BSTR 521, January 18, 2007

Twinning

DefinitionA twinned crystal contains two or more single crystals with identical packing but in different orientations. They are intergrown in such a way that at least some of their lattice directions are parallel.

Why do we care about twinning?It may occur more frequently than reported (2% or more among all crystals?)Systematic diffraction overlapping.

How to monitor twinning

Crystal morphology: concave or “reentrant” crystal faces; not always.

a. Plastocynin crystals. Individual rods are used for data collection. The true space group is P32, but a twinning fraction of ½ gives a diffraction data with Laue symmetry P6/m. b. Perfect twinned crystals of trypanosome variant surface glycoprotein ILTat 1.24. c. Crystals of carboxylase of the pyruvate dehydrogenase complex (from T. Izard and W. Hol). d. Crystals of cytochrome iso-c2.

How to monitor twinning

Crystal morphology: concave or “reentrant” crystal faces; not always;Polarizor: size of twin components may be too small for observation;Diffraction pattern (except merohedral crystals);Statistics of diffraction intensity (merohedral crystals, see below)

Some other warning signs:- Certain space groups;- Cannot merge data collected with different crystals (with the same cell units);- Impossible Patterson map;- Unbelievably difficult refinement,……

Difference of twinned crystals and non-specific crystal clusters

Only crystals that are intergrown in an ordered way are called twinned.

Only rotation twin, but not reflection and inversion twins, can exist in protein crystals.

Rotation twinMost frequently, the twin axis (usually a 2 fold axis) runs parallel to a lattice vector with components u, v, w. The lattice row [uvw] coincides for all twin components, i.e. they have the common zone axis [uvw].

Non-merohedral twins (epitaxial)

In non-merohedral twinned crystals, the separate domain lattices align in fewer than three dimensions (e.g. at a sueface where they meet); the diffraction pattern contains interpenetrating lattices.

Along twin axis

Merohedral twinned crystals

Lattice of two or more distinct domains coincide exactly in all three dimensions. Since the real space lattices coincide, the reciprocal lattices of different domain overlap exactly.

Hemihedral Twinning: -- A special case of merohedral twins: only two distinct orientations are assumed;-- The only merohedral form reported for macromolecule crystals.

For protein crystallography: merohedral = hemihedral

Twin Laws and twin fractions

Two things are needed to describe hemihedral twin crystals: The fractional contribution of each component (twin fraction, α); and the spatial relationship of the two twin components (twin law).

The twin law can be expressed as a matrix that transforms the hkl indices of one species to the other.

Hemihedral twin fraction

Twin fraction (α): the fractional volume of the specimen occupied by domains in the second orientation.

Untwinned crystals: α=0Partial hemihedral twinning α<0.5Perfect hemihedral twinning α=0.5

If each twin domain is large compared to X-ray wavelength, waves diffracted from each domain do not interfere. Therefore each observed intensity is a weighted sum of the intensities of two reflections, h1 and h2 (in the case of hemihedry), that are related by the twinning operation but not by crystallographic symmetry.

Iobs(h1) = (1 - α) I(h1) + α I(h2) (1)Iobs(h2) = α I(h1) + (1 - α) I(h2) (2)

Hemihedral twin laws:

In general, a twin axis can not run parallel to a rotation axis (or a screw axis) of the crystal structure which induces the same rotation angle. For example, a twofold twin axis can not be parallel to a twofold, fourfold, or sixfold axis, but it may run parallel to a threefold axis.

For proteins, merohedral twinning only occurs when the unit cell of the crystal is capable to support a higher symmetry than the true symmetry of the crystal. Here, the twin operator is part of the crystal system but not of the Laue group and, therefore, merohedral twinning only occurs in crystal systems with more than one Laue group (3, 4, 6, 32 and 23 point groups).

What do you do when you have twinned crystals:

Search for untwinned crystals, or find crystallization condition for obtaining different crystal forms;

Non-merohedral crystals are easy to be identified. You can process data with the major lattice and ignore the minor lattice.

When twin operation can be identified, reflections that are expected to suffer from overlap can be identified and either discarded or corrected.

Merohedral crystals: see below;

Pseudo-merohedral (lattices overlap approximately in three dimensions), try every way to compare the result.

Strategies for dealing with merohedral (hemihedral) twinning

Partial twinning does not obscure the true crystallographic symmetry. Statistical analysis can be used to estimate the twin fraction, after which the data can be corrected.

Detwin: Determine twin fraction (α) from observed data set by statistical methods; detwin to get the true intensities and proceed as usual.

Refine with twin fraction: Attempt to solve the structure without knowledge of individual crystallographic intensities. This is possible in practice by molecular replacement, and in theory by isomorphous replacement.

Perfect twinning is more difficult to deal with.

First, detwin is impossible. Second, the symmetry of the twinning operation is imposed on top of the true Laue symmetry to give an erroneously high symmetry.

The Yeates method of detwinning:

Reference: Yeates, T.O. (1988). Acta Cryst. A 44, 142-144.Website: http://www.doe-mbi.ucla.edu/Services/Twinning/

Assume h1 and h2 are related by the twin law.Define: H = | Iobs(h1) - Iobs(h2)| / ( Iobs(h1) + Iobs(h2)) (3)Since the true crystallographic intensities, I(h1) and I(h1), are expected to follow Wilson statistics,Then: <H> = 0.5 - α (4)

<H2> = (1 - 2α)2/3 (5)Thus the twin fraction α can be estimated.

Once have accurately estimated twinning fraction α, we can detwin the diffraction data of partially (hemihedral) twinned crystals:

I(h1) = [(1 - α) Iobs(h1) - α Iobs(h2)] / (1-2α) (6)I(h2) = [-α Iobs(h1) + (1 - α) Iobs(h2)] / (1-2α) (7)

The other robust and widely-used Yeates method to estimate twinning fraction α is the plotting of H versus Cumulative distribution of H (S(H)).

For the definition and calculation of S(H), please check:Yeates, T.O. (1988). Acta Cryst. A 44, 142-144.

Be cautious with data correction (detwinning) of partially twinned crystals:

The caveat of detwinning is that this process magnifies the measurement errors by a factor of 1/(1-2α), which grows rapidly when α approaches ½. In those cases, crystals should be treated as if perfectly twinned.

The twin fraction (α) must be calculated accurately. It may not be a bad idea to estimate α by different methods. Other methods used to estimate αin literatures:

Britton, D. (1972). Acta Cryst. A 28, 296-297.Murray-Rust, P. (1973). Acta Cryst. B 29, 2559-2566.Fisher, R.G. & Sweet, R.M. (1980). Acta Cryst. A 36, 755-760.Rees, D.C. (1982). Acta Cryst. A 38, 201-207.Dumas, P., Ennifar, E. & Walter, P. (1999). Acta Cryst. D 55, 1179-1187.

Perfect hemihedral twinning

Additional symmetry introduced by perfect merohedral twinning.

Detection of perfect twinning

Check Matthew’s coefficient (Vm = volume of assymmetric unit/molecular weight), which should be 1.6 - 3.6 Å3/dalton. Additional symmetry resulted from perfect twinning may produce a Vm below 1.6. Just an indicator for perfect twinning.

Examine the intensity statistics.Wilson Plot: Perfect twinned crystal do not obey the Wilson statistics.Stanley factor: It has been shown (Stanley, E. (1972). J. Appl. Cryst. D 49, 375.)

that for acentric data:<I2>/<I>2 = 2 for untwinned data (8)<I2>/<I>2 = 1.5 for perfectly twinned data

The Stanley factor and Wilson plot can be calculated with TRUNCATE (CCP4).

Molecular replacement with twinned data:

Rotation search can be carried out in the higher observed Laue symmetry (with the twin operation), and is not a problem in many cases. The rotation search should be restricted to the asymmetric region dictated by the apparent Laue symmetry.

Translation function has to be calculated with the true space group. All possible space groups associated with the apparent Laue symmetry (see above table) have to be tested.

MIR with twinned data:

Structural determination by multiple heavy-atom isomorphous replacement (MIR) method with perfectly twinned crystal is theoretically possible (Yeates, T.O. and Rees, D.C. (1987). Acta Cryst. A 43, 30). But no unknown structure has been determined by this method.

Structure refinement with twinning:

Either CNS or SHELXL, both accommodate crystal twinning, can be used for refinement of twinned crystal structures.Refmac ?

A case study:

Use of multiple anomalous dispersion to phase highly merohedrallytwinned crystals of interleukin-1beta.Rudolph, M.G, ……and Wilson, I.A.Acta Crystallogr D Biol Crystallogr 2003 Feb;59(Pt 2):290-8

The crystal structure at 1.54 A resolution of a double mutant ofinterleukin-1beta (F42W/W120F), a cytokine secreted by macrophages, was determined by multiple-wavelength anomalous dispersion (MAD) using data from highly twinned selenomethionine-modified crystals. The space group is P4(3), with unit-cell parameters a = b = 53.9, c = 77.4 A. Self-rotation function analysis and various intensity statistics revealed the presence of merohedral twinning in crystals of both the native (twinning fraction alpha approximately 0.35) and SeMet (alpha approximately 0.40) forms. Structure determination and refinement are discussed with emphasis on the possible reasons for successful phasing using untreated twinned MAD data.

144 residuesSpace group P43

Twin fractions were estimated by CNS and the Yeates twinning server.

Significant anomalous signal up to 1.8 Å (as judged by XPREP (Bruker AXS)).

Six Se sites were determined by SOLVE or SHELX, without detwinning)

After RESOLVE, model was built and refined by ARP/wARP.

Refinement with CNS, using the 1.54 Å native dataset, with a fixed twin factor and maximum likelihood.

Conclusion:

It seems that the presence of twinning neither necessarily prohibits a successful structure determination using SeMet (or other anomalous) data, nor renders refinement impossible.

The success of programs such as SOLVE and SHELXD in determining substructures from twinned MAD data is based on the use of Patterson superposition methods, which are robust because no cross-vectors between the twin domains exist in the anomalous Patterson maps.

If the twin fraction is particularly high, the additional noise introduced into the data by detwinning may more than counterbalance the positive effect of removing the contribution of the minor twin domain. Thus, phasing with twinned MAD data (without detwinning) is a possibility that should not be excluded from consideration. In the present case, attempts to phase using twinned and detwinned MAD data were similarly successful. However, there may well be cases where the twin fraction is so high that detwinning is impossible, while the twinned data can still be phased.

The other successful SeMet case: Yang et al. (2000). Acta Cryst. D56, 959-964.

Summary

General references:

Yeates, T.O. (1997). Detecting and overcoming crystal twinnings. Methods in Enzymology. 276, 344-358.

Yeates, T.O. and Fam, B.C. (1999). Protein crystals and their evil twins. Structure. 7. R25-R29.

Giacovazzo, C. et al. Fundamentals of Crystallography.

International tables for crystallography, volume C, pages 10-14 (Twin Laws).

Sheldrick, GM. And Schneider, T. (1997). SHELXL: high resolution refinement. Methods in Enzymology. 277, 319-343.

A useful website: http://www.doe-mbi.ucla.edu/Services/Twinning