[RASMB] Weak association?

[Arthur Rowe]

Greetings everyone

I have a few further general comments to offer here. For starters, I do  
not see that a few % of dimer in rapid equilibrium with its monomer  
would be "easily visible" in SV. Anything but, I would suggest, since  
what you see is a single boundary, of only slightly odd shape  
(Gilbert-Jenkins). You would of course fail to get the expected 5% (or  
a little more) decrease in s value associated with hydrodynamic  
non-ideality - which is precisely what you observe!

So - let's do the world's simplest curve-fit, on just one point (OK -  
two, I guess, we are assuming the origin). To get the measured s value  
to increase relative to the theoretical s value for a 10 mg/ml  
solution, you need to raise the weight-averaged s value by around 5%,  
so that the 2 effects (Ka vs ks) cancel. This will require the  
weight-averaged M value to go up by 1.05^(3/2) = 1.076 - good old  
two-thirds power rule. For a 714 µM solution (not ~71 µM, I think,  
Jack), the law of mass action tells us that this calls for a Kd = 62mM.  
There's your answer, Andrew! Obviously, had you been dealing with a 140  
Dalton protein rather than a 14 Dalton one, you could not have explored  
an interaction as weak as this with much hope of success.

This value could be refined up a bit - e.g. by knowing the frictional  
ratio, but this 'quick and easy' estimate should be a good deal better  
than ball park. And if it matters, then an SE experiment would increase  
the precision and have NO hard-to-know parameters (as in Vs/vbar in ks  
theory) to worry about. I am giving the (quite trivial) code for doing  
an INVEQ fit for anyone who wishes to paste it into their favoured  
curve-fitting package. Using it, and doing a bit of simulation, you  
will soon find tens of µM in Kd are measurable OK. Or you could do the  
boring thing and read some of the papers I have written using this  
approach.

Regards to all

Arthur


On Feb 2, 2009, at 22:29, John Correia wrote:

> Andrew
>  
> It would be helpful to provide the salt conditions, what is the ionic  
> strength, and the calculated charge at the pH of your runs.  This  
> would put the discussion of nonideality masking association in a real  
> context.  You have done experiments up to ~71 uM so one can guess the  
> Kd might be at least 710 uM and above since 10% association should  
> easily be visible in a velocity run.  In practice affinities of 10^4  
> M-1 are on the edge of measurable.  The suggestion to fit the data to  
> nonassociating vs dimer vs nonideal dimer is reasonable if you  
> constrain the parameters in some reasonable way while comparing rms of  
> the fits.  The nonideal dimer system is intrinsically difficult  
> because nonideality and association strongly correlate.
>  
>
>
> >>> On 2/2/2009 at 8:22 AM, in message <49870199.3050700 at york.ac.uk>,  
> "Leech, AP" <apl3 at york.ac.uk> 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
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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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