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

A novel method of estimating enzyme kinetic parameters is presented using t he Lambert omega function coupled with nonlinear regression. Explicit expre ssions for the substrate and product concentrations in the integrated Micha elis-Menten equation were obtained using the omega function which simplifie d 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 inte grated Michaelis-Menten equation with an accuracy of the order of 10(-16) w hen double precision arithmetic was used. Progress curve data from five dif ferent 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 thos e 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 o mega function approach make it an attractive alternative for parameter esti mation in enzyme kinetics. (C) 1999 Elsevier Science B.V. All rights reserv ed.