From: Arthur Rowe <Arthur.Rowe@nottingham.ac.uk>
  To  : rasmb@alpha.bbri.org
  Date: Wed, 17 Nov 1999 15:36:13 GMT0BST

non-ideality & s values

Hi to all out there !

Libby Resiinger has started quite a hare running with her query about checking out 
assymetry in a protein of known M, using the s value.  Her precise enquiry was:

"We are working on a protein that we believe is asymmetric.  I'm trying to
get sedimentation velocity data to hopefully support this hypothesis.  I
do NOT need an exact, definitive shape, all I am interested in is knowing
that our proposed (asymmetric) model is one way of interpreting the
sedimentation coefficient."

So - the protein being asymmetric is the null hypothesis, and (as Karl Popper 
would have put it) a real s value is the basis for rejection/non-rejection of that 
hypothesis.  In practical terms, an s value means you easily compute f/f0, and if (for 
example) it comes out to be 1.15, then the hypthesis  must be rejected, whilst if it is 
1.38 then the hypothesis survives.  Though it is not actually PROVEN of course.

Does it matter that unless you do an extrapolation to c = 0, your s value will be 
different from the 'true' s value ?  I suggested that in the 1 mg/ml sort of range of 
concentration, one need not bother too much.  Given the further queries which 
have now arisen, might I defend this assertion ?

The limiting coefficient (ks) of linear dependence in s = s0(1 - ks.c) lies numerically 
in the range around 4 - 100 ml/g for PROTEINS.  It can be MUCH higher for NAs 
or carbohydrates. Whilst the limiting coefficient must (by algebra) be the same 
whether one uses a direct or a reciprocal plot, it is better ESTIMATED in most cases 
from the latter. A ks of around 90 ml/g is what one finds for myosin (Emes & 
Rowe, BBA, 537, 110-124, 1978), and single proteins do not come much more 
asymmetric than myosin. Even myosin filaments only just get over 200 ml/g for ks 
(loc cit  125-144).

So - the s value of myosin at 1 mg.ml is around 9% lower than the true 
extrapolated value. For a globular protein, or one even modestly asymmetric, the 
error would be well under 1%.  As one is looking for a quite serious elevation of 
f/f0 to confirm an asymmetric structure, one hardly needs to worry - especially as 
the algebraic sign of the error will magnify the elevation in any case !

As I hinted however, one can also check out the possible presence of an elevated 
f/f0 by looking at the ks value itself, since there is a very simple relationship 
between the two:

ks  =  2*vbar( Vs/vbar  +  (f/f0)^3))            A J Rowe Biopolymers 16, 2595-2611 '77

In rough terms, a ks > 8 ml/g indicates possible asymmetry (with of course the 
usual proviso that a 'hollow' structure with entrained solvent will show the same 
effect, even if perfectly spherical).  If ks is POSITIVE in sign, then one knows a 
self-interaction is going on, which is useful.  Even better, a decent value for ks 
enable one to see if the correct M is echoed back, a pretty rigorous test of absence of 
self-association.

In practical terms - and perhaps my earlier mail could have been better written 
here - I do not think that the ks value for proteins of little to modest asymmetry 
can be reliably estimated from a single run - whether by vHW or any other way.  
You need 3 runs minimum, as I said. Among other problems, pressure effects 
down the column (from 1 to  nearly 100 bar) are much bigger than in SE.   

To finish - though not to repeat things already in the RASMB archive, the 
c-dependence of macromolecular solutes IN THE ABSENCE OF CHARGE EFFECTS 
does have a published, robust theory behind it (see the '77 paper above, extended in 
chapter 21 of the '92 AUC Book.  The general equation given there has been fully 
confirmed so far as numerical values yielded are concerned by the fluid mechanics 
people, it can be coded up in any old plotting package in 2 minutes by anyone who 
wants to.  Charge effects are a different matter.  The original Pedersen theory of the 
'primary charge effect' is very limited, and I know of no modern theory. Does 
anyone else ?

To return to Libby's original query.  The presence of asymmetry in proteins has for 
long been routinely suspected on the basis of elevated f/f0 values - given my 
background, the example of myosin light chains comes to mind.  Its a perfectly 
good way of seeing if a hypothesised asymmetry is defensible as an idea.

Regards to all

Arthur
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Professor Arthur J Rowe
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University of Nottingham
School of Biological Sciences
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Leicestershire LE12 5RD   UK

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