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  From: Dr A.J. Rowe <>
  To  :
  Date: Thu, 30 Apr 1998 11:16:55 +0100 (BST)

re: ks values

Greetings Dave, and all on RASMB !

Whilst the archives have some stuff from me on ks values, let me briefly
summarise the most salient points:


There are two treatments which give an account of the sedimentation at finite
concentration of solute for c values ranging from zero to phi-p (maximum packing
fraction. These are the Brady-Durlovsky treatment (a heavy numerical one, i.e.
an approximation but a quality one) and my own general equation. The numerical
results are essentially identical by both treatments. The limiting slope is
either 5 ml/g (the kinematic ks) or 4 ml/g (the dynamic ks).  Following Fujita,
I personally correct for the solution density, and hence use the latter value,
but fluid mechanics people stick with the kinematic approach. The limiting value
for ks I first published in 1977, in a theory which also gave the theoretical
basis for the well-known Wales-van Holde ratio ks/[eta],  = 1.6 for spheres.

Almost certainly the authority of Batchelor, who had earlier published a
theoretical value of ks = 6.55 (kinematic), made it hard for people to accept my
own much lower predicted value. However, the Brady-Durlovsky paper does a
serious hatchet job on the Batchelor theory, describing it as *aphysical*. It
never *did* agree with empirical evidence, whether from fluid mechancs people or
from the elegant AUC work of Cheng and Schachman. So - I do not now see there is
any reason for dispute as to how spheres behave. For non-spheres, my own
theories remain unique - but they do fit empirical evidence even for very
extended particles such as myosin or fibrinogen.


G K Batchelor  J Fluid Mech  1972   52  p 245
J F Brady & L J Durlovsky   1988    31  pp 717-727
P.Y. Cheng & H.K. Schachman  J Polym Sci  1955  16  p.19
A J Rowe  Biopolymers  1977    16   pp 2595-2611
A J Rowe  in "Analytical Ultracentrifugation in Biochemistry & Polymer Science"
(eds Harding, Rowe & Horton).  Ch 21

{yes, its embarrassing, but in the last reference I had yet to catch up on the
1988 paper !}


Globular proteins can have their ks measured either by the direct or the inverse
plot - it makes little difference (I have checked this out by computer
simulation using the general relationship). However, for extended particles and
possibly for globular ones at higher concentration, the inverse form is better.

Clearly theory predicts that for globular proteins of normal solvation, the ks
values (dynamic) will be about 4 ml/g.  If they are less than that, or go
negative, then self-association is happening. Old published data is of
indifferent quality, often radial dilution has been ignored - this causes ks
values to be too low. Our own experence doing careful work is that somewhere
around 4 ml/g is indeed a fair ball-park value. Values of around 2 would be a
nice measure of weak interaction, I would very much like to find such a system,
please let me know out there if you do - based upon really hard, modern
evidence, that is !


For a start, I am a bit incredulous that you have a ks = 0.18 ml/mg (i.e. = 180
ml/g !!).  Even myosin only makes it to 90 ml/g.  Can you check, is this value
for real ?

An instant question is to what solvent you are working in. ALL the above theory
is restricted to *zero charge effects*.  The primary charge effect, which occurs
when you have a low inoic strength, especially with a lot of charges, has never
been properly quantified.  Even so . . . I just cannot believe a ks = 180 ml/g.
At least for a protein even vaguely thought to be globular.

Perhaps you could clear this question up, prior to any further comment ?

All very best

Arthur Rowe

Dr Arthur J Rowe
UK National Centre for Macromolecular Hydrodynamics
Leicester Laboratory
Adrian Building
University of Leicester
Leicester LE1 7RH    UK

Tel: +44 (0)116 252 3448
Fax: +44 (0)116 252 5260

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