On the difficulties of fitting the double Michaelis-Menten equation to kinetic data

The double Michaelis-Menten equation describes the reaction kinetics of two independent, saturable uptake mechanisms. The use of this equation to describe drug uptake has been reported several times in the literature, and several methods have been published to fit the equation to data. So far, however, confidence intervals on the fitted kinetic parameters have not been provided. We present a grid-search method for fitting the double Michaelis-Menten equation to kinetic uptake data, and a Monte-Carlo procedure for estimating confidence intervals on the fitted parameters. We show that the fitting problem is extremely ill-conditioned, and that very accurate data are required before any confidence can be placed in the fitted parameters.