Three-Dimensional Alignment of Density Maps in Cryo-Electron Microscopy

A common task in cryo-electron microscopy (cryo-EM) is to compare three-dimensional density maps of macromolecules. In this paper, we propose a fast, accurate and robust algorithm for aligning three-dimensional density maps, by exploiting common lines between projection images of the maps. The algorithm is fully automatic and handles rotations, reflections (handedness) and translations between the maps. In addition, the algorithm is applicable to any type of molecular symmetry without requiring any information regarding the symmetry of the maps. We evaluate our alignment algorithm on publicly available density maps, demonstrating its accuracy and efficiency. The algorithm is available at https://github.com/ShkolniskyLab/emalign.