Pseudo translation and Twinning

1. Pseudo translation and Twinning

2. Crystal peculiarities • Pseudo translation • Twin • Order-disorder

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

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

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: Non-merohedral twin Helices, DNA Order-disorder

6. Twinning

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

8. C2 C2 single crystal OD-twin C2221 single crystal Allotwin C2 C2 C2221 C2 Disordered OD-structure C2221 More than three layers, but less than the whole crystal.

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

10. Twins: Self-Rotation Function Figures show sections of the self-rotation function corresponding to two-fold axes Experimental data Model (single domain) Crystallographic two-fold axis • PDB code 1l2h • Spacegroup P43 • 1 molecule per AU • Merohedral twinning Four equivalent twinning two-fold axes Crystallographic two-fold axis • PDB code 1igj • Spacegroup P21 • NCS (Pseudosymmetry): 2 monomers per AU • Pseudo-merohedral twinning Pseudosymmetry and twinning Pseudosymmetry

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

12. Merohedral twinning: • crystal symmetry assumes more symmetric lattice • twinning would not require extra constraints on unit cell dimensions Symmetry environment of twinning • 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 This test is implemented in TRUNCATE Untwinned + pseudosymmetry: test shows no twinning Twin + pseudosymmetry: Test shows only partial Twinning. (decrease of contrast)

14. Partial twinning test Non-linearity 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. This test is implemented in SFCHECK

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

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

17. Effect of twin on electron density: Noise level. Very, very approximate Ft - twinned structure factor FR - structure factor from “correct” crystal FW - 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.