Introduction to Modeling of Biosensors

This chapter introduces mathematical modeling of catalytic biosensors. After a brief tutorial consideration of kinetics of biocatalytic reactions, transducer function of biosensors and a general scheme of biosensor action, a detail mathematical model is then presented for an amperometric biosensor based on a mono-layer of an enzyme immobilized onto the surface of the electrode. The biosensor is modeled by two-component (substrate and product) reaction–diffusion equations containing a nonlinear term related to the Michaelis–Menten kinetics of an enzyme reaction. A few modifications of the mathematical model describing the action of potentiometric, optical and fluorescence biosensors are discussed, too. A special emphasis is placed on the modeling biosensors at steady state and internal or external diffusion limitation with a contribution to the modeling biosensors at non-stationary state at some critical concentrations of the substrate when analytical solution of the governing equations is performed. Using numerical simulation, the influence of the model parameters on the biosensor response is investigated. The simulation of the biosensor operation particularly showed a non-monotonous change of the steady state biosensor current versus the membrane thickness at the various maximal enzymatic rates.