Non-merohedral Twinning in Protein Crystallography

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1 Bruker Users Meeting 2010 Karlsruhe, 22 nd September 2010 Non-merohedral Twinning in Protein Crystallography Regine Herbst-Irmer

2 Definition Twins are regular aggregates consisting of individual crystals of the same species joined together in some definite mutual orientation. from: "Fundamentals of Crystallography", edited by C. Giacovazzo, Union of Crystallography, Oxford University Press 2 nd Edn Simple example for a two-dimensional twin: Twin Law: fractional contribution k 1 for twin domain 1: 5/9 fractional contribution k 2 for twin domain 2: 4/9

3 Four Kinds of Twins (I) 1. Twinning by merohedry Twin operator: symmetry operator of the crystal system but not of the point group of the crystal 1.1. racemic twin 1.2. twin operator: not of the Laue group of the crystal

4 Reciprocal Space Plot l = 0

5 Reciprocal Space Plot l = 0

6 Reciprocal Space Plot l = 0

7 Four Kinds of Twins (I) 1. Twinning by merohedry Twin operator: symmetry operator of the crystal system but not of the point group of the crystal 1.1. racemic twin 1.2. twin operator: not of the Laue group of the crystal - only in tetragonal, trigonal, hexagonal and cubic space groups - exact overlap of the reciprocal lattices - often low value for < E 2-1 > - Laue group and space group determination may be difficult - structure solution may be difficult 2. Twinning by pseudo-merohedry Twin operator: belongs to a higher crystal system than the structure - Metric symmetry higher than Laue symmetry

8 Four Kinds of Twins (II) 3.Twinning by reticular merohedry e.g. obverse/reverse twinning in case of a rhombohedral crystal

9 Reciprocal Space Plot l = 1

10 Reciprocal Space Plot l = 1

11 Reciprocal Space Plot l = 1

12 Four Kinds of Twins (II) 3.Twinning by reticular merohedry e.g. obverse/reverse twinning in case of a rhombohedral crystal - detection of the lattice centring may be difficult - structure solution not as difficult as for merohedral twins. 4. Non-merohedral twins Twin operator: arbitrary operator, often rotation of 180

13 Reciprocal Space Plot k = 2

14 Reciprocal Space Plot k = 2

15 Reciprocal Space Plot k = 2

16 Reciprocal Space Plot k = 2 h 2-4 h 5 l

17 Reflection Pattern Problems with the cell determination Some reflections not indexed Some reflections very close to each other Some split reflections

18 Cell Determination CELL_NOW Reads.spin,.p4p or.drx-files tries to find sets of reciprocal lattice planes that pass close to as many reflections as possible The cell may be rotated to locate further twin domains using only the reflections that have not yet been indexed Determination of the cell and the twin law in one program Writes a.p4p/.spin file for RLATT and SAINT for simultaneous integration of more than one domain Determination of very weak domains possible

19 Integration exact partial nonoverlaps overlaps overlaps

20 Integration exact partial nonoverlaps overlaps overlaps

21 Integration exact partial nonoverlaps overlaps overlaps

22 TWINABS Twin raw file : *.mul, similar to HKLF5 format Special version of SADABS: TWINABS Scaling and absorption correction Merging Output detwinned data file (HKLF4) for structure solution HKLF5 file for the refinement: h' k' l' F 2 (F 2 ) -2 h k l F 2 (F 2 ) 1 with h', k', l' generated by the second orientation matrix

23 Four Kinds of Twins (II) 3.Twinning by reticular merohedry e.g. obverse/reverse twinning in case of a rhombohedral crystal - detection of the lattice centring may be difficult - structure solution not as difficult as for merohedral twins. 4. Non-merohedral twins Twin operator: arbitrary operator, often rotation of no exact overlap of the reciprocal lattices -cell determination problems - cell refinement problems - some reflections sharp, others split - data integration complicated (requires more than one orientation matrix) - structure solution not as difficult as for merohedral twins

24 Bovine Insulin 51 amino acids in the asymmetric unit Madhumati Sevvana, PhD thesis

25 RLATT

26 RLATT

27 CELL_NOW Cell for domain 1: Figure of merit: %(0.1): 51.6 %(0.2): 55.2 %(0.3): 62.6 Orientation matrix: reflections within of an integer index assigned to domain 1, Cell for domain 2: Figure of merit: %(0.1): 91.4 %(0.2): 93.6 %(0.3): 94.5 Orientation matrix: Rotated from first domain by 89.2 degrees about reciprocal axis and real axis Twin law to convert hkl from first to this domain (SHELXL TWIN matrix): reflections within of an integer index assigned to domain 2, 2751 of them exclusively; 184 reflections not yet assigned to a domain

28 d2.spin CELL CELLSD ORT ORT ORT ZEROS ADCOR CELL CELLSD ORT ORT ORT ZEROS ADCOR

29 TWINABS - Scaling data ( unique ) involve domain 1 only, mean I/sigma data ( unique ) involve domain 2 only, mean I/sigma data ( unique ) involve 2 domains, mean I/sigma 13.3

30 TWINABS - Detwinning Unique HKLF 4 data extracted from all observed data Cycle N(1) Rint(1) N(all) Rint(all) Twin fractions Rint = for all observations and Rint = for all observations with I > 3 (I) Rint is based on agreement between observed single and composite intensities and those calculated from refined unique intensities and twin fractions. ** Warning: components may be inconsistently indexed, try reindex option.

31 TWINABS - Detwinning After reindexing the second domain with : Cycle N(1) Rint(1) N(all) Rint(all) Twin fractions Rint = for all observations and Rint = for all observations with I > 3 (I)

32 Structure Solution Resolution to 1.60 Å Cubic symmetry (space group I2 1 3): high redundancy 6 sulfur atoms : structure solution with single wavelength anomalous scattering? Sad Phasing: Redundant data Complete data Twinning??? Precise data (small signal lost easily in the noise) Avoid systematic noise (ice rings, pin in the beam, )

33 Substructure Solution with SHELXD Data truncated to 1.90 Å CC 50.5%, weak CC 28.1% (could also be solved with wrong indexing of the second domain)

34 Bovine Insulin Structure Solution Phasing and Density Modification with SHELXE SHELXE map was traced using ARP/wARP SHELXE map contoured at 1 Final map

35 Final Refinement HKLF 5 HKLF 4 HKLF 5 HKLF5P wrongly indexed R1 (F o > 4 (F o )) R1(free) wr2 (all data) Data Twin fraction R1 (after merging for Fourier) Unique data

36 Glucose Isomerase space group I222 cell: three twin domains rotated by 120 Madhumati Sevvana, PhD thesis

37 Glucose Isomerase

38 TWINABS - Scaling data ( unique ) involve domain 1 only, mean I/sigma data ( unique ) involve domain 2 only, mean I/sigma data ( unique ) involve domain 3 only, mean I/sigma data ( unique ) involve 2 domains, mean I/sigma data ( unique ) involve 3 domains, mean I/sigma 8.8

39 TWINABS - Detwinning Unique HKLF 4 data extracted from all observed data Cycle N(1) Rint(1) N(all) Rint(all) Twin fractions

40 Solution SAD: SHELXD found 2 cations with data truncated to 2.10 Å CC 33.1% and weak CC 21.2

41 Solution SHELXE map contoured at 1 Final map

42 Final Refinement HKLF 4 HKLF 5 HKLF5P R1 (F o > 4 (F o )) R1(free) wr2 (all data) Data Twin fraction Twin fraction R1 (after merging for Fourier) Unique data

43 Summary Non-merohedrally twinned structures can be solved and refined to satisfying results even for marcomolecules More integration programs for twins are needed Refinement against the detwinned HKLF4 data is sufficient for routine structures refinement and in first stages of refinement Refinement against HKLF5 data leads to slightly better results

44 Acknowledgements Madhumati Sevvana, University of Erlangen George Sheldrick, University of Göttingen

Twinning. Andrea Thorn

Twinning. Andrea Thorn Twinning Andrea Thorn OVERVIEW Introduction: Definitions, origins of twinning Merohedral twins: Recognition, statistical analysis: H plot, Yeates Padilla plot Example Refinement and R values Reticular