Abstract
A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.
Highlights
Electrochemical biosensors are used as detectors in several commercial analyzers for the accurate and rapid determination of various metabolites such as urea, glucose, lactate, and creatinine [1,2,3,4,5]
The enzyme layer catalyzes the conversion of metabolite molecules, consuming or producing an electrochemically detectable species
Numerical simulations were developed for modeling the reaction and diffusion processes that arise in the functional enzyme membranes of such systems
Summary
Electrochemical biosensors are used as detectors in several commercial analyzers for the accurate and rapid determination of various metabolites such as urea, glucose, lactate, and creatinine [1,2,3,4,5]. These biosensors are fabricated by immobilizing appropriate bioreagents (i.e., enzymes) in a layer adjacent to the sensing surface of the basic electrochemical transducers. Numerical simulations were developed for modeling the reaction and diffusion processes that arise in the functional enzyme membranes of such systems. The theoretical results agree with simulated data and offer the basis for reliable predictions of response time ranges for enzyme electrodes and enzyme reactors
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