[RASMB] hydrodynamic non-ideality

[Arthur Rowe]

Hi Mitra (and all)

Provided that one is working in pH conditions not too far from neutrality,
and that the neutral salt concentration is of the order of 100 mM, then one
gets an excellent estimate for ks from the relationship

ks = 2*vbar*((Vs/vbar) + F^3)

where Vs/vbar is the swelling ratio - around 1.4 is a good guess for most
proteins) and F is the frictional ratio f/f0. ks is found from the limiting
slope of the s vs c curve, in practice better estimated from the 1/s vs c
curve. Optimally one uses the extended form of the s vs c equation (see my
chapter in the 1992 AUC book - in which there is, sad to say, a typo in the
equation), but up to around 10 mg/mL or so it makes very little difference.
The method of fitting an "isotherm" over the range of c works well even with
weak interactions (see e.g. Patel, Trushar R, Harding, Stephen E,
Ebringerova, Anna, Deszczynski, Marcin, Hromadkova, Zdenka, Togola,
Adiaratoou, Paulsen, Bert Smestad, Morris, Gordon, A and Rowe, Arthur J (
2007) Weak Self-Association in a Carbohydrate System  Biophysical Journal 93
741-749), but clearly the interaction you have got is not all that weak.

I am working on a more extended form of my own fitting function - in
particular I have realised that at the moment it contains one too many
parameters in the general c-dependence equation! As and when I get it
completed, I will have a go and see what it does with your data.

Anyhow - the answers to your queries are (2) AGREED and (3) YES.

Kind regards

Arthur


--
*******************************************************
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
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email:      arthur.rowe at nottingham.ac.uk
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Hi All

Is there anyway I can ignore the hydrodynamic non-ideality? After all
my protein concentrations only go up to ~ 12 mg/ml! :)

Ok that was said in jest or may be half jest since ignoring the ks of
0.009 ml/mg seems to allow me to explain my velocity data by a simple
monomer-trimer equilibrium.

More seriously though -
1. For an isodesmic association model (either the good old N^2(/3)
approach used by Timasheff or the more recent bead modeling used by
Sontag et al. 2004 Biophys. Chem. both used for tubulin
self-association) the s20,w for the oligomers are fixed a priori to
any curve fitting (whether Delta C in SEDANAL or the isotherm)

2. Using the Rowe derivation for ks - one should be theoretically able
to calculate the ks for a given f/f0. Since according to point 1 the
s20,w water for the oligomers is already assumed to be known, one can
calculate the f/f0 for each of the oligomers (I guess this only
applies to bead modeled oligomers since the basis for N^(2/3) is a
constant f/f0).

3. Bottomline - can one use the Rowe equation to calculate the ks for
each of the oligomers and then use this value for fitting the weight
average isotherm? Or am I missing something crucial and there is a
fundamental problem with this approach? Or for the sake of simplicity
can I just presume a ks of 0.009 ml/mg for all oligomers and fit the
data.

If anyone wishes or has the time for it - here are the numbers -
0.03(4.57), 0.37(4.77), 0.745 (5.00), 1.4 (5.3), 3.39 (5.86), 6.65
(6.51), 12.2 (6.99).
The first number is [P] in mg/ml and in brackets the weight-average
s20,w. The best fit I have so far is for a modeled isodesmic
assocation with the relation ln(sn/s1) = 0.5781 ln n - 0.0493 (ln n)^2
. s1 (20,w) ~ 4.53S ks=0.009 mg/ml. Fitted by sedanal Kiso=1.37x10^4.
Isotherm = 1.29x10^4.

Any and all thoughts are welcome. Have a good weekend.
Mitra



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