Theoretical treatment and numerical simulation of potentiometric and amperometric enzyme electrodes and of enzyme reactors. Part 2: Time-dependent concentration profiles, fluxes, and responses

The time-dependent behavior of sensor systems based on enzyme membranes is treated theoretically. The comparative treatment covers traditional potentiometric and amperometric enzyme electrodes as well as enzyme reactors. Theoretical solutions are derived by the method of Laplace transforms. The relationships refer to the analytically useful range of relatively low substrate concentrations where the response signal is a function of the sample concentration. Numerical simulations using finite-difference procedures are applied to verify the theoretical results. Nearly perfect correlations between predicted and simulated concentration profiles, fluxes, and responses are obtained. The response vs. time curves of enzyme electrodes are limited by asymptotic functions that are valid for systems with very high or very low substrate-conversion efficiency. Highly efficient enzyme membranes always exhibit a faster response than poorly efficient ones, and amperometric sensors generally respond faster than potentiometric sensors. An asymptotic time function is also found for the product release from poorly efficient enzyme reactors, whereas no such limit exists for highly efficient reactors. The present theory is capable of predicting the response times of enzyme electrodes and enzyme reactors. For potentiometric sensors the 99% response times (referring to the scale of sensed concentrations and given in units of the trans-membrane diffusion time) are between 3.93 and 5.41 for the most and the least efficient systems, respectively. For amperometric sensors the respective 99% response-time values range between 1.07 and 3.93. The time for reaching 99% of the final outward flux of product species from enzyme reactors are obtained as 1.21 and 5.18 for the most efficient and the least efficient systems studied, respectively. (C) 2011 Elsevier B.V. All rights reserved.