Analytical Expressions for Steady-State Concentrations of Substrate and Oxidized and Reduced Mediator in an Amperometric Biosensor

A mathematical model of modified enzyme-membrane electrode for steady-state condition is discussed. This model contains a nonlinear term related to enzyme kinetics reaction mechanism. The thickness dependence of an amperometric biosensor is presented both analytically and numerically where the biological layer is immobilized between a solid substrate and permeable electrode. The analytical expressions pertaining to the concentration of species and normalized current are obtained using the Adomian decomposition method (ADM). Simple and approximate polynomial expressions of concentrations of an oxidized mediator, substrate, and reduced mediator are derived for all possible values of parameters (Thiele modulus), (normalized surface concentration of oxidized mediator), and (normalized surface concentration of substrate). A comparison of the analytical approximation and numerical simulation is also presented. A good agreement between theoretical predictions and numerical results is observed. 1. Introduction In recent years, polymer membranes are widely used as carriers for immobilization of enzymes [1]. They have been utilized in biomaterials, bioseparators, and biosensors [2]. The membranes provide an ideal support for the immobilization of the biocatalyst. Substrate partition at the membrane/fluid interphase can be used to improve the selectivity of the catalytic reaction towards the desired products [3]. Recently a new method for enzyme immobilization [4], based on a molecular recognition process, has been successfully used for the building of enzymatic biosensors and also of a chemically active membrane [5]. In the recent three decades, much effort has been devoted to the development of various biosensors involving biologically sensitive component and transformers—devices with many fields of applications [6]. Changes in membrane chemistry have been demonstrated by Robeson [7]. The better way of changing the membrane geometry aims to increase the membrane area per volume, thereby speeding the separation. This increased surface area has recently been identified as a high priority research need for membranes [8]. A two-substrate model for enzyme electrode has been devised experimentally [10, 11] where the nonlinear enzyme reaction was taken into account. This model was employed to describe the behaviour of a glucose oxidize (GOx) electrode [12, 13]. It has been found that the mediators could not totally replace the natural cosubstrate when both were present in the assay solution so that here a three-substrate model would be required. In these cases, a