**Mask-Based Approach in Phasing and Restoring of Single-Particle Diffraction Data**
**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, Moscow Region, 142290 Russia*

**Abstract**. The development of experimental techniques, in particular the emergence of the X-ray free-electron lasers, allows one to register the scattering from an isolated particle and, thereby, opens a door to the study of a fine three-dimensional structure of non-crystalline biological objects by X-ray diffraction methods. The possibility to measure non-Bragg reflections makes experimental data mutually dependent and essentially simplifies the structure solution. The sampling of experimental scattering data to a sufficiently fine grid makes the structure determination equivalent to phasing of structure factor magnitudes for a 'virtual' crystal with extremely large solvent content. This makes density modification phasing methods especially powerful supposing the object envelope is known. At the same time, such methods may be sensitive to the accuracy of the predefined envelope and completeness of experimental data and may suffer from non-uniqueness of the solution of the phase problem. The mask-based approach is a preliminary phasing method that performs random search for connected object envelopes possessing of the structure factor magnitudes close to the values observed in X-ray experiment. The alignment and averaging of the phase sets corresponding to selected putative envelopes produce an approximate solution of the phase problem. Beside the estimation of unknown phase values this approach allows one to estimate the values of structure factor magnitudes lost in the experiment, e.g. those corresponding to beam-stop shade zone or to oversaturated reflections.

**Key words**: *biological macromolecules, single-particles, X-ray scattering, X-ray free electron lasers, phase problem, magnitude retrieval, effective resolution*.