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X-ray free-electron lasers (XFELs) open the possibility of obtaining diffraction information from a single biological macromolecule. This is because XFELs can generate extremely intense x-ray pulses that are so short that diffraction data can be collected before the sample is destroyed. By collecting a sufficient number of single-particle diffraction patterns, the three-dimensional electron density of a molecule can be reconstructed ab initio. The quality of the reconstruction depends largely on the number of patterns collected at the experiment. This paper provides an estimate of the number of diffraction patterns required to reconstruct the electron density at a targeted spatial resolution. This estimate is verified by simulations for realistic x-ray fluences, repetition rates, and experimental conditions available at modern XFELs. Employing the bacterial phytochrome as a model system, we demonstrate that sub-nanometer resolution is within reach.

Single-particle structure recovery without crystals or radiation damage is a revolutionary possibility offered by X-ray free-electron lasers, but it involves formidable experimental and data-analytical challenges. Many of these difficulties were encountered during the development of cryogenic electron microscopy of biological systems. Electron microscopy of biological entities has now reached a spatial resolution of about 0.3 nm, with a rapidly emerging capability to map discrete and continuous conformational changes and the energy landscapes of biomolecular machines. Nonetheless, single-particle imaging by X-ray free-electron lasers remains important for a range of applications, including the study of large “electron-opaque” objects and time-resolved examination of key biological processes at physiological temperatures. After summarizing the state of the art in the study of structure and conformations by cryogenic electron microscopy, we identify the primary opportunities and challenges facing X-ray-based single-particle approaches, and possible means for circumventing them.

Determination of fast structural changes of biomolecules is usually performed on crystalline samples in a time-resolved pump-probe experiment. Changes in the structure are found by the difference Fourier method using phases of a known reference structure. As we showed recently, such changes can also be determined from diffraction of uncrystallized molecules in random orientations. In this case, the difference in the angular correlations of the diffraction patterns is used to find structural changes. Similar to the difference Fourier method, there is no need for iterative phasing. We validated this approach previously with simulations in the absence of noise. In this paper, we show that the effects of noise can be adequately suppressed by averaging over a sufficiently large ensemble as they can be obtained using an X-ray free electron laser.