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

Abstract

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.