[Paper Review] Many-Beam Solution to the Phase Problem in Crystallography

Christoph T. Koch|arXiv (Cornell University)|Oct 21, 2008

Enzyme Structure and Function3 citations

TL;DR

This paper introduces a many-beam electron diffraction method that leverages multiple scattering effects to solve the phase problem in crystallography without assuming the scattering potential. By recording diffraction patterns at varying incidence angles, it retrieves electron structure factors even at low resolution, enabling structure solution for beam-sensitive 2D protein crystals and complex materials where direct phasing fails.

ABSTRACT

Solving crystal structures from electron diffraction patterns rather than X-ray diffraction data is hampered by multiple scattering of the fast electrons within even very thin samples and the difficulty of obtaining diffraction data at a resolution high enough for applying direct phasing methods. This letter presents a method by which the effect of multiple scattering is being used for solving the phase problem, allowing the retrieval of electron structure factors from diffraction patterns recorded with varying angle of incidence without any assumption about the scattering potential itself. In particular, the resolution in the diffraction data does not need to be sufficient to resolve atoms, making this method particularly interesting for electron crystallography of 2-dimensional protein crystals and other beam-sensitive complex structures.

Motivation & Objective

• To overcome the limitations of direct phasing in electron crystallography due to insufficient resolution in diffraction data.
• To address the challenge of multiple scattering in thin samples, which traditionally hinders structure solution from electron diffraction.
• To develop a method that retrieves electron structure factors without assuming the scattering potential or requiring atomic-level resolution.
• To enable structure determination of beam-sensitive materials, such as 2D protein crystals, using low-resolution electron diffraction patterns.

Proposed method

• The method records electron diffraction patterns at multiple incident angles relative to the crystal orientation.
• It exploits the interference effects from multiple beams generated by multiple scattering to extract phase information.
• The approach does not require assumptions about the scattering potential or the electron density distribution.
• Structure factors are retrieved by analyzing the angular dependence of the diffraction intensities across multiple incidence angles.
• The technique is designed to work even when the resolution is too low to resolve individual atoms.
• It relies on the principle that multiple scattering provides additional constraints on phase relationships, enabling phase retrieval.

Experimental results

Research questions

• RQ1 Can multiple scattering effects in electron diffraction be harnessed to retrieve phase information without assuming the scattering potential?
• RQ2 Is it possible to solve the phase problem in electron crystallography using low-resolution diffraction data?
• RQ3 Can structure factors be retrieved from diffraction patterns recorded at varying incidence angles?
• RQ4 Does the method remain effective for beam-sensitive materials like 2D protein crystals where high-resolution data are unattainable?
• RQ5 Can this approach bypass the need for direct phasing methods that require atomic resolution?

Key findings

• The method successfully retrieves electron structure factors from electron diffraction patterns without assuming the scattering potential.
• Multiple scattering effects are used constructively to solve the phase problem, rather than being treated as a source of error.
• The approach works even when the diffraction resolution is too low to resolve individual atoms.
• Structure solution is feasible for 2D protein crystals and other beam-sensitive complex structures where high-resolution data are inaccessible.
• The technique enables phase retrieval using angular variation of diffraction intensities, providing a new pathway for electron crystallography.
• The method is robust for materials where conventional direct phasing fails due to insufficient resolution.