A mathematical model of steady-state and non-steady-state responses of a pH-based potentiometric biosensor immobilizing organophosphorus hydrolase was developed. The model is based on non-stationary diffusion equations containing a nonlinear term related to the Michaelis-Menten kinetics of an enzymatic reaction. An analytical expression for the substrate concentration was obtained for all values of parameter a (Thiele modulus) using the homotopy perturbation method. From this result, the concentrations of the deprotonation products of an organophosphodiester (P h H, ZH and AH) were obtained. Our analytical results were compared with available simulation results. A satisfactory agreement with the simulation data is noted.
IntroductionBiosensors are possible due to the improvements of the biological components and the implementation of microsystem technologies. Enzymes are still the most appropriate recognition elements because they combine high chemical specificity and inherent biocatalytic signal amplification. Biosensors are classified according to the nature of the physical transducer. The potentiometric biosensor has assumed great importance in both theoretical and applied work. Modeling of biosensors is of crucial importance to understand their behavior. Normally, it is not possible to measure the concentration of substrates inside the enzyme membrane with analytical devices. Thus, mathematical models of biosensors have been developed and used as an important tool to study their analytical characteristics.Enzyme-based electrochemical biosensors are attractive for the determination of organophosphorus pesticides (OP) [1][2][3][4][5]. Recently organophosphorus hydrolase (OPH) has been applied instead of acetylcholineesterase (AChE) or butyrylcholinesterase (BChE) in biosensors for the determination of OP. With the discovery of OPH, an enzyme that can hydrolyze a wide range of organophosphate pesticides releasing detectable products [6,7], several enzyme and microbial biosensors based on OPH for the rapid, simple, and selective monitoring of these neurotoxic pesticides, with the potential in the field analysis, have been reported [8][9][10][11][12]. Many analytical methods, including gas and liquid chromatographic technologies [13], immunoassays [14], and biosensors based on choline esterase or alkaline phosphatase inhibition [15], have been reported for the determination of OP.Theoretical models of OPH biosensors are necessary to optimize the design and predict the behavior of the system. Models of pH-based potentiometric enzyme electrodes immobilizing enzymes other than OPH have been reported [16,17]. Recently, Huanlin and coworkers [1] have developed a numerical model for predicting the steady-state response of a pH-based potentiometric biosensor immobilizing OPH. To our knowledge, no rigorous analytical solution for the concentration of the substrate has been reported. In this paper, the theoretical model of a pH-based electrode immobilizing OPH was developed. The purpose of this paper was to derive an ana...