On X-ray scattering model for single particles, Part I: The legacy of protein crystallography

TL;DR

This paper reviews and contrasts different X-ray scattering models used in protein crystallography, focusing on their assumptions, limitations, and implications for interpreting scattering patterns of single particles and nanocrystals.

Contribution

It clarifies the assumptions of conventional and rigorous scattering models, highlighting their applicability and limitations for single particle imaging and nanocrystals.

Findings

Conventional models are valid for small crystals but fail for larger or complex particles.

Rigorous models bypass bulk notions and better describe non-classical scattering.

The paper addresses terminology conflicts and sets the stage for further analysis in Part 2.

Abstract

Emerging coherent X-ray scattering patterns of single particles have shown dominant morphological signatures in agreement with predictions of the scattering model used for conventional protein crystallography. The key question is if and to what extent these scattering patterns contain volumetric information, and what model can retrieve it. The scattering model of protein crystallography is valid for very small crystals or those like crystalized biomolecules with small coherent subunits. But in the general case, it fails to model the integrated intensities of diffraction spots, and cannot even find the size of the crystal. The more rigorous and less employed alternative is a purely-classical crystal-specific model, which bypasses the fundamental notion of bulk and hence the non-classical X-ray scattering from bulk. This contribution is Part 1 out of two reports, in which we seek to clarify the assumptions of some different regimes and models of X-ray scattering and their implications for single particle imaging. In this part, first basic concepts and existing models are briefly reviewed. Then the predictions of the conventional and the rigorous models for emerging scattering patterns of protein nanocrystals (intermediate case between conventional crystals and single particles) are contrasted, and the terminology conflict regarding "Diffraction Theory" is addressed. With a clearer picture of crystal scattering, Part 2 will focus on additional concepts, limitations, correction schemes, and alternative models relevant to single particles. Aside from such optical details, protein crystallography is an advanced tool of analytical chemistry and not a self-contained optical imaging technique (despite significant instrumental role of optical data). As such, its final results can be neither confirmed nor rejected on mere optical grounds; i.e., no jurisdiction for optics.