Mathematical Modelling of an Enzyme-Based Biosensor

Abstract

The behavior of biosensors lies on a well-defined physical, chemical and biological reactions, which are specified by nonlinear differential equations. These biosensors have plethora of applications in diverse fields; hence mathematical modeling of the same is highly desirable. This can help in prefiguring its various characteristics. A mathematical model is proposed which studies the cyclic conversion of substrate in an amperometric biosensor. The governing parameters for the Michaelis-Menten kinetics of enzymatic reactions are the enzyme kinetic rate and the diffusion rate across the enzymatic layer. The mathematical model was analytically and numerically solved and simulated in MATLAB® v2016b software using partial differential equation solver pdepe function. . The non-dimensional mathematical model of the amperometric biosensor can be successfully used to investigate the response of biosensors with cyclic substrate conversion. The analytical results are compared with numerically simulated results for various conditions to validate the model parameters. Relative influence of these parameters is decided by a non dimensional number called Damkohler number, which is a ratio of the rate of enzymatic reaction to the rate of diffusion. The effect of Damkohler number on the current density, substrate concentration, and product concentration has been studied. It has been observed that when the Damkohler number is low then enzyme kinetics controls the biosensor response whereas when it is high (of the order of 1) the response is under control of diffusion rate. The current density is found to increase with the decrease in Damkohler number and vice versa.