[RASMB] Weak association?

Tue Feb 3 08:35:06 PST 2009

Hi Tom (and all)

Obviously I am an SE enthusiast when it comes to using the AUC to  
measure Ka values, although SV scores in some cases (our first-ever  
demonstration of a weak carbohydrate-carbohydrate interaction referred  
to by Peter would have floored out SE methods).

But I am not sure that I can go along with the full text of what you  
say could cause the s value at 10 mg/ml of Andrew's sample to be higher  
than predicted. The effects of pressure, and possibly associated change  
in protein solvation and solvent properties are small - but not,  
agreed, negligible. Neil Errington and I published a study on this  
matter a few years back, in which we computed these effects, and showed  
experimentally that with some proteins at least there was a small  
pressure effect on s values. Which we thought could be due to an  
induced change in solvation.

The trouble is - this does not begin to explain the above effect. For  
that, the change in solute/solvent properties would have to be protein  
concentration dependent. I am unaware of any evidence to suggest that  
this is the case. So I will stick by my estimate of around 62 mM for kD  
- with the obvious proviso that I have assumed a minimal value for ks,  
so 62 mM is as weak as you can get, the binding could be stronger. SE  
(or you very good sounding NMR methods) would not be confused by such  
issues.

Regards

Arthur

On Feb 3, 2009, at 16:09, Thomas Jowitt wrote:

> 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
>> University of York                *  Fax   : +44 (0)1904 328804
>> PO Box 373,  York  YO10 5YW       *  Email : apl3 at york.ac.uk
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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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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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