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

Abstract

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.

Authors:
 [1];  [2];  [3]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Dept. of Applied Mathematics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Center for Advanced Mathematics for Energy Research Applications
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Dept. of Applied Mathematics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Center for Advanced Mathematics for Energy Research Applications; Univ. of California, Berkeley, CA (United States). Dept. of Mathematics
  3. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Center for Advanced Mathematics for Energy Research Applications; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Molecular Biophysics and Integrated Bioimaging Division
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); National Institutes of Health (NIH)
OSTI Identifier:
1366768
Alternate Identifier(s):
OSTI ID: 1379908
Grant/Contract Number:
AC02-05CH11231
Resource Type:
Journal Article: Published Article
Journal Name:
Proceedings of the National Academy of Sciences of the United States of America
Additional Journal Information:
Journal Volume: 114; Journal Issue: 28; Journal ID: ISSN 0027-8424
Publisher:
National Academy of Sciences, Washington, DC (United States)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; structure determination; multitiered iterative phasing; single-particle imaging

Citation Formats

Donatelli, Jeffrey J., Sethian, James A., and Zwart, Peter H. Reconstruction from limited single-particle diffraction data via simultaneous determination of state, orientation, intensity, and phase. United States: N. p., 2017. Web. doi:10.1073/pnas.1708217114.
Donatelli, Jeffrey J., Sethian, James A., & Zwart, Peter H. Reconstruction from limited single-particle diffraction data via simultaneous determination of state, orientation, intensity, and phase. United States. doi:10.1073/pnas.1708217114.
Donatelli, Jeffrey J., Sethian, James A., and Zwart, Peter H. Mon . "Reconstruction from limited single-particle diffraction data via simultaneous determination of state, orientation, intensity, and phase". United States. doi:10.1073/pnas.1708217114.
@article{osti_1366768,
title = {Reconstruction from limited single-particle diffraction data via simultaneous determination of state, orientation, intensity, and phase},
author = {Donatelli, Jeffrey J. and Sethian, James A. and Zwart, Peter H.},
abstractNote = {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.},
doi = {10.1073/pnas.1708217114},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 28,
volume = 114,
place = {United States},
year = {Mon Jun 26 00:00:00 EDT 2017},
month = {Mon Jun 26 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1073/pnas.1708217114

Citation Metrics:
Cited by: 1work
Citation information provided by
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  • X-ray free-electron lasers (XFELs) provide new opportunities for structure determination of biomolecules, viruses and nanomaterials. With unprecedented peak brilliance and ultra-short pulse duration, XFELs can tolerate higher X-ray doses by exploiting the femtosecond-scale exposure time, and can thus go beyond the resolution limits achieved with conventional X-ray diffraction imaging techniques. Using XFELs, it is possible to collect scattering information from single particles at high resolution, however particle heterogeneity and unknown orientations complicate data merging in three-dimensional space. Using the Linac Coherent Light Source (LCLS), synthetic inorganic nanocrystals with a core–shell architecture were used as a model system for proof-of-principle coherentmore » diffractive single-particle imaging experiments. To deal with the heterogeneity of the core–shell particles, new computational methods have been developed to extract the particle size and orientation from the scattering data to assist data merging. The size distribution agrees with that obtained by electron microscopy and the merged data support a model with a core–shell architecture.« less
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  • 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 ofmore » 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.« less