Deep learning-based mixed-dimensional Gaussian mixture model for characterizing variability in cryo-EM.

Structural flexibility and/or dynamic interactions with other molecules is a critical aspect of protein function. Cryogenic electron microscopy (cryo-EM) provides direct visualization of individual macromolecules sampling different conformational and compositional states. While numerous methods are available for computational classification of discrete states, characterization of continuous conformational changes or large numbers of discrete state without human supervision remains challenging. Here we present e2gmm, a machine learning algorithm to determine a conformational landscape for proteins or complexes using a three-dimensional Gaussian mixture model mapped onto two-dimensional particle images in known orientations. Using a deep neural network architecture, e2gmm can automatically resolve the structural heterogeneity within the protein complex and map particles onto a small latent space describing conformational and compositional changes. This system presents a more intuitive and flexible representation than other manifold methods currently in use. We demonstrate this method on both simulated data and three biological systems to explore compositional and conformational changes at a range of scales. The software is distributed as part of EMAN2.