Random conical tilt reconstruction without particle picking in cryo-electron microscopy.

A method is proposed to reconstruct the 3D molecular structure from micrographs collected at just one sample tilt angle in the random conical tilt scheme in cryo-electron microscopy. The method uses autocorrelation analysis on the micrographs to estimate features of the molecule which are invariant under certain nuisance parameters such as the positions of molecular projections in the micrographs. This enables the molecular structure to be reconstructed directly from micrographs, completely circumventing the need for particle picking. Reconstructions are demonstrated with simulated data and the effect of the missing-cone region is investigated. These results show promise to reduce the size limit for single-particle reconstruction in cryo-electron microscopy.

Multi-target Detection with an Arbitrary Spacing Distribution.

Motivated by the structure reconstruction problem in single-particle cryo-electron microscopy, we consider the multi-target detection model, where multiple copies of a target signal occur at unknown locations in a long measurement, further corrupted by additive Gaussian noise. At low noise levels, one can easily detect the signal occurrences and estimate the signal by averaging. However, in the presence of high noise, which is the focus of this paper, detection is impossible. Here, we propose two approaches-autocorrelation analysis and an approximate expectation maximization algorithm-to reconstruct the signal without the need to detect signal occurrences in the measurement. In particular, our methods apply to an arbitrary spacing distribution of signal occurrences. We demonstrate reconstructions with synthetic data and empirically show that the sample complexity of both methods scales as SNR-3 in the low SNR regime.

Solving protein structure from sparse serial microcrystal diffraction data at a storage-ring synchrotron source.

In recent years, the success of serial femtosecond crystallography and the paucity of beamtime at X-ray free-electron lasers have motivated the development of serial microcrystallography experiments at storage-ring synchrotron sources. However, especially at storage-ring sources, if a crystal is too small it will have suffered significant radiation damage before diffracting a sufficient number of X-rays into Bragg peaks for peak-indexing software to determine the crystal orientation. As a consequence, the data frames of small crystals often cannot be indexed and are discarded. Introduced here is a method based on the expand-maximize-compress (EMC) algorithm to solve protein structures, specifically from data frames for which indexing methods fail because too few X-rays are diffracted into Bragg peaks. The method is demonstrated on a real serial microcrystallography data set whose signals are too weak to be indexed by conventional methods. In spite of the daunting background scatter from the sample-delivery medium, it was still possible to solve the protein structure at 2.1 Šresolution. The ability of the EMC algorithm to analyze weak data frames will help to reduce sample consumption. It will also allow serial microcrystallography to be performed with crystals that are otherwise too small to be feasibly analyzed at storage-ring sources.

Erratum: Reconstructing three-dimensional protein crystal intensities from sparse unoriented two-axis X-ray diffraction patterns. Corrigendum.

[This corrects the article DOI: 10.1107/S1600576717006537.].

Reconstructing three-dimensional protein crystal intensities from sparse unoriented two-axis X-ray diffraction patterns.

Recently, there has been a growing interest in adapting serial microcrystallography (SMX) experiments to existing storage ring (SR) sources. For very small crystals, however, radiation damage occurs before sufficient numbers of photons are diffracted to determine the orientation of the crystal. The challenge is to merge data from a large number of such 'sparse' frames in order to measure the full reciprocal space intensity. To simulate sparse frames, a dataset was collected from a large lysozyme crystal illuminated by a dim X-ray source. The crystal was continuously rotated about two orthogonal axes to sample a subset of the rotation space. With the EMC algorithm [expand-maximize-compress; Loh & Elser (2009). Phys. Rev. E, 80, 026705], it is shown that the diffracted intensity of the crystal can still be reconstructed even without knowledge of the orientation of the crystal in any sparse frame. Moreover, parallel computation implementations were designed to considerably improve the time and memory scaling of the algorithm. The results show that EMC-based SMX experiments should be feasible at SR sources.

Dragonfly: an implementation of the expand-maximize-compress algorithm for single-particle imaging.

Single-particle imaging (SPI) with X-ray free-electron lasers has the potential to change fundamentally how biomacromolecules are imaged. The structure would be derived from millions of diffraction patterns, each from a different copy of the macromolecule before it is torn apart by radiation damage. The challenges posed by the resultant data stream are staggering: millions of incomplete, noisy and un-oriented patterns have to be computationally assembled into a three-dimensional intensity map and then phase reconstructed. In this paper, the Dragonfly software package is described, based on a parallel implementation of the expand-maximize-compress reconstruction algorithm that is well suited for this task. Auxiliary modules to simulate SPI data streams are also included to assess the feasibility of proposed SPI experiments at the Linac Coherent Light Source, Stanford, California, USA.

Coherent diffraction of single Rice Dwarf virus particles using hard X-rays at the Linac Coherent Light Source.

Single particle diffractive imaging data from Rice Dwarf Virus (RDV) were recorded using the Coherent X-ray Imaging (CXI) instrument at the Linac Coherent Light Source (LCLS). RDV was chosen as it is a well-characterized model system, useful for proof-of-principle experiments, system optimization and algorithm development. RDV, an icosahedral virus of about 70 nm in diameter, was aerosolized and injected into the approximately 0.1 µm diameter focused hard X-ray beam at the CXI instrument of LCLS. Diffraction patterns from RDV with signal to 5.9 Ångström were recorded. The diffraction data are available through the Coherent X-ray Imaging Data Bank (CXIDB) as a resource for algorithm development, the contents of which are described here.

Protein crystal structure from non-oriented, single-axis sparse X-ray data.

X-ray free-electron lasers (XFELs) have inspired the development of serial femtosecond crystallography (SFX) as a method to solve the structure of proteins. SFX datasets are collected from a sequence of protein microcrystals injected across ultrashort X-ray pulses. The idea behind SFX is that diffraction from the intense, ultrashort X-ray pulses leaves the crystal before the crystal is obliterated by the effects of the X-ray pulse. The success of SFX at XFELs has catalyzed interest in analogous experiments at synchrotron-radiation (SR) sources, where data are collected from many small crystals and the ultrashort pulses are replaced by exposure times that are kept short enough to avoid significant crystal damage. The diffraction signal from each short exposure is so 'sparse' in recorded photons that the process of recording the crystal intensity is itself a reconstruction problem. Using the EMC algorithm, a successful reconstruction is demonstrated here in a sparsity regime where there are no Bragg peaks that conventionally would serve to determine the orientation of the crystal in each exposure. In this proof-of-principle experiment, a hen egg-white lysozyme (HEWL) crystal rotating about a single axis was illuminated by an X-ray beam from an X-ray generator to simulate the diffraction patterns of microcrystals from synchrotron radiation. Millions of these sparse frames, typically containing only ∼200 photons per frame, were recorded using a fast-framing detector. It is shown that reconstruction of three-dimensional diffraction intensity is possible using the EMC algorithm, even with these extremely sparse frames and without knowledge of the rotation angle. Further, the reconstructed intensity can be phased and refined to solve the protein structure using traditional crystallographic software. This suggests that synchrotron-based serial crystallography of micrometre-sized crystals can be practical with the aid of the EMC algorithm even in cases where the data are sparse.