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
Positron Emission Tomography (PET), Computed Tomography (CT), PET/CT and Single Photon Emission Tomography (SPECT) are non-invasive imaging tools used for creating two dimensional (2D) cross section images of three dimensional (3D) objects. PET and SPECT have the potential of providing functional or biochemical information by measuring distribution and kinetics of radiolabelled molecules, whereas CT visualizes X-ray density in tissues in the body. PET/CT provides fused images representing both functional and anatomical information with better precision in localization than PET alone.
Images generated by these types of techniques are generally noisy, thereby impairing the imaging potential and affecting the precision in quantitative values derived from the images. It is crucial to explore and understand the properties of noise in these imaging techniques. Here we used autocorrelation function (ACF) specifically to describe noise correlation and its non-isotropic behaviour in experimentally generated images of PET, CT, PET/CT and SPECT.
Experiments were performed using phantoms with different shapes. In PET and PET/CT studies, data were acquired in 2D acquisition mode and reconstructed by both analytical filter back projection (FBP) and iterative, ordered subsets expectation maximisation (OSEM) methods. In the PET/CT studies, different magnitudes of X-ray dose in the transmission were employed by using different mA settings for the X-ray tube. In the CT studies, data were acquired using different slice thickness with and without applied dose reduction function and the images were reconstructed by FBP. SPECT studies were performed in 2D, reconstructed using FBP and OSEM, using post 3D filtering. ACF images were generated from the primary images, and profiles across the ACF images were used to describe the noise correlation in different directions. The variance of noise across the images was visualised as images and with profiles across these images.
The most important finding was that the pattern of noise correlation is rotation symmetric or isotropic, independent of object shape in PET and PET/CT images reconstructed using the iterative method. This is, however, not the case in FBP images when the shape of phantom is not circular. Also CT images reconstructed using FBP show the same non-isotropic pattern independent of slice thickness and utilization of care dose function. SPECT images show an isotropic correlation of the noise independent of object shape or applied reconstruction algorithm. Noise in PET/CT images was identical independent of the applied X-ray dose in the transmission part (CT), indicating that the noise from transmission with the applied doses does not propagate into the PET images showing that the noise from the emission part is dominant. The results indicate that in human studies it is possible to utilize a low dose in transmission part while maintaining the noise behaviour and the quality of the images.
The combined effect of noise correlation for asymmetric objects and a varying noise variance across the image field significantly complicates the interpretation of the images when statistical methods are used, such as with statistical estimates of precision in average values, use of statistical parametric mapping methods and principal component analysis. Hence it is recommended that iterative reconstruction methods are used for such applications. However, it is possible to calculate the noise analytically in images reconstructed by FBP, while it is not possible to do the same calculation in images reconstructed by iterative methods. Therefore for performing statistical methods of analysis which depend on knowing the noise, FBP would be preferred.
We demonstrate that it is feasible to determine high-resolution protein structures by electron crystallography of three-dimensional crystals in an electron cryo-microscope (CryoEM). Lysozyme microcrystals were frozen on an electron microscopy grid, and electron diffraction data collected to 1.7 Å resolution. We developed a data collection protocol to collect a full-tilt series in electron diffraction to atomic resolution. A single tilt series contains up to 90 individual diffraction patterns collected from a single crystal with tilt angle increment of 0.1–1° and a total accumulated electron dose less than 10 electrons per angstrom squared. We indexed the data from three crystals and used them for structure determination of lysozyme by molecular replacement followed by crystallographic refinement to 2.9 Å resolution. This proof of principle paves the way for the implementation of a new technique, which we name ‘MicroED’, that may have wide applicability in structural biology.
X-ray crystallography has been used to work out the atomic structure of a large number of proteins. In a typical X-ray crystallography experiment, a beam of X-rays is directed at a protein crystal, which scatters some of the X-ray photons to produce a diffraction pattern. The crystal is then rotated through a small angle and another diffraction pattern is recorded. Finally, after this process has been repeated enough times, it is possible to work backwards from the diffraction patterns to figure out the structure of the protein.
The crystals used for X-ray crystallography must be large to withstand the damage caused by repeated exposure to the X-ray beam. However, some proteins do not form crystals at all, and others only form small crystals. It is possible to overcome this problem by using extremely short pulses of X-rays, but this requires a very large number of small crystals and ultrashort X-ray pulses are only available at a handful of research centers around the world. There is, therefore, a need for other approaches that can determine the structure of proteins that only form small crystals.
Electron crystallography is similar to X-ray crystallography in that a protein crystal scatters a beam to produce a diffraction pattern. However, the interactions between the electrons in the beam and the crystal are much stronger than those between the X-ray photons and the crystal. This means that meaningful amounts of data can be collected from much smaller crystals. However, it is normally only possible to collect one diffraction pattern from each crystal because of beam induced damage. Researchers have developed methods to merge the diffraction patterns produced by hundreds of small crystals, but to date these techniques have only worked with very thin two-dimensional crystals that contain only one layer of the protein of interest.
Now Shi et al. report a new approach to electron crystallography that works with very small three-dimensional crystals. Called MicroED, this technique involves placing the crystal in a transmission electron cryo-microscope, which is a fairly standard piece of equipment in many laboratories. The normal ‘low-dose’ electron beam in one of these microscopes would normally damage the crystal after a single diffraction pattern had been collected. However, Shi et al. realized that it was possible to obtain diffraction patterns without severely damaging the crystal if they dramatically reduced the normal low-dose electron beam. By reducing the electron dose by a factor of 200, it was possible to collect up to 90 diffraction patterns from the same, very small, three-dimensional crystal, and then—similar to what happens in X-ray crystallography—work backwards to figure out the structure of the protein. Shi et al. demonstrated the feasibility of the MicroED approach by using it to determine the structure of lysozyme, which is widely used as a test protein in crystallography, with a resolution of 2.9 Å. This proof-of principle study paves the way for crystallographers to study protein that cannot be studied with existing techniques.
electron crystallography; electron diffraction; electron cryomicroscopy (cryo-EM); microED; protein structure; microcrystals; None
An iterative phase retrieval algorithm, termed oversampling smoothness (OSS), has been developed to reconstruct fine features in weakly scattered objects such as biological specimens from noisy experimental data. OSS is expected to find application in the rapidly growing coherent diffraction imaging field as well as other disciplines where phase retrieval from noisy Fourier magnitudes is needed.
Coherent diffraction imaging (CDI) is high-resolution lensless microscopy that has been applied to image a wide range of specimens using synchrotron radiation, X-ray free-electron lasers, high harmonic generation, soft X-ray lasers and electrons. Despite recent rapid advances, it remains a challenge to reconstruct fine features in weakly scattering objects such as biological specimens from noisy data. Here an effective iterative algorithm, termed oversampling smoothness (OSS), for phase retrieval of noisy diffraction intensities is presented. OSS exploits the correlation information among the pixels or voxels in the region outside of a support in real space. By properly applying spatial frequency filters to the pixels or voxels outside the support at different stages of the iterative process (i.e. a smoothness constraint), OSS finds a balance between the hybrid input–output (HIO) and error reduction (ER) algorithms to search for a global minimum in solution space, while reducing the oscillations in the reconstruction. Both numerical simulations with Poisson noise and experimental data from a biological cell indicate that OSS consistently outperforms the HIO, ER–HIO and noise robust (NR)–HIO algorithms at all noise levels in terms of accuracy and consistency of the reconstructions. It is expected that OSS will find application in the rapidly growing CDI field, as well as other disciplines where phase retrieval from noisy Fourier magnitudes is needed. The MATLAB (The MathWorks Inc., Natick, MA, USA) source code of the OSS algorithm is freely available from http://www.physics.ucla.edu/research/imaging.
coherent diffraction imaging; lensless imaging; oversampling; phase retrieval; image reconstruction; X-ray free-electron lasers
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 room-temperature structure of lysozyme is determined using 40000 individual diffraction patterns from micro-crystals flowing in liquid suspension across a synchrotron microfocus beamline.
A new approach for collecting data from many hundreds of thousands of microcrystals using X-ray pulses from a free-electron laser has recently been developed. Referred to as serial crystallography, diffraction patterns are recorded at a constant rate as a suspension of protein crystals flows across the path of an X-ray beam. Events that by chance contain single-crystal diffraction patterns are retained, then indexed and merged to form a three-dimensional set of reflection intensities for structure determination. This approach relies upon several innovations: an intense X-ray beam; a fast detector system; a means to rapidly flow a suspension of crystals across the X-ray beam; and the computational infrastructure to process the large volume of data. Originally conceived for radiation-damage-free measurements with ultrafast X-ray pulses, the same methods can be employed with synchrotron radiation. As in powder diffraction, the averaging of thousands of observations per Bragg peak may improve the ratio of signal to noise of low-dose exposures. Here, it is shown that this paradigm can be implemented for room-temperature data collection using synchrotron radiation and exposure times of less than 3 ms. Using lysozyme microcrystals as a model system, over 40 000 single-crystal diffraction patterns were obtained and merged to produce a structural model that could be refined to 2.1 Å resolution. The resulting electron density is in excellent agreement with that obtained using standard X-ray data collection techniques. With further improvements the method is well suited for even shorter exposures at future and upgraded synchrotron radiation facilities that may deliver beams with 1000 times higher brightness than they currently produce.
serial crystallography; room-temperature protein crystallography; radiation damage; CrystFEL; microfocus beamline
We evaluated imaging plates (IPs) and the DITABIS Micron scanner for their use in recording images of negatively stained single-particle specimens and electron diffraction patterns of two-dimensional crystals. We first established the optimal imaging and read-out conditions for images of negatively stained single-particle specimens using the signal-to-noise ratio of the images as the evaluation criterion. We found that images were best recorded on IPs at a magnification of 67 000×, read out with a gain setting of 20 000 and a laser power setting of 30% with subsequent binning over 2 × 2 pixels. Our results show that for images of negatively stained specimens, for which the resolution is limited to ∼20 Å, IPs are a good alternative to EM film. We also compared IPs with a 2K × 2K Gatan charge-coupled device (CCD) camera for their use in recording electron diffraction patterns of sugar-embedded two-dimensional crystals. Diffraction patterns of aquaporin-0 recorded on IPs and with the CCD camera showed reflections beyond 3 Å and had similar RFriedel as well as Rmerge values. IPs can thus be used to collect diffraction patterns, but CCD cameras are more convenient and remain the best option for recording electron diffraction patterns.
imaging plates; negative staining; single-particle electron microscopy; two-dimensional crystals; electron diffraction
A demonstration is given of three-dimensional crystal intensity reconstruction from sparse data, of a nature likely to be encountered in serial microcrystallography experiments at synchrotron sources.
X-ray serial microcrystallography involves the collection and merging of frames of diffraction data from randomly oriented protein microcrystals. The number of diffracted X-rays in each frame is limited by radiation damage, and this number decreases with crystal size. The data in the frame are said to be sparse if too few X-rays are collected to determine the orientation of the microcrystal. It is commonly assumed that sparse crystal diffraction frames cannot be merged, thereby setting a lower limit to the size of microcrystals that may be merged with a given source fluence. The EMC algorithm [Loh & Elser (2009 ▶), Phys. Rev. E, 80, 026705] has previously been applied to reconstruct structures from sparse noncrystalline data of objects with unknown orientations [Philipp et al. (2012 ▶), Opt. Express, 20, 13129–13137; Ayyer et al. (2014 ▶), Opt. Express, 22, 2403–2413]. Here, it is shown that sparse data which cannot be oriented on a per-frame basis can be used effectively as crystallographic data. As a proof-of-principle, reconstruction of the three-dimensional diffraction intensity using sparse data frames from a 1.35 kDa molecule crystal is demonstrated. The results suggest that serial microcrystallography is, in principle, not limited by the fluence of the X-ray source, and collection of complete data sets should be feasible at, for instance, storage-ring X-ray sources.
X-ray serial microcrystallography; sparse data; reconstruction of diffraction intensity; EMC algorithm
X-ray free-electron lasers are being used to determine the three-dimensional structure of objects from random snapshots. The two apparently very different Bayesian algorithms capable of performing this at ultra-low signal are fundamentally the same.
The advent of X-ray free-electron lasers promises the possibility to determine the structure of individual particles such as microcrystallites, viruses and biomolecules from single-shot diffraction snapshots obtained before the particle is destroyed by the intense femtosecond pulse. This program requires the ability to determine the orientation of the particle giving rise to each snapshot at signal levels as low as ~10−2 photons per pixel. Two apparently different approaches have recently demonstrated this capability. Here we show they represent different implementations of the same fundamental approach, and identify the primary factors limiting their performance.
X-ray scattering; single-particle structure determination
A formula for absolute scattering power is derived to include spot fading arising from radiation damage and the crystal volume needed to collect diffraction data to a given resolution is calculated.
In this work, classic intensity formulae were united with an empirical spot-fading model in order to calculate the diameter of a spherical crystal that will scatter the required number of photons per spot at a desired resolution over the radiation-damage-limited lifetime. The influences of molecular weight, solvent content, Wilson B factor, X-ray wavelength and attenuation on scattering power and dose were all included. Taking the net photon count in a spot as the only source of noise, a complete data set with a signal-to-noise ratio of 2 at 2 Å resolution was predicted to be attainable from a perfect lysozyme crystal sphere 1.2 µm in diameter and two different models of photoelectron escape reduced this to 0.5 or 0.34 µm. These represent 15-fold to 700-fold less scattering power than the smallest experimentally determined crystal size to date, but the gap was shown to be consistent with the background scattering level of the relevant experiment. These results suggest that reduction of background photons and diffraction spot size on the detector are the principal paths to improving crystallographic data quality beyond current limits.
radiation damage; minimum crystal size; protein macromolecular crystallography; scattering power
A three-dimensional Bragg diffraction imaging technique, which combines rocking curve imaging with ‘pinhole’ and ‘section’ diffraction topography in the transmission case, allows three-dimensional lattice distortion in the bulk of an ice crystal under compression to be measured.
Rocking curve imaging (RCI) is a quantitative version of monochromatic beam diffraction topography that involves using a two-dimensional detector, each pixel of which records its own ‘local’ rocking curve. From these local rocking curves one can reconstruct maps of particularly relevant quantities (e.g. integrated intensity, angular position of the centre of gravity, FWHM). Up to now RCI images have been exploited in the reflection case, giving a quantitative picture of the features present in a several-micrometre-thick subsurface layer. Recently, a three-dimensional Bragg diffraction imaging technique, which combines RCI with ‘pinhole’ and ‘section’ diffraction topography in the transmission case, was implemented. It allows three-dimensional images of defects to be obtained and measurement of three-dimensional distortions within a 50 × 50 × 50 µm elementary volume inside the crystal with angular misorientations down to 10−5–10−6 rad. In the present paper, this three-dimensional-RCI (3D-RCI) technique is used to study one of the grains of a three-grained ice polycrystal. The inception of the deformation process is followed by reconstructing virtual slices in the crystal bulk. 3D-RCI capabilities allow the effective distortion in the bulk of the crystal to be investigated, and the predictions of diffraction theories to be checked, well beyond what has been possible up to now.
rocking curve imaging (RCI); 3D-RCI; ice crystals; crystal distortion; crystal defects
Dual-energy contrast-enhanced breast tomosynthesis is a promising technique to obtain three-dimensional functional information from the breast with high resolution and speed. To optimize this new method, this study searched for the beam quality that maximized image quality in terms of mass detection performance. A digital tomosynthesis system was modeled using a fast ray-tracing algorithm, which created simulated projection images by tracking photons through a voxelized anatomical breast phantom containing iodinated lesions. The single-energy images were combined into dual-energy images through a weighted log subtraction process. The weighting factor was optimized to minimize anatomical noise, while the dose distribution was chosen to minimize quantum noise. The dual-energy images were analyzed for the signal difference to noise ratio (SdNR) of iodinated masses. The fast ray-tracing explored 523,776 dual-energy combinations to identify which yields optimum mass SdNR. The ray-tracing results were verified using a Monte Carlo model for a breast tomosynthesis system with a selenium-based flat-panel detector. The projection images from our voxelized breast phantom were obtained at a constant total glandular dose. The projections were combined using weighted log subtraction and reconstructed using commercial reconstruction software. The lesion SdNR was measured in the central reconstructed slice. The SdNR performance varied markedly across the kVp and filtration space. Ray-tracing results indicated that the mass SdNR was maximized with a high-energy tungsten beam at 49 kVp with 92.5 μm of copper filtration and a low-energy tungsten beam at 49 kVp with 95 μm of tin filtration. This result was consistent with Monte Carlo findings. This mammographic technique led to a mass SdNR of 0.92 ± 0.03 in the projections and 3.68 ± 0.19 in the reconstructed slices. These values were markedly higher than those for non-optimized techniques. Our findings indicate that dual-energy breast tomosynthesis can be performed optimally at 49 kVp with alternative copper and tin filters, with reconstruction following weighted subtraction. The optimum technique provides best visibility of iodine against structured breast background in dual-energy contrast-enhanced breast tomosynthesis.
Monte Carlo; Dual-energy; Contrast Imaging; Breast Tomosynthesis; Molecular Imaging
We demonstrate the capability of one detector, the Micro-Angiographic Fluoroscope (MAF) detector, to image for two types of applications: nuclear medicine imaging and radiography. The MAF has 1024 × 1024 pixels with an effective pixel size of 35 microns and is capable of real-time imaging at 30 fps. It has a CCD camera coupled by a fiber-optic taper to a light image intensifier (LII) viewing a 300-micron thick CsI phosphor. The large variable gain of the LII provides quantum-limited operation with little additive instrumentation noise and enables operation in both energy-integrating (EI) and sensitive low-exposure single photon counting (SPC) modes. We used the EI mode to take a radiograph, and the SPC mode to image a custom phantom filled with 1 mCi of I-125. The phantom is made of hot rods with diameters ranging from 0.9 mm to 2.3 mm. A 1 mm diameter parallel hole, medium energy gamma camera collimator was placed between the phantom and the MAF and was moved multiple times at equal intervals in random directions to eliminate the grid pattern corresponding to the collimator septa. Data was acquired at 20 fps. Two algorithms to localize the events were used: 1) simple threshold and 2) a weighted centroid method. Although all the hot rods could be clearly identified, the image generated with the simple threshold method shows more blurring than that with the weighted centroid method. With the diffuse cluster of pixels from each single detection event localized to a single pixel, the weighted centroid method shows improved spatial resolution. A radiograph of the phantom was taken with the same MAF in EI mode without the collimator. It shows clear structural details of the rods. Compared to the radiograph, the sharpness of the emission image is limited by the collimator resolution and could be improved by optimized collimator design. This study demonstrated that the same MAF detector can be used in both radioisotope and x-ray imaging, combining the benefits of each.
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.
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
Laser microscopy has generally poor temporal resolution, caused by the serial scanning of each pixel. This is a significant problem for imaging or optically manipulating neural circuits, since neuronal activity is fast. To help surmount this limitation, we have developed a “scanless” microscope that does not contain mechanically moving parts. This microscope uses a diffractive spatial light modulator (SLM) to shape an incoming two-photon laser beam into any arbitrary light pattern. This allows the simultaneous imaging or photostimulation of different regions of a sample with three-dimensional precision. To demonstrate the usefulness of this microscope, we perform two-photon uncaging of glutamate to activate dendritic spines and cortical neurons in brain slices. We also use it to carry out fast (60 Hz) two-photon calcium imaging of action potentials in neuronal populations. Thus, SLM microscopy appears to be a powerful tool for imaging and optically manipulating neurons and neuronal circuits. Moreover, the use of SLMs expands the flexibility of laser microscopy, as it can substitute traditional simple fixed lenses with any calculated lens function.
spines; DOE; MNI-glutamate cortex
X-ray lasers offer new capabilities in understanding the structure of biological systems, complex materials and matter under extreme conditions1–4. Very short and extremely bright, coherent X-ray pulses can be used to outrun key damage processes and obtain a single diffraction pattern from a large macromolecule, a virus or a cell before the sample explodes and turns into plasma1. The continuous diffraction pattern of non-crystalline objects permits oversampling and direct phase retrieval2. Here we show that high-quality diffraction data can be obtained with a single X-ray pulse from a non-crystalline biological sample, a single mimivirus particle, which was injected into the pulsed beam of a hard-X-ray free-electron laser, the Linac Coherent Light Source5. Calculations indicate that the energy deposited into the virus by the pulse heated the particle to over 100,000 K after the pulse had left the sample. The reconstructed exit wavefront (image) yielded 32-nm full-period resolution in a single exposure and showed no measurable damage. The reconstruction indicates inhomogeneous arrangement of dense material inside the virion. We expect that significantly higher resolutions will be achieved in such experiments with shorter and brighter photon pulses focused to a smaller area. The resolution in such experiments can be further extended for samples available in multiple identical copies.
An ultrasensitive Medipix2 detector allowed the collection of rotation electron-diffraction data from single three-dimensional protein nanocrystals for the first time. The data could be analysed using the standard X-ray crystallography programs MOSFLM and SCALA.
When protein crystals are submicrometre-sized, X-ray radiation damage precludes conventional diffraction data collection. For crystals that are of the order of 100 nm in size, at best only single-shot diffraction patterns can be collected and rotation data collection has not been possible, irrespective of the diffraction technique used. Here, it is shown that at a very low electron dose (at most 0.1 e− Å−2), a Medipix2 quantum area detector is sufficiently sensitive to allow the collection of a 30-frame rotation series of 200 keV electron-diffraction data from a single ∼100 nm thick protein crystal. A highly parallel 200 keV electron beam (λ = 0.025 Å) allowed observation of the curvature of the Ewald sphere at low resolution, indicating a combined mosaic spread/beam divergence of at most 0.4°. This result shows that volumes of crystal with low mosaicity can be pinpointed in electron diffraction. It is also shown that strategies and data-analysis software (MOSFLM and SCALA) from X-ray protein crystallography can be used in principle for analysing electron-diffraction data from three-dimensional nanocrystals of proteins.
electron diffraction; electron microscopy; Medipix2; MOSFLM; nanocrystals
The dynamic personalities and structural heterogeneity of proteins are essential for proper functioning. Structural determination of dynamic/heterogeneous proteins is limited by conventional approaches of X-ray and electron microscopy (EM) of single-particle reconstruction that require an average from thousands to millions different molecules. Cryo-electron tomography (cryoET) is an approach to determine three-dimensional (3D) reconstruction of a single and unique biological object such as bacteria and cells, by imaging the object from a series of tilting angles. However, cconventional reconstruction methods use large-size whole-micrographs that are limited by reconstruction resolution (lower than 20 Å), especially for small and low-symmetric molecule (<400 kDa). In this study, we demonstrated the adverse effects from image distortion and the measuring tilt-errors (including tilt-axis and tilt-angle errors) both play a major role in limiting the reconstruction resolution. Therefore, we developed a “focused electron tomography reconstruction” (FETR) algorithm to improve the resolution by decreasing the reconstructing image size so that it contains only a single-instance protein. FETR can tolerate certain levels of image-distortion and measuring tilt-errors, and can also precisely determine the translational parameters via an iterative refinement process that contains a series of automatically generated dynamic filters and masks. To describe this method, a set of simulated cryoET images was employed; to validate this approach, the real experimental images from negative-staining and cryoET were used. Since this approach can obtain the structure of a single-instance molecule/particle, we named it individual-particle electron tomography (IPET) as a new robust strategy/approach that does not require a pre-given initial model, class averaging of multiple molecules or an extended ordered lattice, but can tolerate small tilt-errors for high-resolution single “snapshot” molecule structure determination. Thus, FETR/IPET provides a completely new opportunity for a single-molecule structure determination, and could be used to study the dynamic character and equilibrium fluctuation of macromolecules.
The advantages of a novel wide dynamic range hard X-ray detector are demonstrated for (ptychographic) coherent X-ray diffractive imaging.
Coherent (X-ray) diffractive imaging (CDI) is an increasingly popular form of X-ray microscopy, mainly due to its potential to produce high-resolution images and the lack of an objective lens between the sample and its corresponding imaging detector. One challenge, however, is that very high dynamic range diffraction data must be collected to produce both quantitative and high-resolution images. In this work, hard X-ray ptychographic coherent diffractive imaging has been performed at the P10 beamline of the PETRA III synchrotron to demonstrate the potential of a very wide dynamic range imaging X-ray detector (the Mixed-Mode Pixel Array Detector, or MM-PAD). The detector is capable of single photon detection, detecting fluxes exceeding 1 × 108 8-keV photons pixel−1 s−1, and framing at 1 kHz. A ptychographic reconstruction was performed using a peak focal intensity on the order of 1 × 1010 photons µm−2 s−1 within an area of approximately 325 nm × 603 nm. This was done without need of a beam stop and with a very modest attenuation, while ‘still’ images of the empty beam far-field intensity were recorded without any attenuation. The treatment of the detector frames and CDI methodology for reconstruction of non-sensitive detector regions, partially also extending the active detector area, are described.
pixel array detectors; coherent X-ray diffractive imaging; ptychography
A complex three-dimensional quantitative image of an extended zinc oxide crystal has been obtained using Bragg coherent diffraction imaging integrated with ptychography.
A complex three-dimensional quantitative image of an extended zinc oxide (ZnO) crystal has been obtained using Bragg coherent diffraction imaging integrated with ptychography. By scanning a 2.5 µm-long arm of a ZnO tetrapod across a 1.3 µm X-ray beam with fine step sizes while measuring a three-dimensional diffraction pattern at each scan spot, the three-dimensional electron density and projected displacement field of the entire crystal were recovered. The simultaneously reconstructed complex wavefront of the illumination combined with its coherence properties determined by a partial coherence analysis implemented in the reconstruction process provide a comprehensive characterization of the incident X-ray beam.
three-dimensional quantitative imaging; coherent diffraction imaging; ptychography; zinc oxide
Single-structure models derived from X-ray data do not adequately account for the inherent, functionally important dynamics of protein molecules. We generated ensembles of structures by time-averaged refinement, where local molecular vibrations were sampled by molecular-dynamics (MD) simulation whilst global disorder was partitioned into an underlying overall translation–libration–screw (TLS) model. Modeling of 20 protein datasets at 1.1–3.1 Å resolution reduced cross-validated Rfree values by 0.3–4.9%, indicating that ensemble models fit the X-ray data better than single structures. The ensembles revealed that, while most proteins display a well-ordered core, some proteins exhibit a ‘molten core’ likely supporting functionally important dynamics in ligand binding, enzyme activity and protomer assembly. Order–disorder changes in HIV protease indicate a mechanism of entropy compensation for ordering the catalytic residues upon ligand binding by disordering specific core residues. Thus, ensemble refinement extracts dynamical details from the X-ray data that allow a more comprehensive understanding of structure–dynamics–function relationships.
It has been clear since the early days of structural biology in the late 1950s that proteins and other biomolecules are continually changing shape, and that these changes have an important influence on both the structure and function of the molecules. X-ray diffraction can provide detailed information about the structure of a protein, but only limited information about how its structure fluctuates over time. Detailed information about the dynamic behaviour of proteins is essential for a proper understanding of a variety of processes, including catalysis, ligand binding and protein–protein interactions, and could also prove useful in drug design.
Currently most of the X-ray crystal structures in the Protein Data Bank are ‘snap-shots’ with limited or no information about protein dynamics. However, X-ray diffraction patterns are affected by the dynamics of the protein, and also by distortions of the crystal lattice, so three-dimensional (3D) models of proteins ought to take these phenomena into account. Molecular-dynamics (MD) computer simulations transform 3D structures into 4D ‘molecular movies’ by predicting the movement of individual atoms.
Combining MD simulations with crystallographic data has the potential to produce more realistic ensemble models of proteins in which the atomic fluctuations are represented by multiple structures within the ensemble. Moreover, in addition to improved structural information, this process—which is called ensemble refinement—can provide dynamical information about the protein. Earlier attempts to do this ran into problems because the number of model parameters needed was greater than the number of observed data points. Burnley et al. now overcome this problem by modelling local molecular vibrations with MD simulations and, at the same time, using a course-grain model to describe global disorder of longer length scales.
Ensemble refinement of high-resolution X-ray diffraction datasets for 20 different proteins from the Protein Data Bank produced a better fit to the data than single structures for all 20 proteins. Ensemble refinement also revealed that 3 of the 20 proteins had a ‘molten core’, rather than the well-ordered residues core found in most proteins: this is likely to be important in various biological functions including ligand binding, filament formation and enzymatic function. Burnley et al. also showed that a HIV enzyme underwent an order–disorder transition that is likely to influence how this enzyme works, and that similar transitions might influence the interactions between the small-molecule drug Imatinib (also known as Gleevec) and the enzymes it targets. Ensemble refinement could be applied to the majority of crystallography data currently being collected, or collected in the past, so further insights into the properties and interactions of a variety of proteins and other biomolecules can be expected.
protein; crystallography; structure; function; dynamics; None
Models for the spatial distribution of protein, lipid and water in gap junction structures have been constructed from the results of the analysis of X-ray diffraction data described here and the electron microscope and chemical data presented in the preceding paper (Caspar, D. L. D., D. A. Goodenough, L. Makowski, and W.C. Phillips. 1977. 74:605-628). The continuous intensity distribution on the meridian of the X-ray diffraction pattern was measured, and corrected for the effects of the partially ordered stacking and partial orientation of the junctions in the X-ray specimens. The electron density distribution in the direction perpendicular to the plane of the junction was calculated from the meridional intensity data. Determination of the interference function for the stacking of the junctions improved the accuracy of the electron density profile. The pair-correlation function, which provides information about the packing of junctions in the specimen, was calculated from the interference function. The intensities of the hexagonal lattice reflections on the equator of the X-ray pattern were used in coordination with the electron microscope data to calculate to the two-dimensional electron density projection onto the plane of the membrane. Differences in the structure of the connexons as seen in the meridional profile and equatorial projections were shown to be correlated to changes in lattice constant. The parts of the junction structure which are variable have been distinguished from the invariant parts by comparison of the X-ray data from different specimens. The combination of these results with electron microscope and chemical data provides low resolution three- dimensional representations of the structures of gap junctions.
An expectation maximization algorithm is implemented to resolve the indexing ambiguity which arises when merging data from many crystals in protein crystallography, especially in cases where partial reflections are recorded in serial femtosecond crystallography (SFX) at XFELs.
Crystallographic auto-indexing algorithms provide crystal orientations and unit-cell parameters and assign Miller indices based on the geometric relations between the Bragg peaks observed in diffraction patterns. However, if the Bravais symmetry is higher than the space-group symmetry, there will be multiple indexing options that are geometrically equivalent, and hence many ways to merge diffraction intensities from protein nanocrystals. Structure factor magnitudes from full reflections are required to resolve this ambiguity but only partial reflections are available from each XFEL shot, which must be merged to obtain full reflections from these ‘stills’. To resolve this chicken-and-egg problem, an expectation maximization algorithm is described that iteratively constructs a model from the intensities recorded in the diffraction patterns as the indexing ambiguity is being resolved. The reconstructed model is then used to guide the resolution of the indexing ambiguity as feedback for the next iteration. Using both simulated and experimental data collected at an X-ray laser for photosystem I in the P63 space group (which supports a merohedral twinning indexing ambiguity), the method is validated.
indexing ambiguity; serial femtosecond crystallography (SFX); XFELs; protein crystallography; expectation maximization algorithm
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