Evaluation of enzyme kinetic parameters using explicit analytic approximations to the solution of the Michaelis-Menten equation

The time-course of product accumulation during an enzyme-catalyzed reaction that conforms to the Michaelis-Menten rate equation is expressed by an explicit closed-form equation in terms of the Lambert W(x) function. Unfortunately, the use of direct solution of the Michaelis-Menten equation is limited, because the W(x) function is not widely available in curve-fitting software. The present commentary suggests an alternative to surmount this difficulty. The Lambert W(x) function can be approximated in terms of the elementary mathematical functions that enable the fitting of particular equations on time-course data of the Michaelis-Menten enzyme reaction by any nonlinear regression computer program. Three different demonstrated approximations of the W(x) with relatively high accuracies are shown here to be appropriate for use when progress curves are analyzed by the direct solution of the integrated Michaelis-Menten equation. The elementary and precise nature of these approximations makes them the most user-friendly open candidates for simple, but operative, kinetic parameter estimations from experimental time-course data.