Theoretical treatment and numerical simulation of potentiometric and amperometric enzyme electrodes and of enzyme reactors. Part 1: Steady-state concentration profiles, fluxes, and responses

A unified and comparative treatment of traditional potentiometric and amperometric enzyme electrodes and of enzyme reactors is presented. Exact theoretical descriptions are given for limiting cases, and relatively simple approaches for general cases. The latter approximations are obtained from the respective solutions for a two-segmented membrane model. They allow an explicit description and a full characterization of the response curves by only two kinetic parameters, which are the ratio of overall reaction and diffusion rates and the Michaelis constant. Numerical simulations based on a finite-difference procedure are developed for the functional enzyme membrane being represented by a sufficiently large number of elements (slices). These simulations are applied as virtual experiments for the evaluation of concentration profiles and fluxes of substrate and product species. The response characteristics of potentiometric and amperometric sensor systems, as well as the product release from enzyme reactors, are analyzed, and the influence of the relevant parameters on the steady-state response is demonstrated and discussed. Potentiometric and amperometric enzyme electrodes of identical kinetic properties are shown to exhibit the same response patterns for the actually sensed versus the nominal substrate concentrations. The simulated results are in excellent agreement with the appropriate theories. For all examples studied in this work the standard deviation between computer-simulated and theoretically approximated response curves is in the range of only 0.1-4% with respect to the sensed concentration. (C) 2011 Elsevier B.V. All rights reserved.