NMR for direct determination of K(m) and V(max) of enzyme reactions based on the Lambert W function-analysis of progress curves

Abstract

(1)H 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 41.8mM. 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)=28mM and V(max)=13μM/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)=379μM and k(cat)=0.04s(-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.