Twinning ... some brief notes. (Richard Kingston, Feb 26 2008)
What is it ?
Here’s Giacovazzo’s definition of twinning from “Fundamentals of Crystallography” ...
Twins are regular aggregates consisting of crystals of the same species joined together in some definite
mutual orientation.
Twinned specimens often look exactly like single crystals in the light microscope. However the
presence of twinning can greatly complicate structure determination.
A simple example of a twinned crystal (Adapted from Zbigniew Dauter)
There’s two major types of twinning:
Non-merohedral twinning arises when the lattices associated with the different regions are
not completely coincident. This kind of twinning is easy to recognize, and potentially easy to deal
with, since it results in interpenetrating reciprocal lattices in the diffraction pattern. The presence
of multiple lattices often causes problems for auto-indexing routines. You’ll need to manually
intervene with the peak selection, and remove the contributions from the minor lattice before
indexing. Once you have indexed the diffraction pattern you can integrate and scale the data as
usual, but you should look carefully at the outlier rejection during scaling, since partial overlap of
the lattices will lead to intensity estimates that are quite wrong for a fraction of the reflections, and
it’s important to remove these. Note that some very high profile structures have been determined
from non-merohedral twins (see e.g. (Schulman et al., 2000)). Some groups have partially
automated the data filtering process (see e.g. (Lu et al., 1995; Buts et al., 2004)).
Merohedral twinning is more subtle, and more troublesome. In this case the lattices from the
constituent regions are totally aligned. The diffraction pattern appears normal, but each measured
intensity now contains contributions from two or more reflections, which are not related by the
crystal symmetry. This is not good.
Here’s a diagram which illustrates the two types of twinning (from (Yeates and Fam, 1999) )
The remainder of these notes deal only with merohedrally twinned crystals.
Some Fundamentals of merohedral twinning
If merohedral twinning is present, it is important to characterize it. This means identifying the true
space group of the crystal, and the symmetry operation (the twin operation) which relates the
constituent regions of the twin (the twin domains). We also need to estimate the volume ratio of
the twin domains (the twin fraction). We’ll assume here that there’s only two twin domains related
by a single symmetry operation. Other possibilities exist but are rare (see below)
One effect of merohedral twinning is to introduce additional symmetry (approximate or exact)
into the diffraction pattern - beyond what the space group dictates. The symmetry becomes exact
when the volume of the twin domains is equal. Here’s an example showing how that works
(adapted from Zbigniew Dauter)
Consider our bipyramidal twin shown above Each of the pyramids belongs to space group P4, so
the only symmetry element present is a 4-fold rotation axis.
Here are equivalent slices the diffraction patterns from the two individual pyramids. They are the
same, except that the polar four-fold rotation axis is pointing up or down, respectively.
And here is the diffraction pattern we get by summing these two diffraction patterns, giving equal
weight to each. This is the diffraction pattern that would be observed from the bipyramidal twin.
Note that twinning generates extra symmetry. The diffraction data look like they were collected
from a crystal with P422 symmetry.
Merohedral twinning can only occur when the rotational symmetry of the lattice exceeds that of
the crystal space group. This can occur in the tetragonal, trigonal, hexagonal and cubic crystal
systems. A full catalog of possibilities is given by Chandra et al (Chandra et al., 1999), who also list
the apparent symmetry in the diffraction pattern which will result. In almost all cases the twinning
involves two domains (hemihedral twinning), with the twin operator being a two-fold rotation.
In the case of hemihedral twinning we can write a pair of equations for the twin related reflections
IOBS ]h 1 g = ]1 - a gI ]h 1 g + aI ]h 2g
1a
IOBS ]h 2g = aI ]h 1 g + ]1 - a gI ]h 2g
1b
Where h1 and h2 are the reciprocal-lattice vectors related by the twinning operation, I(h1) and
I(h2) are the true intensities associated with these lattice vectors, IOBS(h1) and IOBS(h2) are the
observed intensities, and α is the twin fraction.
When α is small these linear equations can be solved for the true intensities of the crystal.
However as α approaches 0.5 the system of equations becomes degenerate, and it is impossible to
obtain reliable estimates for the true intensities.
How do I know if it’s a problem?
Sometimes twinning is detected when something goes wrong during structure determination (e.g.
an apparently great heavy atom derivative fails to yield interpretable maps, or an apparently
sensible molecular replacement solution fails to refine to reasonable R-factor, etc etc). Many times
the spacegroup will have been mis-assigned, because of the extra symmetry in the diffraction
pattern generated by twinning. A lot of time can be wasted sorting this out, so it’s better to be
aware of the crystal symmetries that can support merohedral twinning, and to look for it during
data processing.
Fortunately twinning leaves an imprint on the intensities, and intensity statistics calculated from
twinned crystals are quite different to those calculated from untwinned crystals. It’s easy to
appreciate why this is so - twinning effectively “averages” the data, reducing the dispersion in
intensities - there are fewer very weak, and very strong observations.
This has lead to a number of statistical tests, with varying levels of sophistication. One basic
division between these tests is that some of them require you to have processed the data in the
correct, low symmetry space group, and to have identified the twin operator. Others work even if
you’ve processed the data incorrectly, in the higher symmetry space group suggested by the
twinning. The latter class of tests are more useful in the initial stages of an investigation, where you
need to detect the presence of twinning
One of the most useful diagnostic tests, suggested originally by Doug Rees (REES, 1980) is
performed by the program Truncate in the CCP4 program suite. This looks at the cumulative
intensity distribution of acentric reflections. The curve will be distinctly sigmoidal for a perfectly
hemihedrally twinned protein crystal. See below (Figure taken from (REES, 1980))
In this graph “Z” is the Intensity, normalized by the mean Intensity.
What can I do about it?
If possible collect some more data and see if you can find an untwinned crystal. Twinning always
hurts and never helps. It makes structure determination more difficult. and degrades the quality of
the final image. However, if you can’t find an untwinned crystal or can’t collect more data, it is not
hopeless.
If the twin fraction α is low, and the data quality is good, it may be best to “detwin” the data, by
solving the relevant equations (e.g. 1a and 1b above) and deriving the true intensities. With that
done, everything works as usual.
However, if twinning is near perfect, this will not be possible and you’ll have to work with the
twinned data directly. All current methods of phase determination can be applied to twinned
crystals, with some added complications. Structure solution by molecular replacement is relatively
straight forward - a search of NCBI’s PubMed database will pull out several dozen examples.
However if there is more than one molecule to be positioned in the asymmetric unit it gets more
complicated (see e.g.(Breyer et al., 1999)) . Experimental phasing is also possible, if difficult
(Terwisscha van Scheltinga et al., 2003; Barends et al., 2005; Rudolph et al., 2003)
Once a model has been built, there are several programs available which will refine the model
against the twinned data (e.g. SHELXL, PHENIX/CNS and Refmac)
Where do I find more information ?
The are several good reviews in the literature. See (Yeates and Fam, 1999; Yeates, 1997; Chandra et
al., 1999)
References
Barends, T. R., de Jong, R. M., van Straaten, K. E., Thunnissen, A. M., and Dijkstra, B. W. (2005).
Escherichia coli MltA: MAD phasing and refinement of a tetartohedrally twinned protein crystal
structure. Acta Crystallogr D Biol Crystallogr 61, 613-621.
Breyer, W. A., Kingston, R. L., Anderson, B. F., and Baker, E. N. (1999). On the molecular-replacement
problem in the presence of merohedral twinning: structure of the N-terminal half-molecule of
human lactoferrin. Acta Crystallogr. D Biol. Crystallogr. 55, 129-138.
Buts, L., Dao-Thi, M. H., Wyns, L., and Loris, R. (2004). Untangle, a tool for filtering overlapping
diffraction patterns from multicrystals. Acta Crystallogr D Biol Crystallogr 60, 983-984.
Chandra, N., Acharya, K. R., and Moody, P. C. (1999). Analysis and characterization of data from
twinned crystals. Acta Crystallogr D Biol Crystallogr 55, 1750-1758.
Lu, G., Lindqvist, Y., and Schneider, G. (1995). A method for processing diffraction data from twinned
protein crystals and its application in the structure determination of an FAD/NADH-binding
fragment of nitrate reductase. Acta Crystallogr D Biol Crystallogr 51, 13-20.
REES, D. C. (1980). THE INFLUENCE OF TWINNING BY MEROHEDRY ON INTENSITY
STATISTICS. Acta Crystallogr A 36, 578-581.
Rudolph, M. G., Kelker, M. S., Schneider, T. R., Yeates, T. O., Oseroff, V., Heidary, D. K., Jennings, P. A., and
Wilson, I. A. (2003). Use of multiple anomalous dispersion to phase highly merohedrally twinned
crystals of interleukin-1beta. Acta Crystallogr D Biol Crystallogr 59, 290-298.
Schulman, B. A., Carrano, A. C., Jeffrey, P. D., Bowen, Z., Kinnucan, E. R., Finnin, M. S., Elledge, S. J.,
Harper, J. W., Pagano, M., and Pavletich, N. P. (2000). Insights into SCF ubiquitin ligases from the
structure of the Skp1-Skp2 complex. Nature 408, 381-386.
Terwisscha van Scheltinga, A. C., Valegård, K., Hajdu, J., and Andersson, I. (2003). MIR phasing using
merohedrally twinned crystals. Acta Crystallogr D Biol Crystallogr 59, 2017-2022.
Yeates, T. O. (1997). Detecting and overcoming crystal twinning. Meth. Enzymol. 276, 344-358.
Yeates, T. O., and Fam, B. C. (1999). Protein crystals and their evil twins. Structure 7, R25-9.