Analytical expressions of concentration and current in homogeneous catalytic reactions at spherical microelectrodes: Homotopy perturbation approach

Mathematical Analysis of Reaction-Diffusion Equations Modeling the Michaelis-Menten Kinetics in a Micro-Disk Biosensor

In this study, we have investigated the mathematical model of an immobilized enzyme system that follows the Michaelis-Menten (MM) kinetics for a micro-disk biosensor. The film reaction model under steady state conditions is transformed into a couple differential equations which are based on dimensionless concentration of hydrogen peroxide with enzyme reaction (H) and substrate (S) within the biosensor. The model is based on a reaction-diffusion equation which contains highly non-linear terms related to MM kinetics of the enzymatic reaction. Further, to calculate the effect of variations in parameters on the dimensionless concentration of substrate and hydrogen peroxide, we have strengthened the computational ability of neural network (NN) architecture by using a backpropagated Levenberg-Marquardt training (LMT) algorithm. NNs-LMT algorithm is a supervised machine learning for which the initial data set is generated by using MATLAB built in function known as "pdex4". Furthermore, the data set is validated by the processing of the NNs-LMT algorithm to find the approximate solutions for different scenarios and cases of mathematical model of micro-disk biosensors. Absolute errors, curve fitting, error histograms, regression and complexity analysis further validate the accuracy and robustness of the technique.

Electrochemical Performance of Micropillar Array Electrodes in Microflows

The microchip-based electrochemical detection system (μEDS) has attracted plenty of research attention due to its merits including the capability in high-density integration, high sensitivity, fast analysis time, and reduced reagent consumption. The miniaturized working electrode is usually regarded as the core component of the μEDS, since its characteristic directly determines the performance of the whole system. Compared with the microelectrodes with conventional shapes such as the band, ring and disk, the three-dimensional (3D) micropillar array electrode (μAE) has demonstrated significant potential in improving the current response and decreasing the limits of detection due to its much larger reaction area. In this study, the numerical simulation method was used to investigate the performance of the μEDS, and both the geometrical and hydrodynamic parameters, including the micropillars shape, height, arrangement form and the flow rate of the reactant solution, were taken into consideration. The tail effect in μAEs was also quantitatively analyzed based on a pre-defined parameter of the current density ratio. In addition, a PDMS-based 3D μAE was fabricated and integrated into the microchannel for the electrochemical detection. The experiments of cyclic voltammetry (CV) and chronoamperometry (CA) were conducted, and a good agreement was found between the experimental and simulation results. This study would be instructive for the configuration and parameters design of the μEDS, and the presented method can be adopted to analyze and optimize the performance of nanochip-based electrochemical detection system (nEDS).

Characteristics of fast mediated bioelectrocatalytic reaction near microelectrodes

The pseudo-steady-state current due to a mediated enzymatic reaction on a microelectrode is characterized on the basis of theoretical analysis and numerical simulation. The steady-state current is proportional to substrate concentration when the enzymatic reaction is considerably faster than substrate mass transport via nonlinear diffusion. Under such conditions, the reaction plane, where the mass flow of the substrate is converted to that of the mediator, exists near the electrode surface. The steady-state current increases as the diffusion coefficient of the substrate increases. In contrast, the diffusion coefficient and the concentration of the mediator have minor effects on the current. This difference can be explained on the basis of a change in the reaction plane location. When a sufficient amount of enzyme exists in a system, the system can be used as an amperometric biosensor, the response of which is independent of any change in enzyme activity.