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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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The phase problem for one-dimensional crystals.

Rick P Millane1

  • 1Computational Imaging Group, Department of Electrical and Computer Engineering, University of Canterbury, Christchurch, New Zealand.

Acta Crystallographica. Section A, Foundations and Advances
|March 2, 2017
PubMed
Summary
This summary is machine-generated.

Solving the phase problem for one-dimensional crystals is unique, even with limited prior information. This research offers new phasing methods for biomolecular assemblies using X-ray free-electron lasers.

Keywords:
XFELsone-dimensional crystalsphase problem

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Area of Science:

  • Structural biology
  • Crystallography
  • Biophysics

Background:

  • The phase problem is a fundamental challenge in crystallography, hindering direct structure determination from diffraction data.
  • One-dimensional (1D) crystals, common in biological polymers, present unique phasing challenges compared to 3D crystals.
  • Traditional X-ray fiber diffraction requires complex data inversion.

Purpose of the Study:

  • To investigate the uniqueness of solutions to the phase problem for 1D crystals.
  • To explore how a priori information impacts phase retrieval uniqueness.
  • To establish a foundation for ab initio phasing of diffraction data from single 1D biomolecular assemblies.

Main Methods:

  • Analysis of diffraction amplitude phase retrieval for 1D crystals.
  • Characterization of the impact of constraints like positivity, molecular envelope, and helical symmetry.
  • Theoretical framework for ab initio phasing.

Main Results:

  • The phase problem solution for 1D crystals is unique up to a low-dimensional set of solutions without prior information.
  • Minimal additional information significantly enhances solution uniqueness.
  • Positivity, molecular envelope, and helical symmetry effects on uniqueness are systematically defined.

Conclusions:

  • This work provides a theoretical basis for solving the phase problem in 1D crystallography.
  • The findings pave the way for novel ab initio phasing strategies using advanced X-ray sources.
  • This approach bypasses traditional, complex diffraction data inversion methods for 1D structures.