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

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.