Dear Dale,
Am 08.02.2008 um 10:27 schrieb Dale Tronrud:
I'm afraid I have to disagree with summary point (i): that
crystallographic and noncrystallographic symmetry are incomparable.
Crystallographic symmetry is a special case of ncs where the symmetry
happens to synchronize with the lattice symmetry. There are plenty
of cases where this synchronization is not perfect and the ncs is
"nearly" crystallographic.
Yes, I agree with you in the case of non-crystallographic symmetry
that is almost crystallographic symmetry. To decide which one is true
is somewhat arbitrary, then. My statement (i) was more pointing to
the general distinction between local symmetry and global crystal
symmetry.
Best regards,
Dirk.
For some reason this situation seems to be particularly popular
with P21 space group crystals with a dimer in the asymmetric unit.
Quite often the two-fold of the dimer is nearly parallel to the
screw axis resulting in a nearly C2 space group crystal. These
crystals form a bridging case in the continuum between ncs, where
the symmetry is unrelated to the lattice symmetry, and those cases
where the unit cell symmetry is perfectly compatible with the
lattice.
The only saving grace of the "nearly centered" ncs crystals is
that the combination of the crystal and noncrystallographic symmetry
brings the potential "contamination" of a reflection in the working
set back to itself. Unless you have a very high copy number, and
a corresponding large G function, you can't have any feedback from
a working set reflection to a test reflection.
Crystallographic symmetry is just a special case of
noncrystallographic
symmetry, but our computational methods treat them in very different
ways. This choice of ours creates a discontinuity in the treatment
of symmetry that is quite artificial, and I believe, is the root
cause of many of the problems we have with ncs in refinement and
structure solution.
Dale Tronrud
Dirk Kostrewa wrote:
Dear Dean and others,
Peter Zwart gave me a similar reply. This is very interesting
discussion, and I would like to have a somewhat closer look to
this to maybe make things a little bit clearer (please, excuse the
general explanations - this might be interesting for beginners as
well):
1). Ccrystallographic symmetry can be applied to the whole crystal
and results in symmetry-equivalent intensities in reciprocal
space. If you refine your model in a lower space group, there will
be reflections in the test-set that are symmetry-equivalent in the
higher space group to reflections in the working set. If you
refine the (symmetry-equivalent) copies in your crystal
independently, they will diverge due to resolution and data
quality, and R-work and R-free will diverge to some extend due to
this. If you force the copies to be identical, the R-work & R-free
will still be different due to observational errors. In both
cases, however, the R-free will be very close to the R-work.
2). In case of NCS, the continuous molecular transform will
reflect this internal symmetry, but because it is only a local
symmetry, the observed reflections sample the continuous transform
at different points and their corresponding intensities are
generally different. It might, however, happen that a test-set
reflection comes _very_ close in reciprocal space to a "NCS-
related" working-set reflection, and in such a case their
intensities will be very similar and this will make the R-free
closer to the R-work. If you do not apply NCS-averaging in form of
restraints/constraints, these accidentally close reflections will
be the only cases where R-free might be too close to R-work. If
you apply NCS-averaging, then in real space you multiply the
electron density with a mask and average the NCS-related copies
within this mask at all NCS-related positions. In reciprocal
space, you then convolute the Fourier-transform of that mask with
your observed intensities in all NCS-related positions. This will
force to make test-set reflections more similar to NCS-related
working-set reflections and thus the R-free will be heavily based
towards R-work. The range of this influence in reciprocal space
can be approximated by replacing the mask with a sphere and
calculate the Fourier-transform of this sphere. This will give the
so-called G-function, whose radius of the first zero-value
determines its radius of influence in reciprocal space.
To summarize: (i) One can't directly compare crystallographic and
non-crystallographic symmetry
(ii) In case of NCS, I have to admit, that even if you do not
apply NCS-restraints/constraints, there will be some effect on the
R-free by chance. So, my original statement was too strict in this
respect. But only if you really apply NCS-restraints/constraints,
you force to bias the R-free towards the R-work with an approximte
radius of the G-function in reciprocal space.
What an interesting discussion!
Best regards,
Dirk.
Am 07.02.2008 um 18:57 schrieb Dean Madden:
Hi Dirk,
I disagree with your final sentence. Even if you don't apply NCS
restraints/constraints during refinement, there is a serious risk
of NCS "contaminating" your Rfree. Consider the limiting case in
which the "NCS" is produced simply by working in an artificially
low symmetry space-group (e.g. P1, when the true symmetry is P2):
in this case, putting one symmetry mate in the Rfree set, and one
in the Rwork set will guarantee that Rfree tracks Rwork. The same
effect applies to a large extent even if the NCS is not
crystallographic.
Bottom line: thin shells are not a perfect solution, but if NCS
is present, choosing the free set randomly is *never* a better
choice, and almost always significantly worse. Together with
multicopy refinement, randomly chosen test sets were almost
certainly a major contributor to the spuriously good Rfree values
associated with the retracted MsbA and EmrE structures.
Best wishes,
Dean
Dirk Kostrewa wrote:
Dear CCP4ers,
I'm not convinced, that thin shells are sufficient: I think, in
principle, one should omit thick shells (greater than the
diameter of the G-function of the molecule/assembly that is used
to describe NCS-interactions in reciprocal space), and use the
inner thin layer of these thick shells, because only those
should be completely independent of any working set reflections.
But this would be too "expensive" given the low number of
observed reflections that one usually has ...
However, if you don't apply NCS restraints/constraints, there is
no need for any such precautions.
Best regards,
Dirk.
Am 07.02.2008 um 16:35 schrieb Doug Ohlendorf:
It is important when using NCS that the Rfree reflections be
selected is
distributed thin resolution shells. That way application of NCS
should not
mix Rwork and Rfree sets. Normal random selection or Rfree + NCS
(especially 4x or higher) will drive Rfree down unfairly.
Doug Ohlendorf
-----Original Message-----
From: CCP4 bulletin board [mailto:[EMAIL PROTECTED] On
Behalf Of
Eleanor Dodson
Sent: Tuesday, February 05, 2008 3:38 AM
To: CCP4BB@JISCMAIL.AC.UK <mailto:CCP4BB@JISCMAIL.AC.UK>
Subject: Re: [ccp4bb] an over refined structure
I agree that the difference in Rwork to Rfree is quite
acceptable at your resolution. You cannot/ should not use
Rfactors as a criteria for structure correctness.
As Ian points out - choosing a different Rfree set of
reflections can change Rfree a good deal.
certain NCS operators can relate reflections exactly making it
hard to get a truly independent Free R set, and there are other
reasons to make it a blunt edged tool.
The map is the best validator - are there blobs still not
fitted? (maybe side chains you have placed wrongly..) Are there
many positive or negative peaks in the difference map? How well
does the NCS match the 2 molecules?
etc etc.
Eleanor
George M. Sheldrick wrote:
Dear Sun,
If we take Ian's formula for the ratio of R(free) to R(work)
from his paper Acta D56 (2000) 442-450 and make some
reasonable approximations,
we can reformulate it as:
R(free)/R(work) = sqrt[(1+Q)/(1-Q)] with Q = 0.025pd^3(1-s)
where s is the fractional solvent content, d is the
resolution, p is
the effective number of parameters refined per atom after
allowing for
the restraints applied, d^3 means d cubed and sqrt means
square root.
The difficult number to estimate is p. It would be 4 for an
isotropic refinement without any restraints. I guess that
p=1.5 might be an appropriate value for a typical protein
refinement (giving an R-factor
ratio of about 1.4 for s=0.6 and d=2.8). In that case, your R-
factor ratio of 0.277/0.215 = 1.29 is well within the allowed
range!
However it should be added that this formula is almost a self-
fulfilling prophesy. If we relax the geometric restraints we
increase p, which then leads to a larger 'allowed' R-factor
ratio!
Best wishes, George
Prof. George M. Sheldrick FRS
Dept. Structural Chemistry,
University of Goettingen,
Tammannstr. 4,
D37077 Goettingen, Germany
Tel. +49-551-39-3021 or -3068
Fax. +49-551-39-2582
*******************************************************
Dirk Kostrewa
Gene Center, A 5.07
Ludwig-Maximilians-University
Feodor-Lynen-Str. 25
81377 Munich
Germany
Phone: +49-89-2180-76845
Fax: +49-89-2180-76999
E-mail: [EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]
muenchen.de>
*******************************************************
--
Dean R. Madden, Ph.D.
Department of Biochemistry
Dartmouth Medical School
7200 Vail Building
Hanover, NH 03755-3844 USA
tel: +1 (603) 650-1164
fax: +1 (603) 650-1128
e-mail: [EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]>
*******************************************************
Dirk Kostrewa
Gene Center, A 5.07
Ludwig-Maximilians-University
Feodor-Lynen-Str. 25
81377 Munich
Germany
Phone: +49-89-2180-76845
Fax: +49-89-2180-76999
E-mail: [EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]
muenchen.de>
*******************************************************
*******************************************************
Dirk Kostrewa
Gene Center, A 5.07
Ludwig-Maximilians-University
Feodor-Lynen-Str. 25
81377 Munich
Germany
Phone: +49-89-2180-76845
Fax: +49-89-2180-76999
E-mail: [EMAIL PROTECTED]
*******************************************************
