Single-particle cryo-electron microscopy: Mathematical theory, computational challenges, and opportunities

Abstract

In recent years, an abundance of new molecular structures have been elucidated using cryo-electron microscopy (cryo-EM), largely due to advances in hardware technology and data processing techniques. Owing to these new exciting developments, cryo-EM was selected by Nature Methods as Method of the Year 2015, and the Nobel Prize in Chemistry 2017 was awarded to three pioneers in the field. The main goal of this article is to introduce the challenging and exciting computational tasks involved in reconstructing 3-D molecular structures by cryo-EM. Determining molecular structures requires a wide range of computational tools in a variety of fields, including signal processing, estimation and detection theory, high-dimensional statistics, convex and non-convex optimization, spectral algorithms, dimensionality reduction, and machine learning. The tools from these fields must be adapted to work under exceptionally challenging conditions, including extreme noise levels, the presence of missing data, and massively large datasets as large as several Terabytes. In addition, we present two statistical models: multi-reference alignment and multi-target detection, that abstract away much of the intricacies of cryo-EM, while retaining some of its essential features. Based on these abstractions, we discuss some recent intriguing results in the mathematical theory of cryo-EM, and delineate relations with group theory, invariant theory, and information theory.

References in corpus (10)

• Convolutional Neural Networks for Automated Annotation of Cellular Cryo-Electron Tomograms
• A deep convolutional neural network approach to single-particle recognition in cryo-electron microscopy
• Bispectrum Inversion with Application to Multireference Alignment
• Denoising and Covariance Estimation of Single Particle Cryo-EM Images
• Fundamental Limits in Multi-image Alignment
• Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes
• Common lines modeling for reference free ab-initio reconstruction in cryo-EM
• Multi-target detection with application to cryo-electron microscopy
• Unsupervised particle sorting for high-resolution single-particle cryo-EM
• A common lines approach for ab-initio modeling of cyclically-symmetric molecules

Cited by in corpus (15)

• Manifold learning with arbitrary norms
• Multi-reference alignment in high dimensions: sample complexity and phase transition
• The generalized method of moments for multi-reference alignment
• Optimal spectral shrinkage and PCA with heteroscedastic noise
• Multi-target Detection with an Arbitrary Spacing Distribution
• Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms
• An accelerated expectation-maximization algorithm for multi-reference alignment
• Two-dimensional multi-target detection: an autocorrelation analysis approach
• An approximate expectation-maximization for two-dimensional multi-target detection
• Motion Detection in Diffraction Tomography by Common Circle Methods
• Degree bounds for fields of rational invariants of $\mathbb{Z}/p\mathbb{Z}$ and other finite groups
• Efficient high-resolution refinement in cryo-EM with stochastic gradient descent
• Generalized autocorrelation analysis for multi-target detection
• Regularising orientation estimation in Cryo-EM 3D map refinement through measure-based lifting over Riemannian manifolds
• 3D Tomographic Phase Retrieval and Unwrapping