From: James D. Lear <lear@mail.med.upenn.edu>
  To  : Joel Mackay , rasmb@alpha.bbri.org
  Date: Tue, 7 Sep 1999 09:04:17 -0400

Re: significance?

This is a typical problem with fitting AU data to anything but the simplest
models.  It is always true that including another adjustable parameter in
the curve fitting will, at worst, give you the same chisqd and, nearly
always, will make it lower. In my view (and experience!), it is unwise to
rely totally on statistical measures to decide these things. It's all too
easy to apply a test of some kind and come up with an apparantly rigorous,
but totally wrong conclusion.  In your particular case, I'd like to know
how accurately you know the protein's partial specific volume (vbar).  I
think it quite possible that by letting vbar equal zero and allowing the
monomer buoyant molecular weight to float, you might get a better fit for
all the models.  Then you'll need to decide (by calculating vbar from the
known Mw of the monomer) which. if any, vbar is most reasonable.  Measuring
it, of course, is preferable if you can do it accurately enough. Hope this
is helpful.

At 12:33 PM 9/7/99, Joel Mackay wrote:
>Dear all,
>I have a question about deciding which model describes one's data best. I
>have recorded sedimentation equilibrium data at three speeds with three
>different dilutions for a protein which undergoes some self-association. I
>have been fitting the data in NONLIN. If i fit the data by fixing sigma to
>the monomer mass, allowing delta y and lnA values to float, and permitting
>a single association constant to float, i get the best fit with a
>monomer-trimer model (both monomer-dimer and monomer-tetramer have worse
>residuals and higher chi-squared etc according to NONLIN). If I instead
>allow an extra equilibrium constant to float, and call the two associations
>monomer-dimer and monomer-tetramer, i get a slightly lower chi-squared
>(0.0138 vs 0.014 for the monomer-trimer model). My question is, how do i
>decide if the extra complexity of the model is justified. I know there is a
>thing called an F-test, and thought that might be appropriate. If so, how
>does one apply it in this case? What do you all do in these situations? It
>seems that the extra variable is pretty risky, but presumably a
>sufficiantly large reduction in the chi-squared would justify its inclusion.
>cheers and thanks in advance for any help,
>Joel Mackay
>************************************************************************
>Dr Joel Mackay                  ph +61-2-9351-3906
>ARC Research Fellow                     fax +61-2-9351-4726
>Department of Biochemistry
>University of Sydney
>NSW 2006 Australia
>http://www.biochem.usyd.edu.au/~joel/
>************************************************************************

James D. Lear
Department of Biochemistry & Biophysics
Anatomy/Chemistry 309
University of Pennsylvania
36th & Hamilton Walk
Philadelphia, PA 19104-6059
Phone 215-898-2071
Fax   215-573-7229