Noncrystallographic symmetry (NCS) averaging following molecular-replacement phasing is generally the major technique used to solve a structure with several molecules in one asymmetric unit, such as a spherical icosahedral viral particle. As an alternative method to NCS averaging, a new approach to optimize or to refine the electron density directly under NCS constraints is proposed. This method has the same effect as the conventional NCS-averaging method but does not include the process of Fourier synthesis to generate the electron density from amplitudes and the corresponding phases. It has great merit for the solution of structures with limited data that are either twinned or incomplete at low resolution. This method was applied to the case of the T = 1 shell-domain subviral particle of Penaeus vannamei nodavirus with data affected by twinning using the REFMAC5 refinement software.

Helical structures are prevalent in biology. In the PDB, there are many examples where protein molecules are helically arranged, not only according to strict crystallographic screw axes but also according to approximate noncrystallographic screws. The preponderance of such screws is rather striking as helical arrangements in crystals must preserve an integer number of subunits per turn, while intuition and simple packing arguments would seem to favor fractional helices. The article provides insights into such questions, based on stereochemistry, trigonometry, and topology, and illustrates the findings with concrete PDB structures. Updated statistics of Sohncke space groups in the PDB are also presented.

Perfect merohedral twinning of crystals is not uncommon and complicates structural analysis. An iterative method for the deconvolution of data from perfectly merohedrally twinned crystals in the presence of noncrystallographic symmetry (NCS) has been reimplemented. It is shown that the method recovers the data effectively using test data, and an independent metric of success, based on special classes of reflections that are unaffected by the twin operator, is now provided. The method was applied to a real problem with fivefold NCS and rather poor-quality diffraction data, and it was found that even in these circumstances the method appears to recover most of the information. The software has been made available in a form that can be applied to other crystal systems.

Non-POU domain-containing octamer-binding protein (NONO, a.k.a. p54(nrb)) is a central player in nuclear gene regulation with rapidly emerging medical significance. NONO is a member of the highly conserved Drosophila behaviour/human splicing (DBHS) protein family, a dynamic family of obligatory dimeric nuclear regulatory mediators. However, work with the NONO homodimer has been limited by rapid irreversible sample aggregation. Here, it is reported that L-proline stabilizes purified NONO homodimers, enabling good-quality solution small-angle X-ray structure determination and crystallization. NONO crystallized in the apparent space group P21 with a unique axis (b) of 408.9 Å and with evidence of twinning, as indicated by the cumulative intensity distribution L statistic, suggesting the possibility of space group P1. Structure solution by molecular replacement shows a superhelical arrangement of six NONO homodimers (or 12 in P1) oriented parallel to the long axis, resulting in extensive noncrystallographic symmetry. Further analysis revealed that the crystal was not twinned, but the collected data suffered from highly overlapping reflections that obscured the L-test. Optimized data collection on a new crystal using higher energy X-rays, a smaller beam width and an increased sample-to-detector distance produced non-overlapping reflections to 2.6 Å resolution. The steps taken to analyse and overcome this series of practical difficulties and to produce a biologically informative structure are discussed.

Using direct methods starting from random phases, the crystal structure of a 32-base-pair RNA (675 non-H RNA atoms in the asymmetric unit) was determined using only the native diffraction data (resolution limit 1.05 Å) and the computer program SIR2014. The almost three helical turns of the RNA in the asymmetric unit introduced partial or imperfect translational pseudosymmetry (TPS) that modulated the intensities when averaged by the l Miller indices but still escaped automated detection. Almost six times as many random phase sets had to be tested on average to reach a correct structure compared with a similar-sized RNA hairpin (27 nucleotides, 580 non-H RNA atoms) without TPS. More sensitive methods are needed for the automated detection of partial TPS.

One of the great challenges in refining macromolecular crystal structures is a low data-to-parameter ratio. Historically, knowledge from chemistry has been used to help to improve this ratio. When a macromolecule crystallizes with more than one copy in the asymmetric unit, the noncrystallographic symmetry relationships can be exploited to provide additional restraints when refining the working model. However, although globally similar, NCS-related chains often have local differences. To allow for local differences between NCS-related molecules, flexible torsion-based NCS restraints have been introduced, coupled with intelligent rotamer handling for protein chains, and are available in phenix.refine for refinement of models at all resolutions.

The study of virus structures has contributed to methodological advances in structural biology that are generally applicable (molecular replacement and noncrystallographic symmetry are just two of the best known examples). Moreover, structural virology has been instrumental in forging the more general concept of exploiting phase information derived from multiple structural techniques. This hybridization of structural methods, primarily electron microscopy (EM) and X-ray crystallography, but also small-angle X-ray scattering (SAXS) and nuclear magnetic resonance (NMR) spectroscopy, is central to integrative structural biology. Here, the interplay of X-ray crystallography and EM is illustrated through the example of the structural determination of the marine lipid-containing bacteriophage PM2. Molecular replacement starting from an ~13 Å cryo-EM reconstruction, followed by cycling density averaging, phase extension and solvent flattening, gave the X-ray structure of the intact virus at 7 Å resolution This in turn served as a bridge to phase, to 2.5 Å resolution, data from twinned crystals of the major coat protein (P2), ultimately yielding a quasi-atomic model of the particle, which provided significant insights into virus evolution and viral membrane biogenesis.