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.

Observation of substrate diffusion and ligand binding in enzyme crystals using high-repetition-rate mix-and-inject serial crystallography.

Here, we illustrate what happens inside the catalytic cleft of an enzyme when substrate or ligand binds on single-millisecond timescales. The initial phase of the enzymatic cycle is observed with near-atomic resolution using the most advanced X-ray source currently available: the European XFEL (EuXFEL). The high repetition rate of the EuXFEL combined with our mix-and-inject technology enables the initial phase of ceftriaxone binding to the Mycobacterium tuberculosis ß-lactamase to be followed using time-resolved crystallography in real time. It is shown how a diffusion coefficient in enzyme crystals can be derived directly from the X-ray data, enabling the determination of ligand and enzyme-ligand concentrations at any position in the crystal volume as a function of time. In addition, the structure of the irreversible inhibitor sulbactam bound to the enzyme at a 66 ms time delay after mixing is described. This demonstrates that the EuXFEL can be used as an important tool for biomedically relevant research.

Reprint of: Inversion of dynamical Bragg intensities to complex structure factors by iterated projections. For Ultramic. 2020. ("Pico" Festschrift, May 2021).

A method for recovering complex structure factors from many simultaneously excited Bragg beam in- tensities is described. The method is applied to simulated transmission electron diffraction data over a wide range of crystal thickness and beam energies. The method is based on iterated projections between structure and scattering matrices, which are related by a matrix unit ary transformation, exponential, which we invert. The algorithm removes multiple-scattering perturbations from diffraction data and might be extended to other fields, including X-ray and neutron diffraction and cryo-electron microscopy. Because coherent multiple scattering involves interference between Bragg beams, the method also solves the phase problem. Unlike dynamical inversion from electron microscope images or ptychography data, the method, which starts with Bragg beam intensities, provides complex structure factors unaffected by focusing errors or resolution limitations imposed by lenses. We provide inversions from simulated data with 441 simultaneously excited Bragg beams over a range of thickness and beam energy. We discuss the retrieval of chirality information from enantiomorphs, the efficient incorporation of symmetry information using the irreducible representation of the group of structure matrices, and the effect of HOLZ lines to provide three-dimensional information.

Early-stage dynamics of chloride ion-pumping rhodopsin revealed by a femtosecond X-ray laser.

Chloride ion-pumping rhodopsin (ClR) in some marine bacteria utilizes light energy to actively transport Cl- into cells. How the ClR initiates the transport is elusive. Here, we show the dynamics of ion transport observed with time-resolved serial femtosecond (fs) crystallography using the Linac Coherent Light Source. X-ray pulses captured structural changes in ClR upon flash illumination with a 550 nm fs-pumping laser. High-resolution structures for five time points (dark to 100 ps after flashing) reveal complex and coordinated dynamics comprising retinal isomerization, water molecule rearrangement, and conformational changes of various residues. Combining data from time-resolved spectroscopy experiments and molecular dynamics simulations, this study reveals that the chloride ion close to the Schiff base undergoes a dissociation-diffusion process upon light-triggered retinal isomerization.

Synchronous RNA conformational changes trigger ordered phase transitions in crystals.

Time-resolved studies of biomacromolecular crystals have been limited to systems involving only minute conformational changes within the same lattice. Ligand-induced changes greater than several angstroms, however, are likely to result in solid-solid phase transitions, which require a detailed understanding of the mechanistic interplay between conformational and lattice transitions. Here we report the synchronous behavior of the adenine riboswitch aptamer RNA in crystal during ligand-triggered isothermal phase transitions. Direct visualization using polarized video microscopy and atomic force microscopy shows that the RNA molecules undergo cooperative rearrangements that maintain lattice order, whose cell parameters change distinctly as a function of time. The bulk lattice order throughout the transition is further supported by time-resolved diffraction data from crystals using an X-ray free electron laser. The synchronous molecular rearrangements in crystal provide the physical basis for studying large conformational changes using time-resolved crystallography and micro/nanocrystals.

Inversion of dynamical Bragg intensities to complex structure factors by iterated projections. For Ultramic. 2020. ("Pico" Festschrift, May 2021).

A method for recovering complex structure factors from many simultaneously excited Bragg beam in- tensities is described. The method is applied to simulated transmission electron diffraction data over a wide range of crystal thickness and beam energies. The method is based on iterated projections between structure and scattering matrices, which are related by a matrix unit ary transformation, exponential, which we invert. The algorithm removes multiple-scattering perturbations from diffraction data and might be extended to other fields, including X-ray and neutron diffraction and cryo-electron microscopy. Because coherent multiple scattering involves interference between Bragg beams, the method also solves the phase problem. Unlike dynamical inversion from electron microscope images or ptychography data, the method, which starts with Bragg beam intensities, provides complex structure factors unaffected by focusing errors or resolution limitations imposed by lenses. We provide inversions from simulated data with 441 simultaneously excited Bragg beams over a range of thickness and beam energy. We discuss the retrieval of chirality information from enantiomorphs, the efficient incorporation of symmetry information using the irreducible representation of the group of structure matrices, and the effect of HOLZ lines to provide three-dimensional information.

Inversion of Many-Beam Bragg Intensities for Phasing by Iterated Projections: Removal of Multiple Scattering Artifacts from Diffraction Data.

An iterated projection algorithm (N-Phaser) is developed that reconstructs a scattering potential from N-beam multiple Bragg scattered intensities. The method may be used to eliminate multiple scattering artifacts from electron diffraction data, solving the phase problem and increasing the thicknesses of samples used in materials science, solid-state chemistry, and small molecule crystallography. For high-energy transmission electron diffraction, we show that the algorithm recovers accurate complex structure factors from a wide range of thicknesses, orientations, and relativistic beam energies, and does not require known thickness or atomic-resolution data if sufficient multiple scattering occurs. Extensions to Cryo-electron microscopy and Micro-electron diffraction are suggested.

3D printing of gas-dynamic virtual nozzles and optical characterization of high-speed microjets.

Gas dynamic virtual nozzles (GDVNs) produce microscopic flow-focused liquid jets and droplets and play an important role at X-ray free-electron laser (XFEL) facilities where they are used to steer a stream of hydrated biomolecules into an X-ray focus during diffraction measurements. Highly stable and reproducible microjet and microdroplets are desired, as are flexible fabrication methods that enable integrated mixing microfluidics, droplet triggering mechanisms, laser illumination, and other customized features. In this study, we develop the use of high-resolution 3D nano-printing for the production of monolithic, asymmetric GDVN designs that are difficult to fabricate by other means. We also develop a dual-pulsed nanosecond image acquisition and analysis platform for the characterization of GDVN performance, including jet speed, length, diameter, and directionality, among others. We show that printed GDVNs can form microjets with very high degree of reproducibility, down to sub-micron diameters, and with water jet speeds beyond 170 m/s.

Enhanced X-ray diffraction of in vivo-grown µNS crystals by viscous jets at XFELs.

µNS is a 70 kDa major nonstructural protein of avian reoviruses, which cause significant economic losses in the poultry industry. They replicate inside viral factories in host cells, and the µNS protein has been suggested to be the minimal viral factor required for factory formation. Thus, determining the structure of µNS is of great importance for understanding its role in viral infection. In the study presented here, a fragment consisting of residues 448-605 of µNS was expressed as an EGFP fusion protein in Sf9 insect cells. EGFP-µNS(448-605) crystallization in Sf9 cells was monitored and verified by several imaging techniques. Cells infected with the EGFP-µNS(448-605) baculovirus formed rod-shaped microcrystals (5-15 µm in length) which were reconstituted in high-viscosity media (LCP and agarose) and investigated by serial femtosecond X-ray diffraction using viscous jets at an X-ray free-electron laser (XFEL). The crystals diffracted to 4.5 Šresolution. A total of 4227 diffraction snapshots were successfully indexed into a hexagonal lattice with unit-cell parameters a = 109.29, b = 110.29, c = 324.97 Å. The final data set was merged and refined to 7.0 Šresolution. Preliminary electron-density maps were obtained. While more diffraction data are required to solve the structure of µNS(448-605), the current experimental strategy, which couples high-viscosity crystal delivery at an XFEL with in cellulo crystallization, paves the way towards structure determination of the µNS protein.

High-viscosity injector-based pink-beam serial crystallography of microcrystals at a synchrotron radiation source.

Since the first successful serial crystallography (SX) experiment at a synchrotron radiation source, the popularity of this approach has continued to grow showing that third-generation synchrotrons can be viable alternatives to scarce X-ray free-electron laser sources. Synchrotron radiation flux may be increased ∼100 times by a moderate increase in the bandwidth ('pink beam' conditions) at some cost to data analysis complexity. Here, we report the first high-viscosity injector-based pink-beam SX experiments. The structures of proteinase K (PK) and A2A adenosine receptor (A2AAR) were determined to resolutions of 1.8 and 4.2 Šusing 4 and 24 consecutive 100 ps X-ray pulse exposures, respectively. Strong PK data were processed using existing Laue approaches, while weaker A2AAR data required an alternative data-processing strategy. This demonstration of the feasibility presents new opportunities for time-resolved experiments with microcrystals to study structural changes in real time at pink-beam synchrotron beamlines worldwide.

SPIND: a reference-based auto-indexing algorithm for sparse serial crystallography data.

SPIND (sparse-pattern indexing) is an auto-indexing algorithm for sparse snapshot diffraction patterns ('stills') that requires the positions of only five Bragg peaks in a single pattern, when provided with unit-cell parameters. The capability of SPIND is demonstrated for the orientation determination of sparse diffraction patterns using simulated data from microcrystals of a small inorganic molecule containing three iodines, 5-amino-2,4,6-triiodoisophthalic acid monohydrate (I3C) [Beck & Sheldrick (2008 ▸), Acta Cryst. E64, o1286], which is challenging for commonly used indexing algorithms. SPIND, integrated with CrystFEL [White et al. (2012 ▸), J. Appl. Cryst. 45, 335-341], is then shown to improve the indexing rate and quality of merged serial femtosecond crystallography data from two membrane proteins, the human δ-opioid receptor in complex with a bi-functional peptide ligand DIPP-NH2 and the NTQ chloride-pumping rhodopsin (CIR). The study demonstrates the suitability of SPIND for indexing sparse inorganic crystal data with smaller unit cells, and for improving the quality of serial femtosecond protein crystallography data, significantly reducing the amount of sample and beam time required by making better use of limited data sets. SPIND is written in Python and is publicly available under the GNU General Public License from https://github.com/LiuLab-CSRC/SPIND.

Snapshot of an oxygen intermediate in the catalytic reaction of cytochrome c oxidase.

Cytochrome c oxidase (CcO) reduces dioxygen to water and harnesses the chemical energy to drive proton translocation across the inner mitochondrial membrane by an unresolved mechanism. By using time-resolved serial femtosecond crystallography, we identified a key oxygen intermediate of bovine CcO. It is assigned to the PR-intermediate, which is characterized by specific redox states of the metal centers and a distinct protein conformation. The heme a3 iron atom is in a ferryl (Fe4+ = O2-) configuration, and heme a and CuB are oxidized while CuA is reduced. A Helix-X segment is poised in an open conformational state; the heme a farnesyl sidechain is H-bonded to S382, and loop-I-II adopts a distinct structure. These data offer insights into the mechanism by which the oxygen chemistry is coupled to unidirectional proton translocation.

Structural basis for light control of cell development revealed by crystal structures of a myxobacterial phytochrome.

Phytochromes are red-light photoreceptors that were first characterized in plants, with homologs in photosynthetic and non-photosynthetic bacteria known as bacteriophytochromes (BphPs). Upon absorption of light, BphPs interconvert between two states denoted Pr and Pfr with distinct absorption spectra in the red and far-red. They have recently been engineered as enzymatic photoswitches for fluorescent-marker applications in non-invasive tissue imaging of mammals. This article presents cryo- and room-temperature crystal structures of the unusual phytochrome from the non-photosynthetic myxo-bacterium Stigmatella aurantiaca (SaBphP1) and reveals its role in the fruiting-body formation of this photomorphogenic bacterium. SaBphP1 lacks a conserved histidine (His) in the chromophore-binding domain that stabilizes the Pr state in the classical BphPs. Instead it contains a threonine (Thr), a feature that is restricted to several myxobacterial phytochromes and is not evolutionarily understood. SaBphP1 structures of the chromophore binding domain (CBD) and the complete photosensory core module (PCM) in wild-type and Thr-to-His mutant forms reveal details of the molecular mechanism of the Pr/Pfr transition associated with the physiological response of this myxobacterium to red light. Specifically, key structural differences in the CBD and PCM between the wild-type and the Thr-to-His mutant involve essential chromophore contacts with proximal amino acids, and point to how the photosignal is transduced through the rest of the protein, impacting the essential enzymatic activity in the photomorphogenic response of this myxobacterium.

The phase problem for two-dimensional crystals. II. Simulations.

Phasing of diffraction data from two-dimensional crystals using only minimal molecular envelope information is investigated by simulation. Two-dimensional crystals are an attractive target for studying membrane proteins using X-ray free-electron lasers, particularly for dynamic studies at room temperature. Simulations using an iterative projection algorithm show that phasing is feasible with fairly minimal molecular envelope information, supporting recent uniqueness results for this problem [Arnal & Millane (2017). Acta Cryst. A73, 438-448]. The effects of noise and likely requirements for structure determination using X-ray free-electron laser sources are investigated.

X-ray lasers for structure and dynamics in biology.

Recent advances in the application of X-ray lasers to structural biology are providing time-resolved high-resolution imaging of many processes, from enzyme kinetics to the riboswitch in action, drug action, and light-sensitive proteins.

Merging single-shot XFEL diffraction data from inorganic nanoparticles: a new approach to size and orientation determination.

X-ray free-electron lasers (XFELs) provide new opportunities for structure determination of biomolecules, viruses and nanomaterials. With unprecedented peak brilliance and ultra-short pulse duration, XFELs can tolerate higher X-ray doses by exploiting the femtosecond-scale exposure time, and can thus go beyond the resolution limits achieved with conventional X-ray diffraction imaging techniques. Using XFELs, it is possible to collect scattering information from single particles at high resolution, however particle heterogeneity and unknown orientations complicate data merging in three-dimensional space. Using the Linac Coherent Light Source (LCLS), synthetic inorganic nanocrystals with a core-shell architecture were used as a model system for proof-of-principle coherent diffractive single-particle imaging experiments. To deal with the heterogeneity of the core-shell particles, new computational methods have been developed to extract the particle size and orientation from the scattering data to assist data merging. The size distribution agrees with that obtained by electron microscopy and the merged data support a model with a core-shell architecture.

Corrigendum: Diffraction data of core-shell nanoparticles from an X-ray free electron laser.

This corrects the article DOI: 10.1038/sdata.2017.48.

Serial millisecond crystallography of membrane and soluble protein microcrystals using synchrotron radiation.

Crystal structure determination of biological macromolecules using the novel technique of serial femtosecond crystallography (SFX) is severely limited by the scarcity of X-ray free-electron laser (XFEL) sources. However, recent and future upgrades render microfocus beamlines at synchrotron-radiation sources suitable for room-temperature serial crystallography data collection also. Owing to the longer exposure times that are needed at synchrotrons, serial data collection is termed serial millisecond crystallography (SMX). As a result, the number of SMX experiments is growing rapidly, with a dozen experiments reported so far. Here, the first high-viscosity injector-based SMX experiments carried out at a US synchrotron source, the Advanced Photon Source (APS), are reported. Microcrystals (5-20 µm) of a wide variety of proteins, including lysozyme, thaumatin, phycocyanin, the human A2A adenosine receptor (A2AAR), the soluble fragment of the membrane lipoprotein Flpp3 and proteinase K, were screened. Crystals suspended in lipidic cubic phase (LCP) or a high-molecular-weight poly(ethylene oxide) (PEO; molecular weight 8 000 000) were delivered to the beam using a high-viscosity injector. In-house data-reduction (hit-finding) software developed at APS as well as the SFX data-reduction and analysis software suites Cheetah and CrystFEL enabled efficient on-site SMX data monitoring, reduction and processing. Complete data sets were collected for A2AAR, phycocyanin, Flpp3, proteinase K and lysozyme, and the structures of A2AAR, phycocyanin, proteinase K and lysozyme were determined at 3.2, 3.1, 2.65 and 2.05 Šresolution, respectively. The data demonstrate the feasibility of serial millisecond crystallography from 5-20 µm crystals using a high-viscosity injector at APS. The resolution of the crystal structures obtained in this study was dictated by the current flux density and crystal size, but upcoming developments in beamline optics and the planned APS-U upgrade will increase the intensity by two orders of magnitude. These developments will enable structure determination from smaller and/or weakly diffracting microcrystals.

Corrigendum: Double-flow focused liquid injector for efficient serial femtosecond crystallography.

This corrects the article DOI: 10.1038/srep44628.

Coherent soft X-ray diffraction imaging of coliphage PR772 at the Linac coherent light source.

Single-particle diffraction from X-ray Free Electron Lasers offers the potential for molecular structure determination without the need for crystallization. In an effort to further develop the technique, we present a dataset of coherent soft X-ray diffraction images of Coliphage PR772 virus, collected at the Atomic Molecular Optics (AMO) beamline with pnCCD detectors in the LAMP instrument at the Linac Coherent Light Source. The diameter of PR772 ranges from 65-70 nm, which is considerably smaller than the previously reported ~600 nm diameter Mimivirus. This reflects continued progress in XFEL-based single-particle imaging towards the single molecular imaging regime. The data set contains significantly more single particle hits than collected in previous experiments, enabling the development of improved statistical analysis, reconstruction algorithms, and quantitative metrics to determine resolution and self-consistency.