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 ω function coupled with non-linear regression. Explicit expressions for the substrate and product concentrations in the integrated Michaelis-Menten equation were obtained using the ω function which simplified kinetic parameter estimation as root-solving and numerical integration of the Michaelis-Menten equation were avoided. The ω 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 ω function for kinetic parameter estimation. In all cases, the kinetic parameters obtained using the ω function were almost identical to those obtained using the conventional root-solving technique. The availability of highly efficient algorithms makes the computation of ω simpler than root-solving or numerical integration. The accuracy and simplicity of the ω function approach make it an attractive alternative for parameter estimation in enzyme kinetics.