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.
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]>
*******************************************************
--
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]>
*******************************************************
