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

Abstract. The main obstacle to the determination of the atomic structure of a biological macromolecule by X-ray structural analysis is the need to obtain a crystal of the object under study. This need is due to the complexity of the experimental registration of scattering from a separate molecule. However, it is not always possible to get crystals of biological objects. The development of experimental techniques, in particular the emergence of the X-ray free-electron lasers, allows to approach the practical solution of the problem of registration of the scattering from an isolated particle and thereby to obtain information about the three-dimensional structure of non-crystalline biological objects by X-ray diffraction methods. Sampling of experimental scattering data makes the task of the structure determination of a single particle equivalent to the standard problem of biological crystallography, which allows to extend the biological crystallography techniques to the study of isolated biological particles (individual cells, organelles, molecular machines and, in the future, biological macromolecules). This article is devoted to the state of the art in this area, problems and solutions.

Key words: X-ray crystallography, the phase problem, XFEL, single particle diffraction.