Electron cryo-microscopy (cryo-EM) is a powerful method for investigating the structures of protein molecules, with important implications for understanding the molecular processes of life and drug development. In this technique, many noisy, two-dimensional projection images of protein molecules in unknown poses are combined into one or more three-dimensional reconstructions. The presence of multiple structural states in the data represents a major bottleneck in existing processing pipelines, often requiring expert user supervision. Variational auto-encoders (VAEs) have recently been proposed as an attractive means for learning the data manifold of data sets with a large number of different states. These methods are based on a coordinate-based approach, similar to Neural Radiance Fields (NeRF), to make volumetric reconstructions from 2D image data in Fourier-space. Although NeRF is a powerful method for real-space reconstruction, many of the benefits of the method do not transfer to Fourier-space, e.g.

Electron cryo-microscopy (cryo-EM) is a powerful method for investigating the structures of protein molecules, with important implications for understanding the molecular processes of life and drug development. In this technique, many noisy, two-dimensional projection images of protein molecules in unknown poses are combined into one or more three-dimensional reconstructions. The presence of multiple structural states in the data represents a major bottleneck in existing processing pipelines, often requiring expert user supervision. Variational auto-encoders (VAEs) have recently been proposed as an attractive means for learning the data manifold of data sets with a large number of different states. These methods are based on a coordinate-based approach, similar to Neural Radiance Fields (NeRF), to make volumetric reconstructions from 2D image data in Fourier-space.

Cryo-electron microscopy (cryo-EM) is a powerful technique for determining the structure of proteins and other macromolecular complexes at near-atomic resolution. In single particle cryo-EM, the central problem is to reconstruct the three-dimensional structure of a macromolecule from $10^{4-7}$ noisy and randomly oriented two-dimensional projections. However, the imaged protein complexes may exhibit structural variability, which complicates reconstruction and is typically addressed using discrete clustering approaches that fail to capture the full range of protein dynamics. Here, we introduce a novel method for cryo-EM reconstruction that extends naturally to modeling continuous generative factors of structural heterogeneity. This method encodes structures in Fourier space using coordinate-based deep neural networks, and trains these networks from unlabeled 2D cryo-EM images by combining exact inference over image orientation with variational inference for structural heterogeneity. We demonstrate that the proposed method, termed cryoDRGN, can perform ab initio reconstruction of 3D protein complexes from simulated and real 2D cryo-EM image data. To our knowledge, cryoDRGN is the first neural network-based approach for cryo-EM reconstruction and the first end-to-end method for directly reconstructing continuous ensembles of protein structures from cryo-EM images.

Single-particle electron cryomicroscopy is an essential tool for high-resolution 3D reconstruction of proteins and other biological macromolecules. An important challenge in cryo-EM is the reconstruction of non-rigid molecules with parts that move and deform. Traditional reconstruction methods fail in these cases, resulting in smeared reconstructions of the moving parts. This poses a major obstacle for structural biologists, who need high-resolution reconstructions of entire macromolecules, moving parts included. To address this challenge, we present a new method for the reconstruction of macromolecules exhibiting continuous heterogeneity. The proposed method uses projection images from multiple viewing directions to construct a graph Laplacian through which the manifold of three-dimensional conformations is analyzed. The 3D molecular structures are then expanded in a basis of Laplacian eigenvectors, using a novel generalized tomographic reconstruction algorithm to compute the expansion coefficients. These coefficients, which we name spectral volumes, provide a high-resolution visualization of the molecular dynamics. We provide a theoretical analysis and evaluate the method empirically on several simulated data sets.