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Dear Ed,
Thanks for your input and you are of course entirely correct. Even more
general, without NCS reflections still depend on their neighbours as a
result of the G-function, the transform of the molecular shape. That is
what makes solvent flattening work.
However, although it is always desirable to implement the ultimate
correct solution, that doesn't mean that a practical solution cannot be
acceptable. Basically, a healthy suspicion of Rfree statistics is
warranted but not without recognizing that it has been, and still is, a
terrific tool to improve refinement protocols and, in my opinion, in the
great majority of cases it is sufficiently robust to deserve the
confidence we place in it.
Now if overfitting could be estimated from first principles that would
be great, not only to make the procedure more robust and general, but
also because we wouldn't have to sacrifice ~1000 of our reflections just
to calculate a statistic.
Bart
Eaton Lattman wrote:
Hi All-
Phoebe suggested that
"Not all cases of NCS undermine Rfree: There are many where the NCS axis
is roughly parallel to an xtal symmetry axis - e.g. P61 with a non-xtal
twofold running nearly parallel to the xtal 6fold screw, so that
NCS-related reflections are already xtal-symmetry - related. I don't see
how the NCS can affect Rfree in such cases?"
In fact I do think that NCS can affect Rfree even in this case.
Consider a simple example of a crystal in space group P2 which contains
a dimer in the asymmetric unit. Let the NC dimer 2-fold be very closely
parallel to the crystallographic 2-fold. Superficially it would appear
that NCS can add no correlation. Bu the situation is more complex than
it seems. The existence of NCS in this crystal means that one can write
an equation in which the electron density within the boundary of one
monomer equals the (rotated) electron density within the boundary of the
other monomer. In a classic paper by Main and Rossmann the equations
relating identical volumes of electron density were Fourier transformed
to give a set of equations among the structure factors. In this set
each F(p) is equal to a weighted sum over all the other structure
factors F(h). The weights are largest when when the reciprocal lattice
point p is close to the the point h. Thus the coupling by NCS of
reflections in the working and free sets is quite general.
This raises a more general issue of whether Rfree is a
sufficiently robust statistic to deserve the confidence that we place in
it. It seems to me that we need a deeper analysis. How many degrees of
freedom does a refinement really have? Can we derive the distribution
of (Rwork-Rfree) from first principles, so that we know the confidence
limits of this statistic. Should we develop new statistics to describe
the Bayesian refinement targets that many programs use?
Happy New Year.
Ed
Eaton E. Lattman
Dean of Research and Graduate Education
Professor of Biophysics
Zanvyl Krieger School of Arts and Sciences
410.516.8215 (voice); 410.516.4100 (fax)
Mail address:
Johns Hopkins University
3400 North Charles Street
237 Mergenthaler Hall
Baltimore, MD 21218
On Dec 30, 2006, at 12:17 PM, Bart Hazes wrote:
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Hi Phoebe,
Parallel NCS and crystallographic symmetry leads to translational
symmetry and systematic weakening and strengthening of reflections (in
special pseudosymmetry cases it can for instance mimic a centered
space group). I expect that if you just place two monomers with the
proper translational symmetry then you will get a strong correlation
between Fcalc and Fobs and a below-random R-factor even if the model
has major errors. This would apply to both Rwork and Rfree. Thin
shells won't help in this situation and because other basic
assumptions about intensity distributions is violated, ML refinement
may not behave as expected either.
Bart
[EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]> wrote:
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Not all cases of NCS undermine Rfree: There are many where the NCS
axis is roughly parallel to an xtal symmetry axis - e.g. P61 with a
non-xtal twofold running nearly parallel to the xtal 6fold screw, so
that NCS-related reflections are already xtal-symmetry - related. I
don't see how the NCS can affect Rfree in such cases?
Phoebe
At 02:49 PM 12/29/2006, Jan Abendroth wrote:
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A way to avoid biasing Rfree values is to choose the test set in
thin resolution shells whenever NCS is present. Currently, this
precaution is often ignored. It should become a de facto standard
for publication of structures containing NCS.
Hi all,
btw - it would be fantastic and certainly would encourage us to use
it more often if the assignment of free reflections in resolution
shells was incorporated in a ccp4 program. Yes, one can for instance
go through shelxpro, however if one wants to go back to ccp4 this
route is a bit painful.
Cheers
Jan
--
Jan Abendroth
University of Washington
Institute of Biochemistry
1959 NE Pacific Street, K-426
Box 357742
Seattle, WA-98195
phone: +1-206-616-4510
fax: +1-206-685-7002
---------------------------------------------------------------------------------------------------------------------------
Phoebe A. Rice
Assoc. Prof., Dept. of Biochemistry & Molecular Biology
The University of Chicago
phone 773 834 1723
fax 773 702 0439
http://bmb.bsd.uchicago.edu/index.html
http://www.nasa.gov/mission_pages/cassini/multimedia/pia06064.html
--
==============================================================================
Bart Hazes (Assistant Professor)
Dept. of Medical Microbiology & Immunology
University of Alberta
1-15 Medical Sciences Building
Edmonton, Alberta
Canada, T6G 2H7
phone: 1-780-492-0042
fax: 1-780-492-7521
==============================================================================
--
==============================================================================
Bart Hazes (Assistant Professor)
Dept. of Medical Microbiology & Immunology
University of Alberta
1-15 Medical Sciences Building
Edmonton, Alberta
Canada, T6G 2H7
phone: 1-780-492-0042
fax: 1-780-492-7521
==============================================================================
