#### Examples in Serial X-ray Crystallography

Jeffrey J. Donatelli and James A. Sethian

###### Crystal Size Estimation via Analysis of the Shape Transform

In nanocrystallography, one can obtain accurate crystal size information and thus form a partiality estimate by analyzing a finely sampled peak shape profile, e.g., which can be recorded via an extra set of rear detectors placed sufficiently far from the interaction point between the nanocrystal sample and the beam. In particular, the Fourier transform of this shape profile yields the projection of the three-dimensional autocorrelation of the crystal to a two-dimensional plane.

Accurate crystal size iunformation can be obtained by fittting a three-dimensional

model onto this projection. This figure illustrate the shape transform (Left) around a low-angle peak, which is then Fourier transformed to reveal the projected autocorrelated crystal (Middle), which is then segmented (Right).

Enhancing Data via Multi-Modal Analysis and Scaling

If the diffraction data has less symmetry than the crystal lattice, then autoindexing techniques are unable to fully determine the orientation of each image and can only narrow down the orientation to finite list of possibilities, a problem known as the indexing ambiguity. Consequently, the histogram of measured intensities at a given point will take the form of a multi-modal distribution. Due to the extreme amount of shot-to-shot variability, these modes may not be visible in the hisogram. However,

though partiality estimation and multi-modal scaling, these modes may become visible. This figure shows (Left) the histogram of the unscaled data at a point with a partiality estimate applied. (Right) Histogram of the data after scaling, revealing multiple modes.

Iterative Phasing of Nanocrystallographic Diffraction Data

If the diffraction data has less symmetry than the crystal lattice, then autoindexing techniques are unable to fully determine the orientation of each image and can only narrow the orientation down to a finite list of possibilities, a problem known as the indexing ambiguity. Consequently, the histogram of measured intensities at a given point will take the form of a multi-modal distribution. Due to the extreme amount of shot-to-shot variability, these modes may not be visible in the histogram. However, through partiality estimation and multi-modal scaling, these

modes may become visible. This figure presents the result of reconstruction of PuuE Allantoinase via iterative phase retrieval from simulated diffraction images. (Left) Electron density contour of exact structure. (Middle) Electron density contour of the reconstruction. (Right) Overlay of the reconstruction with the atomic model (blue).

Results:

Here we present results that we were able to achieve by applying our autoindexing, crystal size determination, and indexing ambiguity resolution methods to simulated nanocrystal diffraction data for PuuE Allantoinase with varying crystal sizes, beam strength (with an average of Jo photons/square Angstrom), background, and shot noise.