Hierarchical clustering for multiple-crystal macromolecular crystallography experiments: the ccCluster program

Elucidating polymorphs of crystal structures by intensity-based hierarchical clustering analysis of multiple diffraction data sets

In macromolecular structure determination using X-ray diffraction from multiple crystals, the presence of different structures (structural polymorphs) necessitates the classification of the diffraction data for appropriate structural analysis. Hierarchical clustering analysis (HCA) is a promising technique that has so far been used to extract isomorphous data, mainly for single-structure determination. Although in principle the use of HCA can be extended to detect polymorphs, the absence of a reference to define the threshold used to group the isomorphous data sets (the `isomorphic threshold') poses a challenge. Here, unit-cell-based and intensity-based HCAs have been applied to data sets for apo trypsin and inhibitor-bound trypsin that were mixed post data acquisition to investigate the efficacy of HCA in classifying polymorphous data sets. Single-step intensity-based HCA successfully classified polymorphs with a certain `isomorphic threshold'. In data sets for several samples containing an unknown degree of structural heterogeneity, polymorphs could be identified by intensity-based HCA using the suggested `isomorphic threshold'. Polymorphs were also detected in single crystals using data collected using the continuous helical scheme. These findings are expected to facilitate the determination of multiple structural snapshots by exploiting automated data collection and analysis.

Changes in active-site geometry on X-ray photoreduction of a lytic polysaccharide monooxygenase active-site copper and saccharide binding

The recently discovered lytic polysaccharide monooxygenases (LPMOs) are Cu-containing enzymes capable of degrading polysaccharide substrates oxidatively. The generally accepted first step in the LPMO reaction is the reduction of the active-site metal ion from Cu2+ to Cu+. Here we have used a systematic diffraction data collection method to monitor structural changes in two AA9 LPMOs, one from Lentinus similis (LsAA9_A) and one from Thermoascus auranti-acus (TaAA9_A), as the active-site Cu is photoreduced in the X-ray beam. For LsAA9_A, the protein produced in two different recombinant systems was crystallized to probe the effect of post-translational modifications and different crystallization conditions on the active site and metal photoreduction. We can recommend that crystallographic studies of AA9 LPMOs wishing to address the Cu2+ form use a total X-ray dose below 3 × 104 Gy, while the Cu+ form can be attained using 1 × 106 Gy. In all cases, we observe the transition from a hexa-coordinated Cu site with two solvent-facing ligands to a T-shaped geometry with no exogenous ligands, and a clear increase of the θ2 parameter and a decrease of the θ3 parameter by averages of 9.2° and 8.4°, respectively, but also a slight increase in θT. Thus, the θ2 and θ3 parameters are helpful diagnostics for the oxidation state of the metal in a His-brace protein. On binding of cello-oligosaccharides to LsAA9_A, regardless of the production source, the θT parameter increases, making the Cu site less planar, while the active-site Tyr-Cu distance decreases reproducibly for the Cu2+ form. Thus, the θT increase found on copper reduction may bring LsAA9_A closer to an oligosaccharide-bound state and contribute to the observed higher affinity of reduced LsAA9_A for cellulosic substrates.

Probing ligand binding of endothiapepsin by `temperature-resolved' macromolecular crystallography

Continuous developments in cryogenic X-ray crystallography have provided most of our knowledge of 3D protein structures, which has recently been further augmented by revolutionary advances in cryoEM. However, a single structural conformation identified at cryogenic temperatures may introduce a fictitious structure as a result of cryogenic cooling artefacts, limiting the overview of inherent protein physiological dynamics, which play a critical role in the biological functions of proteins. Here, a room-temperature X-ray crystallographic method using temperature as a trigger to record movie-like structural snapshots has been developed. The method has been used to show how TL00150, a 175.15 Da fragment, undergoes binding-mode changes in endothiapepsin. A surprising fragment-binding discrepancy was observed between the cryo-cooled and physiological temperature structures, and multiple binding poses and their interplay with DMSO were captured. The observations here open up new promising prospects for structure determination and interpretation at physiological temperatures with implications for structure-based drug discovery.

Room-temperature serial synchrotron crystallography of Drosophila cryptochrome

Fixed-target serial crystallography allows the high-throughput collection of diffraction data from small crystals at room temperature. This methodology is particularly useful for difficult samples that have sensitivity to radiation damage or intolerance to cryoprotection measures; fixed-target methods also have the added benefit of low sample consumption. Here, this method is applied to the structure determination of the circadian photoreceptor cryptochrome (CRY), previous structures of which have been determined at cryogenic temperature. In determining the structure, several data-filtering strategies were tested for combining observations from the hundreds of crystals that contributed to the final data set. Removing data sets based on the average correlation coefficient among equivalent reflection intensities between a given data set and all others was most effective at improving the data quality and maintaining overall completeness. CRYs are light sensors that undergo conformational photoactivation. Comparisons between the cryogenic and room-temperature CRY structures reveal regions of enhanced mobility at room temperature in loops that have functional importance within the CRY family of proteins. The B factors of the room-temperature structure correlate well with those predicted from molecular-dynamics simulations.

xia2.multiplex: a multi-crystal data-analysis pipeline

In macromolecular crystallography, radiation damage limits the amount of data that can be collected from a single crystal. It is often necessary to merge data sets from multiple crystals; for example, small-wedge data collections from micro-crystals, in situ room-temperature data collections and data collection from membrane proteins in lipidic mesophases. Whilst the indexing and integration of individual data sets may be relatively straightforward with existing software, merging multiple data sets from small wedges presents new challenges. The identification of a consensus symmetry can be problematic, particularly in the presence of a potential indexing ambiguity. Furthermore, the presence of non-isomorphous or poor-quality data sets may reduce the overall quality of the final merged data set. To facilitate and help to optimize the scaling and merging of multiple data sets, a new program, xia2.multiplex, has been developed which takes data sets individually integrated with DIALS and performs symmetry analysis, scaling and merging of multi-crystal data sets. xia2.multiplex also performs analysis of various pathologies that typically affect multi-crystal data sets, including non-isomorphism, radiation damage and preferential orientation. After the description of a number of use cases, the benefit of xia2.multiplex is demonstrated within a wider autoprocessing framework in facilitating a multi-crystal experiment collected as part of in situ room-temperature fragment-screening experiments on the SARS-CoV-2 main protease.

Single-support serial isomorphous replacement phasing

The use of single isomorphous replacement (SIR) has become less widespread due to difficulties in sample preparation and the identification of isomorphous native and derivative data sets. Non-isomorphism becomes even more problematic in serial experiments, because it adds natural inter-crystal non-isomorphism to heavy-atom-soaking-induced non-isomorphism. Here, a method that can successfully address these issues (and indeed can benefit from differences in heavy-atom occupancy) and additionally significantly simplifies the SIR experiment is presented. A single heavy-atom soak into a microcrystalline slurry is performed, followed by automated serial data collection of partial data sets. This produces a set of data collections with a gradient of heavy-atom occupancies, which are reflected in differential merging statistics. These differences can be exploited by an optimized genetic algorithm to segregate the pool of data sets into `native' and `derivative' groups, which can then be used to successfully determine phases experimentally by SIR.

ID23-2: an automated and high-performance microfocus beamline for macromolecular crystallography at the ESRF

ID23-2 is a fixed-energy (14.2 keV) microfocus beamline at the European Synchrotron Radiation Facility (ESRF) dedicated to macromolecular crystallography. The optics and sample environment have recently been redesigned and rebuilt to take full advantage of the upgrade of the ESRF to the fourth generation Extremely Brilliant Source (ESRF-EBS). The upgraded beamline now makes use of two sets of compound refractive lenses and multilayer mirrors to obtain a highly intense (>1013 photons s-1) focused microbeam (minimum size 1.5 µm × 3 µm full width at half-maximum). The sample environment now includes a FLEX-HCD sample changer/storage system, as well as a state-of-the-art MD3Up high-precision multi-axis diffractometer. Automatic data reduction and analysis are also provided for more advanced protocols such as synchrotron serial crystallographic experiments.

Best practices for time-resolved serial synchrotron crystallography

With recent developments in X-ray sources, instrumentation and data-analysis tools, time-resolved crystallographic experiments, which were originally the preserve of a few expert groups, are becoming simpler and can be carried out at more radiation sources, and are thus increasingly accessible to a growing user base. However, these experiments are just that: discrete experiments, not just `data collections'. As such, careful planning and consideration of potential pitfalls is required to enable a successful experiment. Here, some of the key factors that should be considered during the planning and execution of a time-resolved structural study are outlined, with a particular focus on synchrotron-based experiments.

Experimental evidence for the benefits of higher X-ray energies for macromolecular crystallography

X-ray-induced radiation damage is a limiting factor for the macromolecular crystallographer and data must often be merged from many crystals to yield complete data sets for the structure solution of challenging samples. Increasing the X-ray energy beyond the typical 10-15 keV range promises to provide an extension of crystal lifetime via an increase in diffraction efficiency. To date, however, hardware limitations have negated any possible gains. Through the first use of a cadmium telluride EIGER2 detector and a beamline optimized for high-energy data collection, it is shown that at higher energies fewer crystals will be required to obtain complete data, as the diffracted intensity per unit dose increases by a factor of more than two between 12.4 and 25 keV. Additionally, these higher energy data can provide more information, as shown by a systematic increase in the high-resolution cutoff of the data collected. Taken together, these gains point to a high-energy future for synchrotron-based macromolecular crystallography.

Activation of PARP2/ARTD2 by DNA damage induces conformational changes relieving enzyme autoinhibition

Human PARP2/ARTD2 is an ADP-ribosyltransferase which, when activated by 5'-phosphorylated DNA ends, catalyses poly-ADP-ribosylation of itself, other proteins and DNA. In this study, a crystal structure of PARP2 in complex with an activating 5'-phosphorylated DNA shows that the WGR domain bridges the dsDNA gap and joins the DNA ends. This DNA binding results in major conformational changes, including reorganization of helical fragments, in the PARP2 regulatory domain. A comparison of PARP1 and PARP2 crystal structures reveals how binding to a DNA damage site leads to formation of a catalytically competent conformation. In this conformation, PARP2 is capable of binding substrate NAD⁺ and histone PARylation factor 1 that changes PARP2 residue specificity from glutamate to serine when initiating DNA repair processes. The structure also reveals how the conformational changes in the autoinhibitory regulatory domain would promote the flexibility needed by the enzyme to reach the target macromolecule for ADP-ribosylation.

FMX - the Frontier Microfocusing Macromolecular Crystallography Beamline at the National Synchrotron Light Source II

Two new macromolecular crystallography (MX) beamlines at the National Synchrotron Light Source II, FMX and AMX, opened for general user operation in February 2017 [Schneider et al. (2013). J. Phys. Conf. Ser. 425, 012003; Fuchs et al. (2014). J. Phys. Conf. Ser. 493, 012021; Fuchs et al. (2016). AIP Conf. Proc. SRI2015, 1741, 030006]. FMX, the micro-focusing Frontier MX beamline in sector 17-ID-2 at NSLS-II, covers a 5-30 keV photon energy range and delivers a flux of 4.0 × 1012 photons s-1 at 1 Å into a 1 µm × 1.5 µm to 10 µm × 10 µm (V × H) variable focus, expected to reach 5 × 1012 photons s-1 at final storage-ring current. This flux density surpasses most MX beamlines by nearly two orders of magnitude. The high brightness and microbeam capability of FMX are focused on solving difficult crystallographic challenges. The beamline's flexible design supports a wide range of structure determination methods - serial crystallography on micrometre-sized crystals, raster optimization of diffraction from inhomogeneous crystals, high-resolution data collection from large-unit-cell crystals, room-temperature data collection for crystals that are difficult to freeze and for studying conformational dynamics, and fully automated data collection for sample-screening and ligand-binding studies. FMX's high dose rate reduces data collection times for applications like serial crystallography to minutes rather than hours. With associated sample lifetimes as short as a few milliseconds, new rapid sample-delivery methods have been implemented, such as an ultra-high-speed high-precision piezo scanner goniometer [Gao et al. (2018). J. Synchrotron Rad. 25, 1362-1370], new microcrystal-optimized micromesh well sample holders [Guo et al. (2018). IUCrJ, 5, 238-246] and highly viscous media injectors [Weierstall et al. (2014). Nat. Commun. 5, 3309]. The new beamline pushes the frontier of synchrotron crystallography and enables users to determine structures from difficult-to-crystallize targets like membrane proteins, using previously intractable crystals of a few micrometres in size, and to obtain quality structures from irregular larger crystals.

Macromolecular room temperature crystallography

X-ray crystallography enables detailed structural studies of proteins to understand and modulate their function. Conducting crystallographic experiments at cryogenic temperatures has practical benefits but potentially limits the identification of functionally important alternative protein conformations that can be revealed only at room temperature (RT). This review discusses practical aspects of preparing, acquiring, and analyzing X-ray crystallography data at RT to demystify preconceived impracticalities that freeze progress of routine RT data collection at synchrotron sources. Examples are presented as conceptual and experimental templates to enable the design of RT-inspired studies; they illustrate the diversity and utility of gaining novel insights into protein conformational landscapes. An integrative view of protein conformational dynamics enables opportunities to advance basic and biomedical research.

Small-wedge synchrotron and serial XFEL datasets for Cysteinyl leukotriene GPCRs

Structural studies of challenging targets such as G protein-coupled receptors (GPCRs) have accelerated during the last several years due to the development of new approaches, including small-wedge and serial crystallography. Here, we describe the deposition of seven datasets consisting of X-ray diffraction images acquired from lipidic cubic phase (LCP) grown microcrystals of two human GPCRs, Cysteinyl leukotriene receptors 1 and 2 (CysLT₁R and CysLT₂R), in complex with various antagonists. Five datasets were collected using small-wedge synchrotron crystallography (SWSX) at the European Synchrotron Radiation Facility with multiple crystals under cryo-conditions. Two datasets were collected using X-ray free electron laser (XFEL) serial femtosecond crystallography (SFX) at the Linac Coherent Light Source, with microcrystals delivered at room temperature into the beam within LCP matrix by a viscous media microextrusion injector. All seven datasets have been deposited in the open-access databases Zenodo and CXIDB. Here, we describe sample preparation and annotate crystallization conditions for each partial and full datasets. We also document full processing pipelines and provide wrapper scripts for SWSX and SFX data processing.

Measurement(s)	X-ray diffraction data • protein complex • protein structure data • protein crystallization
Technology Type(s)	small-wedge synchrotron crystallography • x-ray crystallography assay • X-ray free electron laser serial femtosecond crystallography
Factor Type(s)	type of G-protein-coupled receptor • type of antagonist

Machine-accessible metadata file describing the reported data: 10.6084/m9.figshare.13128758

Multi-crystal data collection using synchrotron radiation as exemplified with low-symmetry crystals of Dps

Multi-crystal data collection using synchrotron radiation was successfully applied to determine the three-dimensional structure of a triclinic crystal form of Dps from Escherichia coli at 2.0 Å resolution. The final data set was obtained by combining 261 partial diffraction data sets measured from crystals with an average size of approximately 5 µm. The most important features of diffraction data measurement and processing for low-symmetry crystals are discussed.

Making a difference in multi-data-set crystallography: simple and deterministic data-scaling/selection methods

Phasing by single-wavelength anomalous diffraction (SAD) from multiple crystallographic data sets can be particularly demanding because of the weak anomalous signal and possible non-isomorphism. The identification and exclusion of non-isomorphous data sets by suitable indicators is therefore indispensable. Here, simple and robust data-selection methods are described. A multi-dimensional scaling procedure is first used to identify data sets with large non-isomorphism relative to clusters of other data sets. Within each cluster that it identifies, further selection is based on the weighted ΔCC1/2, a quantity representing the influence of a set of reflections on the overall CC1/2 of the merged data. The anomalous signal is further improved by optimizing the scaling protocol. The success of iterating the selection and scaling steps was verified by substructure determination and subsequent structure solution. Three serial synchrotron crystallography (SSX) SAD test cases with hundreds of partial data sets and one test case with 62 complete data sets were analyzed. Structure solution was dramatically simplified with this procedure, and enabled solution of the structures after a few selection/scaling iterations. To explore the limits, the procedure was tested with much fewer data than originally required and could still solve the structure in several cases. In addition, an SSX data challenge, minimizing the number of (simulated) data sets necessary to solve the structure, was significantly underbid.

Millisecond time-resolved serial oscillation crystallography of a blue-light photoreceptor at a synchrotron

The recent development of serial crystallography has popularized time-resolved crystallography as a technique to determine the structure of protein-reaction intermediate states. However, most approaches rely on the availability of thousands to millions of microcrystals. A method is reported here, using monochromatic synchrotron radiation, for the room-temperature collection, processing and merging of X-ray oscillation diffraction data from <100 samples in order to observe the build up of a photoreaction intermediate species. Using this method, we monitored with a time resolution of 63 ms how the population of a blue-light photoreceptor domain in a crystal progressively photoconverts from the dark to the light state. The series of resulting snapshots allows us to visualize in detail the gradual rearrangement of both the protein and chromophore during this process.

Protein crystal structure determination with the crystallophore, a nucleating and phasing agent

Obtaining crystals and solving the phase problem remain major hurdles encountered by bio-crystallographers in their race to obtain new high-quality structures. Both issues can be overcome by the crystallophore, Tb-Xo4, a lanthanide-based molecular complex with unique nucleating and phasing properties. This article presents examples of new crystallization conditions induced by the presence of Tb-Xo4. These new crystalline forms bypass crystal defects often encountered by crystallographers, such as low-resolution diffracting samples or crystals with twinning. Thanks to Tb-Xo4's high phasing power, the structure determination process is greatly facilitated and can be extended to serial crystallography approaches.

A simple and versatile microfluidic device for efficient biomacromolecule crystallization and structural analysis by serial crystallography

Determining optimal conditions for the production of well diffracting crystals is a key step in every biocrystallography project. Here, a microfluidic device is described that enables the production of crystals by counter-diffusion and their direct on-chip analysis by serial crystallography at room temperature. Nine 'non-model' and diverse biomacromolecules, including seven soluble proteins, a membrane protein and an RNA duplex, were crystallized and treated on-chip with a variety of standard techniques including micro-seeding, crystal soaking with ligands and crystal detection by fluorescence. Furthermore, the crystal structures of four proteins and an RNA were determined based on serial data collected on four synchrotron beamlines, demonstrating the general applicability of this multipurpose chip concept.

ZOO: an automatic data-collection system for high-throughput structure analysis in protein microcrystallography

Owing to the development of brilliant microfocus beamlines, rapid-readout detectors and sample changers, protein microcrystallography is rapidly becoming a popular technique for accessing structural information from complex biological samples. However, the method is time-consuming and labor-intensive and requires technical expertise to obtain high-resolution protein crystal structures. At SPring-8, an automated data-collection system named ZOO has been developed. This system enables faster data collection, facilitates advanced data-collection and data-processing techniques, and permits the collection of higher quality data. In this paper, the key features of the functionality put in place on the SPring-8 microbeam beamline BL32XU are described and the major advantages of this system are outlined. The ZOO system will be a major driving force in the evolution of the macromolecular crystallography beamlines at SPring-8.

Resolving polymorphs and radiation-driven effects in microcrystals using fixed-target serial synchrotron crystallography

The ability to determine high-quality, artefact-free structures is a challenge in micro-crystallography, and the rapid onset of radiation damage and requirement for a high-brilliance X-ray beam mean that a multi-crystal approach is essential. However, the combination of crystal-to-crystal variation and X-ray-induced changes can make the formation of a final complete data set challenging; this is particularly true in the case of metalloproteins, where X-ray-induced changes occur rapidly and at the active site. An approach is described that allows the resolution, separation and structure determination of crystal polymorphs, and the tracking of radiation damage in microcrystals. Within the microcrystal population of copper nitrite reductase, two polymorphs with different unit-cell sizes were successfully separated to determine two independent structures, and an X-ray-driven change between these polymorphs was followed. This was achieved through the determination of multiple serial structures from microcrystals using a high-throughput high-speed fixed-target approach coupled with robust data processing.

Choosing your (Friedel) mates wisely: grouping data sets to improve anomalous signal

Single-wavelength anomalous diffraction (SAD) phasing from multiple crystals can be especially challenging in samples with weak anomalous signals and/or strong non-isomorphism. Here, advantage is taken of the combinatorial diversity possible in such experiments to study the relationship between merging statistics and downstream metrics of phasing signals. It is furthermore shown that a genetic algorithm (GA) can be used to optimize the grouping of data sets to enhance weak anomalous signals based on these merging statistics.

Automated data collection and real-time data analysis suite for serial synchrotron crystallography

At the Swiss Light Source macromolecular crystallography (MX) beamlines the collection of serial synchrotron crystallography (SSX) diffraction data is facilitated by the recent DA+ data acquisition and analysis software developments. The SSX suite allows easy, efficient and high-throughput measurements on a large number of crystals. The fast continuous diffraction-based two-dimensional grid scan method allows initial location of microcrystals. The CY+ GUI utility enables efficient assessment of a grid scan's analysis output and subsequent collection of multiple wedges of data (so-called minisets) from automatically selected positions in a serial and automated way. The automated data processing (adp) routines adapted to the SSX data collection mode provide near real time analysis for data in both CBF and HDF5 formats. The automatic data merging (adm) is the latest extension of the DA+ data analysis software routines. It utilizes the sxdm (SSX data merging) package, which provides automatic online scaling and merging of minisets and allows identification of a minisets subset resulting in the best quality of the final merged data. The results of both adp and adm are sent to the MX MongoDB database and displayed in the web-based tracker, which provides the user with on-the-fly feedback about the experiment.

VMXi: a fully automated, fully remote, high-flux in situ macromolecular crystallography beamline

VMXi is a new high-flux microfocus macromolecular crystallography beamline at Diamond Light Source. The beamline, dedicated to fully automated and fully remote data collection of macromolecular crystals in situ, allows rapid screening of hundreds of crystallization plates from multiple user groups. Its main purpose is to give fast feedback at the complex stages of crystallization and crystal optimization, but it also enables data collection of small and delicate samples that are particularly difficult to harvest using conventional cryo-methods, crystals grown in the lipidic cubic phase, and allows for multi-crystal data collections in drug discovery programs. The beamline is equipped with two monochromators: one with a narrow band-pass and fine energy resolution (optimal for regular oscillation experiments), and one with a wide band-pass and a high photon flux (optimal for fast screening). The beamline has a state-of-the-art detector and custom goniometry that allows fast data collection. This paper describes the beamline design, current status and future plans.

Further structural studies of the lytic polysaccharide monooxygenase AoAA13 belonging to the starch-active AA13 family

Lytic polysaccharide monooxygenases (LPMOs) are recently discovered copper enzymes that cleave recalcitrant polysaccharides by oxidation. The structure of an Aspergillus oryzae LPMO from the starch degrading family AA13 (AoAA13) has previously been determined from an orthorhombic crystal grown in the presence of copper, which is photoreduced in the structure. Here we describe how crystals reliably grown in presence of Zn can be Cu-loaded post crystallization. A partly photoreduced structure was obtained by severely limiting the X-ray dose, showing that this LPMO is much more prone to photoreduction than others. A serial synchrotron crystallography structure was also obtained, showing that this technique may be promising for further studies, to reduce even further photoreduction. We additionally present a triclinic structure of AoAA13, which has less occluded ligand binding site than the orthorhombic one. The availability of the triclinic crystals prompted new ligand binding studies, which lead us to the conclusion that small starch analogues do not bind to AoAA13 to an appreciable extent. A number of disordered conformations of the metal binding histidine brace have been encountered in this and other studies, and we have previously hypothesized that this disorder may be a consequence of loss of copper. We performed molecular dynamics in the absence of active site metal, and showed that the dynamics in solution differ somewhat from the disorder observed in the crystal, though the extent is equally dramatic.

High-speed raster-scanning synchrotron serial microcrystallography with a high-precision piezo-scanner

The Frontier Microfocus Macromolecular Crystallography (FMX) beamline at the National Synchrotron Light Source II with its 1 µm beam size and photon flux of 3 × 1012 photons s-1 at a photon energy of 12.66 keV has reached unprecedented dose rates for a structural biology beamline. The high dose rate presents a great advantage for serial microcrystallography in cutting measurement time from hours to minutes. To provide the instrumentation basis for such measurements at the full flux of the FMX beamline, a high-speed, high-precision goniometer based on a unique XYZ piezo positioner has been designed and constructed. The piezo-based goniometer is able to achieve sub-100 nm raster-scanning precision at over 10 grid-linepairs s-1 frequency for fly scans of a 200 µm-wide raster. The performance of the scanner in both laboratory and serial crystallography measurements up to the maximum frame rate of 750 Hz of the Eiger 16M's 4M region-of-interest mode has been verified in this work. This unprecedented experimental speed significantly reduces serial-crystallography data collection time at synchrotrons, allowing utilization of the full brightness of the emerging synchrotron radiation facilities.

Determination of Patterson group symmetry from sparse multi-crystal data sets in the presence of an indexing ambiguity

Combining X-ray diffraction data from multiple samples requires determination of the symmetry and resolution of any indexing ambiguity. For the partial data sets typical of in situ room-temperature experiments, determination of the correct symmetry is often not straightforward. The potential for indexing ambiguity in polar space groups is also an issue, although methods to resolve this are available if the true symmetry is known. Here, a method is presented to simultaneously resolve the determination of the Patterson symmetry and the indexing ambiguity for partial data sets.