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.

The slip-and-slide algorithm: a refinement protocol for detector geometry

Geometry correction is traditionally plagued by mis-fitting of correlated parameters, leading to local minima which prevent further improvements. Segmented detectors pose an enhanced risk of mis-fitting: even a minor confusion of detector distance and panel separation can prevent improvement in data quality. The slip-and-slide algorithm breaks down effects of the correlated parameters and their associated target functions in a fundamental shift in the approach to the problem. Parameters are never refined against the components of the data to which they are insensitive, providing a dramatic boost in the exploitation of information from a very small number of diffraction patterns. This algorithm can be applied to exploit the adherence of the spot-finding results prior to indexing to a given lattice using unit-cell dimensions as a restraint. Alternatively, it can be applied to the predicted spot locations and the observed reflection positions after indexing from a smaller number of images. Thus, the indexing rate can be boosted by 5.8% using geometry refinement from only 125 indexed patterns or 500 unindexed patterns. In one example of cypovirus type 17 polyhedrin diffraction at the Linac Coherent Light Source, this geometry refinement reveals a detector tilt of 0.3° (resulting in a maximal Z-axis error of ∼0.5 mm from an average detector distance of ∼90 mm) whilst treating all panels independently. Re-indexing and integrating with updated detector geometry reduces systematic errors providing a boost in anomalous signal of sulfur atoms by 20%. Due to the refinement of decoupled parameters, this geometry method also reaches convergence.