Analytical Expressions for Steady-State Concentrations of Substrate and Oxidized and Reduced Mediator in an Amperometric Biosensor

Loghambal Shunmugham,L Rajendran

doi:10.1155/2013/812856

Abstract

A mathematical model of modified enzyme-membrane electrode for steady-state condition is discussed. This model contains a nonlinear term related to enzyme kinetics reaction mechanism. The thickness dependence of an amperometric biosensor is presented both analytically and numerically where the biological layer is immobilized between a solid substrate and permeable electrode. The analytical expressions pertaining to the concentration of species and normalized current are obtained using the Adomian decomposition method (ADM). Simple and approximate polynomial expressions of concentrations of an oxidized mediator, substrate, and reduced mediator are derived for all possible values of parametersϕO2(Thiele modulus),BO(normalized surface concentration of oxidized mediator), andBS(normalized surface concentration of substrate). A comparison of the analytical approximation and numerical simulation is also presented. A good agreement between theoretical predictions and numerical results is observed.

Highlights

In recent years, polymer membranes are widely used as carriers for immobilization of enzymes [1]
The average relative error between our analytical result (17) and the numerical result is less than 0.3% for of oxidized mediator various values of φO2 concentration FO
This paper presents a theoretical treatment of an oxidized enzyme-membrane electrode in an amperometric biosensor

Summary

Introduction

Polymer membranes are widely used as carriers for immobilization of enzymes [1]. They have been utilized in biomaterials, bioseparators, and biosensors [2]. A two-substrate model for enzyme electrode has been devised experimentally [10, 11] where the nonlinear enzyme reaction was taken into account. It has been found that the mediators could not totally replace the natural cosubstrate when both were present in the assay solution so that here a three-substrate model would be required In these cases, a complex calibration curve of the enzyme electrode was observed [14, 15]. The information gained from this modeling can be useful in sensor design, optimization, and prediction of the electrode’s response

Mathematical Formulation and Analysis of the Problems

Results and Discussion

Conclusions

Nomenclature