From: John Correia <jcorreia@biochem.umsmed.edu>
  To  : wakeham@itsa.ucsf.edu
  Date: Tue, 12 Sep 2000 10:15:32 -0600

Re: MW Determination for Rod- Shaped Protein(Axial Ratio?)

With all due respect to Bo, sed equil is affected by shape and nonideality
thru a virial coefficient - NONLIN allows you to include a 2nd virial
coefficent B in the fitting along with self-association.  I once measured
B for RNase, a small spherical protein at its pI, so it can be done.  It
does depend upon the optics you use, absorbance probably being too noisey
to get good estimates unless B is large, but interference being very
sensitive to nonideality.

Using similar equation to those Bo alludes to for rods or prolates you can
estimate the size of B for various models and thus calculate if it matters
in your case.  Note B is also influenced by charge.  See vanHoldes book
Physical BioChemistry, 2nd edition, for the approach, and a couple of
papers by Roark & Yphantis in Biochemistry, 10, 3241, 1971 & 11, 2925,
1972 for a detailed theory.  

As to random residuals, it depends upon what you actual did.  How many
data sets do you fit?  Fitting one data set can very easily give you
random residuals with a low MW.  Using Nonlin you can and should fit a
minimum of three data sets and I strongly suggest 9 or more loading
concentrtions &/or different speeds.  This is a much more robust approach
to estimating MW, K's and B.  What you also did not describe is fitting to
a reversible model.  If you are fitting a monomer-dimer system  as single
species, for example, than you should get a lower MW depending upon Kd and
what concentrations you are fitting.  To get the dimer MW you must be >>
100x above Kd.  So a low MW does not actually mean its a nonideality
effect.  It could be a case of just not saturated...& I think that is the
1st hypothesis to test.

The program you use also matters because many people fit to weight average
MW which approaches the nmer MW value much slower than Nonlin, which fits
to a z-average MW.

I suggest fitting multiple data sets globally to reversible models like
1-2 or 1-2-4 and then add B at the end.  We presume you estimated vbar
from the amino acid composition using sednterp and density in the similar
manner??  Temperature can be calibrated using Stafford's method.

Bo is correct sed vel is more sensitive to shape, but if you also have
reversible association then it will be hard to sort out end points for the
monomer and the nmers, if they exist, because you must span a wide
concentration range, easier with interference, and at high concentration
nonideality gets you again.  The shape factor will be in the endpoint
values which may thus be only obtainable by extrapolations.  Depending
upon the model (1-2 or 1-3) you may be able to fit the data with Shuck's
program to estimate the endpoints, but I would be cautious about fitting
to S1 and S2 and K.

-------------------------------------------------------------------
 Dr. John J. "Jack" Correia
 Department of Biochemistry
 University of Mississippi Medical Center
 2500 North State Street
 Jackson, MS  39216
 (601) 984-1522                                 
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 email address: jcorreia@biochem.umsmed.edu     
 homepage location: http://www2.umsmed.edu/dept/biochemistry/correia.html
 
 dept homepage location:   
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