1. Twinning etc Andrey Lebedev YSBL

2. Data prcessing Twinning test: 1) There is twinning 2) The true spacegroup is one of … 3) Find the true spacegroup at the stage of MR 4) Use adequate likelihood / LS target at the refinement MR Twinning refinement Twinning only (MR scenario)

3. Pseudosymmetry: good and bad news for MR The r.m.s.d. between the true structure and the structure refined in a wrong spacegroup is less than the r.m.s.d. between the structure and the search model. Therefore: 1) There is no certainty with the symmetry before model is partially build and refined 2) Model can be partially build and refined in a wrong spacegroup

4. Example: twinning + pseudosymmetry Crystal structure of Ribulose Biphosphate Carboxylase Pdb code: 1upp Cell: 155.9 156.3 200.0 90 90 90 Crystal symmetry: C222 1 Highest possible crystal symmetry according to the symmetry of X-ray data: P4 x 2 x 2 Twinning: pseudomerohedral Pseudotranslation: 1/2, 0, 1/2 15% of origin peak This is an example when pseudomerohedral twinning takes place whereas merohedral twinning cannot be excluded at the stage of X-ray data analysis.

5. 1upp: superposition of the twinning domains An individual single crystal (domain) has symmetry C222 1 The average structure has symmetry I422 with pseudotranslation turned into crystallographic translation Deviation of the domain structure from the average structure is less than 1A 1.34 A

6. 1upp: perturbation of higher symmetry Broken operators of higher symmetry become NCS and twinning operators. NCS 4-folds Twinning 4-fold 3.4° Superposition of two octamers by translation. The Octamers belong to the same twinning domain and are related by crystallographic 2-fold The NCS 4-folds in neighbouring twinning domains are tilted in diferent directions. The latter are related by Twinning 4-fold.

7. Space group* ) C222 1  F222  I422  P4 2 22  P4 2 The number of monomers per asymmetric unit 42124 Starting model I422 - PDBI422 Correlation coefficient after molecular replacement 0.53-0.570.500.51 R after rigid-body refinement0.38-0.430.440.43 R after restrained refinement0.28-0.330.370.36 R-free after restrained refinement0.34-0.410.440.43 1upp: validation of the crystal symmetry Before refinement: I422, F222 are impossible: translational NCS becomes crystallographic translation P4 2 22 is unlikely: perfect twinning test indicates twinning P4 2, C222 1 are equally possible After refinement: C222 1 is the true crystal symmetry * ) subgroup  supergroup Search model had the identity of 99%. With more realistic model the contrast will be worse! What to do?

8. Electron density in a wrong spacegroup The difference map at the missing fragment of the model after refinement in I422. As shown in the previous slide, the structure can be resolved and the correct spacegroup determined after such refinement.

9. RvR-plot A:translational NCS B:mislabeling F  I C,C’:mislabeling I  F Red: (potential) merohedral twins Black: (potential) pseudomerohedral twins non-twins

10. Symmetry environment of twinning – Cases with pseudosymmetry are more frequent in general, and dominate for pseudomerohedral twins. – Among solved structures, pseudomerohedral twinning is less frequent than merohedral. It is likely, that this is partially because of the problems with diagnostic.

11. Perfect twinning test Untwinned + pseudosymmetry: test shows no twinning Twin + pseudosymmetry: Test shows only partial twinning. decrease of contrast

12. Partial twinning test No pseudosymmetry: linear for both twins and non-twins. Tilt shows twinning fraction. The test is useless for perfect twins (cannot distinguish it from higher symmetry) Pseudosymmetry causes non-linearity. Experimental errors + this non-linearity makes the test hardly interpretable in some cases. Non-linearity

13. The last year cases Pure twinning ( choice between P4 x and P2 x 2 x 2 x ) Twinning + pseudosymmetry ( P222 1 / 3* P2 x ) Pseudotranslation ( 2* P4 1 22 / 2* P4 3 22 ) Pseudotranslation ( 2* P3 1 22 / 4* (P3 1 + twinning) ) Statistical orthorombic? ( choice of lattice ) Partial model ( P622 / P322 / … ) Cases where users suspected twinning with no reasons (many!)

14. Data prcessing Twinning test (using data only): 1) Twinning is likely 2) The true spacegroup is one of … 3) Find MR solution in any of these groups 4) Revise the spacegroup later MR Refinement and partial model building Twinning test (using data and pre-refined model): 1) There is twinning 2) The true spacegroup is … Twinning refinement Twinning and pseudo-symmetry (MR scenario)

15. Validation of symmetry: twinning paranoia Cases without pathology message: be happy, work hard with model building Cases with pathology action: correction of the model message: likelihood function to use parameters to refine initial values addressees: refinement program (REFMAC) data reduction program (SCALA, nTRUNCATE) Pathologies to cover Twinning including twinning by reticular merohedry Pseudosymmetry “Statistical” crystals