From: Borries Demeler <demeler@bioc09.v19.uthscsa.edu>
  To  : arthur.rowe@nottingham.ac.uk
  Date: Tue, 16 Nov 1999 07:54:44 -0600 (CST)

Re: s coeff and shape

Dear Libby

I  would like to add a few comments to this:

> The method is simple enough, in principle. Find the frictional ratio
> (f/f0) using SEDNTERP, using your M value, an s value, and vbar if you
> have it (taking it as 0.73 ml/g will be good enough if you don't.  Or,
> of course, use a picket calculator and the relevant equation.
>
> If f/f0 is significantly greater than 1.2, you can be confident that your
> protein is either (i) assymetric, or (ii) swollen, with a substantial
> internal cavity filled with water.  The latter is only really likely
> with a large, oligomeric structure (e.g. a multi-enzyme complex).

I'm not sure what assymmetric means in this context, and I doubt this
conclusion can be drawn from f/f0 values. Non-globular would be more
general. A completely symmetric ellipsoid with an axial ratio > 1 would 
also give rise to f/f0 values > 1.

> As regards that s value.  If you are working at around (say) 1 mg/ml,
> then do not bother about any c-dependence.  

I think that c-dependence can be substantial at this concentration, 
especially for highly charged and non-globular molecules. DNA, for example,
(and even some highly charged proteins) will show a strong concentration 
dependence of s at concentrations much lower than 1 mg/ml.

> Just take the s value at the maximum in your g(s*) profile. 

I tend to disagree. The g(s*) distribution will mask all kinds of problems
with the data, since it isn't diffusion corrected, so you will likely miss
the fact that your data is concentration dependent (or heterogeneous,
or both) and use an S value that is too low. I'm also not aware of any
correction method that will account for concentration dependency in g(s*)
profiles. In my opinion, you were correct, van Holde - Weischet analysis
is the method of choice here.

> You are looking for serious assymetry,
> I gather, so who cares if the s value requires correction by the odd
> percent, or two ?
> 
> I think, incidentally, that you are mis-interpreting your van
> Holde/Weischet plot - I am not aware that it can readily give you a value
> for ks (the c-dependence coefficient).

Absolutely! In fact, vHW is the *only* model-independent approach that
can unambiguously indentify the presence of concentration dependence of S
in a single experiment. However, Arthur raises an important point here,
running multiple experiments at different concentrations is *essential*
in this case, because concentration dependency of S can be masked by
heterogeneity and vice-versa, so even vHW can't tell in every case
*unless* you run multiple concentrations and overlay the integral
distribution plots. If the overall shape of the integral distribution
plot changes from one concentration to the next, you got heterogeneity
on top of concentration dependency.  Even if your equilibrium experiment
seems to indicate homogeneity, it is not a sure thing, since you can
have multiple conformers with different frictional coefficients, which
would give rise to a heterogeneity in S, but still result in the same MW
in an equilibrium experiment.

But vHW can give you a good estimate for ks for any given concentration
range by virtue of the integral distribution plot. The only uncertainty is
caused by the fact that radial dilution is neglected in the concentration
dependency of s in a global vHW fit. But as Arthur says, what is a percent
or so, and the error will actually be much less.  For details, see:

Demeler, B., Saber, S. and J.C. Hansen. Identification and Interpretation
of Complexity in Sedimentation Velocity Boundaries. Biophysical Journal
(1997) 72, 397-407 (http://www.cauma.uthscsa.edu/publications/biophysj-1997/)

Also, you guys might be interested in the van Holde - Weischet tutorial
I have placed online, those issues are discussed there:

http://www.ultrascan.uthscsa.edu/tutorial/

> If you actually want to check
> c-dependence out, its best to do multiplex 3 cells at 3 starting values
> of c, and find the linear dependence of s on c from the g(s*)max values
> plotted against c (corrected for radial dilution).  ks values of around
> 8 ml/g or upwards are again indicative of either assymetry or swelling.

ks is a first order approximation only and hence unlikely to be linear
over a larger concentration range, so this method, while a good indicator
for the presence of conc. dependency of s, will likely give varying
results for different concentrations, i.e., the dependence of s on C
will be linear only for a small concentration range. Only looking at the 
maximum in a g(s*) distribution is still subject to the problems methioned
above.

AFAIK, the only method that would allow you to obtain *some* reliable
shape information would be finite element since it can model concentration
dependency while at the same time provide s and D for the calculation
of MW and f/f0. f/f0 is the *only* shape information you would be able
to derive, it is a measure of globularity. The larger the ratio, the
more non-globular the sample is. This doesn't have anything to do with
asymmetry, by the way, which to my knowledge is impossible to measure with
AUC (even an extended oblate or prolate ellipsoid has axes of symmetry).

Of course, once you obtain f/f0 you can propose hypothetical models based
on some known shapes that have identical f/f0 ratios. But that of course
has to be taken with a grain of salt, since there is no information
that allows you to determine *which* shape is appropriate, there is no
unique solution.

Naturally, only velocity experiments can yield such shape
information.  Both the finite element fitting method and the
prolate/oblate/rod/sphere modeling functions are part of the UltraScan
software, which also yields immediate f/f0 values and hypothetical 
ellipsoid models from your finite element analysis (www.ultrascan.uthscsa.edu)

Keep in mind that a finite element fit to a model for a concentration
dependent system is only warranted if you have good data, and the
system is indeed single-component (at least as long as you only fit
one experiment).  

Hope that helps some, -Borries