[RASMB] averages from SV

[John Philo]

Just to set the record straight, Jack has apparently misinterpreted my paper
(Anal. Biochem. 279, 151 (2000). It does not say that averages higher than
Sw are too noisy to be useful, nor did it attempt to demonstrate that by
simulations. First, the work of Jack and others clearly shows that to be
false. Second, if that were my opinion, why would I have bothered to develop
a new algorithm that gives better estimates of the errors in Sw, Sz, etc. or
to include those computations in my software? 
 
What the paper points out is that when using the standard way of calculating
the error bars for the g(s*) distribution (the original Stafford algorithm),
as you include more scans in the computations the error bars do not reduce
as rapidly as one would expect from fundamental signal/noise considerations
(i.e. the standard algorithm overestimates the error bars and thus
underestimates the true precision of Sw, Sz, etc.). The revised algorithm
described in that paper, and optionally implemented in DCDT+, partially
corrects this problem.
 
Also I should clarify that I was wrong to imply in my earlier response to
Holger that one cannot calculate a formal Sn from g(s*), c(s), etc.  My
program DCDT+ does not calculate that one simply because no one has ever
asked for it, but in response to this discussion I will implement that one
too in the next release.
 
John

-----Original Message-----
From: rasmb-bounces at rasmb.bbri.org [mailto:rasmb-bounces at rasmb.bbri.org] On
Behalf Of John Correia
Sent: Thursday, January 26, 2006 12:29 PM
To: Walter Stafford; Holger Strauss; rasmb at rasmb.bbri.org
Subject: Re: [RASMB] averages from SV


Holger
 
To my knowledge my review from a few years ago is the most recent
comprehensive overview of weight average.  It finishes with a mention of
other averages & who has applied them.  
 
J.J. CORREIA (2000) "The Analysis of Weight Average Sedimentation Data."
Methods in Enzymol., vol 321, 81-100.

 
Soon after I published that review John Philo published a paper claiming
typical data is too noisy for higher averages, and demonstrated so by
simulations.  As Walter mentioned these averages are also calculated in the
DCDT portion of SEDANAL.  Peter Schuck also suggests they are too noisy.
Attached please find a test of those claims, derived from XLA data using
g(s) analysis in SEDANAL.  Clearly if done properly they are not too noisy!
(I have compared this analysis with results from Philo's DCDTplus2 and the
error bars are comparable for Sw, Sz and Sz+1 - John doesn't report Sn.)  
 
As to claims about no theoretical meaning, moments or averages of
distributions are what they are.  One could easily write a program to fit
these moments and compare them to some model.  We have done this but I
generally only attempt such complexity when the system is very complex.  I
find it much more useful to compare weight average fitting with direct
boundary fitting.  For my self association systems the K's derived typically
agree to within 20%.  The direct boundary fitting usually reveals what
causes the disagreement, typically aggregation at the centrifugal edge of
the boundary.
 
Applying these averages to different signals has its pitfalls, but Schachman
1st described absorbance average moments in his book, so the use of
different signals is an old idea and easy to apply as a fitter.  We again
prefer to resort to direct boundary fitting, combining different wavelengths
and extinction coefficients to different components and species.  I strongly
agree the information is in the shape of the sedimenting boundary.  (This
does not necessarily mean the shape of the derived distribution.)
Comparisons to averages should in principle work with the usual caveats
about reversibility, degree of aggregation, the presence of plateaus, etc.  
 
I hope you try this approach, apply your own direct statistical tests, and
convince yourself of its potential utility.  I have no doubts there may be a
system dependency.  My bias continues to be direct boundary fitting is the
most informative, although we use weight average for model building,
extrapolation to end points, and estimation of K's for initial guesses.
 
Good luck!
 
 
-------------------------------------------------------------------
 Dr. John J. "Jack" Correia
 Department of Biochemistry
 University of Mississippi Medical Center
 2500 North State Street
 Jackson, MS  39216
 (601) 984-1522                                 
 fax (601) 984-1501                             
 email address: jcorreia at biochem.umsmed.edu     
 homepage location: http://biochemistry.umc.edu/correia.html
 dept homepage location:    http://biochemistry.umc.edu/
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