Analytical expressions pertaining to the concentration of catechol, o-quinone and current at PPO-modified microcylinder biosensor for diffusion-kinetic model

Abstract

A theoretical model for electroenzymatic process of a modified microcylinder electrode in which polyphenol oxidase occurs for all values of the concentration of catechol and o-quinone is presented. The model is based on system of reaction–diffusion equations containing a non-linear term related to Michaelis–Menten kinetics of the enzymatic reaction. In this paper, we implement a new analytical technique (He’s variational iteration method) is used to solve the system of non-linear differential equations that describe the diffusion coupled with a Michaelis–Menten kinetics law. Herein, we report the closed form of an analytical expressions pertaining to the concentration of catechol and o-quinone and corresponding current in terms of dimensionless reaction–diffusion parameters γE, γS, α, r1/r0(=α1), enzyme kinetics (χr0) and Michaelis–Menten constant (KM). A simple relation between the concentration of catechol and o-quinone also obtained. A good agreement with available limiting case results is noticed. The obtained results are valid for the whole solution domain.