Twinning etc

1
Twinning etc

• Andrey Lebedev
• YSBL

2
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

3
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
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Example twinning pseudosymmetry
Crystal structure of Ribulose Biphosphate
Carboxylase
Pdb code

1upp Cell

155.9 156.3 200.0 90 90 90 Crystal
symmetry

C2221 Highest possible crystal
symmetry according to the symmetry of X-ray
data
P4x2x2 Twinning

pseudomerohedral Pseudotransla
tion
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.
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1upp superposition of the twinning domains
An individual single crystal (domain) has
symmetry C2221 The average structure has
symmetry I422 with pseudotranslation turned into
crystallographic translation Deviation of the
domain structure from the average structure is
less than 1A
1.34 A
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1upp perturbation of higher symmetry
Broken operators of higher symmetry become NCS
and twinning operators.
3.4
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.
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1upp validation of the crystal symmetry
)subgroup ? supergroup
Before refinement I422, F222 are impossible
translational NCS becomes crystallographic
translation P4222 is unlikely
perfect twinning test indicates twinning P42,
C2221 are equally possible After
refinement C2221 is the true crystal symmetry

Search model had the identity of 99. With more
realistic model the contrast will be worse!
What to do?
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Electron density in a wrong spacegroup
The difference map at the missing fragment of the
model after refinement in I422. As shown in the
previous slide, the structure can be resolved and
the correct spacegroup determined after such
refinement.
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RvR-plot
A translational NCS B mislabeling
F?I C,C mislabeling I?F Red (potential)
merohedral twins Black (potential)
pseudomerohedral twins
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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.

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Perfect twinning test
Untwinned pseudosymmetry test shows no
twinning Twin pseudosymmetry Test shows only
partial twinning.
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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) Pseudosymmet
ry causes non-linearity. Experimental errors
this non-linearity makes the test hardly
interpretable in some cases.
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The last year cases
Pure twinning ( choice between P4x and P2x2x2x
) Twinning pseudosymmetry ( P2221 / 3 P2x
) Pseudotranslation ( 2 P4122 / 2 P4322
) Pseudotranslation ( 2 P3122 / 4 (P31
twinning) ) Statistical orthorombic? ( choice of
lattice ) Partial model ( P622 / P322 /
) Cases where users suspected twinning with no
reasons (many!)
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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

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Validation of symmetry twinning paranoia
Cases without pathology message
be happy, work hard with model building
Cases with pathology action
correction of the model message
likelihood function to use
parameters to refine
initial values addressees refinement program
(REFMAC) data reduction
program (SCALA, nTRUNCATE)
Pathologies to cover Twinning including twinning
by reticular merohedry Pseudosymmetry Statistical
crystals