[RASMB] Weak association?

[Arthur Rowe]

Hi Andrew

For a system free of self-interaction, there should indeed be a  
negative slope to the regression of s upon c. The theoretical ks value  
can be computed (see my chapter in the 'Black Book') from

ks = 2*vbar*(Vs/vbar + (f/f0)^3)

which means that for a 'typical globular protein' the ks value will be  
around 5 (the above formula give the dynamic ks value - if you add on a  
vbar value then you get the kinetic ks value: the distinction was made  
theoretically by Burgers in ~1940, and in very elegant practical work  
on PSL spheres by Cheng & Schachman in 1953).

So - in hand-waving terms, there should be a reduction in s value of  
around 5% as c goes up to 10 mg/ml. It is simple enough to fit the  
regression of the weight-averaged s value on c, by incorporating the  
law of mass action (see our paper on weak interaction in carbohydrates  
cited by Peter). But in agreement with Tom I would think that there is  
a little less danger of interference from pressure etc effects if you  
go for low-speed equilibrium. You must of course deconvolute the Ka  
term away from classical 'thermodynamic' i.e. virial coefficient terms.  
Which is do-able. The principles involved have been well described by  
Allen Minton and his colleagues (1) but their practical method as  
described is heroic. The INVEQ fit does it in seconds, from just a  
single run (10 mg/ml is fine), and has been applied to a range of  
systems (see RASMB archives for refs). The fitting equation is simple  
enough - I really owe folks an apology for not having put the software  
up on the RASMB site as yet. I have the original version (in pro Fit  
for Mac) and a Grafit version for Windows. However - it is a trivial  
matter to enter the formula into Sigmaplot, ORIGIN, whatever you have  
in use. Although you will not get under Windows the beautiful range of  
fitting algorithms and error analyses that the mathematical physicists  
have put into pro Fit - at least without going into MatLab.

Finally - a quick offer, if you have an LSE profile, if its  
interference and 'baseline subtracted' and you have a sigma value for  
the monomer, just mail it to me. Doing the analysis will probably take  
me less time than mailing the results back! It's that easy.

Kind regards to you, Tom, and to all

Arthur

(1) Zorilla et al (2004) Biophysical Chemistry 108 89-100.  {we have  
also looked at RNAse and via INVEQ get an identical value for BM to  
that given in this paper}


On Feb 2, 2009, at 14:22, Leech, AP wrote:

> Hello all,
>
> I have done some SV runs at various concentrations 0.3-10 mg/ml on
> a protein (~14 ka) and the sedimentation coefficient appears to
> remain constant (about 1.58). I had expected it to drop slightly at
> higher concentrations, and so I suspect a weak self association.
> Buffer is NaCl/Tris.
>
> Is it reasonable to try and estimate an association coefficient
> from this sort of data, and what is the best way to do it? (Even
> a lower limit would be acceptable, as the intent is to show that
> dimerisation is not significant).
>
> I'm working my way through Gilbert & Gilbert at the moment (Meth.
> Enzymol vol 27, p273) but is there perhaps something more in the
> "global analysis" line?
>
> All comments appreciated,
>
> Andrew
>
> --  
> Dr Andrew Leech                   *  Laboratory Manager
> Technology Facility               *  Molecular Interactions Laboratory
> Department of Biology (Area 15)   *  Tel   : +44 (0)1904 328723
> University of York                *  Fax   : +44 (0)1904 328804
> PO Box 373,  York  YO10 5YW       *  Email : apl3 at york.ac.uk
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>
************************************************************************ 
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Arthur J Rowe
Professor of Biomolecular Technology / Director NCMH Business Centre
School of Biosciences
University of Nottingham
Sutton Bonington
Leics LE12 5RD

TEL:  0115 9516156
FAX:  0115 0516157
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