From: Borries Demeler <demeler@bioc09.uthscsa.edu>
  To  : Houphouet Hy Yarabe <hyarabe@unix1.sncc.lsu.edu>
  Date: Fri, 30 Apr 1999 07:42:02 -0500 (CDT)

Re: Molecular weight (Mw)

> 
> I aggree with him on the principle.  However, in my mind, the diffusion
> coefficients calculated from sedimentation velocity lack accuracy. Could
> somebody give me some input to address this reviewer.
> 
Yarabe,
The reviewer is correct. You should do a whole boundary fit of your data
subject to the following considerations: The accuracy of a diffusion
coefficient calculated from velocity experiments is subject to a couple
criteria:

1. Is the sample really homogeneous?

2. Is there enough signal on the diffusion for it to be accurately
measured/fitted?

Let me elaborate:

On Point 1: If you have a heterogeneous sample, the heterogeneity will
be responsible for some of the boundary spreading, and your (apparent)
diffusion coefficient will be too large. Unless you can account for the
other components (or the system, if there is some interaction going on),
a single component fit will be inappropriate. A good diagnostic is often
to calculate the f/f0 value from the fit, and if it is below one you
*know* the D can't be right.  So, rule #1: assert that you really have
a single component system in your velocity experiment. This is done
unambigously with the van Holde - Weischet analysis. Next, *IF* the
data analysis results in a single component system, fit the data to the
finite element model of a ideal single component system (if the sample
is large enough to give you stable plateaus and deplete the meniscus,
an approximate solution of the Lamm equation can also be used). You should
fit data for the entire cell, i.e., data scans ranging from early in the
experiment with boundaries near the meniscus to scans that are almost 
pelleting, to get maximum signal on your system. If you use an approximate
Lamm solution, you may be better off to exclude scans too close to the 
meniscus or the bottom of the cell, since the solutions are not too 
reliable in these regions. Finite element can be used for all scans.

On Point 2: If you have a sample, say DNA, with very small D values and
large S, you can sediment it in an hour and a half to the bottom of the
cell at moderate to high speed and you get very good resolution on S,
but lousy signal on D, since it had hardly any time to diffuse. In that
case, the result on D may not be as reliable as a run where you sediment
much more slowly at low speed to enhance the signal on D. In the latter
case, you lose resolution in S. Which is why it would be best to fit
to both experiments simultaneously. You could also fit each experiment
individually and use the S from the high speed and the D from the low
speed experiment, since they will have the higher accuracies. In any case,
you need to ascertain if the sample is really homogeneous with van Holde-
Weischet before you fit to the single component component.

Here are some recent references on the subject:

van Holde, K. E. and W. O. Weischet. (1978). Boundary Analysis of
Sedimentation Velocity Experiments with Monodisperse and
Paucidisperse Solutes. Biopolymers, 17:1387-1403

Demeler, B., Saber, H. and J. Hansen. (1997) Identification
and Interpretation of Complexity in Sedimentation Velocity
Boundaries.Biophys. J. 72, 397-407

Demeler, B., Saber, H. and J. Hansen (1997)  Identification
and Interpretation of Complexity in Sedimentation Velocity
Boundaries. Biophys. J. 72, 397-407

Schuck, P., C. E. MacPhee, and G. J. Howlett. (1998) Determination of
sedimentation coefficients for small peptides. Biophys. J. 74, 466-474

Schuck, P. (1998) Sedimentation Analysis of Non-Interacting and
Self-Associating Solutes using Numerical Solutions to the Lamm
Equation. Biophys. J.

Philo, John S. (1997) An Improved Function for Fitting
Sedimentation Velocity Data for Low-Molecular-Weight
Solutes. Biophys. J. 72,435-444

Behlke, J. and Ristau, O. (1997) Molecular Mass Determination
by Sedimentation Velocity Experiments and Direct Fitting of the
Concentration Profiles. Biophys. J. 72, 428-434

Software for analyzing velocity experiments is available from our
website at UTHSCSA: 

http://www.cauma.uthscsa.edu:

* finite element fitting software by Peter Schuck and myself
* software for fitting approximate Lamm solutions by John Philo
* van Holde - Weischet analysis by myself

I should also mention that there are other methods available to get D
from velocity experiments, in particular W. Stafford's method of 
fitting Gaussians to differences of velocity experiments. I don't
use this method, so I prefer if Walt would comment himself on that.

Good luck, -Borries