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Hi Andrew,<br><br>
I guess it depends on your protein whether you want to do SE or SV.
Many proteins I've come across showed poorly reversible or irreversible
aggregates at these high concentrations. With SV they will
hydrodynamically resolve because they will sediment clearly ahead (as
opposed to the reversible dimers that you want to characterize, as
Arthurs pointed out). Likewise, you can see slower fragments from
degradation easily in SV. By low-speed SE, these things are much
more difficult to detect, and if they occur they would end up biasing the
gradients quite a bit. (Also, it takes more time during which
things may aggregate.) For such proteins, based on my experience I
would prefer SV. <br><br>
For sure, compression of the solvent, protein shape, or hydration will
affect the measured s-value, and perhaps partial volume changes in the
complexation may in theory affect the equilibrium constant, but these
factors would not change as a function of protein concentration.
<br><br>
If you go with SV, and can make reasonable assumptions about the
magnitude of the hydrodynamic nonideality, you can estimate the Kd for
dimerization. However, I would not attempt, at least at first, a
direct boundary model with Lamm equation solutions, because any traces of
impurities, aggregates or other degradation products will affect the
boundary shape and bias the result. (You can truncate the data to
exclude what doesn't fit, but that may potentially give you quite
arbitrary results.) Rather, I would determine the weight-average s-value
(from integrating the s-distribution) as a function of concentration, and
analyze this sw isotherm with monomer-dimer model including
non-ideality. That is much simpler and captures all the essential
information from the data. Such a model is readily available for
sw-isotherm analysis in SEDPHAT. <br><br>
Peter<br><br>
<br>
At 11:00 AM 2/2/2009, you wrote:<br>
<blockquote type=cite class=cite cite="">Hi Andrew <br><br>
For a system free of self-interaction, there should indeed be a negative
slope to the regression of s upon c. The theoretical ks value can be
computed (see my chapter in the 'Black Book') from <br><br>
ks = 2*vbar*(Vs/vbar + (f/f0)^3) <br><br>
which means that for a 'typical globular protein' the ks value will be
around 5 (the above formula give the <i>dynamic</i> ks value - if you add
on a vbar value then you get the <i>kinetic</i> ks value: the distinction
was made theoretically by Burgers in ~1940, and in very elegant practical
work on PSL spheres by Cheng & Schachman in 1953). <br>
<br>
So - in hand-waving terms, there should be a reduction in s value of
around 5% as c goes up to 10 mg/ml. It is simple enough to fit the
regression of the weight-averaged s value on c, by incorporating the law
of mass action (see our paper on weak interaction in carbohydrates cited
by Peter). But in agreement with Tom I would think that there is a little
less danger of interference from pressure etc effects if you go for
low-speed equilibrium. You must of course deconvolute the Ka term away
from classical 'thermodynamic' i.e. virial coefficient terms. Which is
do-able. The principles involved have been well described by Allen Minton
and his colleagues (1) but their practical method as described is heroic.
The INVEQ fit does it in seconds, from just a single run (10 mg/ml is
fine), and has been applied to a range of systems (see RASMB archives for
refs). The fitting equation is simple enough - I really owe folks an
apology for not having put the software up on the RASMB site as yet. I
have the original version (in pro Fit for Mac) and a Grafit version for
Windows. However - it is a trivial matter to enter the formula into
Sigmaplot, ORIGIN, whatever you have in use. Although you will not get
under Windows the beautiful range of fitting algorithms and error
analyses that the mathematical physicists have put into pro Fit - at
least without going into MatLab. <br><br>
Finally - a quick offer, if you have an LSE profile, if its interference
and 'baseline subtracted' and you have a sigma value for the monomer,
just mail it to me. Doing the analysis will probably take me less time
than mailing the results back! It's that easy. <br><br>
Kind regards to you, Tom, and to all <br><br>
Arthur <br><br>
(1) Zorilla <u>et al</u> (2004) Biophysical Chemistry 108 89-100. {we
have also looked at RNAse and via INVEQ get an identical value for BM to
that given in this paper} <br><br>
<br>
On Feb 2, 2009, at 14:22, Leech, AP wrote: <br><br>
<blockquote type=cite class=cite cite="">Hello all, <br><br>
I have done some SV runs at various concentrations 0.3-10 mg/ml on <br>
a protein (~14 ka) and the sedimentation coefficient appears to <br>
remain constant (about 1.58). I had expected it to drop slightly at <br>
higher concentrations, and so I suspect a weak self association. <br>
Buffer is NaCl/Tris. <br><br>
Is it reasonable to try and estimate an association coefficient <br>
from this sort of data, and what is the best way to do it? (Even <br>
a lower limit would be acceptable, as the intent is to show that <br>
dimerisation is not significant). <br><br>
I'm working my way through Gilbert & Gilbert at the moment (Meth.
<br>
Enzymol vol 27, p273) but is there perhaps something more in the <br>
"global analysis" line? <br><br>
All comments appreciated, <br><br>
Andrew <br><br>
-- <br>
Dr Andrew
Leech
* Laboratory Manager <br>
Technology
Facility
* Molecular Interactions Laboratory <br>
Department of Biology (Area 15) * Tel : +44 (0)1904 328723
<br>
University of
York
* Fax : +44 (0)1904 328804 <br>
PO Box 373, York YO10 5YW * Email :
apl3@york.ac.uk <br>
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