Abstract
A mathematical model of potentiometric and amperometric enzyme electrodes is discussed. The model is based on the system of non-linear steady-state coupled reaction diffusion equations for Michaelis-Menten formalism that describe the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate, product and corresponding flux response have been derived for all values of parameters using Homotopy analysis method. The obtained solution allow a full characterization of the response curves for only two kinetic parameters (The Michaelis constant and the ratio of overall reaction and the diffusion rates). A simple relation between the concentration of substrate and products for all values of parameter is also reported. All the analytical results are compared with simulation results (Scilab/Matlab program). The simulated results are agreed with the appropriate theories. The obtained theoretical results are valid for the whole solution domain.
Highlights
Theoretical models of enzyme electrodes give information about the mechanism and kinetics of the biosensor
The Homotopy analysis method [38,39] was first proposed by Liao in 1992
We have theoretically analyzed the behavior of potentiometric and amperometric enzyme electrodes, which is previously described in Ref. [33]
Summary
Theoretical models of enzyme electrodes give information about the mechanism and kinetics of the biosensor. Albery and Bartlett [15] studied the steady-state current response of modified enzyme-based sensors where electron transfer from the enzyme to the electrode occurs directly by a redox mediator Later these authors [16] have derived 11 equations to differentiate between 7 limiting cases by offering a complete theoretical treatment of the basic reaction and diffusion processes in homogeneous solution. Rajendran / Natural Science 4 (2012) 1029-1041 concentration of substrate and mediator of ampereometric glucose sensor under steady-state conditions for all values of parameters have been reported The purpose of this communication is to derive approximate analytical expressions for the steady-state concentrations and flux for all values of parameters α, β and γ using Homotopy analysis method.
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