Electron diffraction data processing with DIALS

Abstract

Electron diffraction is a relatively novel alternative to X-ray crystallography for the structure determination of macromolecules from three-dimensional nanometre-sized crystals. The continuous-rotation method of data collection has been adapted for the electron microscope. However, there are important differences in geometry that must be considered for successful data integration. The wavelength of electrons in a TEM is typically around 40 times shorter than that of X-rays, implying a nearly flat Ewald sphere, and consequently low diffraction angles and a high effective sample-to-detector distance. Nevertheless, the DIALS software package can, with specific adaptations, successfully process continuous-rotation electron diffraction data. Pathologies encountered specifically in electron diffraction make data integration more challenging. Errors can arise from instrumentation, such as beam drift or distorted diffraction patterns from lens imperfections. The diffraction geometry brings additional challenges such as strong correlation between lattice parameters and detector distance. These issues are compounded if calibration is incomplete, leading to uncertainty in experimental geometry, such as the effective detector distance and the rotation rate or direction. Dynamic scattering, absorption, radiation damage and incomplete wedges of data are additional factors that complicate data processing. Here, recent features of DIALS as adapted to electron diffraction processing are shown, including diagnostics for problematic diffraction geometry refinement, refinement of a smoothly varying beam model and corrections for distorted diffraction images. These novel features, combined with the existing tools in DIALS, make data integration and refinement feasible for electron crystallography, even in difficult cases.

Keywords: DIALS; diffraction geometry; electron crystallography; electron microscopy; protein nanocrystals.

Figure 1

A diffraction image from data set 1 is shown using dials.image_viewer. The four quads have independent geometry, such that they are not forced to align on a single pixel grid. The upper inset panel shows a zoomed region of the upper left quad where a clear row of diffraction spots is visible. The middle inset panel shows the ‘threshold’ image with default spot-finding settings, which indicates which pixels will be marked as strong during the spot-finding procedure. The lower inset panel shows the same region after spot-finding settings were adjusted for this data set. In this case, this amounted to setting gain=0.833, sigma_strong=1.0 and global_threshold=1 as command-line options for the dials.find_spots program. The detector gain of 3.0 determined by the format class is already applied before the spot-finding operation; hence the spot-finding gain acts as a multiplier for this value.

Figure 2

The Ewald constructions for the electron diffraction and X-ray cases are compared. The cross-hatched circle represents a reciprocal lattice within a limiting sphere of 1 Å resolution. The Ewald sphere for 12 keV X-rays with a wavelength of 1.0332 Å is represented as a complete circle, with the scattering vector s ₁ drawn at the 1 Å limit, forming an angle of 2θ_X = 62.2° from the incident beam direction along s ₀. At this scale, the Ewald sphere for 200 keV electrons, with a wavelength of 0.02508 Å, cannot be shown as a complete circle as it has a radius over 40 times greater. The equivalent scattering vector s ₁ for 1 Å diffraction forms an angle of only 2θ_e = 1.44° from the incident beam direction. It is worth noting that the reciprocal lattice is sampled along an almost planar surface, implying that data from a single image contain no information about the reciprocal-lattice dimension in the direction along the incident beam.

Figure 3

Five reciprocal-lattice points are shown (in black and labelled) along the a ^∗ axis for a crystal with unit-cell dimension a = 10 Å. Arcs representing the surface of the Ewald sphere with a typical X-ray wavelength of λ = 1.0332 Å intersect these points at rotation angles between 15.0° for h = 1 and 27.0° for h = 5, where rotations are assumed to be clockwise from vertical in the plane of the figure. If the modelled rotation axis is inverted then φ centroids of observed spots would be mapped onto Ewald spheres rotated between −15.0 and −27.0°, resulting in a distinct curvature to the reconstructed reciprocal lattice (points shown in blue). In the case of electron diffraction at λ = 0.02508 Å the spots are observed almost simultaneously at rotation angles between 12.1 and 12.4°. For clarity a single Ewald arc is shown for h = 3. If the assumed axis is inverted then φ centroids between −12.1 and −12.4° still result in almost a straight line (points shown in green). It is therefore difficult to determine the correct direction of rotation from the appearance of the reconstructed reciprocal lattice alone.

Figure 4

Geometry refinement against simulated data was performed assuming either typical electron diffraction geometry or X-ray diffraction geometry, as described in the text. Corrgrams were produced for the final step of refinement to provide immediate visual feedback regarding correlations between the effects of refined parameters on the model. The colours and areas of the circles are related to the values of the correlation coefficient, with large blue circles indicating strong correlation and large red circles indicating strong anticorrelation. This plot shows the correlation between the effects of different parameters on the angular residuals (φ − φ_o), with the refined detector parameters excluded from the plots as they have no effect on the φ residuals. The parameter labels are as defined in Waterman et al. (2016 ▸). The upper panel shows the corrgram for the electron diffraction geometry and the lower panel shows the equivalent corrgram for the X-ray diffraction geometry.