From: Gary Knott <knott@civilized.com>
  To  : rasmb@alpha.bbri.org
  Date: Thu,  9 Sep 99 15:19:21 -0400

uniqueness

Dear Rasmb'ers,

Tom Laue's and others comments are certainly appropriate.

I am not very knowledgable about the physics and chemistry
of ultracentrifuge analysis, but I know quite a bit about
curve-fitting.  Given that your minimization code is
adequate (and most are, when properly coddled - but
beware of premature termination due to rolling into a
"flat-place"  (this is equivalent to ill-conditioning)), the
main things you can do to improve your discrimation between
two models are:

1. Use all the statistical tests and other statistical
tools at your disposal (like deviation plots, and various
information criteria), but use
them correctly and with understanding.

2. Use as much data under differing experimental conditions
as you can, so any differences have a chance of becoming
apparent.  (You can even compute sensitivity curves
which help determine where you should collect more data for the
greatest effect. (a sensitivity curve is a plot of
the derivative of a model function with respect to
a parameter, graphed over a suitable range of its
domain (i.e. radial positions) - MLAB can compute
such derivatives symbolically.)

3. Use all the information you have that constrains the
model being studied.  I.e.  Include appropriate
conservation of mass constraints, and do not
neglect non-ideality, or molecular
shape considerations.  Just because your curve-fitter
has trouble with models that have such conditions is
no reason to ignore them.

It is important to use appropriate weights for your data-points.
Marc Lewis' group are experts on this subject, and they
have a device for fitting data with the reference and the
sample O.D. signals given separately; the
errors therein are more nearly normal than are the
Cauchy-distributed errors that result from using the ratio of
these values.  The issue of weights is tied-up with the
issue of outliers; you should take care that outliers
can be justified to be such physically, if possible, and
not just be graphically deviant.

Also, it can be useful to
fit ultracentrifuge models together with models for
other experimental methodology simultaneously, with
shared parameters, such as vbar, as appropriate.
This generally makes better use of the entire complex
of available data than does
using one step to estimate some parameters and then
holding them fixed while you use another step to
estimate other parameters.

You may find the example on fitting a heterogeneous
association model to data found at www.civilized.com
to be of interest.  (click on the "examples and
technical applications" link.)

Cheers, ---
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