A Simulation Study on Designing Experiments to Measure theKmof Michaelis-Menten Kinetics Curves

Simulated data were used to assess the accuracy of determinations ofKmandVmaxof 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 forKmto have an error that is approximately normally distributed: 12 were used routinely in this study. Most published estimates ofKmare not based upon a sufficient number of data points. spaced data points were compared with substrate concentrations spaced logarithmically and inversely proportionally spaced data points. Data sets were spread below theKmaround theKmand above theKm. If the substrate concentrations are all below theKm, the unweighted double reciprocal plot method is unreliable.Kmestimates made using unweighted double reciprocal plots were consistently inferior to estimates made using the direct least squares method. Estimates ofKmusing 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 ofKm. jority ofKmvalues 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.