Spectral decomposition of atomic structures in heterogeneous cryo-EM

Abstract We consider the problem of recovering three-dimensional atomic structure a flexible macromolecule from heterogeneous cryogenic electron microscopy (cryo-EM) dataset. The dataset contains noisy tomographic projections electrostatic potential macromolecule, taken different viewing directions, and in case, each cryo-EM image corresponds to conformation macromolecule. Under assumption that can be modelled as chain, or discrete curve (as it is for instance case protein backbone with single chain amino-acids), we introduce method estimate deformation model respect given conformation, which assumed known priori . Our consists on estimating torsion bond angles linear combination eigenfunctions Laplace operator manifold conformations. These approximated by means well-known technique learning, based construction graph Laplacian using Finally, test our approach synthetic datasets, recover two-dimensional structures simulated images.