Enzyme Reaction Kinetics: Integer and fractional order mathematical models

What is it about?

This groundbreaking study introduces a novel mathematical approximation method that leverages the independent polynomials of complete bipartite graphs to analyze enzyme reaction kinetics. Through rigorous validation and comparison with established solution techniques, the method's reliability and accuracy are thoroughly confirmed. The results hold significant promise for advancing the field of biocatalysis and offer valuable insights for the design of efficient enzyme reactors, paving the way for innovative applications in biotechnology. This could help us make better enzyme reactors for things like medicine and making food.

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Why is it important?

This work is important because it: 1. Addresses a significant gap in the existing literature by introducing fractional derivatives to investigate enzyme reaction kinetics. 2. Develops a novel approximation method (Bipartite Polynomial Approximation Method, BPAM) to analyze substrate concentration and effectiveness factor in enzyme reactions. 3. Provides a practical tool for optimizing enzyme reactor design and operation in industrial settings. 4. Contributes to sustainable production, environmental protection, and healthcare by enabling more efficient biocatalytic processes. What is unique in this work: 1. The use of fractional derivatives to model enzyme reaction kinetics, which is a new approach in the field. 2. The development of the BPAM method, which is a novel and efficient way to solve reaction-diffusion equations. 3. The comprehensive validation of the BPAM method against established methods (BWM, TSM, ADM, and RKM). 4. The investigation of both integer and fractional order Michaelis-Menten modelling for planar, cylindrical, and spherical catalysts. 5. The analysis of the effectiveness factor variability with the Thiele modulus, which provides valuable insights for enzyme reactor design. Overall, this work advances the field of biocatalysis by providing a new mathematical framework and a practical tool for optimizing enzyme reactions, which can lead to more efficient and sustainable industrial processes.