A Common Lines Approach for Ab Initio Modeling of Molecules with Tetrahedral and Octahedral Symmetry

A main task in cryo-electron microscopy single particle reconstruction is to find a three-dimensional model of a molecule given a set of its randomly oriented and positioned projection-images. In this work, we propose an algorithm for ab initio reconstruction for molecules with tetrahedral or octahedral symmetry. The algorithm exploits the multiple common lines between each pair of projection-images as well as self common lines within each image, and integrates the information from all images at once. The applicability of the proposed algorithm is demonstrated using simulated and experimental cryo-electron microscopy data.