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X-ray Crystallography

X-ray Crystallography

The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...

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Updated: Jun 9, 2025

$Microcrystallography of Protein Crystals and In Cellulo Diffraction$

Microcrystallography of Protein Crystals and In Cellulo Diffraction

Published on: July 21, 2017

Analysis of crystallographic phase retrieval using iterative projection algorithms.

Michael J Barnett¹, Rick P Millane², Richard L Kingston¹

¹School of Biological Sciences, University of Auckland, Auckland, New Zealand.

Acta Crystallographica. Section D, Structural Biology

|October 23, 2024

Summary

This summary is machine-generated.

This study explores iterative projection algorithms for X-ray diffraction phase retrieval in protein crystals. Averaging algorithm trajectories after convergence significantly improves density estimation for better crystallographic phasing.

Keywords:

ab initio phase determination crystallographic imaging iterative projection algorithms nonconvex constraint-satisfaction problems

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Published on: May 13, 2020

Area of Science:

Crystallography
Structural Biology
Computational Chemistry

Background:

Protein crystals with high solvent content (>2/3) offer unique constraints for X-ray diffraction data phasing.
Direct phasing is challenging due to the non-convex nature of phase retrieval problems.

Purpose of the Study:

To systematically explore phase retrieval using iterative projection algorithms.
To compare the effectiveness of Difference Map (DM), Relaxed-Reflect-Reflect (RRR), and Relaxed Averaged Alternating Reflectors (RAAR) algorithms.
To establish useful parameter ranges for these algorithms.

Main Methods:

Iterative projection algorithms were applied to X-ray diffraction data, using protein and solvent region density distributions as constraints.
Random errors were added to known phases to test phase recovery capabilities.
The performance of DM, RRR, and RAAR algorithms was compared.

Main Results:

All tested algorithms (DM, RRR, RAAR) proved effective for crystallographic phase retrieval.
Useful operational ranges for algorithm parameters were identified.
Averaging the algorithm trajectory in the stationary region post-convergence enhances density estimation.

Conclusions:

Iterative projection algorithms are powerful tools for X-ray diffraction phase retrieval in protein crystallography.
Post-convergence trajectory averaging offers superior density refinement compared to prior methods.