research papers
TakeTwo: an indexing algorithm suited to still images with known crystal parameters
^{a}Division of Structural Biology, Wellcome Trust Centre for Human Genetics, Roosevelt Drive, Oxford OX3 7BN, England, ^{b}Diamond House, Harwell Science and Innovation Campus, Fermi Avenue, Didcot OX11 0QX, England, ^{c}Deutsches ElektronenSynchrotron, Notkestrasse 85, 22607 Hamburg, Germany, ^{d}Department of Biochemistry, University of Toronto, King's College Circle, Toronto, ON M5S 1A8, Canada, ^{e}Molecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA, ^{f}Department of Molecular Genetics, University of Toronto, King's College Circle, Toronto, ON M5S 1A8, Canada, ^{g}Atomically Resolved Dynamics, MaxPlanckInstitute for Structure and Dynamics of Matter, Luruper Chaussee 149, Hamburg, Germany, ^{h}Hamburg Centre for Ultrafast Imaging, University of Hamburg, Hamburg, Germany, and ^{i}Departments of Physics and Chemistry, University of Toronto, 80 St George Street, Toronto, ON M5S 1H6, Canada
^{*}Correspondence email: dave@strubi.ox.ac.uk
The indexing methods currently used for serial femtosecond crystallography were originally developed for experiments in which crystals are rotated in the Xray beam, providing significant threedimensional information. On the other hand, shots from both Xray freeelectron lasers and serial synchrotron crystallography experiments are still images, in which the few threedimensional data available arise only from the curvature of the
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 unitcell dimensions and 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; data processing; serial crystallography; XFELs; Xray freeelectron lasers.
1. Introduction
Indexing, or deducing the specimen orientation from crystalline diffraction patterns, can potentially be performed with high accuracy and precision owing to the integral nature of the XDS (Kabsch, 1993), iMosflm (Powell et al., 2013), DENZO (Otwinowski & Minor, 2006), LABELIT (Sauter et al., 2004) and DIALS (Gildea et al., 2014) are well established for datacollection strategies that involve crystal rotation, which are typically employed at synchrotron sources. For data collected at Xray freeelectron laser (XFEL) sources, where each image represents diffraction from a separate nonrotating specimen, the measure of success is less well defined. Dataanalysis pipelines sometimes include a preprocessing `hitfinder' step, which distinguishes images without diffraction (blanks) from hits that exceed a certain threshold number of candidate Bragg spots, which is typically set to around 20. The indexing rate is therefore defined as the percentage of hits for which crystal orientations can be determined. Reported indexing rates are often quite low (Barends et al., 2013; Liu et al., 2013; Johansson et al., 2013; Ginn, Brewster et al., 2015; Chapman et al., 2011), although the rate depends on a number of factors, including the strength of diffraction on each image and the diffraction resolution. Our own two analyses of diffraction data from Cypovirus type 17 polyhedrin (CPV17) yielded mediocre indexing rates of 53% (Ginn, Messerschidt et al., 2015) and 36% (Ginn, Brewster et al., 2015). Here, we investigate whether alternate algorithms can help improve the indexing rate, with the overall goal of producing goodquality structures while consuming a minimal amount of crystalline sample and beam time.
at which Bragg reflections are located. Indexing algorithms implemented in programs such asAll indexing methods, regardless of the data source, begin by transforming candidate Bragg spot coordinates measured on the detector into corresponding threedimensional coordinates in ) or by separately computing onedimensional FFTs of the pattern projected onto individual directional axes in and considering all possible directional axes, finely sampled on a spherical grid (Steller et al., 1997). A key success factor is that the specimen rotation provides sufficient sampling in three dimensions to dramatically overdetermine the threedimensional repeat. In contrast, still shots produced at XFEL sources contain only the limited threedimensional information that is afforded by the curvature of the which becomes essentially nonexistent in the lowresolution limit. Another condition making it difficult to detect periodicity from still shots is the minimal number of Bragg spots that meet the especially from crystals with smaller unitcell dimensions.
The periodic arrangement of reciprocallattice points (rlps) is then detected using one of several methods. For rotation data generally, equivalent determinations of the threedimensional periodic repeat can be deduced either by a single threedimensional fast Fourier transformation of the entire reciprocalspace pattern (Campbell, 1998A number of approaches have been adopted to mitigate these inherent difficulties in resolving the cctbx.xfel software suite (Hattne et al., 2014) uses the onedimensional FFT method to identify candidate basis vectors that can potentially span the but then uses prior knowledge of the unitcell parameters to choose a basis set (three vectors combined) that best agrees with the known unitcell lengths and angles. Even if the is initially unknown, a good target cell may be derived from an initial first pass of data reduction (Zeldin et al., 2015). Secondly, a recent method implemented within the DIALS toolbox (Waterman et al., 2013) avoids the onedimensional FFT search altogether (Gildea et al., 2014). The basic idea here is that the FFT is primarily useful to identify the periodic repeat spacing if the unitcell length is completely unknown. However, since the typical unitcell length can be treated as prior knowledge, it is sufficient to perform an exhaustive search for the already known periodic spacings over a grid of directional axes. This method has a high success rate for finding the basis vectors from XFEL still shots, and has also been used to index shots where multiple lattices are present, including CPV polyhedrin diffraction data from Diamond Light Source beamline I24, which eventually resulted in structure solution (Ginn, Messerschmidt et al., 2015). A final adaptation concerns the rocking curve that is normally observed in rotation data sets, as the reciprocallattice point is first rotated into and then out of the exact reflecting condition. At synchrotrons it is easy to collect individual image frames with a fine enough rotational slicing to determine the spot centroid position with high accuracy, but for still data the degree to which the rlps are offset from the is initially unknown. To compensate, parameter targets have been developed (Sauter et al., 2014; Kabsch, 2014) that restrain the orientation (after the basis vectors are chosen) so that the rlps are positioned as close as possible to the Ewald sphere.
for stillshot data. TheIn our efforts to analyse a number of new challenging data sets, including that of Bovine enterovirus (BEV), we revisited the indexing stage of the dataprocessing pipeline. At first, the BEV data appeared to be intractable owing to the low signal to noise and small separation between neighbouring spots. Initial attempts at indexing, specifying the known and produced indexing solutions with that appeared to be of extremely good quality. Finally, however, we realised that the solutions were fundamentally incorrect owing to a large (20 mm) error in the detector distance that initially went undetected.
In the process of developing automated approaches to fix the distance problem, we also sought new ways to detect the basis vectors, considering the sparsity of Bragg spots that potentially precludes the use of FFT methods. Older indexing methods developed around 1990 (Kabsch, 1988; Higashi, 1990; Kabsch, 1993) succeeded without any explicit grid search or FFT method by considering the difference vectors that connect rlps that are close in Kabsch (1988) was able to index rotation data by creating a threedimensional histogram of such difference vectors and identifying clusters which correspond to candidate basis vectors for the lattice.
Inspired by these early experiences with indexing from a limited set of difference vectors, we devised a similar algorithm that allows us to tackle difficult diffraction patterns and correct for errors in the measurements of the experimental geometry. We have named this algorithm TakeTwo, reflecting the underlying idea of taking pairs of spots to form vectors and pairs of vectors to generate indexing solutions. TakeTwo attempts to make maximal use of the information contained within a single still image by considering all interspot vectors that could match to a vector between reflections in This indexing algorithm provides high indexing rates for cubic and hexagonal space groups, and a high degree of success in indexing multiple lattices. TakeTwo is applicable to both serial synchrotron and serial femtosecond crystallography. We expect the TakeTwo algorithm to markedly improve the indexing rates of many of the available XFEL data sets.
2. Materials and methods
2.1. Data acquisition for various protein crystals
A summary of the experimental parameters and crystal symmetry for the various data sets is provided in Table 1. The diffraction patterns used for CPV17 had previously been used for (Ginn, Brewster et al., 2015; Ginn, Messerschmidt et al., 2015). Data were collected at the XPP endstation at the Linac Coherent Light Source (LCLS) under proposal LH90 from BEV crystals on a silicon chip (Roedig et al., 2015; cubic F23, unitcell dimension 437 Å). Reflections were observed to approximately 2.0 Å resolution and the minimum separation of individual reflections was three pixels. The data from thermolysin crystals, collected in 2011, have previously been processed and optimal unitcell dimensions established (Uervirojnangkoorn et al., 2015). All of the above data were recorded using the CSPAD detector. Diffraction patterns from myoglobin crystals crystallized in P2_{1}2_{1}2_{1} provided an example of an orthorhombic and were recorded using a Rayonix MX170HS detector at the XPP endstation using an alternative siliconchip delivery system (Sherrell et al., 2015; ZarrineAfsar et al., 2012; Mueller et al., 2015), which has been shown to support structure solution (Oghbaey et al., 2016).

2.2. Hit finding and spot finding using DIALS
Hits for the CPV17, BEV and thermolysin data sets were determined with cctbx.xfel using the default minimum spot count of 20 to distinguish a hit from a nonuseful image. Images for the myoglobin data set were identified as hits if they had at least 30 spots from DIALS (Waterman et al., 2013) spotfinding analysis, which uses XDS algorithms (Kabsch, 1977). For our indexing algorithm, spots were identified using DIALS, manually finding an optimal combination of spotfinding parameters (Table 2). DIALS produced spotcentroid coordinates on the surface of the detector.

2.3. Generating interspot vectors
Spots were backprojected onto the
using the known experimental parameters (incident energy and detector geometry). Threedimensional vectors were calculated between spots in The coordinates and vectors generated from backprojection onto the are referred to as `observed space', as they come directly from the spots and parameters of the experiment.2.4. Optional filtering of interspot vectors
In cases where substantial amounts of noise are picked up by the spotfinding algorithms or multiple lattices are found on the same image, one can perform an optional filtering of interspot vectors to help prevent spottonoise, noisetonoise or interlattice vectors from being included in pseudopowder pattern generation or indexing. This was performed by tabularing all interspot vectors and removing those which had the fewest neighbours, as explained below.
An interspot vector was considered to be a neighbour of another vector if they were within a certain tolerance of each other. The tolerance was either calculated for a given resolution based on the energy bandwidth and the rlp size, or alternatively a constant tolerance was assumed across the entire image. The variable distance tolerance was chosen as the maximum possible separation between rlps of finite size on opposite sides of the nest of Ewald spheres. This assures that the vector is of a similar length and direction, and is more likely to be a repeated vector from the same p_{t}, which was based on the number of expected lattices for a given image, as follows. The number of expected lattices (n) on the image was calculated based on the number of spots on the image (s) divided by the number expected per (l). The value of l was manually estimated after obtaining a few indexing results as the average number of spots picked by DIALS which were predicted (and removed) by one solution. n was rounded to the nearest integer:
Each vector was assigned a score which was equal to the total number of neighbouring vectors. The vectors were ordered in terms of their score in descending order, and a particular fraction of the vectors were removed if they did not reach a thresholdThe total number of interspot vectors for a single p_{t}) which were likely to originate from a single can therefore be determined:
is proportional to the square of the total number of spots. However, if there were two lattices on an image, each spot could generate a vector either with a member of its own or the other with roughly equal probability. Thus, one would only expect half of the spot vectors to originate between member vectors of the same The proportion of vectors (The threshold t was set so that only the proportion p_{t} of vectors would remain. Since the list is ordered so that those with the most neighbours are at the top, taking this proportion from the top of the list aims to enrich those that originate from the same lattice.
2.5. Theoretical distances for crystal lattices and space groups
Theoretical distances between individual reflections according to the
and unitcell dimension were calculated by considering all and their relation to the origin of Care was taken over those owing to the centring type of the of the crystal prevent some interspot distances from ever appearing, as opposed to axial which do not affect the occurrence of general interspot distances. The reciprocal generated by applying the transformation matrix onto Cartesian coordinates is hereby referred to as `theoretical space'. The indexing solution then defines the orientation matrix which was applied to the transformation matrix to give rise to the spots observed on the detector.2.6. Onedimensional pseudopowder patterns
Onedimensional pseudopowder patterns were generated from a small number of diffraction patterns (Fig. 1) by generating a histogram of interspot distances. These were compared with the predicted reflections given the unitcell dimensions and spacegroup and the wavelength and detector distance were adjusted to ensure a good fit between the theoretical and observed powder diffraction patterns. The beam centre correctness, metrology, detector distance and wavelength parameters all affected the sharpness of the powder rings.
2.7. Interspot vectordistance matching
In order to use the observed space vectors for indexing, they were filtered according to length. Observed space vectors are considered for indexing if they match one or more of the theoretical space vectors in length, within a certain tolerance, calculated as in §2.4.
2.8. First indexing method: rotationmatrix clusters
Two related indexing algorithms based on interspot vectors have been created which are suited to different situations. The TakeTwo algorithm therefore has two branches: the rotationmatrix cluster method and the interspot vectornetwork method.
An indexing solution cannot be determined by one interspot vector alone as this only anchors 2.10. Interspot vectors were considered a candidate for a solution if the angle between them in the observed space matched the angle between matching vectors in the theoretical space within 1°. For each of these pairs of interspot vectors, a matrix was generated which aligns the observed space onto the theoretical space (the opposite transformation was achieved using the inverse). This was combined with the transformation matrix to generate a potential indexing solution. Owing to the presence of noise and multiple lattices on a single image, the map of orientation matrices produced using this method had a low signaltonoise ratio. Indexing solutions were chosen by selecting matrices which were closely surrounded by neighbouring solutions, determined by a reimplementation of the matrix similarity metric contained within XPLOR (Brünger, 1990, 1992), which is reproduced here for clarity. For two rotation matrices P and Q, and n symmetry operators where O_{s} is the rotational component of symmetry operator s, the metric m(P, Q) is defined as
in one axis. An indexing solution must be generated by a minimum of two vectors which are not linearly dependent. This mostly used four spots, but can use three if one spot is shared between the two interspot vectors, as explained in §If this metric has a value below the threshold of 0.25, this corresponds to a rotation of 10° or less and the two are therefore treated as duplicate solutions.
To visualize the indexing solutions generated using this method, a standard unit vector, for example (1, 0, 0), was rotated by an orientation matrix to generate a new vector. This was decomposed into polar coordinates and the two angles (θ, φ) were plotted. Of course, this did not contain all of the information contained within the orientation matrices, but provides a twodimensional representation which was easily plotted to visually identify clusters of orientation matrices (Fig. 3). Clusters were identified by having the highest number of neighbours (calculated using the XPLOR method) within an 8° radius between the central spot and any potential neighbour. Indexing solutions were filtered such that symmetrically identical solutions did not occur more than once, allowing the selection of multiple lattices. Indexing solutions were then selected for initial orientationmatrix according to a previously outlined protocol (Ginn, Messerschmidt et al., 2015).
Indexing solutions were accepted on the basis of the success of the initial orientationmatrix σ_{t} or if the histogram of wavelength peaks had a sufficiently high peak. These thresholds were manually chosen on a casebycase basis for each crystal form and are highly dependent on the other parameters of the initial orientationmatrix refinement.
These initial refinements generate histograms of wavelengths, which are defined as the inverse of the radius on which the centre of the modelled rlp lies. Images were accepted if their standard deviation of rlp midpoint radii were below a certain threshold2.9. Second indexing method: building up an interspot vector network
The second indexing method built up an interconnected network of vectors which were all selfconsistent for a single indexing solution. The network was considered as an indexing solution if the number of vectors reached a certain threshold, to distinguish it from `noise'. This threshold was set to 20 by default. An indexing solution was built up recursively from a starting vector by adding further vectors which belong to the same indexing solution. In most cases, a new vector was not added unless it shared at least one spot with the existing network to increase the likelihood of picking spots from only a single 2.10 and the vector was accepted if it matched within a 8° tolerance of the existing indexing solutions as judged by the XPLOR metric.
However, this could be toggled in cases where only single lattices were suspected to be present. In order to increase the speed of calculation, vectors were `prescreened' to ensure that the angles between the prescreened vector and the current network of existing vectors were consistent. The resulting orientation matrices between the prescreened vector and existing vectors were then calculated according to §2.10. Generating an orientation matrix from two identified interspot vectors
A rotation matrix was generated from two identified interspot vectors i and j. was rotated to line up the first observed vector with the corresponding theoretical vector. The cross product and angle between the observed vector i_{obs} and the theoretical vector i_{thr} were calculated:
We then generated a rotation matrix Q_{a}, rotating by the angle α around the axis C, which aligns one axis in The second axis must be aligned using the second vector j_{obs}. The rotation matrix Q_{b} rotates j_{obs} by an angle β around the axis i_{thr} such that the angle between Q_{b}·j_{obs} and j_{thr} is minimized. Let Q_{c} be Q_{b}Q_{a}. The inverse of Q_{c}, Q_{c}^{−1}, equals Q_{c}^{T}, and is now equivalent to the U matrix defined by Busing & Levy (1967). The unitcell transformation matrix is generated from the unitcell parameters, which is equivalent to the Busing–Levy B matrix. The entire orientation matrix R is calculated as
This matrix R can be applied to integer (h, k, l) values to map them onto rotated Cartesian coordinates in reciprocal space.
2.11. Indexing additional lattices using the interspot vector network
The indexing of additional lattices using the interspot vector network is made possible by a previous method (Gildea et al., 2014) in which spots which are predicted by an existing solution are removed from the data set and indexing is resumed with the remaining spots. Interspot vector networks which lead to a previously determined orientation matrix, or a geometrically equivalent matrix, are rejected. Solutions are scored for their equivalence as described above.
3. Results
3.1. Onedimensional pseudopowder patterns
We find that well defined pseudopowder patterns (generated as described in §2) can be obtained even when true powder patterns cannot be usefully calculated. For instance, when few patterns are available pseudopowder patterns can still be produced. These are not only useful for diffraction patterns with small unitcell dimensions (Fig. 1a), but are still interpretable for diffraction patterns from crystals with large unit cells and very poor reflection separation, as for BEV crystals (Fig. 1c).
An example of the vectors used in a single image to contribute to the overall pseudopowder pattern is shown for CPV17 crystals in Fig. 2. The conventional powder patterns generated by overlaying multiple images may show fewer peaks than the pseudopowder patterns owing to axial The corresponding distances will not be present in a conventional powder pattern, but will appear in the pseudopowder pattern as such vectors occur offaxis.
As the number of BEV crystals was very small (304 images), a conventional powder pattern could not be generated by superimposition of the images, and if it had been possible, the rings would be impossible to distinguish: the unitcell dimension is 437 Å and even the longest reciprocalspace distance in the pseudopowder pattern (50 Å) only spanned 8 mm across the detector and was therefore lost in the unrecorded lowangle region. Only after a onedimensional pseudopowder pattern had been generated was it revealed that the original detectordistance reading was misaligned by 20 mm. This value could be refined manually by observing the effect on the pseudopowder pattern (Figs. 1c and 1d). This enabled indexing of these diffraction patterns in a situation where the presence of this anomaly was otherwise difficult to establish. The BEV images had very poor separation of individual reflections, with the Miller index vector (1, 1, 1) corresponding to only three pixels. Assuming an error in a spot position of ∼0.5 pixels, the error in such a vector will be about 23%, having a major impact on the pseudopowder pattern especially at small reciprocal distance values.
Owing to the orthorhombic nature of myoglobin, powder rings will overlap in ways which are not observed in cubic space groups. This will lead to a degree of uncertainty during the indexing stage when assigning theoretical vectors to observed vectors according to their distances. The pseudopowder pattern for the myoglobin data set is shown in Fig. 1(b).
3.2. Rotationmatrix clusters
The rotationmatrix cluster method, as described in §2, has a poor signaltonoise ratio and can only reliably reach above the level of noise in cubic space groups, where only geometrically equivalent powder rings overlap. Projecting the orientation matrices onto two dimensions shows clusters of orientation matrices which have a high number of neighbours, and these clusters lead to indexing solutions (Fig. 3). However, this method is not well suited to the hexagonal of thermolysin, perhaps because of the less distinct separation of powder rings. A sample of 262 CPV17 images demonstrated a 130% indexing rate (i.e. more than one per hit). Of all the images, 87% provided at least one with data extending to 1.98 Å at the edge of the detector. These images often contained multiple lattices, which were identifiable by the abnormally high numbers of spots (Fig. 4). The indexing rates obtained for these images in the previously published structure (Ginn, Messerschmidt et al., 2015) was 52%.
3.3. Interspot vector networks
Interspot vector networks were successfully applied to all of the test systems. For CPV17, interspot vector distances were considered up to a reciprocal distance of 0.19 Å^{−1}, which was manually chosen to give the optimal indexing rate. When the number of interspot vectors within the network exceeded 20, the corresponding indexing solution was confirmed by initial orientationmatrix (Ginn, Messerschmidt et al., 2015). At this point the majority of interspot vector networks provided a correct indexing solution, as judged by orientationmatrix When indexing was limited to one solution per image, a was found for 92% of images, a higher proportion of indexed images than the result for rotationmatrix clusters. Enabling multiple indexing (up to three distinct lattices on one image) increased the indexing rate to 151%. Of the 29 images which failed to produce any orientations after indexing, 18 were weak or of low resolution, two showed no evidence of diffraction, one had over 1000 spots (at the extreme of the distribution shown in Fig. 4) and eight showed no obvious reasons for indexing failure. Another sample of 1380 CPV17 images which extended to 1.84 Å at the edge of the detector demonstrated an indexing rate of 99.3% when only considering single lattices.
Thermolysin crystals were indexed, selecting vectors with lengths of up to 0.1 Å^{−1} also manually chosen to give the best indexing rates. There was a high incidence of multiple lattices in this data set, which made finding interspot vector networks more difficult (example in Fig. 5). However, when searching for multiple lattices an indexing rate of 90% was achieved for this data set.
BEV crystals performed similarly to CPV17 crystals but had to be processed several times with differing combinations of parameters (Table 3) to achieve the highest indexing rate of 97.6% from a pool of 304 images, despite the spots being much closer together. The greatest distance considered in is 0.06 Å^{−1}. The interspot vector network is likely to comprise more vectors which span an appreciable distance across the detector, including longer vectors where the errors are proportionately lower.

With respect to myoglobin, 69% of the crystals, which were crystallized in P2_{1}2_{1}2_{1} with distinct unitcell axes, generated an indexing solution using the interspot vectornetwork method using a vector distance tolerance of 5 × 10^{−4} Å^{−1}. When searching for multiple lattices, the indexing rate increased to 112%. Interspot vectors were considered within a reciprocallattice distance of 0.15 Å^{−1}. The failed crystals were generally those of lower resolution and had insufficient spots to support indexing with the chosen parameters. Overall, all the images had an average of 148 ± 106 reflections and those which failed to index had a lower average of 80 ± 22 reflections, illustrating the poorer crystal quality of these images.
3.4. Tolerance to errors in experimental parameters
To test the robustness of the algorithm, the experimental parameters were altered and the effect on the indexing success rate was observed using CPV17 data. As the detector distance and beam centre are the most likely to be incorrectly measured at an XFEL beamline, these parameters were varied. The detector distance was varied from its true value of 101.2 mm by 1.0 mm in either direction, and similarly for the beam centre X position. This algorithm had a good tolerance to experimental errors, and although the indexing rates decreased when the model parameters deviated from their true values, this was in the form of a gradual decay. Indexing success only rapidly decreased after moving approximately 0.5 mm from the optimal value for both detector distance and beam centre (Fig. 6). For comparison, the shortest vector for this would have spanned a minimum of 1.77 mm across the detector if it had been located near the beam centre.
4. Discussion and conclusions
For the reliable indexing of diffraction patterns, experimental parameters such as the direct beam position and crystaltodetector position need to be known reasonably accurately. Powder patterns aggregated from a large number of diffraction patterns are useful in establishing these parameters. We have found that in cases where only a small number of images are available, or the
is large enough to obscure the lowresolution rings or prevent adequate separation of rings, a pseudopowder pattern can still be generated by considering the projected threedimensional vectors between spots on the We find that such pseudopowder patterns are generally useful tools for detecting and correcting significant errors in experimental parameters such as the crystaltodetector distance, which can still be poorly estimated at XFEL beamlines.We describe two new approaches to indexing still images such as those derived from serial crystallography. The first approach, termed the rotationcluster method, is well suited to lowresolution data with a small number of reflections, whereas the second method, using interspot vector networks, was found to be more generally robust and particularly suited to the test case in a hexagonal
Taken together, the methods presented here have been shown to be highly effective for cubic (CPV17 and BEV), hexagonal (thermolysin) and orthorhombic (myoglobin) space groups, and are likely to be of general utility. In the test cases chosen, the indexing rate was high and the number of lattices indexed ranged from 80 to 150% of the number of images classified as harbouring diffraction.The large majority of the images which failed to be indexed by the methods described here appeared to originate from weak crystals resulting in diffraction to only low resolution, low XFEL pulse intensity or a combination of these, as judged from the 262image sample of CPV17. This provides reassurance that the images which failed to index would have provided the least amount of useful information for the datareduction stage if they had been successfully indexed.
The TakeTwo algorithm could be incorporated into other XFEL crystallography software suites as an alternative method. Combining the results from multiple algorithms and removing duplicate solutions should lead to a larger indexed percentage than that obtained using any one algorithm alone. We include the TakeTwo algorithm in the cppxfel software suite (Ginn et al., 2016). Potential users may download this software and to do so should visit http://viper.lbl.gov/cctbx.xfel/index.php/Cppxfel.
Acknowledgements
DIS was supported by the Medical Research Council, grant MR/N00065X/1 and previously G1000099. HMG was supported by the Wellcome Trust (studentship 075491/04). NKS was supported by US National Institutes of Health grant R01GM102520. The Canadian Institute for Advanced Research supported RJDM, OPE and DIS. Portions of this research were carried out at the Linac Coherent Light Source (LCLS) at the SLAC National Accelerator Laboratory. The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/20072013) under REA grant agreement No. 623994 (HMW). We are grateful to Helen Duyvesteyn for testing and using the software. LCLS is an Office of Science User Facility operated for the US Department of Energy Office of Science by Stanford University. Administrative support was received from the Wellcome Trust (grant 090532/Z/09/Z). This is a contribution from the Oxford Instruct Centre.
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