Twinning etc Andrey Lebedev YSBL Twinning only MR
Twinning etc Andrey Lebedev YSBL
Twinning only (MR scenario) 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
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
Example: twinning + pseudosymmetry Crystal structure of Ribulose Biphosphate Carboxylase Pdb code: Cell: 1 upp 155. 9 156. 3 200. 0 90 90 90 Crystal symmetry: C 2221 Highest possible crystal symmetry according to the symmetry of X-ray data: P 4 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.
1 upp: superposition of the twinning domains An individual single crystal (domain) has symmetry C 2221 The average structure has symmetry I 422 with pseudotranslation turned into crystallographic translation Deviation of the domain structure from the average structure is less than 1 A 1. 34 A
1 upp: perturbation of higher symmetry Broken operators of higher symmetry become NCS and twinning operators. 3. 4° Twinning 4 -fold NCS 4 -folds 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.
1 upp: validation of the crystal symmetry *)subgroup supergroup Space group*) C 2221 F 222 I 422 P 42 The number of monomers per asymmetric unit 4 2 1 2 4 Starting model I 422 - PDB I 422 Correlation coefficient after molecular replacement 0. 53 - 0. 57 0. 50 0. 51 R after rigid-body refinement 0. 38 - 0. 43 0. 44 0. 43 R after restrained refinement 0. 28 - 0. 33 0. 37 0. 36 R-free after restrained refinement 0. 34 - 0. 41 0. 44 0. 43 Before refinement: I 422, F 222 are impossible: translational NCS becomes crystallographic translation P 4222 is unlikely: perfect twinning test indicates twinning P 42, C 2221 are equally possible After refinement: C 2221 is the true crystal symmetry Search model had the identity of 99%. With more realistic model the contrast will be worse! What to do?
Electron density in a wrong spacegroup The difference map at the missing fragment of the model after refinement in I 422. As shown in the previous slide, the structure can be resolved and the correct spacegroup determined after such refinement.
Rv. R-plot non-twins A: B: C, C’: translational NCS mislabeling F I mislabeling I F Red: (potential) merohedral twins Black: (potential) pseudomerohedral twins
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.
Perfect twinning test Untwinned + pseudosymmetry: test shows no twinning Twin + pseudosymmetry: Test shows only partial twinning. decrease of contrast
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.
The last year cases Pure twinning ( choice between P 4 x and P 2 x 2 x 2 x ) Twinning + pseudosymmetry ( P 2221 / 3* P 2 x ) Pseudotranslation ( 2* P 4122 / 2* P 4322 ) Pseudotranslation ( 2* P 3122 / 4* (P 31 + twinning) ) Statistical orthorombic? ( choice of lattice ) Partial model ( P 622 / P 322 / … ) Cases where users suspected twinning with no reasons (many!)
Twinning and pseudo-symmetry (MR scenario) 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
Validation of symmetry: twinning paranoia Cases without pathology message: be happy, work hard with model building Cases with pathology action: message: correction of the model likelihood function to use parameters to refine initial values addressees: refinement program (REFMAC) data reduction program (SCALA, n. TRUNCATE) Pathologies to cover Twinning including twinning by reticular merohedry Pseudosymmetry “Statistical” crystals
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