Ab initio phasing of the diffraction of crystals with translational disorder.

To date X-ray protein crystallography is the most successful technique available for the determination of high-resolution 3D structures of biological molecules and their complexes. In X-ray protein crystallography the structure of a protein is refined against the set of observed Bragg reflections from a protein crystal. The resolution of the refined protein structure is limited by the highest angle at which Bragg reflections can be observed.

Phase retrieval for multiple objects from their averaged diffraction.

The problem of reconstructing multiple objects from the average of their diffracted intensities is investigated. Reconstruction feasibility (uniqueness) depends on the number of objects, their support shapes and dimensionality, and an appropriately calculated constraint ratio. For objects with sufficiently different supports, and a favorable constraint ratio, the reconstruction problem has a unique solution.

Diffraction by nanocrystals II.

Nanocrystals with more than one molecule in the unit cell will generally crystallize with incomplete unit cells on the crystal surface. Previous results show that the ensemble-averaged diffraction by such crystals consists of a usual Bragg component and two other Bragg-like components due to the incomplete unit cells. Using an intrinsic flexibility in the definition of the incomplete-unit-cell part of a crystal, the problem is formulated such that the magnitude of the Bragg-like components is minimized, which leads to a simpler and more useful interpretation of the diffraction.

Aspects of direct phasing in femtosecond nanocrystallography.

X-ray free-electron laser diffraction patterns from protein nanocrystals provide information on the diffracted amplitudes between the Bragg reflections, offering the possibility of direct phase retrieval without the use of ancillary experimental data. Proposals for implementing direct phase retrieval are reviewed. These approaches are limited by the signal-to-noise levels in the data and the presence of different and incomplete unit cells in the nanocrystals.

Direct phasing in femtosecond nanocrystallography. II. Phase retrieval.

X-ray free-electron laser diffraction patterns from protein nanocrystals provide information on the diffracted amplitudes between the Bragg reflections, offering the possibility of direct phase retrieval without the use of ancillary experimental diffraction data [Spence et al. (2011). Opt.

Direct phasing in femtosecond nanocrystallography. I. Diffraction characteristics.

X-ray free-electron lasers solve a number of difficulties in protein crystallography by providing intense but ultra-short pulses of X-rays, allowing collection of useful diffraction data from nanocrystals. Whereas the diffraction from large crystals corresponds only to samples of the Fourier amplitude of the molecular transform at the Bragg peaks, diffraction from very small crystals allows measurement of the diffraction amplitudes between the Bragg samples. Although highly attenuated, these additional samples offer the possibility of iterative phase retrieval without the use of ancillary experimental data [Spence et al.

Diffraction by nanocrystals.

X-ray femtosecond nanocrystallography is a new, potentially powerful technique for imaging biological macromolecules that uses ensemble-averaged measurements of diffraction of x-ray free-electron laser pulses from nanocrytalline specimens. Nanocrystals have some diffraction characteristics that are distinct from those of macroscopic crystals, due to the presence of different kinds of unit cell in the crystal and of truncated unit cells on the crystal surface. Expressions are derived for diffraction by nanocrystals with variable and incomplete unit cells, averaged over a distribution of crystal sizes and shapes.