[RASMB] RE: DC/Dt vs. sedfit

[Borries Demeler]

Dear RASMB'ers, may I offer you my $0.02...

First, as we show in a chapter of the forthcoming book by Christine
[Brookes, E. and B.  Demeler. Genetic Algorithm Optimization for
obtaining accurate Molecular Weight Distributions from Sedimentation
Velocity Experiments. Analytical Ultracentrifugation VIII, Progr. Colloid
Polym. Sci. C. Wandrey, Editor. Springer], the issue of C(s) producing
misleading peaks under conditions of shape hetereogeneity is very real,
and the examples that Walter mentions are clearly in that category,
as are a host of others that we have come across. For example, of great
interest these days are neurodegenerative diseases, where irreversible
fibrils (aggregates) are formed, each molecule has a different f/f0
ratio, and the difference can be large. In these cases C(s) users
certainly have something to worry about.

IMHO, C(s) only provides reliable results in three cases, two of which can
be verified. One of them Walter already mentioned, it's the trivial case
of a single component. The other case is one where you have heterogeneity
in s, but not in f/f0. This category can be subdivided into two cases:

1) all of the particles are spherical (in which case the average f/f0
will be close to 1.0) and you can rely on both s and MW from C(s) to
be correct if f/f0 comes out to be 1.0.  If the average stays close to
1.0, there is no nonglobular component present (which would increase
the f/f0 average). I have seen systems with great heterogeneity in s,
but perfectly homogeneous in f/f0, all of the particles are spherical,
and the f/f0 will infact come out at 1.0.

2) all molecules have the same shape, but f/f0 is larger than 1.0. In
that case you ought to be sceptical of your results, because residual
deviations may be hidden in experimental noise and hide the fact that
C(s) does not match. Walter's point about the calibration of columns
is well taken.

If you are trying to fit a component with a low f/f0 value by trying
to match it with a solution that forces an f/f0 that is too large, you
will get this peak split into multiple peaks to the left and right of the
where the real peak should be - this is easily verified by simulation -
and regularization just hides, not eliminates this effect. The reason is
that boundary spreading due to diffusion is interpreted as heterogeneity
in s, which of course is not appropriate. Peter claims that you can just look
at the residuals and figure out which hybrid discrete/continuous model
can be used to fix the problem. Yes, perhaps, if you really know what
you are doing, and have a lot of ancillary information supporting your
hypothesis. In my experience the regular user will be quite challenged
to make this decision correctly.

So what can you do?

nonlinear least squares fitting of multiple parameters is hindered by
complicated error surfaces when the parameter space gets too large,
so for all but pauci- or monodisperse systems whole boundary fitting
is not the answer. Genetic Algorithms wonderfully overcome this problem,
but at considerable computational expense.

If you just want diffusion corrected s-value distributions, you should
look at the enhanced van Holde - Weischet analysis, as implemented in
UltraScan. This is completely model independent and doesn't require any
knowledge of f/f0. It is simply a graphical transformation of every
scan in the experiment which eliminates the diffusional boundary
spreading from the result. No assumptions about shape, molecular weight
or vbar have to made (the latter is strictly only true at 20C).

And then there is the two dimensional spectrum analysis (which Peter
has been alluding to), which has been available in UltraScan for quite a
while now. As implemented in UltraScan, this method does reliably resolve
the cases of heterogeneity in shape where C(s) falls short (if vbar's
are known, MW can be obtained as well), and superbly resolves different
aggregation schemes (end-to-end, side-by-side, etc). We will report our
parallel implementation of this approach at the conference in London in a
few weeks. The UltraScan version containing the two-dimensional spectrum
analysis can be downloaded from our website at www.ultrascan.uthscsa.edu

One more thing:
We are exploring a new approach to AUC data analysis - these computationally 
intensive methods are best moved onto remote supercomputers - and accessed
through the web, much like using pubmed, google or NCBI blast. If you
are interested in trying out a preliminary version offering data analysis
through a web interface for the 2-dimensional spectrum analysis or genetic
algorithm method, please get in touch with me off-list. More about that in London.

Best,
-Borries