## Abstract

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.

Original language | English |
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Pages (from-to) | 239-254 |

Number of pages | 16 |

Journal | Journal of Theoretical Biology |

Volume | 178 |

Issue number | 3 |

DOIs | |

Publication status | Published - 7 Feb 1996 |

Externally published | Yes |