Ab initio reconstruction from one-dimensional crystal diffraction data.

Filamentary and rod-like assemblies are ubiquitous in biological systems, and single such assemblies can form one-dimensional (1D) crystals. New, intense X-ray sources, such as X-ray free-electron lasers, make it feasible to measure diffraction data from single 1D crystals. Such experiments would present some advantages, since cylindrical averaging of the diffraction data in conventional fiber diffraction analysis is avoided, there is coherent signal amplification relative to single-particle imaging, and the diffraction data are oversampled compared with those from a 3D crystal so that the phase problem is better determined than for a 3D crystal [Millane (2017). Acta Cryst. A73, 140-150]. Phasing of 1D crystal diffraction data is examined, by simulation, using an iterative projection algorithm. Ab initio phasing is feasible with realistic noise levels and little envelope information is required if a shrink-wrap algorithm is also incorporated. Some practical aspects of the proposed experiments are explored.