Thank you so much Dale,
I am embarrassingly bad at doing transformation matrices. I am going to review and repeat what you did. Your reasoning is making more sense to me. I just wish I had a better handle on this to identify it myself. Do you have any books/resources that might help in this regard (Not necessarily crystallography books)?


On Sat, Apr 19, 2014 at 12:38 AM, Dale Tronrud <detBB@daletronrud.com> wrote:
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Hi,

   In P21 the equivalent positions are:

xyz; -x,y+1/2,-z.

In matrix form the operation to transform chain A onto the symmetry
image of A is:

Transform A -> Symmetry related A
/-1   0   0\  /x\   / 0 \
| 0   1   0 | |y| + |1/2|
\ 0   0  -1/  \z/   \ 0 /

   Now let's assume there are two molecules in the ASU related by
a perfect two-fold, axis parallel to the crystal screw axis, but
with arbitrary translations perpendicular.  The equation to transform
chain B onto A is:

Transform B -> A

/-1   0   0\  /x\   /t1\
| 0   1   0 | |y| + |0 |
\ 0   0  -1/  \z/   \t3/


   Now, the question is "What is the transformation that takes
chain B directly onto the symmetry image of A?"  We can derive
that by transforming B onto A and then transforming that by the
crystal screw axis.

Transform B -> symmetry related A

/-1   0   0\  //-1   0   0\  /x\   /t1\\   / 0 \
| 0   1   0 | || 0   1   0 | |y| + |0 || + |1/2|
\ 0   0  -1/  \\ 0   0  -1/  \z/   \t3//   \ 0 /

Now simplify:

/ 1   0   0\  /x\   /-t1\   / 0 \
| 0   1   0 | |y| + | 0 | + |1/2|
\ 0   0   1/  \z/   \-t3/   \ 0 /

/ 1   0   0\  /x\   /-t1\
| 0   1   0 | |y| + |1/2|
\ 0   0   1/  \z/   \-t3/

   What we get is an identity operator with a translation.

Note, I didn't make any other assumptions.  Whenever you have space
group P21 and two-fold ncs with the same symmetry axis direction you
will get pseudo-translation.

   With your crystal the ncs matrix is not aligned with the y
axis all that well.  I haven't calculated it exactly but it seems
to be about 10 deg away.  That must be enough to wipe out the
Patterson peak and the pseudo-translation check in xtriage.

   As a side note, you mentioned that you didn't think this was
pseudo-translation because the translation was not 0.5.  A translation
of 0.5 could lead to pseudo-centering which is a special case of
pseudo-translation.  If you had that your crystal would be nearly
space group C2 and half your reflections would be systematically
weak and this can cause problems with the free R.

Dale Tronrud



On 4/18/2014 2:16 PM, Yarrow Madrona wrote:
> Hi Dale,
>
> You know a lot more (and probably have forgotten more)
> crystallography theory than I will every know. But I thought that
> rotational and translational NCS can be completely separate from
> the space group symmetry. They can become confused when the NCS
> operator is close to a crystallographic symmetry axis. I have P21
> symmetry between dimers but there is only one dimer in the unit
> cell. They appear to have near perfect 2-fold symmetry between them
> on the b-axis (according to the transformation matrix). However,
> the translation between them is not close to 1/2 of a unit cell as
> would be expected for a 2(1) screw axis. This makes sense because I
> don't see a peak on the patterson map but I do see a peak on the
> self rotation. X-triage also confirms the first part.
>
> I also get a translation of (0, 0.3, 0.3) but I thought this
> wouldn't show up as translational "NCS" because it was not near
> 0.5. I thought the difference between the vectors would not
> perfectly superimpose to give a strong peak on a patterson map.
>
> Please correct me if I am wrong (because I probably am). It is
> entirely possible I sound like an idiot. If so please let me know.
> Otherwise I will never learn more about the fundamentals of
> crystallography. If you have a good reference please let me know.
>
> -Yarrow
>
>
> On Fri, Apr 18, 2014 at 9:34 AM, Dale Tronrud
> <detBB@daletronrud.com <mailto:detBB@daletronrud.com>> wrote:
>
> Hi,
>
> I don't see how you can not have translational ncs.  You are in
> space group P21 and have an ncs two-fold parallel to y. Doesn't
> this combination have to give rise to translational ncs?
>
> I may have screwed up my paper matrix multiplications but I come
> up with a translational ncs of about (0, 0.3, 0.3) in fractional
> coordinates.  If the translation were 0.3333 you would only see
> strong reflections for k+l=3n.  This would result in a lot of weak
> data and higher than expected free R's.
>
> Of course, xtriage should be screaming bloody murder and you
> should be seeing the peak in the Patterson.  I'm confused.
>
> Dale Tronrud
>
> On 4/17/2014 6:05 PM, Yarrow Madrona wrote:
>> There is no significant peaks for translational NCS. I also
>> didn't see anything in the patterson map.
>
>> However, the Multivariate Z score L-test gives 6.218. Also the
>> observed Centric reflections are more intense than they should
>> be but I don't suspect twinning in a monoclinic space group.
>
>> -Yarrow
>
>
>> On Thu, Apr 17, 2014 at 4:37 PM, Paul Adams <pdadams@lbl.gov
> <mailto:pdadams@lbl.gov>
>> <mailto:pdadams@lbl.gov <mailto:pdadams@lbl.gov>>> wrote:
>
>
>> What does triage say about translation NCS?
>
>
>> On Thu, Apr 17, 2014 at 4:25 PM, Yarrow Madrona
>> <amadrona@uci.edu
> <mailto:amadrona@uci.edu>
>> <mailto:amadrona@uci.edu <mailto:amadrona@uci.edu>>> wrote:
>
>> Hello,
>
>> I using the latest stable build of phenx.refine (1.8.4) I
>> recently collected data, processed and obtained an MR solution
>> using phaser. I am stuck trying to refine with an Rfree sitting
>> at 40%
>
>> I really want to know if the high Rfree is due to poor data
>> quality or if non-crystallographic symmetry involving a near
>> perfect two fold rotation between the two molecules in the ASU
>> could somehow impede refinement. Stats and other information is
>> below. Thank you for any help you can give.
>
>> -Yarrow
>
>
>> Visually, the quality of the data is marginal at best
>> (streaky/ice rings in many frames) despite good processing stats
>> from XDS. Processing with mosflm or HKL2000 managed to index but
>> failed pretty bad in integration and scaling.
>
>> Phaser gave high TFZ scores for 2 molecules in the asu (see
>> below).
>
>> Density for a cholesterol like ligand shows up even though not
>> present in the search model.
>
>> MolRep Self rotation shows rotational symmetry.
>
> https://www.dropbox.com/s/2zsajl5o091k50r/CYP142A2-032814_21_rf%20copy.pdf
>
>
>> The 2 molecules in the ASU are related by almost a 2 fold
>> rotation:
>
>> Rotation matrix for chain A to chain B:
>
>> new_ncs_group rota_matrix    1.0000    0.0000    0.0000
>> rota_matrix 0.0000    1.0000    0.0000 rota_matrix    0.0000
>> 0.0000 1.0000 tran_orth     0.0000    0.0000    0.0000
>
>> center_orth   15.2016    0.5245   33.7070
>
>> rota_matrix   -0.9860   -0.1636   -0.0309 rota_matrix   -0.1659
>> 0.9511    0.2605 rota_matrix   -0.0132    0.2620   -0.9650
>> tran_orth      34.3310  -24.0033  107.0457
>
>> center_orth   15.7607    7.2426   77.7512
>
>> RMSD, B onto A = 0.0007 after phaser RMSD, B onto A = 0.347
>> after one round of refinement in phenix
>
>
>> Refinement using aniostropically corrected data (ucla web
>> server: Services.mbi.ucla.edu/anisoscale
> <http://Services.mbi.ucla.edu/anisoscale>
>> <http://Services.mbi.ucla.edu/anisoscale>) did not improve the
>> Rfree in refinement.
>
>
>> Statistics are listed below:
>
>> UNIT CELL: 51.487 88.923 89.592 90 97.15 90 P21
>
>> RESOLUTION     NUMBER OF REFLECTIONS    COMPLETENESS R-FACTOR
>> R-FACTOR COMPARED I/SIGMA   R-meas  CC(1/2)  Anomal  SigAno
>> Nano LIMIT     OBSERVED  UNIQUE  POSSIBLE     OF DATA   observed
>> expected                                      Corr
>
>> 5.99        8280    1927      2087       92.3%       3.1% 3.3%
>> 8246   35.09      3.5%    99.8*    20*   0.909    1296 4.30 14606
>> 3401      3487       97.5%       3.3% 3.5%    14580 33.37
>> 3.8%    99.9*    11*   0.843    2273 3.53       17961 4244
>> 4445       95.5%       3.8% 3.9%    17944   31.11 4.4%    99.8*
>> -2    0.789    2721 3.06       21954    5068 5221       97.1%
>> 4.9% 5.1%    21933   24.81      5.6% 99.7*    -2    0.780    3455
>> 2.74       25741    5830      5933 98.3%       7.6% 7.6%    25713
>> 18.88      8.6%    99.5*    -2 0.782    4165 2.51       27859
>> 6311      6483       97.3% 10.8% 10.8%    27824   14.06     12.3%
>> 99.1*    -2    0.774 4385 2.32       31336    6979      7084
>> 98.5%      14.9% 15.3%    31296   10.49     16.8%    98.5*    -4
>> 0.748    5095 2.17       32396    7347      7567       97.1%
>> 22.3% 22.7% 32341    7.46     25.4%    97.3*    -7    0.728
>> 5055 2.05 32254    7339      8047       91.2%      33.1% 33.5%
>> 32075 5.06     37.5%    94.8*    -6    0.724    5155 total
>> 212387 48446     50354       96.2%       7.8% 7.9%   211952
>> 16.57 8.8%    99.7*    -3    0.768   33600
>
>> Processing with mosflm or HKL2000 managed to index but failed
>> pretty bad in integration and scaling.
>
>
>> Phaser:
>
>> SOLU SET RFZ=27.5 TFZ=24.2 PAK=0 LLG=1711 RF++ TFZ=64.6 PAK=0
>> LLG=3610 LLG=4865
>
>
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> <mailto:phenixbb@phenix-online.org>>
>> http://phenix-online.org/mailman/listinfo/phenixbb
>
>
>
>
>> -- Paul Adams Deputy Division Director, Physical Biosciences
>> Division, Lawrence Berkeley Lab Division Deputy for Biosciences,
>> Advanced Light Source, Lawrence Berkeley Lab Adjunct Professor,
>> Department of Bioengineering, U.C. Berkeley Vice President for
>> Technology, the Joint BioEnergy Institute Laboratory Research
>> Manager, ENIGMA Science Focus Area
>
>> Building 64, Room 248 Tel: 1-510-486-4225 <tel:1-510-486-4225>,
> Fax: 1-510-486-5909 <tel:1-510-486-5909>
>> http://cci.lbl.gov/paul
>
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>
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>
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>
>
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