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Hi-<br>
Only one hydrodynamic parameter may be extracted rigorously from the
sedimentation coefficient extrapolated to zero solute concentration,
and that is the frictional coefficient, f, from which the Stokes
radius, Rs, may be calculated:<br>
f = 6 pi eta Rs, where pi = 3.14, eta is the solvent viscosity and Rs
is the Stokes radius. <br>
<br>
There are several things to note about this-<br>
<ol>
<li>f = 6 pi eta Rs for a solute that exhibits "stick" conditions
with the solvent (i.e. there are favorable solvent/solute surface
interactions). For "slip" conditions, f = 4 pi eta Rs. Where it has
been tested, biological molecules exhibit stick behavior. Given what is
known about the solvent interactions of biomolecules, I am comfortable
that there is no need to worry about using 6. FYI, for rotary
diffusion, the 4 pi term is the one to use.<br>
</li>
<li>The solvent viscosity is used because the calculation of Rs from
f becomes extremely complicated at higher concentrations. By using very
dilute solutions, or extrapolating s to c=0, there is no ambiguity
about what viscosity should be used. At high concentrations, the bulk
viscosity is not an appropriate term for interpreting the frictional
coefficient. To learn more, I recommend Fujita's monograph.</li>
<li>The Stokes radius comes from the solution of the Navier equation,
using Stokes approximation (an incompressible solvent). Solving the
Navier-Stokes equation involves setting a boundary that encloses one
volume of solution from another, then applying the conservation
principles for mass, energy, linear momentum and rotary momentum. There
is little that is instructive in going through the math involved in the
solution. One important point is that conservation of energy includes
conservation of charge, and that conservation of momentum includes
ion-ion momentum transfer through space.</li>
<li>The Stokes radius has been interpreted further, but only by
imposing a model. Perrin determined solutions to Stokes equations from
which the axial ratios for <u>solid, uncharged</u> molecules could be
calculated from the Stokes radius.</li>
<li>Calculation of axial ratios from the Stokes radius inevitably
results in ratios that are larger than would be expected (or that are
known from other data). A rational explanation for the discrepancy is
that there is a layer of solvent carried with the molecule, and that
this solvent layer adds to the molecular size. Hence, the inclusion of
the "solvation" layer, usually described in terms of the number of
grams of water bound per gram of protein. But this approximation needs
to be viewed with care since it is not a rigorous interpretation of Rs
as it is not developed from the Navier-Stokes equation. For starters,
there is only one parameter accessible from s, and now we are trying to
get two- the axial ratio and the extent of solvation. One of these two
terms must be set.<br>
</li>
<li>There is some confusion about the difference between solvation
and hydration. Sednterp estimates the <u>hydration</u> of a protein
using data from Kuntz and Kauffman obtained by proton NMR. Steve
Perkins has shown that the hydration of pretty much every protein is
about 0.3 g/g. However, it is the <u>solvation</u> of the protein that
matters in Rs (and even that is a bit of a kludge), and the solvation
includes the through-space momentum transfer due to charge coupling.
Hence, if you use the hydration values calculated by Sednterp, or if
you use Steve's value for hydration, you will almost inevitably end up
with axial ratio estimates that are large compared to estimates from
other methods. <br>
</li>
</ol>
The long and short of it is that Rs is a valid and valuable quantity
describing both the asymmetry of a protein and its interactions with
the solvent. Comparisons of Rs values for a protein acquired in
different solvents, or between molecules is valid. One should be
careful, though, about interpreting Rs solely in terms of the shape of
a molecule.<br>
Best wishes,<br>
Tom<br>
<a class="moz-txt-link-abbreviated" href="mailto:mitrana@mail.utexas.edu">mitrana@mail.utexas.edu</a> wrote:
<blockquote cite="mid1159156092.4517517ccdc38@webmailapp1.cc.utexas.edu"
type="cite">
<pre wrap="">Hi all
I have a very basic question. How does one get from determining the a/b ratio to
the gross molecular dimensions of the protein molecule. The molecular weight
should place a limit but I am a bit fuzzy as to how exactly this is carried
out.
Mitra
</pre>
</blockquote>
<br>
<pre class="moz-signature" cols="72">--
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</pre>
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