Protocol using similarity score and improved shrink-wrap algorithm for better convergence of phase-retrieval calculation in X-ray diffraction imaging.

In X-ray diffraction imaging (XDI), electron density maps of a targeted particle are reconstructed computationally from the diffraction pattern alone using phase-retrieval (PR) algorithms. However, the PR calculations sometimes fail to yield realistic electron density maps that approximate the structure of the particle. This occurs due to the absence of structure amplitudes at and near the zero-scattering angle and the presence of Poisson noise in weak diffraction patterns. Consequently, the PR calculation becomes a bottleneck for XDI structure analyses. Here, a protocol to efficiently yield realistic maps is proposed. The protocol is based on the empirical observation that realistic maps tend to yield low similarity scores, as suggested in our prior study [Sekiguchi et al. (2017), J. Synchrotron Rad. 24, 1024-1038]. Among independently and concurrently executed PR calculations, the protocol modifies all maps using the electron-density maps exhibiting low similarity scores. This approach, along with a new protocol for estimating particle shape, improved the probability of obtaining realistic maps for diffraction patterns from various aggregates of colloidal gold particles, as compared with PR calculations performed without the protocol. Consequently, the protocol has the potential to reduce computational costs in PR calculations and enable efficient XDI structure analysis of non-crystalline particles using synchrotron X-rays and X-ray free-electron laser pulses.

Similarity score for screening phase-retrieved maps in X-ray diffraction imaging - characterization in reciprocal space.

X-ray diffraction imaging (XDI) is utilized for visualizing the structures of non-crystalline particles in material sciences and biology. In the structural analysis, phase-retrieval (PR) algorithms are applied to the diffraction amplitude data alone to reconstruct the electron density map of a specimen particle projected along the direction of the incident X-rays. However, PR calculations may not lead to good convergence because of a lack of diffraction patterns in small-angle regions and Poisson noise in X-ray detection. Therefore, the PR calculation is still a bottleneck for the efficient application of XDI in the structural analyses of non-crystalline particles. For screening maps from hundreds of trial PR calculations, we have been using a score and measuring the similarity between a pair of retrieved maps. Empirically, probable maps approximating the particle structures gave a score smaller than a threshold value, but the reasons for the effectiveness of the score are still unclear. In this study, the score is characterized in terms of the phase differences between the structure factors of the retrieved maps, the usefulness of the score in screening the maps retrieved from experimental diffraction patterns is demonstrated, and the effective resolution of similarity-score-selected maps is discussed.

Ultrastructure and fractal property of chromosomes in close-to-native yeast nuclei visualized using X-ray laser diffraction.

Genome compaction and activity in the nucleus depend on spatiotemporal changes in the organization of chromatins in chromosomes. However, the direct imaging of the chromosome structures in the nuclei has been difficult and challenging. Herein, we directly visualized the structure of chromosomes in frozen-hydrated nuclei of budding yeast in the interphase using X-ray laser diffraction. The reconstructed projection electron density maps revealed inhomogeneous distributions of chromosomes, such as a 300 nm assembly and fibrous substructures in the elliptic-circular shaped nuclei of approximately 800 nm. In addition, from the diffraction patterns, we confirmed the absence of regular arrangements of chromosomes and chromatins with 400-20 nm spacing, and demonstrated that chromosomes were composed of self-similarly assembled substructural domains with an average radius of gyration of 58 nm and smooth surfaces. Based on these analyses, we constructed putative models to discuss the organization of 16 chromosomes, carrying DNA of 4.1 mm in 800 nm ellipsoid of the nucleus at the interphase. We anticipate the structural parameters on the fractal property of chromosomes and the experimental images to be a starting point for constructing more sophisticated 3D structural models of the nucleus.

Common architectures in cyanobacteria Prochlorococcus cells visualized by X-ray diffraction imaging using X-ray free electron laser.

Visualization of intracellular structures and their spatial organization inside cells without any modification is essential to understand the mechanisms underlying the biological functions of cells. Here, we investigated the intracellular structure of cyanobacteria Prochlorococcus in the interphase by X-ray diffraction imaging using X-ray free-electron laser. A number of diffraction patterns from single cells smaller than 1 µm in size were collected with high signal-to-noise ratio with a resolution of up to 30 nm. From diffraction patterns, a set of electron density maps projected along the direction of the incident X-ray were retrieved with high reliability. The most characteristic structure found to be common among the cells was a C-shaped arrangement of 100-nm sized high-density spots, which surrounded a low-density area of 100 nm. Furthermore, a three-dimensional map reconstructed from the projection maps of individual cells was non-uniform, indicating the presence of common structures among cyanobacteria cells in the interphase. By referring to the fluorescent images for distributions of thylakoid membranes, nucleoids, and carboxysomes, we inferred and represented their spatial arrangements in the three-dimensional map. The arrangement allowed us to discuss the relevance of the intracellular organization to the biological functions of cyanobacteria.

siRNA potency enhancement via chemical modifications of nucleotide bases at the 5'-end of the siRNA guide strand.

Small interfering RNAs (siRNAs) can be utilized not only as functional biological research tools but also as therapeutic agents. For the clinical use of siRNA as drugs, various chemical modifications have been used to improve the activity of siRNA drugs, and further chemical modifications are expected to improve the utility of siRNA therapeutics. As the 5' nucleobase of the guide strand affects the interaction between an siRNA and AGO2 and target cleavage activity, structural optimization of this specific position may be a useful strategy for improving siRNA activity. Here, using the in silico model of the complex between human AGO2 MID domain and nucleoside monophosphates, we screened and synthesized an original adenine-derived analog, 6-(3-(2-carboxyethyl)phenyl)purine (6-mCEPh-purine), that fits better than the natural nucleotide bases into the MID domain of AGO2. Introduction of the 6-mCEPh-purine analog at the 5'-end of the siRNA guide strand significantly enhanced target knockdown activity in both cultured cell lines and in vivo animal models. Our findings can help expand strategies for rationally optimizing siRNA activity via chemical modifications of nucleotide bases.

Domain Organization in Plant Blue-Light Receptor Phototropin2 of Arabidopsis thaliana Studied by Small-Angle X-ray Scattering.

Phototropin2 (phot2) is a blue-light (BL) receptor protein that regulates the BL-dependent activities of plants for efficient photosynthesis. Phot2 is composed of two light-oxygen-voltage sensing domains (LOV1 and LOV2) to absorb BL, and a kinase domain. Photo-activated LOV domains, especially LOV2, play a major role in photo-dependent increase in the phosphorylation activity of the kinase domain. The atomic details of the overall structure of phot2 and the intramolecular mechanism to convert BL energy to a phosphorylation signal remain unknown. We performed structural studies on the LOV fragments LOV1, LOV2, LOV2-linker, and LOV2-kinase, and full-length phot2, using small-angle X-ray scattering (SAXS). The aim of the study was to understand structural changes under BL irradiation and discuss the molecular mechanism that enhance the phosphorylation activity under BL. SAXS is a suitable technique for visualizing molecular structures of proteins in solution at low resolution and is advantageous for monitoring their structural changes in the presence of external physical and/or chemical stimuli. Structural parameters and molecular models of the recombinant specimens were obtained from SAXS profiles in the dark, under BL irradiation, and after dark reversion. LOV1, LOV2, and LOV2-linker fragments displayed minimal structural changes. However, BL-induced rearrangements of functional domains were noted for LOV2-kinase and full-length phot2. Based on the molecular model together with the absorption measurements and biochemical assays, we discuss the intramolecular interactions and domain motions necessary for BL-enhanced phosphorylation activity of phot2.

Structure-guided screening strategy combining surface plasmon resonance with nuclear magnetic resonance for identification of small-molecule Argonaute 2 inhibitors.

Argonaute (AGO) proteins are the key component of the RNA interference machinery that suppresses gene expression by forming an RNA-induced silencing complex (RISC) with microRNAs (miRNAs). Each miRNA is involved in various cellular processes, such as development, differentiation, tumorigenesis, and viral infection. Thus, molecules that regulate miRNA function are expected to have therapeutic potential. In addition, the biogenesis of miRNA is a multistep process involving various proteins, although the complete pathway remains to be elucidated. Therefore, identification of molecules that can specifically modulate each step will help understand the mechanism of gene suppression. To date, several AGO2 inhibitors have been identified. However, these molecules were identified through a single screening method, and no studies have specifically evaluated a combinatorial strategy. Here, we demonstrated a combinatorial screening (SCR) approach comprising an in silico molecular docking study, surface plasmon resonance (SPR) analysis, and nuclear magnetic resonance (NMR) analysis, focusing on the strong binding between the 5'-terminal phosphate of RNA and the AGO2 middle (MID) domain. By combining SPR and NMR, we identified binding modes of amino acid residues binding to AGO2. First, using a large chemical library (over 6,000,000 compounds), 171 compounds with acidic functional groups were screened using in silico SCR. Next, we constructed an SPR inhibition system that could analyze only the 5'-terminal binding site of RNA, and nine molecules that strongly bound to the AGO2 MID domain were selected. Finally, using NMR, three molecules that bound to the desired site were identified. The RISC inhibitory ability of the "hit" compounds was analyzed in human cell lysate, and all three hit compounds strongly inhibited the binding between double-stranded RNA and AGO2.

Measurement of the horizontal beam emittance of undulator radiation by tandem-double-slit optical system.

A tandem-double-slit optical system was constructed to evaluate the practical beam emittance of undulator radiation. The optical system was a combination of an upstream slit (S1) and downstream slit (S2) aligned on the optical axis with an appropriate separation. The intensity distribution after the double slits, I(x1, x2), was measured by scanning S1 and S2 in the horizontal direction. Coordinates having 1/\sqrt e intensity were extracted from I(x1, x2), whose contour provided the standard deviation ellipse in the x1-x2 space. I(x1, x2) was converted to the corresponding distribution in the phase space, I(x1, x1'). The horizontal beam emittance was evaluated to be 3.1 nm rad, which was larger than the value of 2.4 nm rad estimated by using ray-tracing. It was found that the increase was mainly due to an increase in beam divergence rather than size.

Methods and application of coherent X-ray diffraction imaging of noncrystalline particles.

Microscopic imaging techniques have been developed to visualize events occurring in biological cells. Coherent X-ray diffraction imaging is one of the techniques applicable to structural analyses of cells and organelles, which have never been crystallized. In the experiment, a single noncrystalline particle is illuminated by an X-ray beam with almost complete spatial coherence. The structure of the particle projected along the direction of the beam is, in principle, retrieved from a finely recorded diffraction pattern alone by using iterative phase-retrieval algorithms. Here, we describe fundamental theory and experimental methods of coherent X-ray diffraction imaging and the recent application in structural studies of noncrystalline specimens by using X-rays available at Super Photon Ring of 8-Gev and SPring-8 Angstrom Compact Free Electron Laser in Japan.

Inverse-phase composite zone plate providing deeper focus than the normal diffraction-limited depth of X-ray microbeams.

A novel type of zone plate (ZP), termed an inverse-phase composite ZP, is proposed to gain a deeper focus than the standard diffraction-limited depth of focus, with little reduction in spatial resolution. The structure is a combination of an inner ZP functioning as a conventional phase ZP and an outer ZP functioning with third-order diffraction with opposite phase to the inner ZP. Two-dimensional complex amplitude distributions neighboring the focal point were calculated using a wave-optical approach of diffraction integration with a monochromatic plane-wave illumination, where one dimension is the radial direction and the other dimension is the optical-axis direction. The depth of focus and the spatial resolution were examined as the main focusing properties. Two characteristic promising cases regarding the depth of focus were found: a pit-intensity focus with the deepest depth of focus, and a flat-intensity focus with deeper depth of focus than usual ZPs. It was found that twice the depth of focus could be expected with little reduction in the spatial resolution for 10 keV X-ray energy, tantalum zone material, 84 nm minimum fabrication zone width, and zone thickness of 2.645 µm. It was also found that the depth of focus and the spatial resolution were almost unchanged in the photon energy range from 8 to 12 keV. The inverse-phase composite ZP has high potential for use in analysis of practical thick samples in X-ray microbeam applications.

Developing a MEMS Device with Built-in Microfluidics for Biophysical Single Cell Characterization.

This study combines the high-throughput capabilities of microfluidics with the sensitive measurements of microelectromechanical systems (MEMS) technology to perform biophysical characterization of circulating cells for diagnostic purposes. The proposed device includes a built-in microchannel that is probed by two opposing tips performing compression and sensing separately. Mechanical displacement of the compressing tip (up to a maximum of 14 µm) and the sensing tip (with a quality factor of 8.9) are provided by two separate comb-drive actuators, and sensing is performed with a capacitive displacement sensor. The device is designed and developed for simultaneous electrical and mechanical measurements. As the device is capable of exchanging the liquid inside the channel, different solutions were tested consecutively. The performance of the device was evaluated by introducing varying concentrations of glucose (from 0.55 mM (0.1%) to 55.5 mM (10%)) and NaCl (from 0.1 mM to 10 mM) solutions in the microchannel and by monitoring changes in the mechanical and electrical properties. Moreover, we demonstrated biological sample handling by capturing single cancer cells. These results show three important capabilities of the proposed device: mechanical measurements, electrical measurements, and biological sample handling. Combined in one device, these features allow for high-throughput multi-parameter characterization of single cells.

Diffraction apparatus and procedure in tomography X-ray diffraction imaging for biological cells at cryogenic temperature using synchrotron X-ray radiation.

X-ray diffraction imaging is a technique for visualizing the structure of biological cells. In X-ray diffraction imaging experiments using synchrotron radiation, cryogenic conditions are necessary in order to reduce radiation damage in the biological cells. Frozen-hydrated biological specimens kept at cryogenic temperatures are also free from drying and bubbling, which occurs in wet specimens under vacuum conditions. In a previous study, the diffraction apparatus KOTOBUKI-1 [Nakasako et al. (2013), Rev. Sci. Instrum. 84, 093705] was constructed for X-ray diffraction imaging at cryogenic temperatures by utilizing a cryogenic pot, which is a cooling device developed in low-temperature physics. In this study a new cryogenic pot, suitable for tomography experiments, has been developed. The pot can rotate a biological cell over an angular range of ±170° against the direction of the incident X-ray beam. Herein, the details and the performance of the pot and miscellaneous devices are reported, along with established experimental procedures including specimen preparation. The apparatus has been used in tomography experiments for visualizing the three-dimensional structure of a Cyanidioschyzon merolae cell with an approximate size of 5 µm at a resolution of 136 nm. Based on the experimental results, the necessary improvements for future experiments and the resolution limit achievable under experimental conditions within a maximum tolerable dose are discussed.

Atmospheric coherent X-ray diffraction imaging for in situ structural analysis at SPring-8 Hyogo beamline BL24XU.

Coherent X-ray diffraction imaging (CXDI) is a promising technique for non-destructive structural analysis of micrometre-sized non-crystalline samples at nanometre resolutions. This article describes an atmospheric CXDI system developed at SPring-8 Hyogo beamline BL24XU for in situ structural analysis and designed for experiments at a photon energy of 8 keV. This relatively high X-ray energy enables experiments to be conducted under ambient atmospheric conditions, which is advantageous for the visualization of samples in native states. The illumination condition with pinhole-slit optics is optimized according to wave propagation calculations based on the Fresnel-Kirchhoff diffraction formula so that the sample is irradiated by X-rays with a plane wavefront and high photon flux of ∼1 × 1010 photons/16 µmø(FWHM)/s. This work demonstrates the imaging performance of the atmospheric CXDI system by visualizing internal voids of sub-micrometre-sized colloidal gold particles at a resolution of 29.1 nm. A CXDI experiment with a single macroporous silica particle under controlled humidity was also performed by installing a home-made humidity control device in the system. The in situ observation of changes in diffraction patterns according to humidity variation and reconstruction of projected electron-density maps at 5.2% RH (relative humidity) and 82.6% RH at resolutions of 133 and 217 nm, respectively, were accomplished.

Common structural features of toxic intermediates from α-synuclein and GroES fibrillogenesis detected using cryogenic coherent X-ray diffraction imaging.

The aggregation and deposition of α-synuclein (αSyn) in neuronal cells is correlated to pathogenesis of Parkinson's disease. Although the mechanism of αSyn aggregation and fibril formation has been studied extensively, the structural hallmarks that are directly responsible for toxicity toward cells are still under debate. Here, we have compared the structural characteristics of the toxic intermediate molecular species of αSyn and similar toxic species of another protein, GroES, using coherent X-ray diffraction analysis. Using coherent X-ray free electron laser pulses of SACLA, we analysed αSyn and GroES fibril intermediate species and characterized various aggregate structures. Unlike previous studies where an annular oligomeric form of αSyn was identified, particle reconstruction from scattering traces suggested that the specific forms of the toxic particles were varied, with the sizes of the particles falling within a specific range. We did however discover a common structural feature in both αSyn and GroES samples; the edges of the detected particles were nearly parallel and produced a characteristic diffraction pattern in the diffraction experiments. The presence of parallel-edged particles in toxic intermediates of αSyn and GroES fibrillogenesis pointed towards a plausible common molecular interface that leads to the formation of mature fibrils.

Blue Light-excited Light-Oxygen-Voltage-sensing Domain 2 (LOV2) Triggers a Rearrangement of the Kinase Domain to Induce Phosphorylation Activity in Arabidopsis Phototropin1.

Phototropin1 is a blue light (BL) receptor in plants and shows BL-dependent kinase activation. The BL-excited light-oxygen-voltage-sensing domain 2 (LOV2) is primarily responsible for the activation of the kinase domain; however, the molecular mechanism by which conformational changes in LOV2 are transmitted to the kinase domain remains unclear. Here, we investigated BL-induced structural changes of a minimum functional fragment of Arabidopsis phototropin1 composed of LOV2, the kinase domain, and a linker connecting the two domains using small-angle x-ray scattering (SAXS). The fragment existed as a dimer and displayed photoreversible SAXS changes reflected in the radii of gyration of 42.9 Å in the dark and 48.8 Å under BL irradiation. In the dark, the molecular shape reconstructed from the SAXS profiles appeared as two bean-shaped lobes in a twisted arrangement that was 170 Å long, 80 Å wide, and 50 Å thick. The molecular shape under BL became slightly elongated from that in the dark. By fitting the crystal structure of the LOV2 dimer and a homology model of the kinase domain to their inferred shapes, the BL-dependent change could be interpreted as the positional shift in the kinase domain relative to that of the LOV2 dimer. In addition, we found that lysine 475, a functionally important residue, in the N-terminal region of LOV2 plays a critical role in transmitting the structural changes in LOV2 to the kinase domain. The interface between the domains is critical for signaling, suitably changing the structure to activate the kinase in response to conformational changes in the adjoining LOV2.

TAKASAGO-6 apparatus for cryogenic coherent X-ray diffraction imaging of biological non-crystalline particles using X-ray free electron laser at SACLA.

Coherent X-ray diffraction imaging (CXDI) is a technique for structure analyses of non-crystalline particles with dimensions ranging from micrometer to sub-micrometer. We have developed a diffraction apparatus named TAKASAGO-6 for use in single-shot CXDI experiments of frozen-hydrated non-crystalline biological particles at cryogenic temperature with X-ray free electron laser pulses provided at a repetition rate of 30 Hz from the SPring-8 Angstrom Compact free-electron LAser. Specimen particles are flash-cooled after being dispersed on thin membranes supported by specially designed disks. The apparatus is equipped with a high-speed translation stage with a cryogenic pot for raster-scanning of the disks at a speed higher than 25 µm/33 ms. In addition, we use devices assisting the easy transfer of cooled specimens from liquid-nitrogen storages to the cryogenic pot. In the current experimental procedure, more than 20 000 diffraction patterns can be collected within 1 h. Here we report the key components and performance of the diffraction apparatus. Based on the efficiency of the diffraction data collection and the structure analyses of metal particles, biological cells, and cellular organelles, we discuss the future application of this diffraction apparatus for structure analyses of biological specimens.

Cryogenic coherent X-ray diffraction imaging of biological samples at SACLA: a correlative approach with cryo-electron and light microscopy.

Coherent X-ray diffraction imaging at cryogenic temperature (cryo-CXDI) allows the analysis of internal structures of unstained, non-crystalline, whole biological samples in micrometre to sub-micrometre dimensions. Targets include cells and cell organelles. This approach involves preparing frozen-hydrated samples under controlled humidity, transferring the samples to a cryo-stage inside a vacuum chamber of a diffractometer, and then exposing the samples to coherent X-rays. Since 2012, cryo-coherent diffraction imaging (CDI) experiments have been carried out with the X-ray free-electron laser (XFEL) at the SPring-8 Ångstrom Compact free-electron LAser (SACLA) facility in Japan. Complementary use of cryo-electron microscopy and/or light microscopy is highly beneficial for both pre-checking samples and studying the integrity or nature of the sample. This article reports the authors' experience in cryo-XFEL-CDI of biological cells and organelles at SACLA, and describes an attempt towards reliable and higher-resolution reconstructions, including signal enhancement with strong scatterers and Patterson-search phasing.

Coherent X-Ray Diffraction Imaging of Chloroplasts from Cyanidioschyzon merolae by Using X-Ray Free Electron Laser.

Coherent X-ray diffraction imaging (CXDI) is a lens-less technique for visualizing the structures of non-crystalline particles with the dimensions of submicrometer to micrometer at a resolution of several tens of nanometers. We conducted cryogenic CXDI experiments at 66 K to visualize the internal structures of frozen-hydrated chloroplasts of Cyanidioschyzon merolae using X-ray free electron laser (XFEL) as a coherent X-ray source. Chloroplast dispersed specimen disks at a number density of 7/(10×10 µm(2)) were flash-cooled with liquid ethane without staining, sectioning or chemical labeling. Chloroplasts are destroyed at atomic level immediately after the diffraction by XFEL pulses. Thus, diffraction patterns with a good signal-to-noise ratio from single chloroplasts were selected from many diffraction patterns collected through scanning specimen disks to provide fresh specimens into the irradiation area. The electron density maps of single chloroplasts projected along the direction of the incident X-ray beam were reconstructed by using the iterative phase-retrieval method and multivariate analyses. The electron density map at a resolution of 70 nm appeared as a C-shape. In addition, the fluorescence image of proteins stained with Flamingo™ dye also appeared as a C-shape as did the autofluorescence from Chl. The similar images suggest that the thylakoid membranes with an abundance of proteins distribute along the outer membranes of chloroplasts. To confirm the present results statistically, a number of projection structures must be accumulated through high-throughput data collection in the near future. Based on the results, we discuss the feasibility of XFEL-CXDI experiments in the structural analyses of cellular organelles.

Magnetic resonance imaging of tumor with a self-traceable phosphorylcholine polymer.

Polymers are concentration-amplified with respect to the monomeric units. We show here that a phosphorylcholine polymer enriched with (13)C/(15)N at the methyl groups is self-traceable by multiple-resonance (heteronuclear-correlation) NMR in tumor-bearing mice inoculated with the mouse rectal cancer cell line (colon 26). Preliminary measurements indicated that the present polymeric nanoprobe was satisfactorily distinguished from lipids and detectable with far sub-micromolar spectroscopic and far sub-millimolar imaging sensitivities. Detailed ex vivo and in vivo studies for the tumor-bearing mice administered the probe with a mean molecular weight of 63,000 and a mean size of 13 nm, revealed the following: (1) this probe accumulates in the tumor highly selectively (besides renal excretion) and efficiently (up to 30% of the injected dose), (2) the tumor can thus be clearly in vivo imaged, the lowest clearly imageable dose of the probe being 100 mg/kg or 2.0 mg/20-g mouse, and (3) the competition between renal excretion and tumor accumulation is size-controlled; that is, the larger (higher molecular-weight) and smaller (lower molecular-weight) portions of the probe undergo tumor accumulation and renal excretion, respectively. The observed size dependence suggests that the efficient tumor-targeting of the present probe is stimulated primarily by the so-called enhanced permeability and retention (EPR) effect, that is, size-allowed invasion of the probe into the tumor tissue via defective vascular wall. Self-traceable polymers thus open an important area of magnetic resonance imaging (MRI) of tumors and may provide a highly potential tool to visualize various delivery/localization processes using synthetic polymers.

Signal enhancement and Patterson-search phasing for high-spatial-resolution coherent X-ray diffraction imaging of biological objects.

In this decade coherent X-ray diffraction imaging has been demonstrated to reveal internal structures of whole biological cells and organelles. However, the spatial resolution is limited to several tens of nanometers due to the poor scattering power of biological samples. The challenge is to recover correct phase information from experimental diffraction patterns that have a low signal-to-noise ratio and unmeasurable lowest-resolution data. Here, we propose a method to extend spatial resolution by enhancing diffraction signals and by robust phasing. The weak diffraction signals from biological objects are enhanced by interference with strong waves from dispersed colloidal gold particles. The positions of the gold particles determined by Patterson analysis serve as the initial phase, and this dramatically improves reliability and convergence of image reconstruction by iterative phase retrieval. A set of calculations based on current experiments demonstrates that resolution is improved by a factor of two or more.