We present two computational methods for cryo-EM: (1) 2D to 3D reconstruction and (2) 3D map alignment. (1) Our reconstruction method employs stochastic variational inference, with a forward model simulator that incorporates microscope defocus, global 3D pose, and deformations from an anisotropic network model. The variational posterior is characterized by neural networks that amortize over single particle 2D images. The simulator is evaluated every gradient step during training. We explain how to made this computationally feasible on synthetic and experimental data, as well as how frequency marching improves the training. (2) Our alignment method, AlignOT, relies on computational optimal transport to stochastically search for an optimal rotation between two maps, represented as point clouds. We benchmark the precision and accuracy of AlignOT on a selection of experimental maps of diverse conformational heterogeneity and geometry. We anticipate that our non-Euclidean method can be applied to align 3D EM maps when an atomic model is lacking.
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