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Twinning and other pathologies Andrey Lebedev University of York

Twinning and other pathologies Andrey Lebedev University of York. Examples of crystal pathologies Twinning by (pseudo)merohedry Statistics of one observation Statistics of two observations Twinning tests summary Space group validation. Examples of crystal pathologies

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Twinning and other pathologies Andrey Lebedev University of York

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  1. Twinning and other pathologies Andrey Lebedev University of York

  2. Examples of crystal pathologies Twinning by (pseudo)merohedry Statistics of one observation Statistics of two observations Twinning tests summary Space group validation

  3. Examples of crystal pathologies Twinning by (pseudo)merohedry Statistics of one observation Statistics of two observations Twinning tests summary Space group validation

  4. Crystal disorder Diffraction: Twinning & Disorder = Missing global periodicity Sizes of ordered domains decrease 1- 2- and 3-dimensional disorder Single crystal Twinned crystal Partially disordered crystal OD-structures

  5. OD-structures S2 S1 S1 S1 - identical layers - identical interfaces between the layers - but: two or more ways of packing adjacent layers *) MX: "identical" means Ca r.m.s.d. < 1 A *)S1 and S2. are called stacking vectors - two-dimensional periodicity - a potential for disorder in the third dimension

  6. Examples Single crystal Single crystal Partially disordered OD-structure Allotwin OD-twin P21 C2 P21 C2 P212121 Example 1 Example 2 Example 3

  7. Example 1: OD-twin (twin by lattice pseudomerohedy) C2 C2 Indexing in C2 Indexing in C2 Rye et al. (2007) Acta Cryst.D67 L-2-haloacid dehalogenase from Sulfolobus tokodaii The diffraction images can be indexed in C2 with two different orientation of the crystal The problem with the data is that some of the reflections from two lattices overlap. The presence of layers of overlapping reflections is the reason of non-origin peaks in the Patterson map.

  8. OD-twin: real and reciprocal lattices C2 C2 c a Example1

  9. OD-twin: demodulation C2 C2 Example1 IT1 = q'(h) I1 q'(h) = p0 + p1 cos(2th) + p2 cos(4th) + ... q'(h) R / R-free Original data 0.21 / 0.27 Demodulated data 0.16 / 0.23 v = w = 0

  10. Example 2: allotwin P21 P212121 Crystals of Lon protease Resolution 3Å Dauter et al. (2005). Acta Cryst. D61, 967-975. P21 R / R-free = 0.21 / 0.31 P212121 R / R-free = 0.19 / 0.35

  11. Example 3: partially disordered OD-structure Wang et al. (2005). Acta Cryst. D61, 67-74. a* The translation symmetry is perturbed in the direction a*. The diffraction pattern is characterised by the presence of the diffuse streaks along a*. Crystals of Phi29 DNA polymerase Resolution 2.2Å The structure was solved using demodulated data and experimental phasing Refinement against corrected data: R=0.28 P21

  12. Example 4: Four types of domains Patterson maps at Z=0 P21 structure (1k7u, 1k7v) 1k7v 1k7u Putative C2 structure Interpretation of the Patterson map for 1k7v: four types of domains - P21 (orientation 1) - P21 (orientation 2) - C2 (orientation 1) contribute to some of the P21 spots, - C2 (orientation 2) hence non-origin Patterson peaks Twinned P21 data

  13. Example 5: Conserved one-dimensional substructures crystal soaking twinned orthorhombic crystal twinned tetragonal crystal Roberto Steiner, Kings college, University of London

  14. Examples of crystal pathologies Twinning by (pseudo)merohedry Statistics of one observation Statistics of two observations Twinning tests summary Space group validation

  15. Twins by reticular merohedry (inc some OD-twins), allotwins, disordered structures - Can be readily seen in images with predictions Important special case: twinning by (pseudo)merohedry - All spots overlap with related spots from another individual crystal - Detection requires analysis of intensity statistics - Significant effect on model if ignored

  16. Examples of crystal pathologies Twinning by (pseudo)merohedry Statistics of one observation Statistics of two observations Twinning tests summary Space group validation

  17. Theoretical intensity statistics Single crystal Partial twin Partial twin Perfect twin Acentric reflections Centric reflections <Z2> <Z2> <Z2> <Z2> s s s s

  18. Two good, two bad PDB entry 1i1j single crystal C-terminal domain of gp2 protein from phage SPP1 (unpublished) perfect twin

  19. Bad example 1 PDB code 1l2h partial twin

  20. Bad example 2 human deoxycytidine kinase single crystal

  21. Twinning tests in CCP4I (ctruncate) 1 5 6 2 3 4

  22. Cumulative intensity distribution in Ctruncate Z ≈ |E|2 To compare: Red: Acentric theoretical, Blue: Acentric observed Untwinned data Twinned data > Cumulative intensity distribution > Cumulative ... (Centric and acentric)

  23. Second moments of Z (fourth moments of |E|) in Ctruncate To compare with the line <E4> = 2 Untwinned data Twinned data > Acentric moments of E for k=1,3,4 > 4th moments of E ...

  24. Examples of crystal pathologies Twinning by (pseudo)merohedry Statistics of one observation Statistics of two observations Twinning tests summary Space group validation

  25. H-test and L-test H = | J1 – J2 | / ( J1 + J2 ) L = | J1 – J2 | / ( J1 + J2 ) J1 J1 J2 J2 sublattices with strong and weak reflections (pseudotranslation) twin axes

  26. Theoretical distribution of H Single crystal Perfect twin Partial twin P(H) P(H) P(H) H H H

  27. Distribution of H can be perturbed by NCS and weak observations Blue: ideal distribution for partial twin P(H) Green: blue + effect of NCS axis || twin axis Red: green + effect of intensities with small I/ sig(I) H

  28. Examples of experimental P(H) Despite NCS and effect of weak observations correct interpretation is possible

  29. Theoretical distribution of L Single crystal Partial twin Perfect twin 1.0 1.0 1.0 P(L) P(L) P(L) 0.5 0.5 0.5 0.0 0.0 0.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 L L L

  30. Distribution of L can be strongly perturbed by weak observations <sig(F)> / <F> Cell: 64.2 109.2 100.2 90 93.8 90 Spacegroup: P21 No pseudo symmetry Pseudomerohedral twinning is impossible All data: as if a perfect twin Data below 3A: untwinned 1.0 1.0 P(L) P(L) Resolution, A 0.5 0.5 0.0 0.0 0.0 0.5 1.0 0.0 0.5 1.0 L L Nevertheless the L-test is very useful when performed with right resolution range (or with several ranges)

  31. Statistics of one intensity are strongly affected by pseudotranslation PDB:1jjk: Pseudotranslation results in clearly seen alteration of strong and weak reflections > Acentric moments of E for k=1,3,4 > 4th moments of E ...

  32. L-test and H-test are not affected by pseudotranslation > L test for twinning > cumulative distribution function for |L| > H test for twinning (operator ...) > cumulative distribution function for |H|

  33. Examples of crystal pathologies Twinning by (pseudo)merohedry Statistics of one observation Statistics of two observations Twinning tests summary Space group validation

  34. Why so many tests?

  35. Are these tests always sufficient? Pseudosymmetry may behave as exact symmetry (and may obscure twinning) Weak observations may obscure twinning How to handle the cases with strong pseudosymmetry? Low Resolution High Validation of crystallographic symmetry instead of twinning tests: refinement in space groups compatible with - unit cell - current model (considered as at least approximately correct)

  36. Examples of crystal pathologies Twinning by (pseudo)merohedry Statistics of one observation Statistics of two observations Twinning tests summary Space group validation

  37. http://www.ysbl.york.ac.uk/YSBLPrograms/index.jsp Zanuda

  38. Submitting Zanuda job 1yup.mtz 1yup.pdb

  39. Zanuda output Download of output pdb- and mtz-files Symmetry analysis

  40. An example of symmetry correction PDB code: 1yup spacegroup (PDB): P1 8 molecules per a.u. spacegroup (true): P21 4 molecules per a.u. Pseudo-symmetry spacegroup: C2 2 molecules per a.u. (because of pseudo-translation)

  41. Monoclinic structures related to 1yup Crystallographic axes NCS axes Positions of molecules Spacegroup and its relation to the structure 1yup C2 Pseudo-symmetry spacegroup P2 False spacegroup P21 True spacegroup

  42. Structure solution and symmetry validation Data processing ( 2/m ) Data processing ( -1 ) PDB: 1yup Zanuda Molecular replacement ( P2 ) Molecular replacement ( P1 ) ( P21 ) R-free = 0.33 Refinement ( P2 ) R-free ≈ 0.37 Refinement ( P1 ) R / R-free = 0.24 / 0.31 PDB: 1yup ( P1 )

  43. Spacegroup validation: step 1 if this value is too big value (>1.5), then convergency is unlikely, and the results will almost certainly be unreliable

  44. Spacegroup validation: step 2 2-axis 21-axis C2 crystallographic crystallographic P2 crystallographic NCS P21 NCS crystallographic

  45. spacegroup validation: step 3 Output (P21)

  46. Zanuda protocol is not perfect Assumptions: - The pseudosymmetry is very strong (r.m.s.d. from exact symmetry ≈ 1A) - The structure is almost correct (although it might have been refined / rebuilt in an incorrect spacegroup) If it is not so, the results will likely to be wrong. Things go wrong way

  47. CCP4I interface Refinement > Symmetry validation This is not jet in the ccp4i distribution

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