A simulation study on designing experiments to measure the K_m of Michaelis-Menten kinetics curves

Simulated data were used to assess the accuracy of determinations of K_m and V_max of the Michaelis-Menten equation using exhaustive Monte Carlo modelling of error variances in data sets. Curves were fitted using a direct least squares fit and the unweighted double reciprocal plot (commonly but incorrectly called the Lineweaver-Burk plot). At least 10 pairs of data points are needed in an experiment for K_m to have an error that is approximately normally distributed: 12 were used routinely in this study. Most published estimates of K_m are not based upon a sufficient number of data points. Evenly spaced data points were compared with substrate concentrations spaced logarithmically and inversely proportionally spaced data points. Data sets were spread below the K_m around the K_m and above the K_m. If the substrate concentrations are all below the K_m, the unweighted double reciprocal plot method is unreliable. K_m estimates made using unweighted double reciprocal plots were consistently inferior to estimates made using the direct least squares method. Estimates of K_m using the direct least squares fit are normally distributed under a wide range of experimental error conditions. Errors can be independent of substrate concentration, have a constant relative error, or be inversely proportional to the velocity (rate). Substrate concentrations are best evenly spaced; inversely proportionally spaced and logarithmically spaced substrates lead to skewed estimates of K_m. The majority of K_m values published are based on the statistically unsatisfactory unweighted double reciprocal plot. If similar data are analysed using the double reciprocal "Lineweaver-Burk" plot and the least squares methods, the least squares method can give useful results when the other does not.