NMR for direct determination of Km and Vmax of enzyme reactions based on the Lambert W function-analysis of progress curves
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1H NMR spectroscopy was used to follow the cleavage of sucrose by invertase. The parameters of the enzyme's kinetics, Km and Vmax, 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 Km and Vmax were fitted to obtain the experimental progress curve and resulted in Km = 28 mM and Vmax = 13 ¦ÌM/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 Km = 379 ¦ÌM and kcat = 0.04 s?#xA0;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.
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