Approximate analytical solution for non-linear reaction diffusion equations in a mono-enzymatic biosensor involving Michaelis–Menten kinetics

Abstract

Here we consider the case where the enzyme reacts with an electroinactive substrate to produce an electroactive product which is quickly oxidized or reduced at the electrode/film interface. This model is based on the system of non-linear reaction diffusion equations containing a nonlinear term related to the Michaelis Menten kinetic of the enzymatic reaction. In this paper the powerful analytical method, called the recent approach of Homotopy analysis method is applied to solve the non-linear reaction diffusion equations in amperometric biosensors. A simple and closed-form of analytical expression for concentrations of substrate, product and corresponding current response in the case of an enzyme immobilized into a planar film onto an electrode have been derived. The effect of various parameters on current density is discussed. Numerical simulation (Matlab) for the concentration profile for non-steady state condition was carried out and compared with the analytical results. A satisfactory agreement is noted. A graphical procedure for estimating the kinetic parameters and sensitivity analysis of the parameters from current density is suggested.