Method of moments for 3D single particle ab initio modeling with non-uniform distribution of viewing angles

  title={Method of moments for 3D single particle ab initio modeling with non-uniform distribution of viewing angles},
  author={Nir Sharon and Joe Kileel and Yuehaw Khoo and Boris Landa and Amit Singer},
  journal={Inverse Problems},
Single-particle reconstruction in cryo-electron microscopy (cryo-EM) is an increasingly popular technique for determining the 3D structure of a molecule from several noisy 2D projections images taken at unknown viewing angles. Most reconstruction algorithms require a low-resolution initialization for the 3D structure, which is the goal of ab initio modeling. Suggested by Zvi Kam in 1980, the method of moments (MoM) offers one approach, wherein low-order statistics of the 2D images are computed… 

Toward single particle reconstruction without particle picking: Breaking the detection limit

This paper contends that the structure could, in principle, be reconstructed directly from the micrographs, without intermediate detection, and as a result, even small molecules should be within reach for cryo-EM.

Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms

It is proved that molecular structures modeled as sums of idealized point masses are uniquely determined by the second-order autocorrelation of their projection images, implying that the sample complexity is proportional to the square of the variance of the noise.

Computational Methods for Single-Particle Cryo-EM

Computational methods for structure determination by single-particle cryo-EM and their guiding principles from statistical inference, machine learning, and signal processing that also play a significant role in many other data science applications are discussed.

Learning to recover orientations from projections in single-particle cryo-EM

The proposed method offers a novel learning-based take on orientation recovery in SPA, and demonstrates that orientations can be accurately recovered from projections that are shifted and corrupted with a high level of noise.

The sample complexity of sparse multi-reference alignment and single-particle cryo-electron microscopy

The second moment of the MRA and cryo-EM models is analyzed, showing that in both models the second moment determines the signal up to a set of unitary matrices, whose dimension is governed by the decomposition of the space of signals into irreducible representations of the group.

Orthogonal Matrix Retrieval with Spatial Consensus for 3D Unknown-View Tomography

This work proposes to jointly recover the density map and the orthogonal matrices by requiring that they be mutually consistent, and designs an easy-to-compute initial density map which effectively mitigates the non-convexity of the reconstruction problem.

Fast Principal Component Analysis for Cryo-EM Images

A fast method for estimating a compressed representation of the 2-D covariance matrix of noisy cryo-electron microscopy projection images that enables fast PCA computation, based on a new algorithm for expanding images in the Fourier-Bessel basis.

Regularising orientation estimation in Cryo-EM 3D map refinement through measure-based lifting over Riemannian manifolds

Motivated by the trade-off between noise-robustness and data-consistency for joint 3D map reconstruction and rotation estimation in single particle cryogenic-electron microscopy (Cryo-EM), we propose

3D Unknown View Tomography Via Rotation Invariants

The method obviates the need to recover the projection angles by extracting a set of rotation-invariant features from the noisy projection data by reconstructing the density map through a constrained nonconvex optimization.

Motion Detection in Diffraction Tomography by Common Circle Methods

The method of common lines is a well-established reconstruction technique in cryogenic electron microscopy (cryo-EM), which can be used to extract the relative orientations of an object in



Angular reconstitution: a posteriori assignment of projection directions for 3D reconstruction.

A method of "angular reconstitution" is described, which allows the a posteriori determination of the relative angular orientations of the projections and thus enables the three-dimensional reconstruction of the object to be calculated.

Non-Uniformity of Projection Distributions Attenuates Resolution in Cryo-EM

This work shows how inhomogeneity in any projection distribution scheme attenuates the global Fourier Shell Correlation (FSC) in relation to the number of particles and a single geometrical parameter, which is termed the sampling compensation factor (SCF).

Three-Dimensional Structure Determination from Common Lines in Cryo-EM by Eigenvectors and Semidefinite Programming

Two algorithms for finding the unknown imaging directions of all projections by minimizing global self-consistency errors are described and are optimal in the sense that they reach the information theoretic Shannon bound up to a constant for an idealized probabilistic model.

Single‐particle cryo‐EM—Improved ab initio 3D reconstruction with SIMPLE/PRIME

The refined method for identification of homogeneous subsets of images in accurate register substantially improves the resolution of the cluster centers and of the ab initio 3D reconstructions derived from them.

Structural Variability from Noisy Tomographic Projections

A shrinkage procedure is incorporated by the recent success of eigenvalue shrinkage procedures for high-dimensional covariance matrix estimation that improves accuracy at lower signal-to-noise ratios and compares favorably in runtime with respect to previously proposed nonconsistent estimators.

RELION: Implementation of a Bayesian approach to cryo-EM structure determination

  • S. Scheres
  • Computer Science
    Journal of structural biology
  • 2012

Iterative phasing for fluctuation X-ray scattering

A multitiered iterative phasing algorithm to determine the underlying structure of the scattering object from FXS data is developed, which allows one to visualize structural details that may be inaccessible through traditional methods.

Measuring the effects of particle orientation to improve the efficiency of electron cryomicroscopy

The efficiency measures the ability of the distribution to provide uniform information and resolution in all directions of the reconstruction, independent of other factors, allows rapid and rigorous evaluation of specimen preparation methods, assisting structure determination to high resolution with minimal data.