[Paper Review] Reconstructing continuous distributions of 3D protein structure from cryo-EM images

Ellen D. Zhong, Tristan Bepler+2 more|arXiv (Cornell University)|Sep 11, 2019

Advanced Electron Microscopy Techniques and ApplicationsBiochemistry, Genetics and Molecular Biology37 references45 citations

TL;DR

cryoDRGN is a neural network-based method that reconstructs a continuous distribution of 3D protein structures directly from unlabeled 2D cryo-EM images by combining exact pose inference with variational inference over structural heterogeneity.

ABSTRACT

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.

Motivation & Objective

• Motivate addressing continuous structural heterogeneity in cryo-EM beyond discrete multiclass refinement.
• Propose a neural network framework that models 3D volumes as a continuous latent manifold learned from unlabeled 2D cryo-EM images.
• Disentangle intrinsic structural variability from extrinsic imaging pose using a Fourier-space decoder and exact pose inference.
• Demonstrate ab initio reconstruction capability on simulated and real cryo-EM data.
• Show that cryoDRGN can recover continuous conformational landscapes and compare with traditional multiclass approaches.

Proposed method

• Encode 3D volumes in Fourier space using a coordinate-based neural network decoder parameterized by a latent variable z.
• Use a variational autoencoder to infer the latent variable z from 2D cryo-EM images.
• Perform exact inference over image pose (R, t) via a branch-and-bound global search over SO(3) × R2.
• Represent image formation via the Fourier slice theorem to relate 2D projections to 3D volumes.
• Provide a fixed neural architecture where the decoder outputs a Gaussian over Fourier-domain volumes for given k and z, with positional encoding of k.
• Train the model end-to-end with a variational lower bound, sampling z and optimizing pose for each image.

Experimental results

Research questions

• RQ1 Can a neural network learn a continuous manifold of 3D protein structures directly from unlabeled 2D cryo-EM images?
• RQ2 Does explicit disentangling of imaging pose from intrinsic structural variability enable ab initio reconstruction of continuous heterogeneity?
• RQ3 How does cryoDRGN perform on homogeneous versus heterogeneous datasets and how does it compare to multiclass cryo-EM methods?
• RQ4 Can tilt-series information improve pose invariance and reconstruction quality in unsupervised heterogeneous settings?

Key findings

• CryoDRGN enables ab initio reconstruction of continuous distributions of 3D volumes from unlabeled cryo-EM images.
• On homogeneous data, cryoDRGN matches state-of-the-art pose accuracy and volume reconstruction as measured by FSC and pose errors.
• On heterogeneous real data, cryoDRGN recovers known major structural states and aligns latent space with discrete cryoSPARC clusters.
• In fully unsupervised tests with synthetic continuous heterogeneity, cryoDRGN reconstructs continuous deformations along the true reaction coordinates and outperforms discrete multiclass methods.
• Using tilt-series pairs further improves reconstruction accuracy for continuous heterogeneity tasks.