Assessing Uncertainties in X-ray Single-particle Three-dimensional reconstructions

TL;DR

This paper evaluates the uncertainties in 3D reconstructions of biological nanoparticles from X-ray diffraction data, introduces bootstrap methods for uncertainty assessment, and suggests improvements for current computational algorithms.

Contribution

It provides a detailed analysis of uncertainty sources in the Expansion-Maximization-Compression scheme and introduces bootstrap procedures for practical uncertainty quantification in real data reconstructions.

Findings

Uncertainty sources significantly affect reconstruction quality.

Bootstrap methods effectively assess reconstruction uncertainty.

Proposed improvements enhance algorithm robustness.

Abstract

Modern technology for producing extremely bright and coherent X-ray laser pulses provides the possibility to acquire a large number of diffraction patterns from individual biological nanoparticles, including proteins, viruses, and DNA. These two-dimensional diffraction patterns can be practically reconstructed and retrieved down to a resolution of a few \angstrom. In principle, a sufficiently large collection of diffraction patterns will contain the required information for a full three-dimensional reconstruction of the biomolecule. The computational methodology for this reconstruction task is still under development and highly resolved reconstructions have not yet been produced. We analyze the Expansion-Maximization-Compression scheme, the current state of the art approach for this very challenging application, by isolating different sources of uncertainty. Through numerical experiments on synthetic data we evaluate their respective impact. We reach conclusions of relevance for handling actual experimental data, as well as pointing out certain improvements to the underlying estimation algorithm. We also introduce a practically applicable computational methodology in the form of bootstrap procedures for assessing reconstruction uncertainty in the real data case. We evaluate the sharpness of this approach and argue that this type of procedure will be critical in the near future when handling the increasing amount of data.