  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.
