Approximation of intra-particle reaction/diffusion effects of immobilized enzyme system following reverse Michaelis–Menten (rMM) mechanism: third degree polynomial and Akbari–Ganji methods

Two approximate analytical expressions based on third degree polynomial and Akbari–Ganji’s method (AGM) were derived for the reaction/difusion controlled kinetics of an immobilized enzyme (IE) systems. The approximation methods predict substrate concentration profle and efectiveness factor (ղ) in a porous spherical particle. The reaction is assumed to follow reverse Michaelis–Menten (rMM) kinetics. The approximate methods predictions were comparable to that of numerical solution (using the Matlab fnite diference function, bvp4c) at wide range of ز and y_o especially at low ز and high y_o (polynomial equation) and low ز and low y_o (AGM equation). Although the approximate solution was derived for rMM kinetics, the results can be used to describe other important enzymatic reaction kinetics such as simple Michaelis–Menten (MM) kinetics and MM with competitive product inhibition kinetics. A necessary design equation should be satisfed when using polynomial or AGM approximation for diferent enzyme kinetic equations. In this work, two examples of enzymatic reactions of industrial interest were studied, namely glucose-fructose isomerization follows rMM kinetics and hydrolysis of lactose follows Michaelis–Menten (MM) equation with competitive product (galactose) inhibition. Predictions of the developed third degree polynomial and AGM approximation equations agree with that of numerical solution, the percentage relative error for the efectiveness factor was less than 11 in comparison with the numerical solution. Good agreement between approximate and numerical estimations demonstrates the validity of these approximation methods.

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Published in: Reaction Kinetics, Mechanisms and Catalysis
License: https://creativecommons.org/licenses/by/4.0
See article on publisher's website: https://dx.doi.org/10.1007/s11144-023-02496-8