Theory on the accurate estimation of Michaelis-Menten enzyme kinetic parameters from steady state and progress curve datasets

We show that neither pure steady state nor pure progress curve analysis yield reliable estimate of enzyme KM values since these methods are valid only at specific timescales and also use different type of datasets. All the currently proposed validity conditions of these methods assume a priori knowledge on KM. Hence, there is no way to check whether the obtained KM from a given dataset is a reliable estimate or not. Here we propose an integrated approach in which the same time course dataset will be analysed both in the progress curve as well as steady state perspectives at different reaction timescales across replications and substrate concentrations. Our theory shows that there exists an optimum reaction time at which the error in the estimation of KM using various progress curve and steady state methods show the least possible value so that the coefficient of variation of the median KM values obtained across various methods attains a minimum. Using detailed stochastic simulations, we confirm that the KM value obtained with minimum coefficient of variation across various methods is actually the reliable estimate that is close to the original KM value. We further show that using multiple nonlinear regression methods, the type of inhibition viz. competitive, uncompetitive and mixed can be accurately classified apart from obtaining the accurate inhibitor constants and IC50 values from Dixon type average velocity steady state datasets.