From: John Philo <jphilo@mailway.com>
  To  : John Correia <jcorreia@biochem.umsmed.edu>
  Date: Fri, 27 Jul 2001 16:31:20 -0700

RE: small peptides, offsets

Jack and RASMB,

No, I did not mean that for the sorts of low-curvature (very low sigma)
equilibrium absorbance data we have been discussing you can only correctly
analyze single species (non-associating) systems or that one can't (or
shouldn't) do global fitting. You can handle even the most complex systems
with low sigma data. There's no doubt, however, that higher sigma will
usually give better discrimination of models and association constants
because there is more physical separation.

With regard to global analysis and cross-correlation between offsets and all
other parameters, that definitely is a problem in general. Indeed my point
about needing to fix the offsets with low-curvature data can perhaps be
better stated by saying that under those conditions the cross-correlation
between the offset and the masses and/or association constants goes to 1, so
you absolutely cannot get reliable mass/association results with floating
offsets.

However, even for higher curvature data the cross-correlation between the
offsets and the more interesting parameters is much higher than one wants.
Just try doing a NONLIN-type analysis with and without floating offsets and
you'll often get very different answers. If you compare the fitted value of
an offset with an actual experimental determination from over-speeding, they
unfortunately often differ quite a bit.  That is one reason why I am a
strong advocate of getting an experimental value and fixing it, especially
for complex associations with lots of other floating parameters.

Jack, you imply that using global fitting of multiple rotor speeds helps to
constrain the offsets, but that's just the problem, the usual approach does
no such thing. Logically, a true offset should be independent of rotor
speed, but if you float them and look at the numbers, all too often they
vary significantly for the same channel at different speeds. In my own
versions of NONLIN when I do have to fit an offset I have the ability to
constrain the offset for the same channel at different speeds to be the same
(as I discussed briefly in a Methods. Enzymol. article last year), and I
think that's an important thing to do. When you have to use reductants, of
course, one unfortunately can't make this assumption.

With regard to what is a reasonable value for an absorbance offset, I must
say that IMHO unless you have reductants in there, if you get offsets of
0.05 AU then there is something wrong with your samples or your instrument.
Usually a large offset means there is some contaminating small molecule
contributing to the absorbance, and in such cases you may see a strong
correlation of the offset with the protein concentration. One source of such
contaminants are those *!*#!! color-coded plastic tubes some labs are found
of (throw them out!).

Yes, you are right that the conservation of mass (signal) approaches to
fitting equilibrium data do tend to force lower rotor speeds, again as I
discussed in that Methods. Enzymol. article. Hence you will see that many of
my studies of hetero-associating systems use fairly low sigma. That, in
fact, proves my first point that even the most complex systems can be
studied using low curvature data, if (and only if) you measure and fix the
offsets.

Phew. Now it's time for me to go on vacation (yay!).

John
-----Original Message-----
From: John Correia [jcorreia@biochem.umsmed.edu]">mailto:jcorreia@biochem.umsmed.edu]
Sent: Friday, July 27, 2001 2:07 PM
To: jphilo@mailway.com
Cc: rasmb@alpha.bbri.org
Subject: RE: small peptides


John - let me rephrase your comment to clarify - if there is no association
and using absorbance optics, assuming a small offset will accurately
determine MW from a single channel fit - or in a LnC vs r2/2 plot the slope
of the linear line will correctly give back the correct MW.

On my machine it is not unusual to have offsets of 0.002 up to 0.05 in
global fits of self associating data sets.  I typically do 9 loading
concentrations at one speed (lately all my data for a monomer-dimer-trimer
system I am working on is also two wavelengths).

So in practise how dependable is this offset assumption?

My understanding of globally fitting many channels of data, conc or speed,
is in part to help constrain the offsets and the Ao or meniscus
concentrations, thus giving the best global MW and/or association constants.
If the system is (reversible and) associating, then assuming offsets or
neglecting offsets sets up an error propagation between offset and Ao and
thus K.  When fiitting associating systems more curvature helps to determine
all parameters in a global sense, especially the Nmer values, although I
must admit I do not compare wide ranges of curvature, wide ranges of sigma,
to see the effect on Ks.  (A caveat in this is the fractionation of monomer
from polymer - too much curvature may mean the polymer is pelleting - I
usually try to spin at speeds where the largest Nmer has a sigma less than 4
to 5)

An additional point worth making, although not necessarily for the small
peptide case, if one uses conservation of concentration fitting methods,
then one must in fact spin al lower speeds and thus less curvature to avoid
loss of material.  This may be especially critical for analysis of
hetero-associating cases.  The conservation of mass in part compensates for
the information lost in the low curvature plus the complexity of having two
thermodynamic species.