On 30 Dec, Dean Madden wrote:
> It's also a good point that NCS can help improve the quality of  
> structures in a lot of other ways. If properly accounted for, its  
> benefits clearly outweigh any drawbacks. 

Yes, in fact excluding NCS-related reflections is undesirable ideally,
because of the benefits of NCS-symmetry averaging, and because their
amplitude is likely to be high.  Excluding such reflections in a sphere
is also likely to lead to systematic errors, although such errors might
be small. 

It is important to note that coupling is not a problem if _all_ of the 
NCS-related reflections are included in the phase calculations.  In that
case the R-free set would obviously be independent of the coupled set.

NCS-related reflections pile up in narrow slabs of reciprocal space that
are not coincident to the reciprocal space axes.  A better
way to account for the coupling problem would be to choose a random
R-free set, which excludes these slabs, so that _all_ of the NCS-related
data can be included in the phase calculation. The random selection of
the R-free set would then be unbiased with respect to the working set
including _all_ of the NCS-related reflections, and the full benefit of
NCS would be realized while solving the problem of coupling.

If one insists on excluding some NCS-related reflections, then
intersections between the slabs and thin resolution spheres could be
used.  This intersection could be included in the R-free set, since
these reflections obviously have some degree of coupling, and if they
are excluded from the calculation, they should be excluded together.  I
am troubled by the possibility however that there may be additional
coupling between reflections within these NCS-symmetry related
reciprocal space slabs which are not restricted to the same resolution
sphere.  Moreover a spherical intersection is not a random intersection
of the set of NCS-related reflections.  It seems to me that none of
them should be included in the R-free set ideally.

Now, one of us needs to figure out the width of the slab and write some
code ;-}.

Regards,
Michael L. Love Ph.D
Department of Biophysics and Biophysical Chemistry
School of Medicine
Johns Hopkins University
725 N. Wolfe Street
Room 608B WBSB
Baltimore MD 21205-2185

Interoffice Mail: 608B WBSB, SoM

office: 410-614-2267
lab:    410-614-3179
fax:    410-502-6910
cell:   443-824-3451
http://www.gnu-darwin.org/


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