Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Equivariant amortized inference of poses for cryo-EM

Larissa de Ruijter, Gabriele Cesa

TL;DR

This work tackles cryo-EM pose estimation under high noise and unknown orientations by introducing an equivariant amortized inference framework. A $D_4$-equivariant encoder, built with steerable CNNs, enforces planar symmetries and enables faster convergence and more accurate pose estimation, improving the Fourier-space reconstruction via FourierNet. The authors show that the $D_4$-equivariant model can render the symmetric loss unnecessary while delivering superior FSC-based resolution and pose accuracy, with robustness across varying noise levels. These findings highlight a scalable approach to rapid, high-resolution cryo-EM reconstructions using geometric priors to address convergence challenges.

Abstract

Cryo-EM is a vital technique for determining 3D structure of biological molecules such as proteins and viruses. The cryo-EM reconstruction problem is challenging due to the high noise levels, the missing poses of particles, and the computational demands of processing large datasets. A promising solution to these challenges lies in the use of amortized inference methods, which have shown particular efficacy in pose estimation for large datasets. However, these methods also encounter convergence issues, often necessitating sophisticated initialization strategies or engineered solutions for effective convergence. Building upon the existing cryoAI pipeline, which employs a symmetric loss function to address convergence problems, this work explores the emergence and persistence of these issues within the pipeline. Additionally, we explore the impact of equivariant amortized inference on enhancing convergence. Our investigations reveal that, when applied to simulated data, a pipeline incorporating an equivariant encoder not only converges faster and more frequently than the standard approach but also demonstrates superior performance in terms of pose estimation accuracy and the resolution of the reconstructed volume. Notably, $D_4$-equivariant encoders make the symmetric loss superfluous and, therefore, allow for a more efficient reconstruction pipeline.

Equivariant amortized inference of poses for cryo-EM

TL;DR

This work tackles cryo-EM pose estimation under high noise and unknown orientations by introducing an equivariant amortized inference framework. A -equivariant encoder, built with steerable CNNs, enforces planar symmetries and enables faster convergence and more accurate pose estimation, improving the Fourier-space reconstruction via FourierNet. The authors show that the -equivariant model can render the symmetric loss unnecessary while delivering superior FSC-based resolution and pose accuracy, with robustness across varying noise levels. These findings highlight a scalable approach to rapid, high-resolution cryo-EM reconstructions using geometric priors to address convergence challenges.

Abstract

Cryo-EM is a vital technique for determining 3D structure of biological molecules such as proteins and viruses. The cryo-EM reconstruction problem is challenging due to the high noise levels, the missing poses of particles, and the computational demands of processing large datasets. A promising solution to these challenges lies in the use of amortized inference methods, which have shown particular efficacy in pose estimation for large datasets. However, these methods also encounter convergence issues, often necessitating sophisticated initialization strategies or engineered solutions for effective convergence. Building upon the existing cryoAI pipeline, which employs a symmetric loss function to address convergence problems, this work explores the emergence and persistence of these issues within the pipeline. Additionally, we explore the impact of equivariant amortized inference on enhancing convergence. Our investigations reveal that, when applied to simulated data, a pipeline incorporating an equivariant encoder not only converges faster and more frequently than the standard approach but also demonstrates superior performance in terms of pose estimation accuracy and the resolution of the reconstructed volume. Notably, -equivariant encoders make the symmetric loss superfluous and, therefore, allow for a more efficient reconstruction pipeline.
Paper Structure (46 sections, 39 equations, 12 figures, 2 tables)

This paper contains 46 sections, 39 equations, 12 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Contributions
  3. Image formation model
  4. Related work
  5. Amortized inference of poses for cryo-EM
  6. Homoemorphic Encoders and Equivariance
  7. Method
  8. Equivariant amortized inference of poses
  9. Pipeline overview
  10. Equivariant encoder
  11. Symmetric loss function
  12. Experiments
  13. Convergence of original pipeline
  14. Impact of equivariance on convergence of pipeline
  15. Higher noise levels
  16. ...and 31 more sections

Figures (12)

  • Figure 1: Images in the same equivalence class differ only by an in-plane rotation and/or reflection. Source: cesa2022symmetries.
  • Figure 2: The MSE and MedSE over time for each of the five runs on the noiselessspliceosome dataset.
  • Figure 3: Fourier Shell Correlation (FSC) curves and reconstruction visualizations comparing the reconstruction to the ground truth (GT) for the top-performing seeds in 6000-second runs across four simulated datasets. Each dataset is represented by two curves and two visualizations: one from the best run using the $D_4$-equivariant model and one from the best run with the standard cryoAI pipeline. The volume visualisations were made with software ChimeraX (meng2023ucsf). The $D_4$-equivariant model consistently improves the FSC score over the non-equivariant cryoAI baseline.
  • Figure 4: Visualization of the two volumes that were used to generate the datasets. The visualisations were made with software ChimeraX meng2023ucsf
  • Figure 5: Examples of images from our datasets generated with the plasmodium falciparum 80S ribosome volume with different noise levels.
  • ...and 7 more figures