1. Pseudo translation and Twinning

2. Crystal peculiarities Pseudo translation Twin Order-disorder

3. Pseudo translation Real space Reciprocal space a b Distance between spots: 1/a, 1/b Distance between spots: 1/(2a), 1/b Every second reflection is weak.

4. Pseudo-translation P0 0.125 P0 Patterson Pst-vector Cell

5. Pseudo translation (PST) may cause problems in molecular replacement. Refinement usually does not have much problem. However in the presence of PST the solution may be in wrong origin. There may be other sources of pseudotranslation: 1)Non-merohedral twin 2)Helices, DNA 3)Order-disorder

6. Twinning

7. merohedral and pseudo-merohedral twinning Crystal symmetry: P3 P2 P2 Constrain: - β = 90º - Lattice symmetry *: P622 P222 P2 (rotations only) Possible twinning: merohedral pseudo-merohedral - Domain 1 Domain 2 Twinning operator - Crystal lattice is invariant with respect to twinning operator. The crystal is NOT invariant with respect to twinning operator.

8. More than three layers, but less than the whole crystal. C2 single crystal C2 OD-twin C2 C222 1 single crystal C222 1 Allotwin C2 C222 1 Disordered OD-structure

9. The whole crystal: twin or polysynthetic twin? A single crystal can be cut out of the twin: twin yes polysynthetic twin no The shape of the crystal suggested that we dealt with polysynthetic OD-twin

10. Experimental data Model (single domain) Twins: Self-Rotation Function PDB code 1l2h Spacegroup P4 3 1 molecule per AU Merohedral twinning Crystallographic two-fold axis Four equivalent twinning two-fold axes Figures show sections of the self- rotation function corresponding to two-fold axes PDB code 1igj Spacegroup P2 1 NCS (Pseudosymmetry): 2 monomers per AU Pseudo-merohedral twinning Crystallographic two-fold axis Pseudosymmetry and twinning Pseudosymmetry

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

12. Symmetry environment of twinning Merohedral twinning: – crystal symmetry assumes more symmetric lattice – twinning would not require extra constraints on unit cell dimensions Conclusions: – 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.

13. Perfect twinning test Untwinned + pseudosymmetry: test shows no twinning Twin + pseudosymmetry: Test shows only partial Twinning. (decrease of contrast) This test is implemented in TRUNCATE

14. 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 This test is implemented in SFCHECK

15. Electron density: 1rxf We will see occasionally this “refmac” map“twin” map

16. Electron density: 1jrg More usual and boring case “refmac” map “twin” map

17. Effect of twin on electron density: Noise level. Very, very approximate F t - twinned structure factor F R - structure factor from “correct” crystal F W - structure factor from “wrong” crystal The first term is correct electron density the second term corresponds to noise. When twin and NCS are parallel then the second term is even smaller.