Statistics of spatial rotations and projection directions considering molecular symmetry in 3D electron cryo-microscopy

Abstract

Electron cryo-microscopy (cryoEM) three-dimensional (3D) reconstruction is based on estimations of orientations of projection images or 3D volumes. It is common that the macromolecules studied by cryoEM have molecular symmetry. However, for neither spatial rotations nor projection directions, cur- rently there is no statistics and classification method which takes molecular symmetry into consideration. This limits the applications of advanced statistical methods in cryoEM. In this research, based on the concept of non-unique-games (NUG), we propose statistics and classification methods of both spatial rotations and projection directions when molecular symmetry is considered. Such methods are realized in the open-source python package pySymStat.