km determination

Dr. Peter Gegenheimer PGegen at UKans.nolospamare.edu
Mon Dec 7 22:45:52 EST 1998


On Sun, 6 Dec 1998 04:02:53, keith at eve.cchem.berkeley.edu (Keith Rickert) wrote:

> In <7opiGDf98QgB-pn2-dy9Z1ZHxmmZ4 at rnaworld.bio.ukans.edu> PGegen at UKans.nolospamare.edu (Dr. Peter Gegenheimer) writes:
>
> >Yes -- it IS _always_ most accurate to fit the untransformed data to the equation
> >which describes the relationship between X and Y; you are guaranteed to get the best
> >estimate for the kinetic constants. Not only for the reasons Simon mentions, but also
> >because when you transform the variables, you also transform their experimental error
> >so that it no longer has a ~Gaussian distribution. Further, the transformations in
> >which one axis contains both V and S violate the assumtions of regression analysis,
> >in that the X and Y axis variables are no longer separate (you no longer have an
> >independent and a  dependent variable), and (so certain transforms) the experimental
> >error is no longer exclusively in the Y axis.
>
> While I generally agree with all of these points, I have to say
> that I still think there's a place for the linear transform plots.
> If your data has some kind of systematic deviation from
> Michaelis-Menten kinetics, it's often much easier to recognize
> that on a linear transform than on the non-linear plot.
> So I generally do both plots, but only derive constants from
> the nonlinear fit.

I forgot to discuss this point: in any nonlinear curvefitting, you have to examine
the plot of residuals. Indeed, the residual plot should be published along with the
fitted curve. The residual plot is exactly what you'd get if you pulled the curve
like a string to make it straight, and all the data points moved along with it -- in
other words, it's a linear plot of the deviation of the data points from the fitted
curve. For exactly the reason Keith Rickert gives, it is much easier to tell the
goodness of fit from the residual plot.

(I should acknowledge that the various linear plots are convenient ways to visualize
various types of enzyme inhibition mechanisms. I've never used them.)

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