Transcript Twinning and other pathologies

Twinning and other pathologies
Andrey Lebedev
University of York
Examples of crystal pathologies
Twinning by (pseudo)merohedry
Statistics of one observation
Statistics of two observations
Twinning tests summary
Space group validation
Examples of crystal pathologies
Twinning by (pseudo)merohedry
Statistics of one observation
Statistics of two observations
Twinning tests summary
Space group validation
Crystal disorder
Diffraction:
Sizes of ordered domains
decrease
Single crystal
Twinning & Disorder =
Missing global periodicity
12- and
3-dimensional disorder
Twinned crystal
Partially disordered crystal
OD-structures
OD-structures
- identical layers
- identical interfaces between the layers
- but: two or more ways of packing adjacent layers
*) MX: "identical" means Ca r.m.s.d. < 1 A
S1
S1
*) S1 and S2. are called stacking vectors
- two-dimensional periodicity
- a potential for disorder in the third dimension
S2
S1
Examples
Single crystal
Single crystal
OD-twin
Allotwin
Partially
disordered
OD-structure
C2
P21
P21
C2
Example 1
P212121
Example 2
Example 3
Example 1: OD-twin (twin by lattice pseudomerohedy)
C2
Indexing in C2
C2
Indexing in C2
Rye et al. (2007) Acta Cryst. D67
L-2-haloacid dehalogenase
from Sulfolobus tokodaii
The diffraction images can be indexed
in C2 with two different orientation of
the crystal
The problem with the data is that
some of the reflections from two
lattices overlap.
The presence of layers of overlapping
reflections is the reason of non-origin
peaks in the Patterson map.
OD-twin: real and reciprocal lattices
Example1
C2
C2
c
a
OD-twin: demodulation
Example1
C2
IT1 = q'(h) I1
C2
q'(h) = p0 + p1 cos(2th) + p2 cos(4th) + ...
q'(h)
R / R-free
Original
data
0.21 / 0.27
Demodulated
data
0.16 / 0.23
v=w=0
Example 2: allotwin
Crystals of Lon protease
Resolution 3Å
P21
P212121
Dauter et al. (2005).
Acta Cryst. D61, 967-975.
P21
R / R-free = 0.21 / 0.31
P212121
R / R-free = 0.19 / 0.35
Example 3: partially disordered OD-structure
Crystals of Phi29 DNA polymerase
Resolution 2.2Å
The structure was solved using demodulated
data and experimental phasing
Refinement against corrected data: R=0.28
Wang et al. (2005).
Acta Cryst. D61, 67-74.
P21
a*
The translation symmetry is perturbed in
the direction a*.
The diffraction pattern is characterised
by the presence of the diffuse streaks
along a*.
Example 4: Four types of domains
Patterson maps at Z=0
P21 structure (1k7u, 1k7v)
1k7u
1k7v
Putative C2 structure
Interpretation of the Patterson map for 1k7v: four types of domains
- P21 (orientation 1)
Twinned P21 data
- P21 (orientation 2)
- C2 (orientation 1)
contribute to some of the P21 spots,
- C2 (orientation 2)
hence non-origin Patterson peaks
Example 5: Conserved one-dimensional substructures
crystal
soaking
twinned orthorhombic crystal
twinned tetragonal crystal
Roberto Steiner, Kings college, University of London
Examples of crystal pathologies
Twinning by (pseudo)merohedry
Statistics of one observation
Statistics of two observations
Twinning tests summary
Space group validation
Twins by reticular merohedry (inc some OD-twins), allotwins, disordered structures
- Can be readily seen in images with predictions
Important special case: twinning by (pseudo)merohedry
- All spots overlap with related spots from another individual crystal
- Detection requires analysis of intensity statistics
- Significant effect on model if ignored
Examples of crystal pathologies
Twinning by (pseudo)merohedry
Statistics of one observation
Statistics of two observations
Twinning tests summary
Space group validation
Theoretical intensity statistics
Partial twin
s
s
Acentric reflections
Centric reflections
Perfect twin
<Z2>
Partial twin
<Z2>
<Z2>
<Z2>
Single crystal
s
s
Two good, two bad
PDB entry 1i1j
single crystal
C-terminal domain of gp2
protein from phage SPP1
(unpublished)
perfect twin
Bad example 1
PDB code 1l2h
partial twin
Bad example 2
human deoxycytidine
kinase single crystal
Twinning tests in CCP4I (ctruncate)
1
5
6
2
3
4
Cumulative intensity distribution in Ctruncate
To compare: Red: Acentric theoretical, Blue: Acentric observed
Untwinned data
> Cumulative intensity distribution
> Cumulative ... (Centric and acentric)
Twinned data
Z ≈ |E|2
Second moments of Z (fourth moments of |E|) in Ctruncate
To compare with the line <E4> = 2
Untwinned data
> Acentric moments of E for k=1,3,4
> 4th moments of E ...
Twinned data
Examples of crystal pathologies
Twinning by (pseudo)merohedry
Statistics of one observation
Statistics of two observations
Twinning tests summary
Space group validation
H-test and L-test
H = | J1 – J2 | / ( J1 + J2 )
L = | J1 – J2 | / ( J1 + J2 )
J1
J1
J2
J2
sublattices with strong and weak
reflections (pseudotranslation)
twin axes
Theoretical distribution of H
H
Perfect twin
P(H)
Partial twin
P(H)
P(H)
Single crystal
H
H
Distribution of H can be perturbed by NCS and weak observations
Blue:
ideal distribution for
partial twin
P(H)
Green:
blue + effect of
NCS axis || twin axis
Red:
green + effect of
intensities with small I/ sig(I)
H
Examples of experimental P(H)
Despite NCS and effect of weak observations correct interpretation is possible
Theoretical distribution of L
Single crystal
Partial twin
0.5
0.0
0.0
0.5
L
1.0
1.0
P(L)
1.0
P(L)
P(L)
1.0
Perfect twin
0.5
0.0
0.0
0.5
L
1.0
0.5
0.0
0.0
0.5
L
1.0
Distribution of L can be strongly perturbed by weak observations
Cell: 64.2 109.2 100.2 90 93.8 90
Spacegroup: P21
No pseudo symmetry
Pseudomerohedral twinning is impossible
All data:
as if a perfect twin
Data below 3A:
untwinned
Resolution, A
1.0
P(L)
P(L)
1.0
0.5
0.0
0.0
<sig(F)> / <F>
0.5
L
1.0
0.5
0.0
0.0
Nevertheless the L-test is
very useful when performed
with right resolution range
(or with several ranges)
0.5
L
1.0
Statistics of one intensity are strongly affected by pseudotranslation
PDB:1jjk: Pseudotranslation results in
clearly seen alteration of strong and
weak reflections
> Acentric moments of E for k=1,3,4
> 4th moments of E ...
L-test and H-test are not affected by pseudotranslation
> L test for twinning
> cumulative distribution function for |L|
> H test for twinning (operator ...)
> cumulative distribution function for |H|
Examples of crystal pathologies
Twinning by (pseudo)merohedry
Statistics of one observation
Statistics of two observations
Twinning tests summary
Space group validation
Why so many tests?
Statistics of one
observation
Statistics of two
observations
P(Z)
<Z^2>
H-test
L-test
Specific for a given
operation
–
–
+
–
Insensitive to
pseudotranslation
–
–
+/–
+
Insensitive to
anisotropy
–
–
+/–
+
Specific for a given
resolution shell
–
+
–
–
Insensitive to weak
reflections at high
resolution
–
(–)
–
–
Are these tests always sufficient?
Pseudosymmetry may
behave as exact symmetry
(and may obscure twinning)
Low
Weak observations
may obscure twinning
Resolution
High
How to handle the cases with strong pseudosymmetry?
Validation of crystallographic symmetry instead of twinning tests:
refinement in space groups compatible with
- unit cell
- current model (considered as at least approximately correct)
Examples of crystal pathologies
Twinning by (pseudo)merohedry
Statistics of one observation
Statistics of two observations
Twinning tests summary
Space group validation
http://www.ysbl.york.ac.uk/YSBLPrograms/index.jsp
Zanuda
Submitting Zanuda job
1yup.mtz
1yup.pdb
Zanuda output
Download of output
pdb- and mtz-files
Symmetry analysis
An example of symmetry correction
PDB code:
1yup
spacegroup (PDB):
P1
8 molecules per a.u.
spacegroup (true):
P21
4 molecules per a.u.
Pseudo-symmetry spacegroup:
(because of pseudo-translation)
C2
2 molecules per a.u.
Monoclinic structures related to 1yup
Positions of
molecules
Crystallographic axes
NCS axes
Spacegroup and its relation
to the structure 1yup
C2
Pseudo-symmetry
spacegroup
P2
False spacegroup
P21
True spacegroup
Structure solution and symmetry validation
Data processing
( 2/m )
Data processing
( -1 )
Molecular replacement
( P2 )
Molecular replacement
( P1 )
Refinement
( P2 )
R-free ≈ 0.37
Refinement
( P1 )
R / R-free = 0.24 / 0.31
PDB: 1yup ( P1 )
PDB: 1yup
Zanuda
( P21 )
R-free = 0.33
Spacegroup validation: step 1
if this value is too big value (>1.5), then convergency is unlikely,
and the results will almost certainly be unreliable
Spacegroup validation: step 2
2-axis
C2
P2
P21
crystallographic
crystallographic
NCS
21-axis
crystallographic
NCS
crystallographic
spacegroup validation: step 3
Output (P21)
Zanuda protocol is not perfect
Assumptions:
- The pseudosymmetry is very strong (r.m.s.d. from exact symmetry ≈ 1A)
- The structure is almost correct
(although it might have been refined / rebuilt in an incorrect spacegroup)
If it is not so, the results will likely to be wrong.
Things go wrong way
CCP4I interface
Refinement > Symmetry validation
This is not jet in the ccp4i distribution