Center of Mass Operators for Cryo-EM—Theory and Implementation

A central task in recovering the structure of a macromolecule using cryo-electron microscopy is to determine a three-dimensional model of the macromolecule from many of its two-dimensional projection images, taken from random and unknown directions. We have recently proposed the globally consistent angular reconstitution (GCAR) [7], which allows to determine a three-dimensional model of the molecule without assuming any prior knowledge on the reconstructed molecule or the distribution of its viewing directions. In this chapter we briefly introduce the idea behind the algorithm [7], and describe several improvements and implementation details required in order to apply it on experimental data. In particular, we extend GCAR with self-stabilizing refinement iterations that increase its robustness to noise, modify the common lines detection procedure to handle the relative (unknown) shifts between images, and demonstrate the algorithm on real data obtained by an electron microscope.