Pseudo translation and Twinning

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Pseudo translation and Twinning
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Crystal peculiarities

• Pseudo translation
• Twin
• Order-disorder

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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.
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Pseudo-translation
Cell
P0

Patterson
0.125 P0

Pst-vector
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• 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

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Twinning
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merohedral and pseudo-merohedral twinning
Crystal symmetry P3 P2
P2 Constrain - ß 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.
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More than three layers, but less than the whole
crystal.
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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
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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
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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

• Merohedral twinning
• crystal symmetry assumes more symmetric lattice
• twinning would not require extra constraints on
  unit cell dimensions

• 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.

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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)
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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.
This test is implemented in SFCHECK
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Electron density 1rxfWe will see occasionally
this
refmac map
twin map
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Electron density 1jrgMore usual and boring case
refmac map
twin map
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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.