Last week, I was asked to review a new case study for W.H. Freeman for their 7th edition of Lenninger's Biochemistry. The study involved using enzyme kinetics to discover the identiy of a poisoner using an unnamed inhibitor. Alas, I had a difficult time getting the correct maximum enzyme velocity and Michaelis constant.

Initially, I did the usual non-linear regression of the kinetics plot in R using
`nls`

, but that wasn't right. Next I tried a Hanes-Woolf plot because
of it's relative accuracy at finding constants. As a last chance effort I made a
Lineweaver-Burk plot which had the "correct" values.

Educationally, the Lineweaver-Burk plot is used as a mostly accurate determination of the kinetics constants while being easy to both construct and read. However, the differences in computed constants between a Lineweaver-Burk, Hanes-Woolf, and basic non-linear regression seems non-trivial. Just how different are they?

Let's start with an example kinetic experiment:

Concentration of Substrate | Concentration of Products |
---|---|

1 | 0.11 |

3 | 0.25 |

5 | 0.34 |

10 | 0.45 |

30 | 0.58 |

50 | 0.61 |

and let's plot this out into a nice curve.

Following the non-linear least squares regression, the curve has an equation of

This can then be compared to curves derived from Lineweaver-Burk and Hanes-Woolf plots:

This figure gives an impression of accuracy, but it doesn't give the whole story. To that end, the standard errors for each model were calculated and tabulated below.

Model Type | Standard Error |
---|---|

Non-linear Regression | 5.85e-6 |

Lineweaver-Burk | 2.29e-5 |

Hanes-Woolf | 6.41e-6 |

It was said to me by a professor that the best solution isn't the most accurate, but rather the best mix of easy and accurate. The Lineweaver-Burk may be the least accurate derivation tested with my limited dataset, but an error of only ~0.00001 compared to the best model makes it more than accurate enough for quick kinetics work.