Modeling Immobilized Enzyme Reactions: Nonlinear Kinetics With Fractional- and Integer-Order Analysis

Abstract

This research investigates the immobilization of enzymes within porous materials of varying geometries, such as spherical and cylindrical pellet-shaped catalysts. The study focuses on modeling enzyme reactions using reaction–diffusion equations that capture the irreversible Michaelis–Menten kinetics, emphasizing the nonlinear nature of the process. A distinctive feature of this work is the incorporation of fractional derivatives to enhance the understanding of enzymatic reaction kinetics. To achieve this, a novel computational framework utilizing Laguerre wavelets is developed to compute substrate concentrations and effectiveness factors over a broad range of parameter values. The proposed Laguerre wavelet method (LAWM) is rigorously compared against established analytical and numerical approaches, including the Hermite wavelet method (HWM), Taylor series method (TSM), Adomian decomposition method (ADM), and the fourth-order Runge–Kutta method (RKM). The findings reveal a high degree of accuracy and consistency across all methods, underscoring the reliability and efficiency of the LAWM. This study offers new insights into enzyme kinetics within porous catalysts and highlights the potential of fractional-order models for advancing biocatalytic applications. The outcomes provide a robust theoretical foundation for optimizing the design and performance of immobilized enzyme reactors in industrial and biotechnological settings.