Solution of steady-state substrate concentration in the action of biosensor response at mixed enzyme kinetics

A mathematical modeling of an amperometric biosensor at mixed enzyme kinetics and diffusion limitation in the case of substrate inhibition is developed. The model is based on non-stationary diffusion equation containing a non-linear term related to non-Michaelis–Menten kinetics of the enzymatic reaction. This paper presents the complex numerical methods (He's variational iteration method and Homotopy perturbation method) to solve the non-linear differential equations that describe the diffusion coupled with a non-linear reaction terms. Approximate analytical expressions for substrate concentration have been derived for all values of parameters α, β and K.