Iterative phasing for fluctuation X-ray scattering

Donatelli, Jeffrey J.; Zwart, Peter H.; Sethian, James A.

doi:10.1073/pnas.1513738112

Cited by 57 publications

(67 citation statements)

References 26 publications

(25 reference statements)

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“…The integration for the Fourier transform, spherical harmonic transform, and their inverses are numerically computed on this grid using the quadratures described in ref. 21. In particular, we note that the numerical integration scheme for the Fourier transform is a direct approximation of Eq.…”

Section: M-tipmentioning

confidence: 98%

“…Here we outline an alternative approach, based on M-TIP (21). In this single-particle version of M-TIP, we iteratively modify a set of models for the density, intensity function, orientations, and states to be consistent with specified constraints and the measured data.…”

Section: M-tipmentioning

confidence: 99%

“…This approach is an extension of the multitiered iterative phasing (M-TIP) algorithm, originally introduced in ref. 21 for fluctuation X-ray scattering reconstruction. Our single-particle version of M-TIP is formulated in a polar framework, using spherical harmonics for fast orientational alignment and spectrally accurate assembly of a 3D intensity function from a sparse set of 2D images.…”

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confidence: 99%

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Reconstruction from limited single-particle diffraction data via simultaneous determination of state, orientation, intensity, and phase

Donatelli

Sethian

Zwart

2017

Proc. Natl. Acad. Sci. U.S.A.

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Free-electron lasers now have the ability to collect X-ray diffraction patterns from individual molecules; however, each sample is delivered at unknown orientation and may be in one of several conformational states, each with a different molecular structure. Hit rates are often low, typically around 0.1%, limiting the number of useful images that can be collected. Determining accurate structural information requires classifying and orienting each image, accurately assembling them into a 3D diffraction intensity function, and determining missing phase information. Additionally, single particles typically scatter very few photons, leading to high image noise levels. We develop a multitiered iterative phasing algorithm to reconstruct structural information from singleparticle diffraction data by simultaneously determining the states, orientations, intensities, phases, and underlying structure in a single iterative procedure. We leverage real-space constraints on the structure to help guide optimization and reconstruct underlying structure from very few images with excellent global convergence properties. We show that this approach can determine structural resolution beyond what is suggested by standard Shannon sampling arguments for ideal images and is also robust to noise.single-particle imaging | multitiered iterative phasing | structure determination S ingle-particle X-ray diffraction aims to determine the structures of biological molecules from an ensemble of diffraction patterns, each collected from a single particle per shot. Particles are delivered to the beam at random orientations through either a liquid medium (1) or aerosolization (2). Large-scale experimental facilities, such as the Linac Coherent Light Source (3), have been developed to perform these experiments, with initial results indicating the feasibility of single-particle diffraction as a viable technique to address challenges in the health, material, and energy sciences (4, 5).A fundamental challenge in single-particle imaging is that the orientation of each imaged particle is unknown and must be recovered to determine structural information. Additionally, many biological samples display conformational flexibility and may exist in one of many possible structural states. To account for varying structural states and avoid a loss of resolution due to averaging of states, the diffraction patterns may need to be classified to the correct state. Furthermore, single particles scatter very few photons; hence the images are heavily contaminated by shot noise, often with less than a photon per Shannon pixel at high scattering angles.Current approaches typically determine states, orientations, and structures in separate consecutive steps. Classification work includes manifold mapping (6), spectral clustering (7), principal component analysis, and support vector machines (8). Orientation methods include common curve approaches (9-12), expectation maximization (13-15), and manifold embedding (16)(17)(18)(19). Once images are classified, oriented, and assemb...

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Section: M-tipmentioning

confidence: 98%

Section: M-tipmentioning

confidence: 99%

mentioning

confidence: 99%

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Reconstruction from limited single-particle diffraction data via simultaneous determination of state, orientation, intensity, and phase

Donatelli

Sethian

Zwart

2017

Proc. Natl. Acad. Sci. U.S.A.

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“…The goals of past SPI experiments mainly focused on light source and instruments optimization, sample preparations and delivery Recently, great progress has been made in real-space image reconstruction phase retrieval algorithms, multi-tiered iterative phasing (M-TIP) [207]. M-TIP is an extension of standard iterative phasing algorithms, which recover the 3D internal intensity directly from fluctuation X-ray scattering data [208]. The angular cross-correlations method makes a valuable statistical tool for structural analysis.…”

Section: Summary and Future Prospectsmentioning

confidence: 99%

Current Status of Single Particle Imaging with X-ray Lasers

Sun

Fan

et al. 2018

Applied Sciences

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Abstract:The advent of ultrafast X-ray free-electron lasers (XFELs) opens the tantalizing possibility of the atomic-resolution imaging of reproducible objects such as viruses, nanoparticles, single molecules, clusters, and perhaps biological cells, achieving a resolution for single particle imaging better than a few tens of nanometers. Improving upon this is a significant challenge which has been the focus of a global single particle imaging (SPI) initiative launched in December 2014 at the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, USA. A roadmap was outlined, and significant multi-disciplinary effort has since been devoted to work on the technical challenges of SPI such as radiation damage, beam characterization, beamline instrumentation and optics, sample preparation and delivery and algorithm development at multiple institutions involved in the SPI initiative. Currently, the SPI initiative has achieved 3D imaging of rice dwarf virus (RDV) and coliphage PR772 viruses at~10 nm resolution by using soft X-ray FEL pulses at the Atomic Molecular and Optical (AMO) instrument of LCLS. Meanwhile, diffraction patterns with signal above noise up to the corner of the detector with a resolution of~6 Ångström (Å) were also recorded with hard X-rays at the Coherent X-ray Imaging (CXI) instrument, also at LCLS. Achieving atomic resolution is truly a grand challenge and there is still a long way to go in light of recent developments in electron microscopy. However, the potential for studying dynamics at physiological conditions and capturing ultrafast biological, chemical and physical processes represents a tremendous potential application, attracting continued interest in pursuing further method development. In this paper, we give a brief introduction of SPI developments and look ahead to further method development.

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“…It has been claimed that the recently proposed multi-tiered itrerative phasing (MTIP) algorithm [23] would not need to assume azimuthal symmetry. Since it is supposed to determine the the magnitudes of the quantities characterized by different magnetic quantum numbers, in principle, it is capable of deducing that m = 0.…”

Section: Reconstruction Of Diffraction Pattern Of Nanoricementioning

confidence: 99%

Algorithm for Reconstruction of 3D Images of Nanorice Particles from Diffraction Patterns of Two Particles in Independent Random Orientations with an X-ray Laser

2017

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Abstract:The method of angular correlations recovers quantities from diffraction patterns of randomly oriented particles, as expected to be measured with an X-ray free electron laser (XFEL), proportional to quadratic functions of the spherical harmonic expansion coefficients of the diffraction volume of a single particle. We have previously shown that it is possible to reconstruct a randomly oriented icosahedral or helical virus from the average over all measured diffraction patterns of such correlations. We point out in this paper that a structure of even simpler particles of 50 Å or so in diameter and consisting of heavier atomic elements (to enhance scattering) that has been used as a test case for reconstructions from XFEL diffraction patterns can also be solved by this technique. Even though there has been earlier work on similar objects (prolate spheroids), one advantage of the present technique is its potential to also work with diffraction patterns not only due to single particles as has been suggested on the basis on nonoverlapping delta functions of angular scattering. Accordingly, we calculated from the diffraction patterns the angular momentum expansions of the pair correlations and triple correlations for general particle images and reconstructed those images in the standard way. Although the images looked pretty much the same, it is not totally clear to us that the angular correlations are exactly the same as different numbers of particles due to the possibility of constructive or destructive interference between the scattered waves from different particles. It is of course known that, for a large number of particles contributing to a diffraction parttern, the correlations converge to that of a single particle. It could be that the lack of perfect agreement between the images reconstructed with one and two particles is due to uncancelling constructive and destructive conditions that are not found in the case of solution scattering.

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Iterative phasing for fluctuation X-ray scattering

Cited by 57 publications

References 26 publications

Reconstruction from limited single-particle diffraction data via simultaneous determination of state, orientation, intensity, and phase

Reconstruction from limited single-particle diffraction data via simultaneous determination of state, orientation, intensity, and phase

Current Status of Single Particle Imaging with X-ray Lasers

Algorithm for Reconstruction of 3D Images of Nanorice Particles from Diffraction Patterns of Two Particles in Independent Random Orientations with an X-ray Laser

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