Bayesian Structure Determination From Ultrafast Single Molecule X-Ray Diffraction

Single molecule X-Ray diffraction experiments are a promising new method for the structure determination of biomolecules. In the experiments, a stream of single molecules enters a femtosecond high-intensity X-Ray free electron laser beam, and for each molecule the scattered photons are recorded as an image. The reconstruction of the structure from this data is quite challenging: The orientations of the molecules during the scattering events are unknown, the signal to noise ratio is very low, and the recorded images are sparse, with typically less than 10-50 photons per image. Previously available analysis methods require at least 100 photons per image, or a very large number (e.g. 10⁹) of images. We present a novel Bayesian approach that requires fewer photons per image and, at the same time, a relatively few images. It is flexible in that many different representations of the electron density can be used, both in Fourier space and directly in real space. Using synthetic data, we demonstrated the method is able to recover the atomic structure of (fictional) 20-atom molecules using only 5000 images with on average 15 photons each. Scaling up to larger molecules is work in progress.