Table of Contents
ISRN Biochemistry
Volume 2014, Article ID 582675, 11 pages
Research Article

Analysis of Mathematical Modelling on Potentiometric Biosensors

1Department of Mathematics, K.L.N. College of Engineering, Sivagangai, Tamil Nadu, India
2Department of Mathematics, The Madura College, Madurai, Tamil Nadu 625 011, India

Received 25 February 2014; Accepted 30 March 2014; Published 7 May 2014

Academic Editors: T. Kietzmann and Y. Zhang

Copyright © 2014 N. Mehala and L. Rajendran. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.