Determination of crystallographic intensities from sparse data

Abstract

X-ray serial microcrystallography involves the collection and merging of frames of diffraction data from randomly oriented protein microcrystals. The number of diffracted X-rays in each frame is limited by radiation damage, and this number decreases with crystal size. The data in the frame are said to be sparse if too few X-rays are collected to determine the orientation of the microcrystal. It is commonly assumed that sparse crystal diffraction frames cannot be merged, thereby setting a lower limit to the size of microcrystals that may be merged with a given source fluence. The EMC algorithm [Loh & Elser (2009), Phys. Rev. E, 80, 026705] has previously been applied to reconstruct structures from sparse noncrystalline data of objects with unknown orientations [Philipp et al. (2012), Opt. Express, 20, 13129-13137; Ayyer et al. (2014), Opt. Express, 22, 2403-2413]. Here, it is shown that sparse data which cannot be oriented on a per-frame basis can be used effectively as crystallographic data. As a proof-of-principle, reconstruction of the three-dimensional diffraction intensity using sparse data frames from a 1.35 - kDa molecule crystal is demonstrated. The results suggest that serial microcrystallography is, in principle, not limited by the fluence of the X-ray source, and collection of complete data sets should be feasible at, for instance, storage-ring X-ray sources.