[RASMB] Weak association?

Tue Feb 3 08:30:59 PST 2009

Hi Andrew,

I guess it depends on your protein whether you want to do SE or SV.  Many 
proteins I've come across showed poorly reversible or irreversible 
aggregates at these high concentrations.  With SV they will 
hydrodynamically resolve because they will sediment clearly ahead (as 
opposed to the reversible dimers that you want to characterize, as Arthurs 
pointed out).  Likewise, you can see slower fragments from degradation 
easily in SV.  By low-speed SE, these things are much more difficult to 
detect, and if they occur they would end up biasing the gradients quite a 
bit.  (Also, it takes more time during which things may aggregate.)  For 
such proteins, based on my experience I would prefer SV.

For sure, compression of the solvent, protein shape, or hydration will 
affect the measured s-value, and perhaps partial volume changes in the 
complexation may in theory affect the equilibrium constant, but these 
factors would not change as a function of protein concentration.

If you go with SV, and can make reasonable assumptions about the magnitude 
of the hydrodynamic nonideality, you can estimate the Kd for 
dimerization.  However, I would not attempt, at least at first, a direct 
boundary model with Lamm equation solutions, because any traces of 
impurities, aggregates or other degradation products will affect the 
boundary shape and bias the result.  (You can truncate the data to exclude 
what doesn't fit, but that may potentially give you quite arbitrary 
results.) Rather, I would determine the weight-average s-value (from 
integrating the s-distribution) as a function of concentration, and analyze 
this sw isotherm with monomer-dimer model including non-ideality.  That is 
much simpler and captures all the essential information from the 
data.  Such a model is readily available for sw-isotherm analysis in SEDPHAT.

Peter

At 11:00 AM 2/2/2009, you wrote:
>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
>>_______________________________________________
>>RASMB mailing list
>>RASMB at rasmb.bbri.org
>><http://rasmb.bbri.org/mailman/listinfo/rasmb>http://rasmb.bbri.org/mailman/listinfo/rasmb 
>>
>>
>******************************************************************************* 
>
>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
>******************************************************************************* 
>
>
><br>
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