Crystallography

Resolution beyond the diffraction limit

A method has been devised that extends the resolution of X-ray crystal structures beyond the diffraction limit. This might help to improve the visualization of structures of proteins that form 'poorly diffracting' crystals. See Letter p.202

In 1913, Lawrence Bragg described the law that characterizes the diffraction of X-ray beams by crystalline materials1. Since then, crystallographers have used this law to solve the atomic structures of a wealth of compounds, ranging from simple table salt to extremely complex biomacromolecules. The resolution at which a structure can be visualized depends on the diffraction limit (or the Bragg limit), which in turn depends on the regular arrangement of molecules within crystalline materials. The degree of this regularity is often low in crystals of biomacromolecules, and this creates a major barrier to visualizing these molecules at the atomic level. On page 202 of this issue, Ayyer et al.2 report an approach to solving molecular structures at resolutions higher than the diffraction limit.

The X-ray diffraction defined by Bragg's law is the sum total of diffraction patterns from molecules that strictly occupy the positions of a crystal's lattice units. Obtaining such a strictly ordered crystal often represents a big obstacle to the study of hydrophobic, membrane-spanning proteins and their complexes, limiting the resolution at which the structures of these biologically important molecules can be solved. The low degree of order in protein crystals can be caused by translational and rotational displacements of the protein molecules from their ideal positions, and by dynamic motions within the molecules.

Ayyer and colleagues propose that molecules in crystalline materials can be considered as rigid units, and that the disorder is caused by translational displacements of these units from their crystal-lattice positions. These displacements cause scattered X-rays to deviate from the trajectories generated by a perfectly ordered crystal lattice, giving rise to a vague pattern of light and shadowy regions, instead of a sharp diffraction pattern with distinct spots (see Figure 1 of the paper2). This vague picture constitutes a kind of 'continuous' diffraction2,3,4 pattern, and contains information about the structure of the molecules in the crystals at resolutions extending well beyond the limit of Bragg diffraction.

Figure 1: Electron-density maps of a section of photosystem II.
figure1

Ayyer et al.2 have developed a method that improves the resolution of X-ray crystal structures by analysing information from both conventional Bragg diffraction and continuous diffraction — which occurs when molecules in crystals deviate from their exact lattice positions only through translational displacements. a, Here, the structure of an α-helix chain of photosystem II, a photosynthetic protein complex, is superimposed on the electron-density map (grey mesh) of the chain obtained by analysing only Bragg X-ray diffraction. The resolution is 4.5 Å. b, Using the authors' method, the resolution of the electron-density map is improved to 3.5 Å, and the molecular structure fits more precisely into the map.

Continuous diffraction has frequently been observed in diffraction patterns of protein crystals, but had not previously been used for structural determination. Ayyer and co-workers' approach is similar to that used for single-molecule imaging5 to obtain structural information from the continuous diffraction pattern, working on the basis that the diffraction arises from the sum of aligned single-molecule diffraction patterns.

The authors' method requires both Bragg and continuous diffraction data, and treats these diffractions separately. First, the Bragg diffractions were analysed using conventional techniques, generating an electron-density map of the target molecule at low resolution. The researchers used this map to generate a low-resolution outline of the 3D molecular structure. This, in turn, was used to constrain a higher-resolution 3D image of the electron density, generated from the continuous diffraction data using an 'iterative phasing' algorithm6,7. The structure was finally refined using a procedure similar to that used for single-particle cryo-electron microscopy data8.

Ayyer et al. used this approach to extend the resolution of the structure of photosystem II (PSII), an extremely large, dimeric membrane-protein complex (the molecular weight of the dimer is about 700 kilodaltons). PSII splits water into electrons, protons and oxygen during photosynthesis, thereby sustaining aerobic life on Earth by providing oxygen and converting light energy into biologically useful chemical energy. The structure of PSII has previously been solved at a resolution of 1.9 ångströms using X-rays from a conventional synchrotron source9, and at a resolution of 1.95 Å using femtosecond X-ray pulses (1 femtosecond is 10−15 s) from a free-electron laser (XFEL)10. These structures indicated that the PSII molecules are rigid within the crystals, at least up to this level of resolution. However, some of Ayyer and colleagues' PSII crystals diffracted to only 4.5 Å resolution, limiting the authors' ability to study the complex's reaction dynamics.

To obtain better resolution, the researchers collected a data set from a stream of micrometre-scale PSII crystals using powerful femtosecond XFEL pulses, and thus obtained an X-ray structure of 4.5 Å based on Bragg diffractions. They then refined this to 3.5 Å resolution using their method based on continuous diffraction data. The resulting electron-density map showed more-detailed features of many amino-acid side chains (Fig. 1) and cofactors associated with the large protein complex, compared with the structure derived from Bragg diffraction data alone. This great improvement hints at the potential of this approach for extending resolution limited by Bragg diffraction.

The extent to which rotational displacements and dynamic motions in crystals can generally be ignored remains to be seen — this will determine how useful continuous diffraction data will be for improving resolutions. Nevertheless, the authors' approach might find broad applications, from structural analysis beyond Bragg diffractions to single-molecule imaging, and help to improve the accuracy of structures derived from X-ray data. In particular, the technique is potentially a great step forward for those seeking high-resolution structural information for many 'poorly diffracting' protein crystals and their complexes.

It will be interesting to see how much further resolution can be improved by incorporating continuous diffraction data with X-ray data collected from both XFEL and synchrotron sources. Meanwhile, the reported iterative-phasing approach may allow structures to be solved without the use of additional methods to retrieve phase information from diffraction data. It is also to be hoped that the reported iterative-phasing algorithms will be made user-friendly and widely available.Footnote 1

Notes

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Shen, J. Resolution beyond the diffraction limit. Nature 530, 168–169 (2016). https://doi.org/10.1038/530168a

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