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

Area of Science:

• Biotechnology
• Biochemical Engineering
• Computational Biology

Background:

• Biosensors are crucial for detecting analytes.
• Immobilized enzyme systems are widely used in biosensors.
• Modeling enzyme kinetics, like Michaelis-Menten, is essential for biosensor performance.

Purpose of the Study:

• To develop and analyze a mathematical model for an immobilized enzyme system in a micro-disk biosensor.
• To investigate the reaction-diffusion dynamics under steady-state conditions.
• To apply advanced computational methods for solving the model.

Main Methods:

• Developed a steady-state film reaction model for immobilized enzymes following Michaelis-Menten kinetics.
• Transformed the model into coupled differential equations based on dimensionless concentrations of hydrogen peroxide and substrate.
• Employed a neural network (NN) architecture trained with the Levenberg-Marquardt (LMT) algorithm for computational analysis.
• Generated initial datasets using MATLAB's 'pdex4' function and validated solutions with NNs-LMT.

Main Results:

• The NNs-LMT algorithm effectively calculated the effects of parameter variations on substrate and hydrogen peroxide concentrations.
• The model accurately represents the non-linear reaction-diffusion processes governed by Michaelis-Menten kinetics.
• Validation through error analysis, curve fitting, and regression confirmed the accuracy and robustness of the NNs-LMT approach.

Conclusions:

• The study successfully modeled an immobilized enzyme system for micro-disk biosensors using Michaelis-Menten kinetics.
• The NNs-LMT algorithm provides a powerful and accurate tool for solving complex biosensor models.
• This approach enhances the understanding and design of biosensors by enabling precise analysis of kinetic and diffusion parameters.