Bayesian electron density determination from sparse and noisy single-molecule X-ray scattering images

Abstract

Single molecule X-ray scattering experiments using free electron lasers hold the potential to resolve both single structures and structural ensembles of biomolecules. However, molecular electron density determination has so far not been achieved due to low photon counts, high noise levels and low hit rates. Most analysis approaches therefore focus on large specimen like entire viruses, which scatter substantially more photons per image, such that it becomes possible to determine the molecular orientation for each image. In contrast, for small specimen like proteins, the molecular orientation cannot be determined for each image, and must be considered random and unknown. Here we developed and tested a rigorous Bayesian approach to overcome these limitations, and also taking into account intensity fluctuations, beam polarization, irregular detector shapes, incoherent scattering and background scattering. We demonstrate using synthetic scattering images that it is possible to determine electron densities of small proteins in this extreme high noise Poisson regime. Tests on published experimental data from the coliphage PR772 achieved the detector-limited resolution of $9\mathrm{nm}$, using only $0.01\%$ of the available photons per image.

arXiv comment27 pages, 4 figures

References in corpus (8)

• Relaxed Averaged Alternating Reflections for Diffraction Imaging
• Gas Dynamic Virtual Nozzle for Generation of Microscopic Droplet Streams
• A reconstruction algorithm for single-particle diffraction imaging experiments
• Reconstructing an Icosahedral Virus from Single-Particle Diffraction Experiments
• Low-signal limit of X-ray single particle imaging
• Three dimensional structure from intensity correlations
• Femtosecond reduction of atomic scattering factors triggered by intense x-ray pulse
• Expansion-maximization-compression algorithm with spherical harmonics for single particle imaging with X-ray lasers

Cited by in corpus (1)

• Structure determination from single-molecule X-ray scattering images using stochastic gradient ascent