The advent of the X-ray free-electron laser (XFEL) has made it possible to record diffraction snapshots of biological entities injected into the X-ray beam before the onset of radiation damage. Algorithmic means must then be used to determine the snapshot orientations and thence the three-dimensional structure of the object. Existing Bayesian approaches are limited in reconstruction resolution typically to 1/10 of the object diameter, with the computational expense increasing as the eighth power of the ratio of diameter to resolution. We present an approach capable of exploiting object symmetries to recover three-dimensional structure to high resolution, and thus reconstruct the structure of the satellite tobacco necrosis virus to atomic level. Our approach offers the highest reconstruction resolution for XFEL snapshots to date and provides a potentially powerful alternative route for analysis of data from crystalline and nano-crystalline objects.
macromolecular assemblies; symmetry; X-ray lasers; manifold embedding; dimensionality reduction
We have mimicked the 4%-energy-bandpass mode of the SwissFEL beam at a synchrotron facility, collected snapshots of randomly oriented multi-crystal samples, and developed a methodology to index and process such non-monochromatic data for materials science applications.
New opportunities for studying (sub)microcrystalline materials with small unit cells, both organic and inorganic, will open up when the X-ray free electron laser (XFEL) presently being constructed in Switzerland (SwissFEL) comes online in 2017. Our synchrotron-based experiments mimicking the 4%-energy-bandpass mode of the SwissFEL beam show that it will be possible to record a diffraction pattern of up to 10 randomly oriented crystals in a single snapshot, to index the resulting reflections, and to extract their intensities reliably. The crystals are destroyed with each XFEL pulse, but by combining snapshots from several sets of crystals, a complete set of data can be assembled, and crystal structures of materials that are difficult to analyze otherwise will become accessible. Even with a single shot, at least a partial analysis of the crystal structure will be possible, and with 10–50 femtosecond pulses, this offers tantalizing possibilities for time-resolved studies.
serial snapshot crystallography; multi-microcrystal diffraction; indexing; broad-bandpass beam; XFEL
X-ray diffraction patterns may be obtained from individual submicron protein nanocrystals using a femtosecond pulse from a free-electron X-ray laser. Many “single-shot” patterns are read out every second from a stream of nanocrystals lying in random orientations. The short pulse terminates before significant atomic (or electronic) motion commences, minimizing radiation damage. Simulated patterns for Photosystem I nanocrystals are used to develop a method for recovering structure factors from tens of thousands of snapshot patterns from nanocrystals varying in size, shape and orientation. We determine the number of shots needed for a required accuracy in structure factor measurement and resolution, and investigate the convergence of our Monte-Carlo integration method.
Emerging X-ray free-electron lasers with femtosecond pulse duration enable single-shot snapshot imaging almost free from sample damage by outrunning major radiation damage processes. In bioimaging, it is essential to keep the sample close to its natural state. Conventional high-resolution imaging, however, suffers from severe radiation damage that hinders live cell imaging. Here we present a method for capturing snapshots of live cells kept in a micro-liquid enclosure array by X-ray laser diffraction. We place living Microbacterium lacticum cells in an enclosure array and successively expose each enclosure to a single X-ray laser pulse from the SPring-8 Angstrom Compact Free-Electron Laser. The enclosure itself works as a guard slit and allows us to record a coherent diffraction pattern from a weakly-scattering submicrometre-sized cell with a clear fringe extending up to a 28-nm full-period resolution. The reconstructed image reveals living whole-cell structures without any staining, which helps advance understanding of intracellular phenomena.
Live cell imaging at high resolution is very challenging because cells die upon prolonged radiation exposure. Kimura et al. overcome this problem by using pulsed coherent X-ray diffraction to image live microbacterium in a nanofabricated liquid enclosure at resolution far exceeding optical methods.
A complete set of structure factors has been extracted from hundreds of thousands of femtosecond X-ray diffraction patterns from randomly oriented Photosystem I membrane protein nanocrystals, using the Monte Carlo method of intensity integration. The data, collected at the Linac Coherent Light Source, are compared with conventional single-crystal data collected at a synchrotron source, and the quality of each data set was found to be similar.
A complete set of structure factors has been extracted from hundreds of thousands of femtosecond single-shot X-ray microdiffraction patterns taken from randomly oriented nanocrystals. The method of Monte Carlo integration over crystallite size and orientation was applied to experimental data from Photosystem I nanocrystals. This arrives at structure factors from many partial reflections without prior knowledge of the particle-size distribution. The data were collected at the Linac Coherent Light Source (the first hard-X-ray laser user facility), to which was fitted a hydrated protein nanocrystal injector jet, according to the method of serial crystallography. The data are single ‘still’ diffraction snapshots, each from a different nanocrystal with sizes ranging between 100 nm and 2 µm, so the angular width of Bragg peaks was dominated by crystal-size effects. These results were compared with single-crystal data recorded from large crystals of Photosystem I at the Advanced Light Source and the quality of the data was found to be similar. The implications for improving the efficiency of data collection by allowing the use of very small crystals, for radiation-damage reduction and for time-resolved diffraction studies at room temperature are discussed.
nanocrystals; femtosecond diffraction; free-electron lasers; Monte Carlo methods; protein microdiffraction
Bragg diffraction achieved from two-dimensional protein crystals using femtosecond X-ray laser snapshots is presented.
X-ray diffraction patterns from two-dimensional (2-D) protein crystals obtained using femtosecond X-ray pulses from an X-ray free-electron laser (XFEL) are presented. To date, it has not been possible to acquire transmission X-ray diffraction patterns from individual 2-D protein crystals due to radiation damage. However, the intense and ultrafast pulses generated by an XFEL permit a new method of collecting diffraction data before the sample is destroyed. Utilizing a diffract-before-destroy approach at the Linac Coherent Light Source, Bragg diffraction was acquired to better than 8.5 Å resolution for two different 2-D protein crystal samples each less than 10 nm thick and maintained at room temperature. These proof-of-principle results show promise for structural analysis of both soluble and membrane proteins arranged as 2-D crystals without requiring cryogenic conditions or the formation of three-dimensional crystals.
two-dimensional protein crystal; femtosecond crystallography; single layer X-ray diffraction; membrane protein
The diversity of nanoparticle shapes generated by condensation from gaseous matter reflects the fundamental competition between thermodynamic equilibration and the persistence of metastable configurations during growth. In the kinetically limited regime, intermediate geometries that are favoured only in early formation stages can be imprinted in the finally observed ensemble of differently structured specimens. Here we demonstrate that single-shot wide-angle scattering of femtosecond soft X-ray free-electron laser pulses allows three-dimensional characterization of the resulting metastable nanoparticle structures. For individual free silver particles, which can be considered frozen in space for the duration of photon exposure, both shape and orientation are uncovered from measured scattering images. We identify regular shapes, including species with fivefold symmetry and surprisingly large aspect ratio up to particle radii of the order of 100 nm. Our approach includes scattering effects beyond Born’s approximation and is remarkably efficient—opening up new routes in ultrafast nanophysics and free-electron laser science.
The occurrence of thermodynamically metastable nanoparticles determines the particle growth in nature, but capturing them is experimentally challenging. Barke et al. identify the three-dimensional shape of metastable silver nanoparticles in gas phase, characterized by X-ray free-electron laser.
The software suite SITENNO is developed for processing diffraction data collected in coherent X-ray diffraction imaging experiments of non-crystalline particles using an X-ray free-electron laser.
Coherent X-ray diffraction imaging is a promising technique for visualizing the structures of non-crystalline particles with dimensions of micrometers to sub-micrometers. Recently, X-ray free-electron laser sources have enabled efficient experiments in the ‘diffraction before destruction’ scheme. Diffraction experiments have been conducted at SPring-8 Angstrom Compact free-electron LAser (SACLA) using the custom-made diffraction apparatus KOTOBUKI-1 and two multiport CCD detectors. In the experiments, ten thousands of single-shot diffraction patterns can be collected within several hours. Then, diffraction patterns with significant levels of intensity suitable for structural analysis must be found, direct-beam positions in diffraction patterns determined, diffraction patterns from the two CCD detectors merged, and phase-retrieval calculations for structural analyses performed. A software suite named SITENNO has been developed to semi-automatically apply the four-step processing to a huge number of diffraction data. Here, details of the algorithm used in the suite are described and the performance for approximately 9000 diffraction patterns collected from cuboid-shaped copper oxide particles reported. Using the SITENNO suite, it is possible to conduct experiments with data processing immediately after the data collection, and to characterize the size distribution and internal structures of the non-crystalline particles.
coherent X-ray diffraction imaging; X-ray free-electron laser; structure analysis of non-crystalline particles
The advent of hard X-ray free-electron lasers has opened a new chapter in macromolecular crystallography. Recent results, developments and prospects of serial femtosecond crystallography are described.
Protein crystallography using synchrotron radiation sources has had a tremendous impact on biology, having yielded the structures of thousands of proteins and given detailed insight into their mechanisms. However, the technique is limited by the requirement for macroscopic crystals, which can be difficult to obtain, as well as by the often severe radiation damage caused in diffraction experiments, in particular when using tiny crystals. To slow radiation damage, data collection is typically performed at cryogenic temperatures. With the advent of free-electron lasers (FELs) capable of delivering extremely intense femtosecond X-ray pulses, this situation appears to be remedied, allowing the structure determination of undamaged macromolecules using either macroscopic or microscopic crystals. The latter are exposed to the FEL beam in random orientations and their diffraction data are collected at cryogenic or room temperature in a serial fashion, since each crystal is destroyed upon a single exposure. The new approaches required for crystal growth and delivery, and for diffraction data analysis, including de novo phasing, are reviewed. The opportunities and challenges of SFX are described, including applications such as time-resolved measurements and the analysis of radiation damage-prone systems.
serial femtosecond crystallography; SFX; X-ray lasers; FELs; time-resolved crystallography; microcrystals; radiation damage
X-ray free-electron laser crystallography relies on the collection of still-shot diffraction patterns. New methods are developed for optimal modeling of the crystals’ orientations and mosaic block properties.
X-ray diffraction patterns from still crystals are inherently difficult to process because the crystal orientation is not uniquely determined by measuring the Bragg spot positions. Only one of the three rotational degrees of freedom is directly coupled to spot positions; the other two rotations move Bragg spots in and out of the reflecting condition but do not change the direction of the diffracted rays. This hinders the ability to recover accurate structure factors from experiments that are dependent on single-shot exposures, such as femtosecond diffract-and-destroy protocols at X-ray free-electron lasers (XFELs). Here, additional methods are introduced to optimally model the diffraction. The best orientation is obtained by requiring, for the brightest observed spots, that each reciprocal-lattice point be placed into the exact reflecting condition implied by Bragg’s law with a minimal rotation. This approach reduces the experimental uncertainties in noisy XFEL data, improving the crystallographic R factors and sharpening anomalous differences that are near the level of the noise.
X-ray free-electron lasers; single-shot exposures
An updated partiality model and post-refinement algorithm for XFEL snapshot diffraction data is presented and confirmed by observing anomalous density for S atoms at an X-ray wavelength of 1.3 Å.
Research towards using X-ray free-electron laser (XFEL) data to solve structures using experimental phasing methods such as sulfur single-wavelength anomalous dispersion (SAD) has been hampered by shortcomings in the diffraction models for X-ray diffraction from FELs. Owing to errors in the orientation matrix and overly simple partiality models, researchers have required large numbers of images to converge to reliable estimates for the structure-factor amplitudes, which may not be feasible for all biological systems. Here, data for cytoplasmic polyhedrosis virus type 17 (CPV17) collected at 1.3 Å wavelength at the Linac Coherent Light Source (LCLS) are revisited. A previously published definition of a partiality model for reflections illuminated by self-amplified spontaneous emission (SASE) pulses is built upon, which defines a fraction between 0 and 1 based on the intersection of a reflection with a spread of Ewald spheres modelled by a super-Gaussian wavelength distribution in the X-ray beam. A method of post-refinement to refine the parameters of this model is suggested. This has generated a merged data set with an overall discrepancy (by calculating the R
split value) of 3.15% to 1.46 Å resolution from a 7225-image data set. The atomic numbers of C, N and O atoms in the structure are distinguishable in the electron-density map. There are 13 S atoms within the 237 residues of CPV17, excluding the initial disordered methionine. These only possess 0.42 anomalous scattering electrons each at 1.3 Å wavelength, but the 12 that have single predominant positions are easily detectable in the anomalous difference Fourier map. It is hoped that these improvements will lead towards XFEL experimental phase determination and structure determination by sulfur SAD and will generally increase the utility of the method for difficult cases.
post-refinement; free-electron laser; partiality
X-ray crystallography provides the vast majority of macromolecular structures, but the success of the method relies on growing crystals of sufficient size. In conventional measurements, the necessary increase in X-ray dose to record data from crystals that are too small leads to extensive damage before a diffraction signal can be recorded1-3. It is particularly challenging to obtain large, well-diffracting crystals of membrane proteins, for which fewer than 300 unique structures have been determined despite their importance in all living cells. Here we present a method for structure determination where single-crystal X-ray diffraction ‘snapshots’ are collected from a fully hydrated stream of nanocrystals using femtosecond pulses from a hard-X-ray free-electron laser, the Linac Coherent Light Source4. We prove this concept with nanocrystals of photosystem I, one of the largest membrane protein complexes5. More than 3,000,000 diffraction patterns were collected in this study, and a three-dimensional data set was assembled from individual photosystem I nanocrystals (~200 nm to 2 μm in size). We mitigate the problem of radiation damage in crystallography by using pulses briefer than the timescale of most damage processes6. This offers a new approach to structure determination of macromolecules that do not yield crystals of sufficient size for studies using conventional radiation sources or are particularly sensitive to radiation damage.
We describe a new generation of algorithms capable of mapping the structure and conformations of macromolecules and their complexes from large ensembles of heterogeneous snapshots, and demonstrate the feasibility of determining both discrete and continuous macromolecular conformational spectra. These algorithms naturally incorporate conformational heterogeneity without resort to sorting and classification, or prior knowledge of the type of heterogeneity present. They are applicable to single-particle diffraction and image datasets produced by X-ray lasers and cryo-electron microscopy, respectively, and particularly suitable for systems not easily amenable to purification or crystallization.
macromolecular structure; macromolecular conformations; X-ray lasers; cryo-electron microscopy; manifold embedding; dimensionality reduction
A serial femtosecond crystallography based method has been proposed, which enables simultaneous X-ray phase identification and structure solution for multiphase polycrystalline samples. Test results from simulating calculations are encouraging.
Serial femtosecond crystallography (SFX) is capable of collecting three-dimensional single-crystal diffraction data using polycrystalline samples. This may dramatically enhance the power of X-ray powder diffraction. In this paper a test has been performed using simulated diffraction patterns. The test sample is a mixture of two zeolites with crystal grain sizes from 100 to 300 nm. X-ray diffraction snapshots by SFX were simulated and processed using the program suite CrystFEL. Identification according to the primitive unit-cell volume determined from individual snapshots was able to separate the whole set of snapshots into two subsets, which correspond to the two zeolites in the sample. Monte Carlo integration in CrystFEL was then applied to them separately. This led to two sets of three-dimensional single-crystal diffraction intensities, based on which crystal structures of the two zeolites were solved easily by direct methods implemented in the program SHELXD.
serial crystallography; X-ray powder diffraction; phase identification; structure solution
The invention of Free Electron X-ray Lasers has opened a new era for membrane protein structure determination with the recent first proof-of-principle of the new concept of femtosecond nanocrystallography. Structure determination is based on thousands of diffraction snapshots that are collected on a fully hydrated stream of nanocrystals. This review provides a summary of the method and describes how femtosecond X-ray crystallography overcomes the radiation damage problem in X-ray crystallography, avoids the need for growth and freezing of large single crystals while offering a new method for direct digital phase determination by making use of the fully coherent nature of the X-ray beam. We briefly review the possibilities for time-resolved crystallography, and the potential for making “molecular movies” of membrane proteins at work.
Schemes for X-ray imaging single protein molecules using new x-ray sources, like x-ray free electron lasers (XFELs), require processing many frames of data that are obtained by taking temporally short snapshots of identical molecules, each with a random and unknown orientation. Due to the small size of the molecules and short exposure times, average signal levels of much less than 1 photon/pixel/frame are expected, much too low to be processed using standard methods. One approach to process the data is to use statistical methods developed in the EMC algorithm (Loh & Elser, Phys. Rev. E, 2009) which processes the data set as a whole. In this paper we apply this method to a real-space tomographic reconstruction using sparse frames of data (below 10−2 photons/pixel/frame) obtained by performing x-ray transmission measurements of a low-contrast, randomly-oriented object. This extends the work by Philipp et al. (Optics Express, 2012) to three dimensions and is one step closer to the single molecule reconstruction problem.
(000.2190) Experimental physics; (040.7480) X-rays, soft x-rays, extreme ultraviolet (EUV); (100.6950) Tomographic image processing; (110.4155) Multiframe image processing; (110.4280) Noise in imaging systems; (110.6955) Tomographic imaging; (110.7440) X-ray imaging; (340.7440) X-ray imaging
Membrane proteins are very important for all living cells, being involved in respiration, photosynthesis, cellular uptake and signal transduction, amongst other vital functions. However, less than 300 unique membrane protein structures have been determined to date, often due to difficulties associated with the growth of sufficiently large and well-ordered crystals. This work has been focused on showing the first proof of concept for using membrane protein nanocrystals and microcrystals for high-resolution structure determination. Upon determining that crystals of the membrane protein Photosystem I, which is the largest and most complex membrane protein crystallized to date, exist with only a hundred unit cells with sizes of less than 200 nm on an edge, work was done to develop a technique that could exploit the growth of the Photosystem I nanocrystals and microcrystals. Femtosecond X-ray protein nanocrystallography was developed for use at the first high-energy X-ray free electron laser, the LCLS at SLAC National Accelerator Laboratory, in which a liquid jet brought fully-hydrated Photosystem I nanocrystals into the interaction region of the pulsed X-ray source. Diffraction patterns were recorded from millions of individual PSI nanocrystals and data from thousands of different, randomly oriented crystallites were integrated using Monte Carlo integration of the peak intensities. The short pulses (~ 70 fs) provided by the LCLS allowed the possibility to collect the diffraction data before the onset of radiation damage, exploiting the diffract-before-destroy principle. During the initial experiments at the AMO beamline using 6.9-Å wavelength, Bragg peaks were recorded to 8.5-Å resolution, and an electron-density map was determined that did not show any effects of X-ray-induced radiation damage [Chapman H.N., et al. Femtosecond X-ray protein nanocrystallography, Nature 470 (2011) 73–81]. Many additional techniques still need to be developed to explore the femtosecond nanocrystallography technique for experimental phasing and time-resolved X-ray crystallography experiments. The first proof-of-principle results for the femtosecond nanocrystallography technique indicate the incredible potential of the technique to offer a new route to the structure determination of membrane proteins.
membrane proteins; structure determination; femtosecond nanocrystallography; protein nanocrystals; X-ray crystallography; XFEL
Viscous sample delivery that decreases the net protein consumed in serial femtosecond crystallography is described. The agarose stream has a low background, is compatible with membrane proteins and can be used at a wide range of temperatures.
Serial femtosecond crystallography (SFX) has opened a new era in crystallography by permitting nearly damage-free, room-temperature structure determination of challenging proteins such as membrane proteins. In SFX, femtosecond X-ray free-electron laser pulses produce diffraction snapshots from nanocrystals and microcrystals delivered in a liquid jet, which leads to high protein consumption. A slow-moving stream of agarose has been developed as a new crystal delivery medium for SFX. It has low background scattering, is compatible with both soluble and membrane proteins, and can deliver the protein crystals at a wide range of temperatures down to 4°C. Using this crystal-laden agarose stream, the structure of a multi-subunit complex, phycocyanin, was solved to 2.5 Å resolution using 300 µg of microcrystals embedded into the agarose medium post-crystallization. The agarose delivery method reduces protein consumption by at least 100-fold and has the potential to be used for a diverse population of proteins, including membrane protein complexes.
serial femtosecond crystallography; viscous crystal delivery; protein complexes; membrane proteins; femtosecond studies; nanocrystals; coherent X-ray diffractive imaging; free-electron laser
X-ray free-electron lasers (X-FELs) produce X-ray pulses with extremely brilliant peak intensity and ultrashort pulse duration. It has been proposed that radiation damage can be “outrun” by using an ultra intense and short X-FEL pulse that passes a biological sample before the onset of significant radiation damage. The concept of “diffraction-before-destruction” has been demonstrated recently at the Linac Coherent Light Source, the first operational hard X-ray FEL, for protein nanocrystals and giant virus particles. The continuous diffraction patterns from single particles allow solving the classical “phase problem” by the oversampling method with iterative algorithms. If enough data are collected from many identical copies of a (biological) particle, its three-dimensional structure can be reconstructed. We review the current status and future prospects of serial femtosecond crystallography (SFX) and single-particle coherent diffraction imaging (CDI) with X-FELs.
Single-particle imaging experiments of biomolecules at x-ray free-electron lasers (XFELs) require processing hundreds of thousands of images that contain very few x-rays. Each low-fluence image of the diffraction pattern is produced by a single, randomly oriented particle, such as a protein. We demonstrate the feasibility of recovering structural information at these extremes using low-fluence images of a randomly oriented 2D x-ray mask. Successful reconstruction is obtained with images averaging only 2.5 photons per frame, where it seems doubtful there could be information about the state of rotation, let alone the image contrast. This is accomplished with an expectation maximization algorithm that processes the low-fluence data in aggregate, and without any prior knowledge of the object or its orientation. The versatility of the method promises, more generally, to redefine what measurement scenarios can provide useful signal.
(040.7480) X-rays, soft x-rays, extreme ultraviolet (EUV); (110.7440) X-ray imaging; (000.2190) Experimental physics; (110.3055) Information theoretical analysis; (110.4155) Multiframe image processing; (040.0040) Detectors
A new method for the treatment of partial reflections from X-ray snapshots is implemented in the program package nXDS, which yields intensity data of almost the same quality as those obtained by the classical rotation method.
A functional expression is introduced that relates scattered X-ray intensities from a still or a rotation snapshot to the corresponding structure-factor amplitudes. The new approach was implemented in the program nXDS for processing monochromatic diffraction images recorded by a multi-segment detector where each exposure could come from a different crystal. For images containing indexable spots, the intensities of the expected reflections and their variances are obtained by profile fitting after mapping the contributing pixel contents to the Ewald sphere. The varying intensity decline owing to the angular distance of the reflection from the surface of the Ewald sphere is estimated using a Gaussian rocking curve. This decline is dubbed ‘Ewald offset correction’, which is well defined even for still images. Together with an image-scaling factor and other corrections, an explicit expression is defined that predicts each recorded intensity from its corresponding structure-factor amplitude. All diffraction parameters, scaling and correction factors are improved by post-refinement. The ambiguous case of a lower point group than the lattice symmetry is resolved by a method reminiscent of the technique of ‘selective breeding’. It selects the indexing alternative for each image that yields, on average, the highest correlation with intensities from all other images. Processing a test set of rotation images by XDS and treating the same images by nXDS as snapshots of crystals in random orientations yields data of comparable quality, clearly indicating an anomalous signal from Se atoms.
We demonstrate the use of an X-ray free electron laser synchronized with an optical pump laser to obtain X-ray diffraction snapshots from the photoactivated states of large membrane protein complexes in the form of nanocrystals flowing in a liquid jet. Light-induced changes of Photosystem I-Ferredoxin co-crystals were observed at time delays of 5 to 10 μs after excitation. The result correlates with the microsecond kinetics of electron transfer from Photosystem I to ferredoxin. The undocking process that follows the electron transfer leads to large rearrangements in the crystals that will terminally lead to the disintegration of the crystals. We describe the experimental setup and obtain the first time-resolved femtosecond serial X-ray crystallography results from an irreversible photo-chemical reaction at the Linac Coherent Light Source. This technique opens the door to time-resolved structural studies of reaction dynamics in biological systems.
We demonstrate the use of an X-ray free electron laser synchronized with an optical pump laser to obtain X-ray diffraction snapshots from the photoactivated states of large membrane protein complexes in the form of nanocrystals flowing in a liquid jet. Light-induced changes of Photosystem I-Ferredoxin co-crystals were observed at time delays of 5 to 10 µs after excitation. The result correlates with the microsecond kinetics of electron transfer from Photosystem I to ferredoxin. The undocking process that follows the electron transfer leads to large rearrangements in the crystals that will terminally lead to the disintegration of the crystals. We describe the experimental setup and obtain the first time-resolved femtosecond serial X-ray crystallography results from an irreversible photo-chemical reaction at the Linac Coherent Light Source. This technique opens the door to time-resolved structural studies of reaction dynamics in biological systems.
(170.7160) Ultrafast technology; (170.7440) X-ray imaging; (140.3450) Laser-induced chemistry; (140.7090) Ultrafast lasers; (170.0170) Medical optics and biotechnology
A new algorithm is developed for reconstructing the high-resolution three-dimensional diffraction intensity function of a globular biological macromolecule from many quantum-noise-limited two-dimensional X-ray laser diffraction patterns, each for an unknown orientation. The structural resolution is expressed as a function of the incident X-ray intensity and quantities characterizing the target molecule.
A new two-step algorithm is developed for reconstructing the three-dimensional diffraction intensity of a globular biological macromolecule from many experimentally measured quantum-noise-limited two-dimensional X-ray laser diffraction patterns, each for an unknown orientation. The first step is classification of the two-dimensional patterns into groups according to the similarity of direction of the incident X-rays with respect to the molecule and an averaging within each group to reduce the noise. The second step is detection of common intersecting circles between the signal-enhanced two-dimensional patterns to identify their mutual location in the three-dimensional wavenumber space. The newly developed algorithm enables one to detect a signal for classification in noisy experimental photon-count data with as low as ∼0.1 photons per effective pixel. The wavenumber of such a limiting pixel determines the attainable structural resolution. From this fact, the resolution limit due to the quantum noise attainable by this new method of analysis as well as two important experimental parameters, the number of two-dimensional patterns to be measured (the load for the detector) and the number of pairs of two-dimensional patterns to be analysed (the load for the computer), are derived as a function of the incident X-ray intensity and quantities characterizing the target molecule.
biological macromolecules; classification of two-dimensional diffraction patterns; common intersecting circles; attainable structural resolution
A code with an algorithm for high-speed classification of X-ray diffraction patterns has been developed. Results obtained for a set of 1 × 106 simulated diffraction patterns are also reported.
Single-particle coherent X-ray diffraction imaging using an X-ray free-electron laser has the potential to reveal the three-dimensional structure of a biological supra-molecule at sub-nanometer resolution. In order to realise this method, it is necessary to analyze as many as 1 × 106 noisy X-ray diffraction patterns, each for an unknown random target orientation. To cope with the severe quantum noise, patterns need to be classified according to their similarities and average similar patterns to improve the signal-to-noise ratio. A high-speed scalable scheme has been developed to carry out classification on the K computer, a 10PFLOPS supercomputer at RIKEN Advanced Institute for Computational Science. It is designed to work on the real-time basis with the experimental diffraction pattern collection at the X-ray free-electron laser facility SACLA so that the result of classification can be feedback for optimizing experimental parameters during the experiment. The present status of our effort developing the system and also a result of application to a set of simulated diffraction patterns is reported. About 1 × 106 diffraction patterns were successfully classificatied by running 255 separate 1 h jobs in 385-node mode.
X-ray free-electron laser; K computer; single-particle coherent diffraction imaging; classification of diffraction patterns; big-data analysis