Whole-pattern fitting technique in serial femtosecond nanocrystallography

Crystal diffraction prediction and partiality estimation using Gaussian basis functions

The recent diversification of macromolecular crystallographic experiments including the use of pink beams, convergent electron diffraction and serial snapshot crystallography has shown the limitations of using the Laue equations for diffraction prediction. This article gives a computationally efficient way of calculating approximate crystal diffraction patterns given varying distributions of the incoming beam, crystal shapes and other potentially hidden parameters. This approach models each pixel of a diffraction pattern and improves data processing of integrated peak intensities by enabling the correction of partially recorded reflections. The fundamental idea is to express the distributions as weighted sums of Gaussian functions. The approach is demonstrated on serial femtosecond crystallography data sets, showing a significant decrease in the required number of patterns to refine a structure to a given error.

Beyond integration: modeling every pixel to obtain better structure factors from stills

Most crystallographic data processing methods use pixel integration. In serial femtosecond crystallography (SFX), the intricate interaction between the reciprocal lattice point and the Ewald sphere is integrated out by averaging symmetrically equivalent observations recorded across a large number (104-106) of exposures. Although sufficient for generating biological insights, this approach converges slowly, and using it to accurately measure anomalous differences has proved difficult. This report presents a novel approach for increasing the accuracy of structure factors obtained from SFX data. A physical model describing all observed pixels is defined to a degree of complexity such that it can decouple the various contributions to the pixel intensities. Model dependencies include lattice orientation, unit-cell dimensions, mosaic structure, incident photon spectra and structure factor amplitudes. Maximum likelihood estimation is used to optimize all model parameters. The application of prior knowledge that structure factor amplitudes are positive quantities is included in the form of a reparameterization. The method is tested using a synthesized SFX dataset of ytterbium(III) lysozyme, where each X-ray laser pulse energy is centered at 9034 eV. This energy is 100 eV above the Yb3+ L-III absorption edge, so the anomalous difference signal is stable at 10 electrons despite the inherent energy jitter of each femtosecond X-ray laser pulse. This work demonstrates that this approach allows the determination of anomalous structure factors with very high accuracy while requiring an order-of-magnitude fewer shots than conventional integration-based methods would require to achieve similar results.

Serial electron crystallography: merging diffraction data through rank aggregation

Serial electron crystallography is being developed as an alternative way to collect diffraction data on beam-sensitive polycrystalline materials. Merging serial diffraction data from a large number of snapshots is difficult, and the dynamical nature of electron diffraction prevents the use of existing methods that rely on precise measurement of kinematical reflection intensities. To overcome this problem, an alternative method that uses rank aggregation to combine the rankings of relative reflection intensities from a large number of snapshots has been developed. The method does not attempt to accurately model the diffraction intensity, but instead optimizes the most likely ranking of reflections. As a consequence, the problem of scaling individual snapshots is avoided entirely, and requirements for the data quality and precision are low. The method works best when reflections can be fully measured, but the benefit over measuring partial intensities is small. Since there were no experimental data available for testing rank-based merging, the validity of the approach was assessed through a series of simulated serial electron diffraction datasets with different numbers of frames and varying degrees of errors. Several programs have been used to show that these rank-merged simulated data are good enough forab initiostructure determination using several direct methods programs.