Institute of Mathematical Problems of Biology RAS, Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Pushchino, Russia

Abstract. X-ray diffraction analysis is the main experimental approach to determining the atomic structure of biological macromolecules and their complexes. The most serious limitation of its applicability, to date, is the need to prepare a sample of the object under study in the form of a single crystal, which is caused by the extremely low intensity of rays scattered by a single molecule. The commissioning of X-ray Free-Electron Lasers with their super-powerful (by many orders of magnitude exceeding the brightness of modern synchrotrons) and ultra-short (less than 100 fs) pulse is an experimental breakthrough that allows us to expect to obtain diffraction patterns from individual biological particles and then determine their structure. The first experimental results demonstrate the fundamental possibility of such an approach and are accompanied by the publication of a significant number of articles on various aspects of the development of the method. The purpose of this article is to discuss the current state of art in this area, evaluate the results achieved and discuss the prospects for further development of the method based on the analysis of publications in the world scientific literature of recent years and the experience of work carried out by the review authors and their colleagues.

Key words: biological macromolecules, single particle, X-ray diffraction, X-ray Free-electrons Lasers, the phase problem, biological crystallography.