Enzymatic synthesis of amoxicillin: avoiding limitations of the mechanistic approach for reaction kinetics

A recurrent doubt that occurs to the enzyme-kinetics modeler is, When should I stop adding parameters to my mechanistic model in order to fit a non-conventional behavior? This problem becomes more and more involving when the complexity of the reaction network increases. This work intends to show how the use of artificial neural networks may circumvent the need of including an overwhelming number of parameters in the rate equations obtained through the classical, mechanistic approach. We focus on the synthesis of amoxicillin by the reaction of p-OH-phenylglycine methyl ester and 6-aminopenicillanic acid, catalyzed by penicillin G acylase immobilized on glyoxyl-agarose, at 25 degrees C and pH 6.5. The reaction was carried on a batch reactor. Three kinetic models of this system were compared: a mechanistic, a semi-empiric, and a hybrid-neural network (NN). A semi-empiric, simplified model with a reasonable number of parameters was initially built-up. It was able to portray many typical process conditions. However, it either underestimated or overestimated the rate of synthesis of amoxicillin when substrates' concentrations were low. A more complex, full-scale mechanistic model that could span all operational conditions was intractable for all practical purposes. Finally, a hybrid model, that coupled artificial neural networks (NN) to mass-balance equations was established, that succeeded in representing all situations of interest. Particularly, the NN could predict with accuracy reaction rates for conditions where the semi-empiric model failed, namely, at low substrate concentrations, a situation that would occur, for instance, at the end of a fed-batch industrial process.