Numerical Modeling of Multilayer Biosensor with Degrading Substrate and Product

Abstract

Numerical simulations of multilayer electrochemical biosensor with degradation of substrate and/or product have been presented. Action of the enzyme has been assumed to be a Michaelis--Menten process. Two cases: when product diffuses out of the biosensor and when the outer membrane is impermeable for product have been dealt with by adjusting boundary conditions in the mathematical model. A few versions of numerical algorithm, based on the Crank--Nicolson method, have been elaborated. Computed curves of current density have demonstrated analogous profiles to those observed in real experiments. Numerical evidence has shown that if uniform grid is employed to partition the time variable, the algorithm produces some oscillatory artifacts (in the profile of substrate concentration) near boundary of the outer layer. Counter intuitively, employing non-uniform grid in the direction of coordinate variable (distance to the biosensor electrode), can also result in such oscillations. However, these artifacts do not appear in any other part of substrate or product concentration profiles, also, they do not propagate to the electrode, hence they have no effect on evaluation of biosensor response. For best results we recommend to use uniform grid in coordinate direction and non-uniform (finer at the starting moment of modeling) grid in time direction.