Bayesian structure determination from fluctuation X-ray scattering experiments

Abstract

Fluctuation X-ray scattering is an emerging method for biomolecular structure determination, where scattering data of an ensemble of molecules in a dilute solution is collected using ultra-short X-ray pulses below rotational tumbling times. This allows to capture structural information in angular intensity correlations that are absent in traditional solution X-ray scattering methods, while also keeping the more biological conditions in solution compared to single-molecule X-ray scattering. However, the reconstruction of the molecular structure of the sample using the scattering images poses a significant challenge, since the orientations of the individual molecules in the solution are unknown and the low signal-to-noise ratio has to be overcome. We present a rigorous Bayesian framework that finds the molecular structure that has the largest probability given all recorded scattering images. In this approach, the orientation of each molecule explicitly appears in the likelihood function. We formally integrate out the unknown individual orientations, and to reduce the computational cost, this integration is approximated by a finite sum over randomly chosen orientations of each molecule. We show that our method can recover the molecular structure of a fictitious 12-atom molecule up to 4-Å resolution, using 2000 synthetic noise-free images of 50 randomly oriented copies each.