results

Conclusion