<div dir="ltr"><span style="font-family:arial,sans-serif;font-size:16px">Thank you so much Dale,</span><div style="font-family:arial,sans-serif;font-size:16px">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)?</div>
<div class="" style="font-family:arial,sans-serif;font-size:16px"></div></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Sat, Apr 19, 2014 at 12:38 AM, Dale Tronrud <span dir="ltr"><<a href="mailto:detBB@daletronrud.com" target="_blank">detBB@daletronrud.com</a>></span> wrote:<br>
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Hi,<br>
<br>
</div> In P21 the equivalent positions are:<br>
<br>
xyz; -x,y+1/2,-z.<br>
<br>
In matrix form the operation to transform chain A onto the symmetry<br>
image of A is:<br>
<br>
Transform A -> Symmetry related A<br>
/-1 0 0\ /x\ / 0 \<br>
| 0 1 0 | |y| + |1/2|<br>
\ 0 0 -1/ \z/ \ 0 /<br>
<br>
Now let's assume there are two molecules in the ASU related by<br>
a perfect two-fold, axis parallel to the crystal screw axis, but<br>
with arbitrary translations perpendicular. The equation to transform<br>
chain B onto A is:<br>
<br>
Transform B -> A<br>
<br>
/-1 0 0\ /x\ /t1\<br>
| 0 1 0 | |y| + |0 |<br>
\ 0 0 -1/ \z/ \t3/<br>
<br>
<br>
Now, the question is "What is the transformation that takes<br>
chain B directly onto the symmetry image of A?" We can derive<br>
that by transforming B onto A and then transforming that by the<br>
crystal screw axis.<br>
<br>
Transform B -> symmetry related A<br>
<br>
/-1 0 0\ //-1 0 0\ /x\ /t1\\ / 0 \<br>
| 0 1 0 | || 0 1 0 | |y| + |0 || + |1/2|<br>
\ 0 0 -1/ \\ 0 0 -1/ \z/ \t3// \ 0 /<br>
<br>
Now simplify:<br>
<br>
/ 1 0 0\ /x\ /-t1\ / 0 \<br>
| 0 1 0 | |y| + | 0 | + |1/2|<br>
\ 0 0 1/ \z/ \-t3/ \ 0 /<br>
<br>
/ 1 0 0\ /x\ /-t1\<br>
| 0 1 0 | |y| + |1/2|<br>
\ 0 0 1/ \z/ \-t3/<br>
<br>
What we get is an identity operator with a translation.<br>
<br>
Note, I didn't make any other assumptions. Whenever you have space<br>
group P21 and two-fold ncs with the same symmetry axis direction you<br>
will get pseudo-translation.<br>
<br>
With your crystal the ncs matrix is not aligned with the y<br>
axis all that well. I haven't calculated it exactly but it seems<br>
to be about 10 deg away. That must be enough to wipe out the<br>
Patterson peak and the pseudo-translation check in xtriage.<br>
<br>
As a side note, you mentioned that you didn't think this was<br>
pseudo-translation because the translation was not 0.5. A translation<br>
of 0.5 could lead to pseudo-centering which is a special case of<br>
pseudo-translation. If you had that your crystal would be nearly<br>
space group C2 and half your reflections would be systematically<br>
weak and this can cause problems with the free R.<br>
<br>
Dale Tronrud<br>
<div class=""><br>
<br>
<br>
On 4/18/2014 2:16 PM, Yarrow Madrona wrote:<br>
> Hi Dale,<br>
><br>
> You know a lot more (and probably have forgotten more)<br>
> crystallography theory than I will every know. But I thought that<br>
> rotational and translational NCS can be completely separate from<br>
> the space group symmetry. They can become confused when the NCS<br>
> operator is close to a crystallographic symmetry axis. I have P21<br>
> symmetry between dimers but there is only one dimer in the unit<br>
> cell. They appear to have near perfect 2-fold symmetry between them<br>
> on the b-axis (according to the transformation matrix). However,<br>
> the translation between them is not close to 1/2 of a unit cell as<br>
> would be expected for a 2(1) screw axis. This makes sense because I<br>
> don't see a peak on the patterson map but I do see a peak on the<br>
> self rotation. X-triage also confirms the first part.<br>
><br>
> I also get a translation of (0, 0.3, 0.3) but I thought this<br>
> wouldn't show up as translational "NCS" because it was not near<br>
> 0.5. I thought the difference between the vectors would not<br>
> perfectly superimpose to give a strong peak on a patterson map.<br>
><br>
> Please correct me if I am wrong (because I probably am). It is<br>
> entirely possible I sound like an idiot. If so please let me know.<br>
> Otherwise I will never learn more about the fundamentals of<br>
> crystallography. If you have a good reference please let me know.<br>
><br>
> -Yarrow<br>
><br>
><br>
> On Fri, Apr 18, 2014 at 9:34 AM, Dale Tronrud<br>
</div><div class="">> <<a href="mailto:detBB@daletronrud.com">detBB@daletronrud.com</a> <mailto:<a href="mailto:detBB@daletronrud.com">detBB@daletronrud.com</a>>> wrote:<br>
><br>
> Hi,<br>
><br>
> I don't see how you can not have translational ncs. You are in<br>
> space group P21 and have an ncs two-fold parallel to y. Doesn't<br>
> this combination have to give rise to translational ncs?<br>
><br>
> I may have screwed up my paper matrix multiplications but I come<br>
> up with a translational ncs of about (0, 0.3, 0.3) in fractional<br>
> coordinates. If the translation were 0.3333 you would only see<br>
> strong reflections for k+l=3n. This would result in a lot of weak<br>
> data and higher than expected free R's.<br>
><br>
> Of course, xtriage should be screaming bloody murder and you<br>
> should be seeing the peak in the Patterson. I'm confused.<br>
><br>
> Dale Tronrud<br>
><br>
> On 4/17/2014 6:05 PM, Yarrow Madrona wrote:<br>
>> There is no significant peaks for translational NCS. I also<br>
>> didn't see anything in the patterson map.<br>
><br>
>> However, the Multivariate Z score L-test gives 6.218. Also the<br>
>> observed Centric reflections are more intense than they should<br>
>> be but I don't suspect twinning in a monoclinic space group.<br>
><br>
>> -Yarrow<br>
><br>
><br>
>> On Thu, Apr 17, 2014 at 4:37 PM, Paul Adams <<a href="mailto:pdadams@lbl.gov">pdadams@lbl.gov</a><br>
> <mailto:<a href="mailto:pdadams@lbl.gov">pdadams@lbl.gov</a>><br>
</div><div class="">>> <mailto:<a href="mailto:pdadams@lbl.gov">pdadams@lbl.gov</a> <mailto:<a href="mailto:pdadams@lbl.gov">pdadams@lbl.gov</a>>>> wrote:<br>
><br>
><br>
>> What does triage say about translation NCS?<br>
><br>
><br>
>> On Thu, Apr 17, 2014 at 4:25 PM, Yarrow Madrona<br>
>> <<a href="mailto:amadrona@uci.edu">amadrona@uci.edu</a><br>
> <mailto:<a href="mailto:amadrona@uci.edu">amadrona@uci.edu</a>><br>
</div><div><div class="h5">>> <mailto:<a href="mailto:amadrona@uci.edu">amadrona@uci.edu</a> <mailto:<a href="mailto:amadrona@uci.edu">amadrona@uci.edu</a>>>> wrote:<br>
><br>
>> Hello,<br>
><br>
>> I using the latest stable build of phenx.refine (1.8.4) I<br>
>> recently collected data, processed and obtained an MR solution<br>
>> using phaser. I am stuck trying to refine with an Rfree sitting<br>
>> at 40%<br>
><br>
>> I really want to know if the high Rfree is due to poor data<br>
>> quality or if non-crystallographic symmetry involving a near<br>
>> perfect two fold rotation between the two molecules in the ASU<br>
>> could somehow impede refinement. Stats and other information is<br>
>> below. Thank you for any help you can give.<br>
><br>
>> -Yarrow<br>
><br>
><br>
>> Visually, the quality of the data is marginal at best<br>
>> (streaky/ice rings in many frames) despite good processing stats<br>
>> from XDS. Processing with mosflm or HKL2000 managed to index but<br>
>> failed pretty bad in integration and scaling.<br>
><br>
>> Phaser gave high TFZ scores for 2 molecules in the asu (see<br>
>> below).<br>
><br>
>> Density for a cholesterol like ligand shows up even though not<br>
>> present in the search model.<br>
><br>
>> MolRep Self rotation shows rotational symmetry.<br>
><br>
> <a href="https://www.dropbox.com/s/2zsajl5o091k50r/CYP142A2-032814_21_rf%20copy.pdf" target="_blank">https://www.dropbox.com/s/2zsajl5o091k50r/CYP142A2-032814_21_rf%20copy.pdf</a><br>
><br>
><br>
>> The 2 molecules in the ASU are related by almost a 2 fold<br>
>> rotation:<br>
><br>
>> Rotation matrix for chain A to chain B:<br>
><br>
>> new_ncs_group rota_matrix 1.0000 0.0000 0.0000<br>
>> rota_matrix 0.0000 1.0000 0.0000 rota_matrix 0.0000<br>
>> 0.0000 1.0000 tran_orth 0.0000 0.0000 0.0000<br>
><br>
>> center_orth 15.2016 0.5245 33.7070<br>
><br>
>> rota_matrix -0.9860 -0.1636 -0.0309 rota_matrix -0.1659<br>
>> 0.9511 0.2605 rota_matrix -0.0132 0.2620 -0.9650<br>
>> tran_orth 34.3310 -24.0033 107.0457<br>
><br>
>> center_orth 15.7607 7.2426 77.7512<br>
><br>
>> RMSD, B onto A = 0.0007 after phaser RMSD, B onto A = 0.347<br>
>> after one round of refinement in phenix<br>
><br>
><br>
>> Refinement using aniostropically corrected data (ucla web<br>
>> server: <a href="http://Services.mbi.ucla.edu/anisoscale" target="_blank">Services.mbi.ucla.edu/anisoscale</a><br>
> <<a href="http://Services.mbi.ucla.edu/anisoscale" target="_blank">http://Services.mbi.ucla.edu/anisoscale</a>><br>
>> <<a href="http://Services.mbi.ucla.edu/anisoscale" target="_blank">http://Services.mbi.ucla.edu/anisoscale</a>>) did not improve the<br>
>> Rfree in refinement.<br>
><br>
><br>
>> Statistics are listed below:<br>
><br>
>> UNIT CELL: 51.487 88.923 89.592 90 97.15 90 P21<br>
><br>
>> RESOLUTION NUMBER OF REFLECTIONS COMPLETENESS R-FACTOR<br>
>> R-FACTOR COMPARED I/SIGMA R-meas CC(1/2) Anomal SigAno<br>
>> Nano LIMIT OBSERVED UNIQUE POSSIBLE OF DATA observed<br>
>> expected Corr<br>
><br>
>> 5.99 8280 1927 2087 92.3% 3.1% 3.3%<br>
>> 8246 35.09 3.5% 99.8* 20* 0.909 1296 4.30 14606<br>
>> 3401 3487 97.5% 3.3% 3.5% 14580 33.37<br>
>> 3.8% 99.9* 11* 0.843 2273 3.53 17961 4244<br>
>> 4445 95.5% 3.8% 3.9% 17944 31.11 4.4% 99.8*<br>
>> -2 0.789 2721 3.06 21954 5068 5221 97.1%<br>
>> 4.9% 5.1% 21933 24.81 5.6% 99.7* -2 0.780 3455<br>
>> 2.74 25741 5830 5933 98.3% 7.6% 7.6% 25713<br>
>> 18.88 8.6% 99.5* -2 0.782 4165 2.51 27859<br>
>> 6311 6483 97.3% 10.8% 10.8% 27824 14.06 12.3%<br>
>> 99.1* -2 0.774 4385 2.32 31336 6979 7084<br>
>> 98.5% 14.9% 15.3% 31296 10.49 16.8% 98.5* -4<br>
>> 0.748 5095 2.17 32396 7347 7567 97.1%<br>
>> 22.3% 22.7% 32341 7.46 25.4% 97.3* -7 0.728<br>
>> 5055 2.05 32254 7339 8047 91.2% 33.1% 33.5%<br>
>> 32075 5.06 37.5% 94.8* -6 0.724 5155 total<br>
>> 212387 48446 50354 96.2% 7.8% 7.9% 211952<br>
>> 16.57 8.8% 99.7* -3 0.768 33600<br>
><br>
>> Processing with mosflm or HKL2000 managed to index but failed<br>
>> pretty bad in integration and scaling.<br>
><br>
><br>
>> Phaser:<br>
><br>
>> SOLU SET RFZ=27.5 TFZ=24.2 PAK=0 LLG=1711 RF++ TFZ=64.6 PAK=0<br>
>> LLG=3610 LLG=4865<br>
><br>
><br>
>> _______________________________________________ phenixbb mailing<br>
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>> <mailto:<a href="mailto:phenixbb@phenix-online.org">phenixbb@phenix-online.org</a>><br>
</div></div>>> <mailto:<a href="mailto:phenixbb@phenix-online.org">phenixbb@phenix-online.org</a><br>
<div class="">> <mailto:<a href="mailto:phenixbb@phenix-online.org">phenixbb@phenix-online.org</a>>><br>
>> <a href="http://phenix-online.org/mailman/listinfo/phenixbb" target="_blank">http://phenix-online.org/mailman/listinfo/phenixbb</a><br>
><br>
><br>
><br>
><br>
>> -- Paul Adams Deputy Division Director, Physical Biosciences<br>
>> Division, Lawrence Berkeley Lab Division Deputy for Biosciences,<br>
>> Advanced Light Source, Lawrence Berkeley Lab Adjunct Professor,<br>
>> Department of Bioengineering, U.C. Berkeley Vice President for<br>
>> Technology, the Joint BioEnergy Institute Laboratory Research<br>
>> Manager, ENIGMA Science Focus Area<br>
><br>
</div>>> Building 64, Room 248 Tel: <a href="tel:1-510-486-4225" value="+15104864225">1-510-486-4225</a> <tel:<a href="tel:1-510-486-4225" value="+15104864225">1-510-486-4225</a>>,<br>
> Fax: <a href="tel:1-510-486-5909" value="+15104865909">1-510-486-5909</a> <tel:<a href="tel:1-510-486-5909" value="+15104865909">1-510-486-5909</a>><br>
<div class="">>> <a href="http://cci.lbl.gov/paul" target="_blank">http://cci.lbl.gov/paul</a><br>
><br>
>> Lawrence Berkeley Laboratory 1 Cyclotron Road BLDG 64R0121<br>
>> Berkeley, CA 94720, USA.<br>
><br>
>> Executive Assistant: Louise Benvenue [ <a href="mailto:LBenvenue@lbl.gov">LBenvenue@lbl.gov</a><br>
> <mailto:<a href="mailto:LBenvenue@lbl.gov">LBenvenue@lbl.gov</a>><br>
</div>>> <mailto:<a href="mailto:LBenvenue@lbl.gov">LBenvenue@lbl.gov</a> <mailto:<a href="mailto:LBenvenue@lbl.gov">LBenvenue@lbl.gov</a>>> ][<br>
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><br>
><br>
><br>
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