Orthogonal Matrix Retrieval in Cryo-Electron Microscopy

In single particle reconstruction (SPR) from cryo-electron microscopy (cryo-EM), the 3D structure of a molecule needs to be determined from its 2D projection images taken at unknown viewing directions. Zvi Kam showed already in 1980 that the autocorrelation function of the 3D molecule over the rotation group SO(3) can be estimated from 2D projection images whose viewing directions are uniformly distributed over the sphere. The autocorrelation function determines the expansion coefficients of the 3D molecule in spherical harmonics up to an orthogonal matrix of size $(2l+1)\times (2l+1)$ for each $l=0,1,2,...$. In this paper we show how techniques for solving the phase retrieval problem in X-ray crystallography can be modified for the cryo-EM setup for retrieving the missing orthogonal matrices. Specifically, we present two new approaches that we term Orthogonal Extension and Orthogonal Replacement, in which the main algorithmic components are the singular value decomposition and semidefinite programming. We demonstrate the utility of these approaches through numerical experiments on simulated data.Comment: Modified introduction and summary. Accepted to the IEEE International Symposium on Biomedical Imagin

CRYO-ELECTRON MICROSCOPY SYMPOSIUM

A Revolution for Structural Biology: Electron Microscopy of Macromolecules at Atomic Resolutionhttps://digitalcommons.rockefeller.edu/posters/1199/thumbnail.jp

Cryo-electron microscopy of viruses

Thin vitrified layers of unfixed, unstained and unsupported virus suspensions can be prepared for observation by cryo-electron microscopy in easily controlled conditions. The viral particles appear free from the kind of damage caused by dehydration, freezing or adsorption to a support that is encountered in preparing biological samples for conventional electron microscopy. Cryo-electron microscopy of vitrified specimens offers possibilities for high resolution observations that compare favourably with any other electron microscopical method

Common lines ab-initio reconstruction of D2D_2-symmetric molecules

Cryo-electron microscopy is a state-of-the-art method for determining high-resolution three-dimensional models of molecules, from their two-dimensional projection images taken by an electron microscope. A crucial step in this method is to determine a low-resolution model of the molecule using only the given projection images, without using any three-dimensional information, such as an assumed reference model. For molecules without symmetry, this is often done by exploiting common lines between pairs of images. Common lines algorithms have been recently devised for molecules with cyclic symmetry, but no such algorithms exist for molecules with dihedral symmetry. In this work, we present a common lines algorithm for determining the structure of molecules with $D_{2}$ symmetry. The algorithm exploits the common lines between all pairs of images simultaneously, as well as common lines within each image. We demonstrate the applicability of our algorithm using experimental cryo-electron microscopy data

Cryo-electron microscopy of chromatin biology

The basic unit of chromatin, the nucleosome core particle (NCP), controls how DNA in eukaryotic cells is compacted, replicated and read. Since its discovery, biochemists have sought to understand how this protein-DNA complex can help to control so many diverse tasks. Recent electron-microscopy (EM) studies on NCP-containing assemblies have helped to describe important chromatin transactions at a molecular level. With the implementation of recent technical advances in single-particle EM, our understanding of how nucleosomes are recognized and read looks to take a leap forward. In this review, the authors highlight recent advances in the architectural understanding of chromatin biology elucidated by EM