Analytical Expressions Pertaining to the Concentration of Substrates and Product in Phenol-Polyphenol Oxidase System Immobilized in Laponite Hydrogels: A Reciprocal Competitive Inhibition Process

Theoretical analysis corresponding to the diffusion and kinetics of substrate and product in an amperometric biosensor is developed and reported in this paper. The nonlinear coupled system of diffusion equations was analytically solved by Homotopy perturbation method. Herein, we report the approximate analytical expressions pertaining to substrate concentration, product concentration, and current response for all possible values of diffusion and kinetic parameters. The numerical solution of this problem is also reported using Scilab/Matlab program. Also, we found excellent agreement between the analytical results and numerical results upon comparison. 1. Introduction Theoretical modeling of biosensors usually provides some important insight into understanding the functioning of a biosensor. Usually, with the aid of an analytical device, it is not possible to measure the concentration of substrates inside the enzyme membranes. As a result, theoretical model in biosensors has been developed and employed as an important tool to study the analytical characteristics of biosensors. Initially, Goldman et al. [1] reported the theoretical modeling on biosensor. In that report [1], they have published an extensive theoretical treatment corresponding to substrate and product distribution in membranes containing enzymes. Later, Sundaram and Laidler [2] reported equations that describe the kinetics of reaction in an enzyme membrane immersed in a substrate solution. Kasche and coworkers [3] presented a model and equations that describe steady-state catalysis by an enzyme immobilized in spherical gel particles. Furthermore, they have demonstrated that the catalysis by a bounded enzyme at low substrate concentrations differs from the catalysis brought about by an unbound enzyme. Blaedel et al. [4] derived equations for steady-state fluxes of substrates and product through a membrane in simple systems. Catalytic biosensors are sensors that use enzymes which catalyse a specific conversion of analyte [5]. The analysis of the action of the biosensors containing one and two enzymes was performed under internal diffusion limitation in [6]. Gough et al. [7] have simulated the performance of a cylindrical biosensor employed for glucose monitoring at steady state. Jobst et al. [8] reported a finite difference scheme for the discretization of the model equation. Bacha et al. [9, 10] have developed a model that takes into account a variety of configuration designs to describe the behaviour of an amperometric biosensor for glucose monitoring. Recently, Baronas et al. [11–14] have