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|
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|
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.