[RASMB] fringe deviation

[Arthur Rowe]

Dear Barbara

Both sedimentation velocity and sedimentation equilibrium can work well when
it comes to determining Ka/Kd values, but there is a real problem with
currently used software when it comes to estimating weak interactions - and
I take it from the concentration range in c that you are using that it is a
truly weak interaction that you are looking at. The contributions from the
thermodynamic non-ideality (BM) term can be of the same order of magnitude
to those arising from Ka, and since (in the approximated forms of the
equation often used, as in WinNONLIN, they are additive, plainly one can
never unscramble these two effects.

As regards SE vs SV, I use both. I have to disagree with John Philo when he
asserts that "non-ideality effects are much stronger in velocity than in
equilibrium". This is incorrect. For ideal spheres, the limiting
concentration dependence coefficient for velocity is 4.0 ml/g (the kinetic
ks - see my chapter 21 in "Analytical Ultracentrifugation in Biochemistry
and Polymer Science" 1992) whilst the corresponding coefficient for (1/M) in
equilibrium is 8.0 ml/g (value for 2BM - see any good physical chemistry
text). The shape-dependence of these coefficients is not at all identical,
so for a non-globular protein it is probably true that one can find 2BM to
be bigger than ks. But - either way - you have to unscramble Ka away from
non-ideality. And as Allen Minton has correctly said, you will not find
WinNONLIN of any use here.

So - how to do it?  Let us look at the two possibilities:

(1) SV

There are problems with trying to unscramble c-effects out of single runs.
Among other things, the effects of pressure on the solvent and on the system
are not negligible (see [1]). But this does not matter. Within a single
rotor you can do 3 experiments over whatever range of c you can get.
Strictly control all the parameters (e.g. scans used) to be equivalent
between your 3 channels. Find the s(w) for each - various methods, but Peter
Schuck's c(s) gives you the s(w) by simple integration . Providing you know
the s value for the monomer (no problem with a weakly interacting system -
do another run on one or more low c samples) you can fit s(w) vs c with
stability using Ka as a floated parameter and get an excellent estimate for
Ka - since the ks factor is readily incorporated into the fitted equation. I
am happy supply the equations for this approach - they can be used in any
decent fitting program.

This method works at even 2+ logs away from Kd - so no need to use
impossibly high c values. The precision with which s values can be measured
relative to each other in the same rotor is amazing (<0.1%) so that is why 3
channels are plenty. I like this method - it is very 'visual', you can see
whether your fit makes sense or not. And sorry about another contradiction
(John, Borries) - but you do not need a vast range in c. I have a litter of
data around in which I have successfully used e.g. 0.5, 1.0 and 2.0 mg/ml
(for systems with a significant c-dependence of s).

(2) SE

A big advantage of SE is that just one channel with a minimal volume of
solution suffices - at least provided you have sorted out that you system is
an equilibrium, not a mixture. I am currently working on souped-up software
which segregates Ka away from 2BM. I will be releasing same very soon. But
what is publicly available right now is of limited (or even no) use for this
purpose. Perhaps Allen can fill us in on the 'correct' treatments which he
says are available?

To sum up: in your case, I would use SV. The suggestion from John Philo that
you use absorption optics off-peak is a good one - but bear in mind that the
numerical aperture of the XL-I/A optics is very limited, so in early stages
of a higher-c run you are liable to get 'schlieren' effects, in which you
see a peak where you expect to see just an integral boundary! Using 3 mm
centrepieces limits this problem. And you can always discard a few early
scans, just so long as you stick to the same regime for all channels.

All best with your researches. Weak interactions may be a pain -
methodologically - but from the point of view of biology, signalling and all
that, they are important.

Kind regards

Arthur Rowe

[1] N Errington, P. Mistry & A J Rowe (2002) "Protein hydration varies with
protein crowding and with applied pressure: a sedimentation velocity study"
Progr Colloid Polym Sci 119 58-63


--
*******************************************************
Arthur J Rowe
Professor of Biomolecular Technology
NCMH Business Centre
University of Nottingham
School of Biosciences
Sutton Bonington
Leicestershire LE12 5RD   UK

Tel:        +44 (0)115 951 6156
            +44 (0)116 271 4502
Fax:        +44 (0)115 951 6157
email:      arthur.rowe at nottingham.ac.uk
            arthur.rowe at connectfree.co.uk (home)
Web:        www.nottingham.ac.uk/ncmh/business
*******************************************************



Hello!

I am trying to determine the association constant for a monomer-dimer
equilibrium. I know the association occurs because I've seen it by velocity
experiments.

I run equilibrium at 3 concentrations and 3 speeds, my conc. are high and
therefore I used interference optics. I have a fringe displacement at
equilibrium of up to 50 fringes. I fit my data with WinNonlin and at the
best I can get a SQUARE ROOT OF VARIANCE=9.3317E-02.  Since I have such a
big fringe displacement when I plot deviation vs. indipendent variable, in
the worst case I have a deviation of -0.25 to 0.375 fringes, is it
reasonable?

thanks 
barbara

---
Barbara Lelj Garolla Di Bard
Dr. Mauk's Lab
Dept. of Biochemistry and Molecular Biology
University of British Columbia
2146 Health Sciences Mall
Vancouver, B.C. V6T 1Z3
Phone: (604) 822-2526


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