Parameter estimation using a direct solution of the integrated Michaelis-Menten equation.

A novel method of estimating enzyme kinetic parameters is presented using the Lambert omega function coupled with nonlinear regression. Explicit expressions for the substrate and product concentrations in the integrated Michaelis-Menten equation were obtained using the omega function which simplified kinetic parameter estimation as root-solving and numerical integration of the Michaelis-Menten equation were avoided. The omega function was highly accurate in describing the substrate and product concentrations in the integrated Michaelis-Menten equation with an accuracy of the order of 10(-16) when double precision arithmetic was used. Progress curve data from five different experimental systems were used to demonstrate the suitability of the omega function for kinetic parameter estimation. In all cases, the kinetic parameters obtained using the omega function were almost identical to those obtained using the conventional root-solving technique. The availability of highly efficient algorithms makes the computation of omega simpler than root-solving or numerical integration. The accuracy and simplicity of the omega function approach make it an attractive alternative for parameter estimation in enzyme kinetics.