Analytical expressions of steady-state concentrations of species in potentiometric and amperometric biosensor

Abstract

A mathematical model of potentiometric and amperometric enzyme electrodes is discussed. The model is based on the system of non-linear steady-state coupled reaction diffusion equations for Michaelis-Menten formalism that describe the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate, product and corresponding flux response have been derived for all values of parameters using Homotopy analysis method. The obtained solution allow a full characterization of the response curves for only two kinetic parameters (The Michaelis constant and the ratio of overall reaction and the diffusion rates). A simple relation between the concentration of substrate and products for all values of parameter is also reported. All the analytical results are compared with simulation results (Scilab/Matlab program). The simulated results are agreed with the appropriate theories. The obtained theoretical results are valid for the whole solution domain

Analysis of Mathematical Modelling on Potentiometric Biosensors

“…It is obvious from Figure 1(c) that when α increases the concentration u decreases and if α is very small, the concentration of the substrate is uniform and the curve becomes a straight line. Recently, Sivasankari and Rajendran [ 23 ] discussed the same mathematical model of potentiometric biosensors for the steady state and according to them when the diffusion parameter γ s is very small, the diffusion of the substrate concentration will be uniform and the curve becomes straight line. This reveals that the parameter time t has greater impact on diffusion.…”