Derivation and identification of a mechanistic model for a branched enzyme-catalyzed carboligation

The kinetic description of enzyme-catalyzed reactions is a core task in biotechnology and biochemical engineering. In particular, mechanistic kinetic models help from the discovery of the biocatalyst throughout its application. Chemo- or enantioselective enzyme reactions often undergo two alternative pathways for the release of two different products from a central intermediate. For these types of reaction, no explicit reaction equations have been derived so far. To this end, we extend the commonly used Cleland's notation for branched reaction pathways and explicitly derive the rate expressions for two-coupled ordered bi-uni reactions. This mechanism also leads to a ping-pong bi-bi mechanism for a transfer reaction between the two products via the same central intermediate of the reaction system. Using the cross-ligation of benzaldehyde and propanal catalyzed by the thiamine diphosphate-dependent enzyme benzaldehyde lyase from Pseudomonas fluorescens yielding (R)-2-hydroxy-1-phenylbutan-1-one as a case study, we performed model-based experimental analysis to show that such a reaction mechanism can be modeled mechanistically and leads to reasonable kinetic parameters.