Cryo-EM image alignment based on nonuniform fast Fourier transform

Abstract

In single particle analysis, two-dimensional (2-D) alignment is a fundamental step intended to put into register various particle projections of biological macromolecules collected at the electron microscope. The efficiency and quality of three-dimensional (3-D) structure reconstruction largely depends on the computational speed and alignment accuracy of this crucial step. In order to improve the performance of alignment, we introduce a new method that takes advantage of the highly accurate interpolation scheme based on the gridding method, a version of the nonuniform Fast Fourier Transform, and utilizes a multi-dimensional optimization algorithm for the refinement of the orientation parameters. Using simulated data, we demonstrate that by using less than half of the sample points and taking twice the runtime, our new 2-D alignment method achieves dramatically better alignment accuracy than that based on quadratic interpolation. We also apply our method to image to volume registration, the key step in the single particle EM structure refinement protocol. We find that in this case the accuracy of the method not only surpasses the accuracy of the commonly used real-space implementation, but results are achieved in much shorter time, making griddingbased alignment a perfect candidate for efficient structure determination in single particle analysis.

Assembly of macromolecular complexes by satisfaction of spatial restraints from electron microscopy images

“…The specific noise σ j is presumed to be constant for all images. We define the em2D score as the minimal difference between the image and a model projection (28,29):…”

“…In the refinement step, the k vectors α ij for image d i obtained from the coarse search are sorted by descending value of the corresponding ccc, and the first l ≤ k of them are refined (typically, l = 2). Each α ij is refined by the Simplex algorithm to maximize the ccc between image d i and projection p j (28). The vector α ij that gives the maximum ccc after the refinement is used to compute the em2D score.…”

Cryogenic Electron Microscopy and Single-Particle Analysis

“…However, the key advances contributed by EMAN were the user-friendly Unix toolbox-style command-line interface and the graphical user interface, which offered newcomers a welcoming environment. SPARX (83) is another all-purpose package that contributed new algorithms for improved interpolation accuracy (112,113), statistical methods for sorting single-particle projections aligned in 3D according to conformational or compositional state (12), and robust 2D alignment and clustering procedures (48). The FREALIGN program for high-resolution refinement advanced the projection matching algorithm by introducing continuous orientation search for alignment of individual particle images, eliminating the need for class averaging altogether (59).…”

Three-dimensional reconstruction for coherent diffraction patterns obtained by XFEL

“…There are currently two main strategies for estimating the 3D orientation of particles. One is called projection matching (Penczek et al, 1994;Sorzano et al, 2004;Grigorieff, 2007;Yang & Penczek, 2008), where the best angular parameters are estimated by finding an image which has a maximum correlation coefficient in the reference library and is used to construct a new volume. Another widely used strategy is the maximum-likelihoodbased algorithm (Scheres et al, 2007;Sigworth et al, 2010;Scheres, 2012;Lyumkis et al, 2013).…”