NMR for direct determination of Km and Vmax of enzyme reactions based on the Lambert W function-analysis of progress curves

¹H NMR spectroscopy was used to follow the cleavage of sucrose by invertase. The parameters of the enzyme's kinetics, K_m and V_max, were directly determined from progress curves at only one concentration of the substrate. For comparison with the classical Michaelis-Menten analysis, the reaction progress was also monitored at various initial concentrations of 3.5 to 41.8 mM. Using the Lambert W function the parameters K_m and V_max were fitted to obtain the experimental progress curve and resulted in K_m = 28 mM and V_max = 13 μM/s. The result is almost identical to an initial rate analysis that, however, costs much more time and experimental effort. The effect of product inhibition was also investigated. Furthermore, we analyzed a much more complex reaction, the conversion of farnesyl diphosphate into (+)-germacrene D by the enzyme germacrene D synthase, yielding K_m = 379 μM and k_cat = 0.04 s^− 1. The reaction involves an amphiphilic substrate forming micelles and a water insoluble product; using proper controls, the conversion can well be analyzed by the progress curve approach using the Lambert W function.