Single Particle Study by X-Ray Diffraction: Crystallographic Approach
Lunin V.Y., Lunina N.L., Petrova T.E.
Institute of Mathematical Problems of Biology RAS, Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Pushchino, Russia
Abstract. An increase in the power of X-ray sources, in particular, the commissioning of X-ray free electron lasers, opens up the possibility of recording the diffraction by single macromolecular biological particles. These opportunities open the way to weakening, and, ideally, removal, of the main limitation of X-ray structure analysis, namely, the need to prepare the sample in the single-crystal form. However, the possibility of the practical recording of diffraction by a single particle is currently limited to a very low-resolution zone, what is one of the main obstacles in the development of this approach. This paper discusses the similarities and differences in the study of crystal samples and single particles. It is shown that the problem of the determination of the structure of a single particle can be formulated as a standard problem of biological crystallography, namely, as the problem of retrieval the electron density distribution in some unit cell from the magnitudes of its Fourier coefficients. This makes it possible to apply the entire range of the methods of biological crystallography to the study of isolated particles. At the same time, the possibility of recording continuous diffraction pattern for a single particle (as opposed to a discrete set of Bragg reflections in the case of a crystal) significantly increases the amount of information derived from the experiment. The analytical properties of the continuous diffraction pattern create a potential opportunity both to restore the structure factors phases (lost in the diffraction experiment), and to extrapolate the experimentally observed pattern onto a wider area, which allows to increase the resolution of Fourier syntheses for the electron density distribution.
Key words: biological macromolecules, single-particles, X-ray scattering, X-ray free electron lasers, phase problem, resolution of Fourier syntheses.