[RASMB] Weak association?

[Thomas Jowitt]

Hi

This is a good discussion and I would like to add some points. I have been down this road a few times, which was why my first answer was fairly abrupt. There needs to be quite a bit of caution when looking for oligomerisation in the high mM ranges using sedimentation velocity. There have been several good reports on it by yourself Arthur, Peter, and Christene Ebel. For a change as low as this, you are you basing the lack of change in s vs concentration on several effects. This could in reality be contributed to by hydration, compression of the solvent as well as the shape of the protein (is hydration effecting conformation slightly?). This is not to say that there isn't a difference but a 5% difference could easily be reduced to 2% or less, meaning a much lower association. 

Certainly equilibrium measurements are much more sensitive for the analysis of fast interactions, and that isn't just sedimentation equilibrium, but equilibrium relaxation NMR and also, as I am currently doing, vibrational frequency dissipation measurements, again at equilibrium, would tell you if your interactions are indeed real or not and certainly would be a more rigorous test. 

All the best

Tom J

-----Original Message-----
From: rasmb-bounces at rasmb.bbri.org [mailto:rasmb-bounces at rasmb.bbri.org] On Behalf Of Arthur Rowe
Sent: 03 February 2009 14:53
To: John Correia
Cc: RASMB
Subject: Re: [RASMB] Weak association?

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

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