Amperometric biosensors in an uncompetitive inhibition processes: a complete theoretical and numerical analysis

A mathematical model of an amperometric biosensor response for uncompetitive inhibition detection is discussed. The model is based on a system of reaction–diffusion equations containing a nonlinear term related to Michaelis–Menten kinetics of the enzymatic reaction. Two highly accurate and easily accessible analytical methods are used to solve the nonlinear differential equations that describe the diffusion coupled with a reaction term. Semi-analytical expressions for the concentrations of substrate, inhibitor, and product in addition to the corresponding current response are derived. The effects of various parameters such as layer thickness, bulk substrate concentration, Michaelis–Menten constant, maximum reaction velocity on current, and the sensitivity and resistance of a biosensor are investigated. A direct comparison with a numerical solution of the governing system is presented to confirm the accuracy of the derived approximate analytical solutions.