From: John Correia <jcorreia@biochem.umsmed.edu>
  To  : j.mackay@biochem.usyd.edu.au
  Date: Tue, 07 Sep 1999 17:54:55 -0600

the significance of a fit is the heart of the matter

Joel

Mike Johnson is better to answer this (does he subscribe to rasmb?) since
he developed Nonlin, but Nonlin, at least the versions from UCONN,
determine an F statistic and properly correct the rms of the fit for the
increase in the number of parameters.   A marginal improvement in rms
(0.0138 vs 0.0140) is not enough reason to abandon 1-3 for 1-2-4.

That is not to say the question then comes down to statistical opinions,
which incidentally is the only way we can ultimately judge any fitting
exercise.  

First I would ask questions like why only 3 concentrations - Nonlin will
fit up to 15 data sets so why limit the range to just 9.  More
specifically, the ability to discriminate between a trimer & a tetramer is often due
to the concentration and the degree of saturation of the largest species. 
Thus, higher concentrations, possibly requiring a change in wavelength,
might improve resolution.

I & others like to make a species plot that essentially shows fraction of
each polymer vs total conc and allows you to judge the degree of
saturation.

Unfortunately, for my systems there always seems to be something else that
appears, like 1-2-4-8 thus confusing the 1-2-3 vs 1-2-4 question.  I
usually revert to the simplest model and/or indicate the range of
uncertainty.

The suggestion about a two species plot is on the mark, except Dennie
Roark & Dave Yphantis developed it in the late 60's.  Walter does have one
of the best paper discussing graphical methods including 2-species plots
(Biophy J, 1980, 29, p 149) & he is the major user of these techniques.  
(We use them to get a start on easy issues like reversibility.)   The
problem is if concentration is limiting resolution the same uncertainty
will apply.  Furthermore, two species plots have more error intrinsic to
them than direct fitting; the data are transformed to sliding MW's and
then ratios are plotted, each a step that contributes uncertainty.  If
Nonlin can't resolve it Biospin analysis is unlikely to.  (Incidently,
Walter & Jeff Lary have a PC version of Dennie's Biospin they might make
available???)

The references to vbar really only say sigma is uncertain - so vary sigma
+/- the error in vbar and see what you get.  Float sigma & see what you
get.  Does it fall in the +/- for vbar.


-------------------------------------------------------------------
 Dr. John J. "Jack" Correia
 Department of Biochemistry
 University of Mississippi Medical Center
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