[RASMB] averages from SV

[Peter Schuck]

Holger,

to be honest, to me these averages do not make much sense, with the 
exception of the weight-average sw.

Sw, of course, reflects mass balance and therefore a thermodynamically 
well-defined value of the sedimenting molecules.  I have studied this for 
differential sedimentation coefficient distributions (Anal Biochem 320 
(2003) 104-124), and shown that they can actually be derived from 
differential sedimentation coefficient distributions, provided that they 
imply a faithful representation of the boundary (or the area under the 
boundary).  This condition is *not* automatically fulfilled, for example, 
with dcdt or ls-g*(s), but requires comparison with the original 
sedimentation data.  (To facilitate this test, I've build into sedfit a 
tool that can take dcdt-derived distributions and compare them with direct 
boundary data.)  As far as I know, nobody has demonstrated a theoretical 
connection of a thermodynamically well-defined sw with what you would get 
from taking a formal weight average over the van-Holde Weischet 
distribution, and I doubt there is such a connection because of the neglect 
of absolute boundary height information in the original method (perhaps one 
could empirically compare).

As far as the other averages are concerned, I believe they do not actually 
represent well the sedimenting molecules, but
depend very much on the analysis method and the data acquisition.  For 
example, the width and shape of the peaks will be dominated by signal-noise 
ratio, rotor speed, and  the extent to which diffusion was deconvoluted, 
regularization level (if used), and for dcdt and ls-g*(s) the timepoints 
from which the distribution is derived.  There might be situations where it 
can be useful to empirically compare the width of a peak from samples that 
are run side-by-side in the same experiment and detected and analyzed in 
exactly the same way.  For that purpose, there's a second central moment 
calculated in the integration tool in sedfit.

Just to be specific, this applies to sedimentation coefficient 
distributions and the way they can be determined in AUC.  An exception is 
the case of very large particles, such as cells or dispersions, where 
things are easier because diffusion is virtually absent on the time-scale 
of sedimentation.  If the sedimentation coefficient distribution is not 
distorting, and data acquisition takes place with good signal-noise ratio, 
then these averages could be calculated.  But even then, I would rather 
compare simply the shape of the whole distribution, which in my opinion is 
more informative than extracting averages.

Generally, I think it is important to realize that taking formal averages 
does not necessarily mean that the numbers reflect a real property of the 
sedimenting sample!

Sorry if that comment will generate a flood of email in your 
inbox...  maybe somebody else knows some recent examples where these 
averages - of course other than sw - have been useful?

Regards,
Peter