Structure Determination from Single-Molecule X-ray Scattering Images Using Stochastic Gradient Ascent.

Scattering experiments using ultrashort X-ray free electron laser pulses have opened a new path for structure determination of a wide variety of specimens, including nanocrystals and entire viruses, approaching atomistic spatial and femtoseconds time resolution. However, random and unknown sample orientations as well as low signal-to-noise ratios have so far prevented a successful application to smaller specimens like single biomolecules. We here present resolution-annealed stochastic gradient ascent (RASTA), a new approach for direct atomistic electron density determination, which utilizes our recently developed rigorous Bayesian treatment of single-particle X-ray scattering. We demonstrate electron density determination at 2 Å resolution of various small proteins from synthetic scattering images with as low as 15 photons per image.