Modeling of nonlinear boundary value problems in enzyme-catalyzed reaction diffusion processes

Abstract

A mathematical model of steady state mono-layer potentiometric biosensor is developed. The model is based on non stationary diffusion equations containing a non linear term related to Michaelis-Menten kinetics of the enzymatic reaction. This paper presents a complex numerical method (He’s variational iteration method) to solve the non-linear differential equations that describe the diffusion coupled with a Michaelis-Menten kinetics law. Approximate analytical expressions for substrate concentration and corresponding current response have been derived for all values of saturation parameter α and reaction diffusion parameter K using variational iteration method. These results are compared with available limiting case results and are found to be in good agreement. The obtained results are valid for the whole solution domain.