Mathematical Modeling of Amoxicillin Synthesis in Batch and Semi-Batch Reactor: Application of Bayesian Statistics...

This study investigates the enzymatic synthesis of amoxicillin, focusing on its kinetic properties and their influence on antibiotic production in a batch-operated enzymatic reactor. The reaction is catalyzed by penicillin G acylase (PGA, E.C.3.5.1.11), which is immobilized on glyoxyl-agarose. The reaction involves the p-hydroxyphenylglycyne methyl ester and 6-aminopenicillanic acid (6-APA) for amoxicillin formation. Under kinetic control, parallel hydrolytic pathways lead to product loss. Two kinetic models were evaluated: one based on Michaelis-Menten kinetics and another incorporating reaction and equilibrium constants for the process steps. Parameter estimation for the models was performed at different concentrations using two mathematical approaches: the Markov chain Monte Carlo (MCMC) method, rooted in Bayesian statistics and characterized as nondeterministic, and genetic algorithm, an evolutionary computation method incorporating crossover, mutation, and selection operators. The relative root mean squared error (rRMSE) was selected as the metric for evaluating the predictive performance of the models. MCMC presented the best results for low ester concentrations, with rRMSE values ranging from 1.48% to 6.10% for the Michaelis-Menten-based model. The mathematical model was validated using data from an enzymatic reactor operating in semi-batch mode, demonstrating a satisfactory capacity to predict the system's dynamic behavior under this operational condition.