Mathematical model for kinetics of enzymatic conversion of benzaldehyde and pyruvate to ( R)-phenylacetylcarbinol

Abstract

A mathematical model for the enzymatic biotransformation of benzaldehyde and pyruvate to R-phenylacetylcarbinol (PAC) and its associated by-products has been developed using a schematic method devised by King and Altman [E.L. King, C. Altman, A schematic method of deriving the rate laws for enzyme catalysed reactions, J. Phys. Chem. 60 (1956) 1375–1378] for deriving the rate equations for a complex enzyme-catalysed reaction. PAC is the commercial intermediate for the production of ephedrine and pseudoephedrine. A combinatorial theorem was applied using Visual Basic to create all of the possible reaction patterns for a simplified form of the pyruvate decarboxylase (PDC) biotransformation mechanism. The rate equations for substrates, product, and by-products have been derived from the patterns for yeast PDC and combined with a deactivation model for PDC from Candida utilis. The batch biotransformation profile generated by the model validated previously for a data set at initial substrate concentrations 50–150 mM benzaldehyde and 60–180 mM pyruvate, provided an acceptable fit for published data at initial concentrations of 400 mM benzaldehyde and 600 mM pyruvate.