Although conventional X-ray crystallography has been used extensively to determine atomic structure, it is limited to objects that can be formed into large crystal samples (>10 μm). An appealing alternative, made possible by recent advances in light source technology, is serial crystallography, which is able to image structures resistant to large crystallization, such as membrane proteins, by substituting a large ensemble of easier to build nanocrystals or microcrystals, often delivered to the beam via a liquid jet. However, the beam power required to retrieve sufficient

X-Ray Nanocrystallographic Reconstruction

Jeffrey J. Donatelli and James A. Sethian

information destroys the crystal, hence ultrafast pulses (~ 70 fs) are required to collect data before damage effects alter the signal. Using such smaller crystals introduces several challenges. Due to the small crystal size, reflection peaks are smeared out, and there is noticeable signal between peaks. In particular, one is only able to measure partial peak reflections, which effectively attenuates the recorded intensity by a random amount. Variations in crystal size and incident photon flux density, unknown orientations, shot noise, and background signal from the liquid and detector add additional uncertainty to the data.

A class of methods, known as autoindexing techniques, can be used to determine crystal orientation up to symmetry of the lattice from the location of a sufficient number of peaks. However, such approaches typically face difficulties in the presence of partial and inter-peak reflections. Furthermore, these techniques only narrow down orientation to a list of possibilities when the diffraction pattern has less symmetry than the lattice, leading to an ambiguity in the image orientation. This is  known as the indexing ambiguity. If the data is processed without resolving this indexing ambiguity then the collected data will appear to be perfectly twinned, i.e., averaged over multiple crystal orientations. We have developed computational methods, utilizing techniques from graph theory, computational harmonic analysis, and maximum likelihood estimation, to address these issues and enhance the fidelity of serial crystallographic reconstruction.