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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
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



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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]>
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-- 
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]


*******************************************************
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]
*******************************************************