Real-Time Enzyme Kinetics by Quantitative NMR Spectroscopy and Determination of the Michaelis–Menten Constant Using the Lambert-W Function

Enzyme kinetics is an essential part of a chemistry curriculum, especially for students interested in biomedical research or in health care fields. Though the concept is routinely performed in undergraduate chemistry/biochemistry classrooms using other spectroscopic methods, we provide an optimized approach that uses a real-time monitoring of the kinetics by quantitative NMR (qNMR) spectroscopy and a direct analysis of the time course data using Lambert-W function. The century old Michaelis–Menten equation, one of the fundamental concepts in biochemistry, relates the time derivative of the substrate to two kinetic parameters (the Michaelis constant KM and the maximum rate Vmax) and to the concentration of the substrate. The exact solution to the Michaelis–Menten equation, in terms of the Lambert-W function, is not available in standard curve-fitting tools. The high-quality of the real-time qNMR data on the enzyme kinetics enables a revisit of the concept of applying the progress curve analysis. This is particularly made feasible with the advent of analytical approximations of the Lambert-W function. Thus, the combination of NMR experimental time-course data with progress curve analysis is demonstrated in the case of enzyme (invertase) catalyzed hydrolysis reaction (conversion of sucrose to fructose and glucose) to provide students with direct and simple estimations of kinetic parameters of Michaelis–Menten. Complete details on how to implement the experiment and perform data analysis are provided in the Supporting Information.