Bayesian algorithms for recovering structure from single-particle diffraction snapshots of unknown orientation: a comparison.

Brian Moths,Abbas Ourmazd

doi:10.1107/s0108767311019611

Abstract

The advent of X-ray free-electron lasers promises the possibility to determine the structure of individual particles such as microcrystallites, viruses and biomolecules from single-shot diffraction snapshots obtained before the particle is destroyed by the intense femtosecond pulse. This program requires the ability to determine the orientation of the particle giving rise to each snapshot at signal levels as low as ~10(-2) photons per pixel. Two apparently different approaches have recently demonstrated this capability. Here we show they represent different implementations of the same fundamental approach, and identify the primary factors limiting their performance.

Highlights

X-ray free-electron lasers promise to move crystallography beyond crystals
Moves are afoot to determine the structure of biological molecules and their assemblies by exposing a succession of individual single particles to intense femtosecond pulses of X-rays (Solem & Baldwin, 1982; Neutze et al, 2004; Gaffney & Chapman, 2007)
The large number of pixels used as components of a vector representing a snapshot ensures, via the central limit theorem (CLT), that a Gaussian model is appropriate regardless of the specific noise spectrum present in each pixel

Summary

Introduction

X-ray free-electron lasers promise to move crystallography beyond crystals. For example, moves are afoot to determine the structure of biological molecules and their assemblies by exposing a succession of individual single particles to intense femtosecond pulses of X-rays (Solem & Baldwin, 1982; Neutze et al, 2004; Gaffney & Chapman, 2007). Once diffraction-pattern orientations have been discovered, the three-dimensional diffraction volume can be assembled and the particle structure recovered by standard phasing algorithms (Gerchberg & Saxton, 1972; Feinup, 1978; Miao et al, 2001; Shneerson et al, 2008; Fung et al, 2009; Loh & Elser, 2009). Loh & Elser (2009) demonstrated structure recovery from simulated diffraction snapshots by an apparently different approach, using a so-called expansion–maximization–compression (EMC) algorithm (Loh & Elser, 2009). Both approaches have been validated with experimental data.

Conceptual outline of orientation recovery

Exploiting the information content of the data set

Bayesian inference and likelihood maximization

Constraints to guide expectation–maximization

Scaling behavior

Summary and conclusions