When you say that "NCS is only a local, not global, crystal symmetry"
what you actually mean is that "NCS is only a local not global *group*
symmetry", i.e. NCS symmetry obviously *is* global if symmetry is
defined (as in physics) as *any* operator which superposes (more or
less) 2 copies of the monomer. In fact this isn't correct either
because even the localised NCS symmetry operators may not form a group,
so the correct statement is "NCS operators can only form a local not
global symmetry group, though this is not a necessary condition for
NCS.".
It follows that the important feature of NCS is *not* whether it's local
or global, but whether or not it forms a group. Clearly only in the
case that it forms a group is it possible for it to synchronise with the
lattice symmetry and approximate to crystallographic symmetry (though of
course in the majority of cases the NCS group doesn't synchronise with
the lattice).
This isn't just nit-picking semantics, the same issue arises when
analysing self-rotation functions. Many people, believing that the only
NCS operators that need to be considered are the local group operators,
look only at the kappa sections which may contain peaks corresponding to
the group symmetry operators (e.g. kappa = 60, 72, 90, 120, 180) and
completely ignore all the other sections which may contain peaks
corresponding to all the non-group operators (which often outnumber the
group operator peaks), and thus miss potentially valuable information.
-- Ian
> -----Original Message-----
> From: [log in to unmask]
> [mailto:[log in to unmask]] On Behalf Of Dirk Kostrewa
> Sent: 08 February 2008 10:10
> To: CCP4BB
> Subject: Re: [ccp4bb] an over refined structure
>
> 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:[log in to unmask]] On Behalf Of
> Eleanor Dodson
> Sent: Tuesday, February
> 05, 2008 3:38 AM
> To:
> [log in to unmask] <mailto:[log in to unmask]>
> 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:
> [log in to unmask] <mailto:[log in to unmask]>
>
> *******************************************************
>
>
> --
> 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: [log in to unmask]
> <mailto:[log in to unmask]>
>
> *******************************************************
> 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: [log in to unmask]
> <mailto:[log in to unmask]>
> *******************************************************
>
>
>
>
> *******************************************************
> 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: [log in to unmask]
> *******************************************************
>
>
>
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