Simplifying the Analysis of Enzyme Kinetics of Cytochrome c Oxidase by the Lambert-W Function

Conventional analysis of enzyme-catalyzed reactions uses a set of initial rates of product formation or substrate decay at a variety of substrate concentrations. Alternatively to the conventional methods, attempts have been made to use an in- tegrated Michaelis-Menten equation to assess the values of the Michaelis-Menten KM and turnover kcat constants di- rectly from a single time course of an enzymatic reaction. However, because of weak convergence, previous fits of the integrated Michaelis-Menten equation to a single trace of the reaction have no proven records of success. Here we pro- pose a reliable method with fast convergence based on an explicit solution of the Michaelis- Menten equation in terms of the Lambert-W function with transformed variables. Tests of the method with stopped-flow measurements of the cata- lytic reaction of cytochrome c oxidase, as well as with simulated data, demonstrate applicability of the approach to de- termine KM and kcat constants free of any systematic errors. This study indicates that the approach could be an alterna- tive solution for the characterization of enzymatic reactions, saving time, sample and efforts. The single trace method can greatly assist the real time monitoring of enzymatic activity, in particular when a fast control is mandatory. It may be the only alternative when conventional analysis does not apply, e.g. because of limited amount of sample