Transcript Twinning in macromolecular crystals

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:
1upp
155.9 156.3 200.0 90 90 90
Crystal symmetry:
C222 1
Highest possible crystal symmetry
according to the symmetry of X-ray data:
P4x2x2
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.
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
1upp: 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.
1upp: validation of the crystal symmetry
*)subgroup  supergroup
Space group*)
C2221

F222 
I422
 P4222 
P42
The number of monomers per
asymmetric unit
4
2
1
2
4
Starting model
I422
-
PDB
I422
I422
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:
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?
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.

RvR-plot
non-twins
Rtwin
| I(h)  I(S


2 I(h)
twin
h
h
obs
Rtwin
:: I  I obs
calc
twin
R
:: I  I
calc
h) |
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 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!)
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, nTRUNCATE)
Pathologies to cover
Twinning including twinning by reticular merohedry
Pseudosymmetry
“Statistical” crystals