TakeTwo: an indexing algorithm suited to still images with known crystal parameters

Abstract

The indexing methods currently used for serial femtosecond crystallography were originally developed for experiments in which crystals are rotated in the X-ray beam, providing significant three-dimensional information. On the other hand, shots from both X-ray free-electron lasers and serial synchrotron crystallography experiments are still images, in which the few three-dimensional data available arise only from the curvature of the Ewald sphere. Traditional synchrotron crystallography methods are thus less well suited to still image data processing. Here, a new indexing method is presented with the aim of maximizing information use from a still image given the known unit-cell dimensions and space group. Efficacy for cubic, hexagonal and orthorhombic space groups is shown, and for those showing some evidence of diffraction the indexing rate ranged from 90% (hexagonal space group) to 151% (cubic space group). Here, the indexing rate refers to the number of lattices indexed per image.

Keywords: TakeTwo; X-ray free-electron lasers; XFELs; data processing; serial crystallography.

Figure 1

CPV17 at 101.2 mm detector distance (a), myoglobin (b) and BEV pseudo-powder patterns (c, d) generated using optimized experimental parameters without spot-vector filtering. The blue line is generated from experimental data, whereas the pink line is the expected pseudo-powder pattern given the unit-cell and space-group information. The height of the magenta line denotes the relative number of Miller indices which give rise to the particular inter-spot vector length; the absolute values are not shown for clarity. The CPV17 powder pattern was generated from 262 images. Owing to the higher mosaicity of the myoglobin crystals (464 images), the experimental peaks for each powder ring in (b) are broadened compared with the CPV17 powder pattern (a). For the BEV pseudo-powder patterns (304 images), the pattern in (c) was generated from the recorded detector distance of 105 mm. However, the pattern in (d), which shows a better fit to the pseudo-powder pattern, was obtained at a detector distance of 85 mm. The peaks are less well separated owing to the high error associated with measuring spot vectors between extremely close spots.

Figure 2

An example CPV17 crystal diffraction image at 101.2 mm detector distance with vectors picked between spots which lie within 0.1 Å⁻¹ of each other. This will contribute a small portion of the pseudo-powder pattern as seen in Fig. 1 ▸. The Miller index (0, 0, 0) is also included in the analysis to boost the number of inter-spot vectors identified within the image.

Figure 3

Matrix-cluster solutions decomposed into two dimensions, showing one strong (denoted by blue circles) and one weak solution (denoted by red circles) on the same image. Darker areas show matrices which have a high number of neighbouring solutions within an 8° angle, whereas yellow solutions have the lowest number of neighbours within the 8° angle and are likely to be noise. Both circles correspond to solutions which lead to a successful, unique indexing solution. Each solution has six symmetry-related solutions generated by indexing relative to geometrically equivalent axes. The image is from a CPV17 sample at 101.2 mm.

Figure 4

Left: a histogram of frequency of images with a given number of spots for the CPV17 sample at 101.2 mm detector distance. Images with higher numbers of spots typically have larger numbers of lattices. The graph is cropped at a maximum of 400 spots for clarity. Right: the frequency of spots on the same images grouped by the number of successfully indexed lattices. Images which fail to index typically have significantly larger spot counts.

Figure 5

Map of inter-spot vectors within an image of a thermolysin crystal diffraction pattern which contribute to a correct indexing solution. The Miller index translation between the spots is marked beside each vector. The total number of vectors was limited to 80.

Figure 6

Tolerance of the indexing algorithm to the detector-distance parameter (filled circles) and beam-centre X parameter (crosses) are shown. Indexing success decreases significantly after 0.5 mm displacement from the optimal detector distance. The CSPAD detector pixel size is 0.11 mm. Calculated for the CPV17 sample at 101.2 mm detector distance.