From: Borries Demeler <demeler@bioc09.v19.uthscsa.edu>
  To  : Diane Wakeham <wakeham@itsa.ucsf.edu>
  Date: Tue, 12 Sep 2000 07:00:07 -0500 (CDT)

Re: MW Determination for Rod- Shaped Protein(Axial Ratio?)

> 
> I am a rather inexperienced user of an XL-A analytical ultracentrifuge
> to assess the assembly state of a highly nonspherical protein (approx
> dimensions 115 x 28 x 24 angstroms, essentially rod shaped and rather
> large) likely to form dimers or possibly tetramers.  Using the simplest
> fits to my sedimentation equilibrium data with Optima software the
> molecular weight I obtain is about 10- 20 kD less than I would expect
> the actual protein size to be.  I checked the weight using mass spec to
> confirm that this was not due to degradation of the sample.

What percent error in MW does that turn out to be? A small percentage
can be expected, and can be due to other factors such as incorrect
determination of the partial specific volume, or incorrect temperature
and buffer correction. If the sample exhibits concentration dependency
and it is not part of the model, a reduction in MW is likely, but the 
fit would show that in terms of non-random residuals.

> I have many questions:  (1) Is it possible for molecular shape to affect
> the parameters this much 

sedimentation equilibrium is completely insensity to frictional factors
resulting from shape, since there is no net flow of solute at equilibrium,
hence no effect from frictional factors. If fact, SE is so insensitive 
to shape that even if you have a mixture of different shapes (but same
MW's), they can all be fit with the same SE model.

> (2) What software do you recommend (preferably
> free?) to fit this nonspherical data with?  

Any equilibrium software should work with spherical or non-spherical solutes
equally well.

> (3) Is there are a software
> package available to estimate the axial ratio, from estimated size
> parameters or from a crystal structure?

UltraScan will do that.

>  I tried to simulate the size using Ultrascan but found that it can't
> handle an axial ratio lower than 6.  If I divide the two largest
> dimensions in half as a crude estimate of radius for the axial a and b,
> my ratio is closer to 4.  Your input would be very useful as I assess
> how to interpret this data.

The reason UltraScan won't give you rod-shaped values for axial ratios
less than 6 is because the model for rod-shape doesn't hold up for 
such small ratios. An axial ratio below 6 doesn't suggest a rod shape
anyway, it is probably better modeled by a prolate ellipsoid or an
oblate ellipsoid. Keep in mind that those models are based on perfect
shapes and practically never approached in reality. They can be used
to get a general idea about shape, but not as absolute determinants.
A more sophisticated approach for modeling shape can be accmplished
with Kirkwood theory or bead modeling. Take a look at the program "hydro".

One last comment: If you are interested in the shape of your sample, you
should use sedimentation velocity or laser light scattering experiments,
since those experiments *are* sensitive to shape, while SE experiments
are not. Finite Element analysis (also available in UltraScan) will allow
you to determine the molecular weight, s20,W, D20,W amd the frictional
coefficient of the molecule from a SV experiment. It works well for 
single component systems such as yours.

Good luck, -Borries
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* Borries Demeler                                                             *
* The University of Texas Health Science Center at San Antonio                *
* Dept. of Biochemistry, 7703 Floyd Curl Drive, San Antonio, Texas 78229-3900 *
* Voice: 210-567-6592, Fax: 210-567-4575, Email: demeler@biochem.uthscsa.edu  *
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