(September 2001)
I have a dataset that I scales equally well in P4 and P422. In order to resolve this ambiguity I looked at the P4 scaled data in HKLVIEW and found mirror planes in all the right places suggesting that the Laue class was 4/m mm, therefore P422. All the moments and intensity statistics in SCALA/TRUNCATE look fine when the data is scaled in P422, but not quite as good in P4. Just for the hell of it, I ran the DETWIN program on the P4 scaled data, and DETWIN reckons my data is pretty much a perfect twin. So... if the true space group is P422, and you put P4 data through DETWIN, will it appear twinned (as 'perfectly' twinned P4 data can appear to be P422...)? The UCLA twinning server indicates that my data is not perfectly twinned when tested in P422... so now I'm getting two conflicting results and I'm confused... (basically... is my data twinned or not!!!)
The enquirer kindly provided plots from TRUNCATE (click on thumb-nails to enlarge):
P4
cumulative intensity distribution
1st&3rd moments 2nd moment P422
cumulative intensity distribution
1st&3rd moments 2nd moment
Perhaps packing considerations can help you out with your twinning problem: In P4 there are 4 a.u. per unit cell, in P422 it would be 8 a.u./unit cell. If the true space group was P4 and you have a perfect twin, and assume you have one protein molecule per asym. unit, then when you calculate Matthews parameters for both P4 and P422, they would look alright for P4 and one molecule, but for P422 you would obtain a reasonable Matthews parameter only for 0.5 molecules per a.u. The other way around: the wrong assumption of P422 caused by perfect twinning means that the lattice is too small to accommodate the number of molecules required by this space group. Think this was what made Luecke et al. suspicious about the possibility of twinning in the case of bacteriorhodopsin ( Luecke, H., Richter, H.T., and Lanyi, J.K. (1998). Proton transfer pathways in bacteriorhodopsin at 2.3 angstrom resolution. Science 280, 1934-1937.) It would become a bit more difficult when the true space group is P4, and you have 2 molecules in the asym. unit, connected by two- fold NCS. Then you obtain normal Matthews parameter for the true space group and 2 mol. per asym. unit, but also for the wrong sp.gr. P422 with 1 mol. per a.u. However, if you are lucky and the NCS axes do not run parallel to the crystallographic axes, you should then be able to differentiate between NCS and pseudo-crystallographic two-fold axes (caused by perfect twinning) by examination of the self rotation function. The self rotation peaks of data processed in P4 should be at kappa 180, omega 90, and phi _exactly_ at 0°,45°,90° etc. only in the case of perfect twinning. If they are off 0°, then it is NCS and thus not perfect twinning.
Note from the enquirer: Unfortunately, I am not that lucky. I have 2mols per asu in P422 (therefore 4 in P4) - everything SHOULD fit. My NCS two fold does run parallel to my crystallographic axes, as I have rather nice looking pseudo-translation peaks on my native patterson...
The DETWIN program indicated a near perfect twin for the P4 scaled data. As there are no twinning operators for P422, I could not use DETWIN on this data. The UCLA twinning server allows you to detect presence of a perfect twin using your higher space group (for me, P422). The perfect twin test gave a resounding "NO, you are not twinned!". However, the partial twin test using P4 data gave a "yes, you are greater than 45% twinned" answer. Which is right?!
A piece of wisdom: one should always go for the highest symmetry that gives consistent results. If the true symmetry is P4, you might be looking at twice as many molecules in the asymmetric unit, with an 'accidental' packing that looks like P422. To distinguish between them, you might want to do rigid body refinement of the P422 derived model in P4 (using the appropriate 422 symmetry operator to complete the contents of the P4 asymmetric unit), and then observe how far apart the two are. If there are genuine differences, go for the lower sp. gr. However, Rigid Body refinement only tells you about gross errors in positioning the molecules. This might not be significant. So you might have to go further and do a full refinement in both sp. gr. and observe particularly the side chains near interfaces that make lattice contacts. A few of these differences would force a lower symmetry (P4), but if you assume the higher symmetry (P422) you would not notice in the statistics, always taking into account the degree of difference (the resolution obviously has a great deal of impact on the significance of the differences). 'Accidental' packing that looks like a higher sp.gr. usually gives a slightly odd N(z) plot in TRUNCATE, where the observed graphs are to the left of the theoretical ones. If they are to the right of the theoretical graphs, especially in the bottom left corner, then you should suspect twinning. The solution (?): Following on from my problems regarding tetragonal twinning and some ambiguity between P4 (twinned) and P422 (non-twinned), we took an un-scaled MTZ file from a solved/published structure from our college that was solved in P422 (4/m mm). This
integrated MTZ file was in P4. We then re-indexed this in P422 and repeated SCALA/TRUNCATE/DETWIN on both P4 and P422 datasets. Both my data and the solved data scale equally well in P4 and P422 (sensible stats, very few rejections...) The P4 centric intensity distribution was also a little odd, whereas the P422 looks fine. All the various moments in P4 and P422 indicated that the data was not twinned. Detwin also indicated that, in P4, this data was an almost perfect twin. The UCLA perfect twinning test for P422 indicated "no twin", but the partial test in P4 indicated almost perfect