Kinetic Modeling of Enzymatic Cephalexin Synthesis with Neural ODEs and Surrogate-Accelerated Bayesian Inference

Abstract α-Amino ester hydrolases offer a promising route to the stereoselective synthesis of β-lactams such as cephalexin. However, published kinetic studies have encountered difficulty when extended beyond fitting of the data, indicating practical nonidentifiability of the underlying kinetic models. Here, we address this issue using Bayesian inference combined with a reaction-consistent neural ordinary differential equation surrogate that substantially accelerates parameter estimation. This framework enables efficient development of complex enzyme kinetic models even on limited hardware while providing rigorous uncertainty quantification of all parameters. To account for batch-dependent differences in active enzyme concentration, it was treated as a free parameter in each time series. Using this approach, the number of kinetic parameters was reduced from 12 to 9, and a useful kinetic model was obtained, which is identifiable and mechanistically consistent even under high substrate conditions.