Unsupervised learning approaches to characterizing heterogeneous samples using X-ray single-particle imaging

One of the outstanding analytical problems in X-ray single-particle imaging (SPI) is the classification of structural heterogeneity, which is especially difficult given the low signal-to-noise ratios of individual patterns and the fact that even identical objects can yield patterns that vary greatly when orientation is taken into consideration. Proposed here are two methods which explicitly account for this orientation-induced variation and can robustly determine the structural landscape of a sample ensemble. The first, termed common-line principal component analysis (PCA), provides a rough classification which is essentially parameter free and can be run automatically on any SPI dataset. The second method, utilizing variation auto-encoders (VAEs), can generate 3D structures of the objects at any point in the structural landscape. Both these methods are implemented in combination with the noise-tolerant expand–maximize–compress (EMC) algorithm and its utility is demonstrated by applying it to an experimental dataset from gold nanoparticles with only a few thousand photons per pattern. Both discrete structural classes and continuous deformations are recovered. These developments diverge from previous approaches of extracting reproducible subsets of patterns from a dataset and open up the possibility of moving beyond the study of homogeneous sample sets to addressing open questions on topics such as nanocrystal growth and dynamics, as well as phase transitions which have not been externally triggered.

Crystallography relevant to Mars and Galilean icy moons: crystal behavior of kieserite-type monohydrate sulfates at extraterrestrial conditions down to 15 K

Monohydrate sulfate kieserites (M 2+SO4·H2O) and their solid solutions are essential constituents on the surface of Mars and most likely also on Galilean icy moons in our solar system. Phase stabilities of end-member representatives (M 2+ = Mg, Fe, Co, Ni) have been examined crystallographically using single-crystal X-ray diffraction at 1 bar and temperatures down to 15 K, by means of applying open He cryojet techniques at in-house laboratory instrumentation. All four representative phases show a comparable, highly anisotropic thermal expansion behavior with a remarkable negative thermal expansion along the monoclinic b axis and a pronounced anisotropic expansion perpendicular to it. The lattice changes down to 15 K correspond to an `inverse thermal pressure' of approximately 0.7 GPa, which is far below the critical pressures of transition under hydrostatic compression (Pc ≥ 2.40 GPa). Consequently, no equivalent structural phase transition was observed for any compound, and neither dehydration nor rearrangements of the hydrogen bonding schemes have been observed. The M 2+SO4·H2O (M 2+ = Mg, Fe, Co, Ni) end-member phases preserve the kieserite-type C2/c symmetry; hydrogen bonds and other structural details were found to vary smoothly down to the lowest experimental temperature. These findings serve as an important basis for the assignment of sulfate-related signals in remote-sensing data obtained from orbiters at celestial bodies, as well as for thermodynamic considerations and modeling of properties of kieserite-type sulfate monohydrates relevant to extraterrestrial sulfate associations at very low temperatures.

Tracing electron density changes in langbeinite under pressure

Pressure is well known to dramatically alter physical properties and chemical behaviour of materials, much of which is due to the changes in chemical bonding that accompany compression. Though it is relatively easy to comprehend this correlation in the discontinuous compression regime, where phase transformations take place, understanding of the more subtle continuous compression effects is a far greater challenge, requiring insight into the finest details of electron density redistribution. In this study, a detailed examination of quantitative electron density redistribution in the mineral langbeinite was conducted at high pressure. Langbeinite is a potassium magnesium sulfate mineral with the chemical formula [K2Mg2(SO4)3], and crystallizes in the isometric tetartoidal (cubic) system. The mineral is an ore of potassium, occurs in marine evaporite deposits in association with carnallite, halite and sylvite, and gives its name to the langbeinites, a family of substances with the same cubic structure, a tetrahedral anion, and large and small cations. Single-crystal X-ray diffraction data for langbeinite have been collected at ambient pressure and at 1 GPa using a combination of in-house and synchrotron techniques. Experiments were complemented by theoretical calculations within the pressure range up to 40 GPa. On the basis of changes in structural and thermal parameters, all ions in the langbeinite structure can be grouped into `soft' (potassium cations and oxygens) and `hard' (sulfur and magnesium). This analysis emphasizes the importance of atomic basins as a convenient tool to analyse the redistribution of electron density under external stimuli such as pressure or temperature. Gradual reduction of completeness of experimental data accompanying compression did not significantly reduce the quality of structural, electronic and thermal parameters obtained in experimental quantitative charge density analysis.

Crystal structure of CmABCB1 multi-drug exporter in lipidic mesophase revealed by LCP-SFX

CmABCB1 is a Cyanidioschyzon merolae homolog of human ABCB1, a well known ATP-binding cassette (ABC) transporter responsible for multi-drug resistance in various cancers. Three-dimensional structures of ABCB1 homologs have revealed the snapshots of inward- and outward-facing states of the transporters in action. However, sufficient information to establish the sequential movements of the open–close cycles of the alternating-access model is still lacking. Serial femtosecond crystallography (SFX) using X-ray free-electron lasers has proven its worth in determining novel structures and recording sequential conformational changes of proteins at room temperature, especially for medically important membrane proteins, but it has never been applied to ABC transporters. In this study, 7.7 monoacylglycerol with cholesterol as the host lipid was used and obtained well diffracting microcrystals of the 130 kDa CmABCB1 dimer. Successful SFX experiments were performed by adjusting the viscosity of the crystal suspension of the sponge phase with hydroxypropyl methylcellulose and using the high-viscosity sample injector for data collection at the SACLA beamline. An outward-facing structure of CmABCB1 at a maximum resolution of 2.22 Å is reported, determined by SFX experiments with crystals formed in the lipidic cubic phase (LCP-SFX), which has never been applied to ABC transporters. In the type I crystal, CmABCB1 dimers interact with adjacent molecules via not only the nucleotide-binding domains but also the transmembrane domains (TMDs); such an interaction was not observed in the previous type II crystal. Although most parts of the structure are similar to those in the previous type II structure, the substrate-exit region of the TMD adopts a different configuration in the type I structure. This difference between the two types of structures reflects the flexibility of the substrate-exit region of CmABCB1, which might be essential for the smooth release of various substrates from the transporter.

Modeling a unit cell: crystallographic refinement procedure using the biomolecular MD simulation platform Amber

A procedure has been developed for the refinement of crystallographic protein structures based on the biomolecular simulation program Amber. The procedure constructs a model representing a crystal unit cell, which generally contains multiple protein molecules and is fully hydrated with TIP3P water. Periodic boundary conditions are applied to the cell in order to emulate the crystal lattice. The refinement is conducted in the form of a specially designed short molecular-dynamics run controlled by the Amber ff14SB force field and the maximum-likelihood potential that encodes the structure-factor-based restraints. The new Amber-based refinement procedure has been tested on a set of 84 protein structures. In most cases, the new procedure led to appreciably lower R free values compared with those reported in the original PDB depositions or obtained by means of the industry-standard phenix.refine program. In particular, the new method has the edge in refining low-accuracy scrambled models. It has also been successful in refining a number of molecular-replacement models, including one with an r.m.s.d. of 2.15 Å. In addition, Amber-refined structures consistently show superior MolProbity scores. The new approach offers a highly realistic representation of protein–protein interactions in the crystal, as well as of protein–water interactions. It also offers a realistic representation of protein crystal dynamics (akin to ensemble-refinement schemes). Importantly, the method fully utilizes the information from the available diffraction data, while relying on state-of-the-art molecular-dynamics modeling to assist with those elements of the structure that do not diffract well (for example mobile loops or side chains). Finally, it should be noted that the protocol employs no tunable parameters, and the calculations can be conducted in a matter of several hours on desktop computers equipped with graphical processing units or using a designated web service.