A Modified Cross Correlation Algorithm for Reference-free Image Alignment of Non-Circular Projections in Single-Particle Electron Microscopy

In this paper we propose a modified cross correlation method to align images from the same class in single-particle electron microscopy of highly non-spherical structures. In this new method, First we coarsely align projection images, and then re-align the resulting images using the cross correlation (CC) method. The coarse alignment is obtained by matching the centers of mass and the principal axes of the images. The distribution of misalignment in this coarse alignment can be quantified based on the statistical properties of the additive background noise. As a consequence, the search space for re-alignment in the cross correlation method can be reduced to achieve better alignment. In order to overcome problems associated with false peaks in the cross correlations function, we use artificially blurred images for the early stage of the iterative cross correlation method and segment the intermediate class average from every iteration step. These two additional manipulations combined with the reduced search space size in the cross correlation method yield better alignments for low signal-to-noise ratio images than both classical cross correlation and maximum likelihood(ML) methods.Comment: 29page

Rotationally Invariant Image Representation for Viewing Direction Classification in Cryo-EM

We introduce a new rotationally invariant viewing angle classification method for identifying, among a large number of Cryo-EM projection images, similar views without prior knowledge of the molecule. Our rotationally invariant features are based on the bispectrum. Each image is denoised and compressed using steerable principal component analysis (PCA) such that rotating an image is equivalent to phase shifting the expansion coefficients. Thus we are able to extend the theory of bispectrum of 1D periodic signals to 2D images. The randomized PCA algorithm is then used to efficiently reduce the dimensionality of the bispectrum coefficients, enabling fast computation of the similarity between any pair of images. The nearest neighbors provide an initial classification of similar viewing angles. In this way, rotational alignment is only performed for images with their nearest neighbors. The initial nearest neighbor classification and alignment are further improved by a new classification method called vector diffusion maps. Our pipeline for viewing angle classification and alignment is experimentally shown to be faster and more accurate than reference-free alignment with rotationally invariant K-means clustering, MSA/MRA 2D classification, and their modern approximations

Alignment, Classification, and Three-Dimensional Reconstruction of Single Particles Embedded in Ice

Cryo-electron microscopy of single biological particles poses new challenges to digital image processing due to the low signal-to-noise ratio of the data. New tools have been devised to deal with important aspects of 3-D reconstruction following the random-conical data collection scheme: (a) a new shift-invariant function has been derived, which promises to facilitate alignment and classification of single particle projections; (b) a new method of orientation search is proposed, which makes it possible to relate random-conical data sets to one another prior to reconstruction; and (c) the foundation is laid for a 3-D variance estimation which utilizes the oversampling of 3-D angular space by projections in the random-conical reconstruction scheme

Contributions To Automatic Particle Identification In Electron Micrographs: Algorithms, Implementation, And Applications

Three dimensional reconstruction of large macromolecules like viruses at resolutions below 8 Ã… - 10 Ã… requires a large set of projection images and the particle identification step becomes a bottleneck. Several automatic and semi-automatic particle detection algorithms have been developed along the years. We present a general technique designed to automatically identify the projection images of particles. The method utilizes Markov random field modelling of the projected images and involves a preprocessing of electron micrographs followed by image segmentation and post processing for boxing of the particle projections. Due to the typically extensive computational requirements for extracting hundreds of thousands of particle projections, parallel processing becomes essential. We present parallel algorithms and load balancing schemes for our algorithms. The lack of a standard benchmark for relative performance analysis of particle identification algorithms has prompted us to develop a benchmark suite. Further, we present a collection of metrics for the relative performance analysis of particle identification algorithms on the micrograph images in the suite, and discuss the design of the benchmark suite

Three-dimensional structure and flexibility of a membrane-coating module of the nuclear pore complex.

The nuclear pore complex mediates nucleocytoplasmic transport in all eukaryotes and is among the largest cellular assemblies of proteins, collectively known as nucleoporins. Nucleoporins are organized into distinct subcomplexes. We optimized the isolation of a putative membrane-coating subcomplex of the nuclear pore complex, the heptameric Nup84 complex, and analyzed its structure by EM. Our data confirmed the previously reported 'Y' shape. We discerned additional structural details, including specific hinge regions at which the particle shows great flexibility. We determined the three-dimensional structures of two conformers, mapped the localization of two nucleoporins within the subcomplex and docked known crystal structures into the EM maps. The free ends of the Y-shaped particle are formed by beta-propellers; the connecting segments consist of alpha-solenoids. Notably, the same organizational principle is found in the clathrin triskelion, which may share a common evolutionary origin with the heptameric complex

Automatic particle detection in digitized electron micrographs

High resolution structural analysis of biological complexes can be carried out by single particle electron microscopy where a large number of particle images are available. Many approaches to automate the process of selection of particle positions from digitized electron micrograph images have been described, but so far none has proved as good as manual selection. This thesis describes a method which I have developed to locate such biological complexes by matching small boxed areas to a set of reference images using the radius of gyration, complemented by a series of other simple criteria. From the reference images, parameters such as the ratio between the average density of the central area and that in its surrounding band, and the density sum and variance are calculated. They are compared with corresponding values from a moving square window of densities extracted from the micrograph, and the coordinates of successfully matched candidate squares are recorded. Since the same particle is detected in a series of overlapping windows, candidates found to be within close proximity are grouped, and the best-fitting one is selected from each cluster. Along with a small stack of boxed reference images, a few specified parameter values, such as the particle radius and the minimum acceptable distance between particle centres are required to select the windows. Micrograph labels and other areas that do not contain appropriate specimens are automatically ignored in order to minimize false positives, and reduce the computing time. A computer program SLEUTH written to carry out this method of automatic particle detection includes a graphical user interface to assist the user in setting up the parameter values. The program has been tested successfully on a variety of different biological structures, from both negatively stained and ice-embedded specimens

3D reconstruction of biological structures: automated procedures for alignment and reconstruction of multiple tilt series in electron tomography

Transmission electron microscopy allows the collection of multiple views of specimens and their computerized three-dimensional reconstruction and analysis with electron tomography. Here we describe development of methods for automated multi-tilt data acquisition, tilt-series processing, and alignment which allow assembly of electron tomographic data from a greater number of tilt series, yielding enhanced data quality and increasing contrast associated with weakly stained structures. This scheme facilitates visualization of nanometer scale details of fine structure in volumes taken from plastic-embedded samples of biological specimens in all dimensions. As heavy metal-contrasted plastic-embedded samples are less sensitive to the overall dose rather than the electron dose rate, an optimal resampling of the reconstruction space can be achieved by accumulating lower dose electron micrographs of the same area over a wider range of specimen orientations. The computerized multiple tilt series collection scheme is implemented together with automated advanced procedures making collection, image alignment, and processing of multi-tilt tomography data a seamless process. We demonstrate high-quality reconstructions from samples of well-described biological structures. These include the giant Mimivirus and clathrin-coated vesicles, imaged in situ in their normal intracellular contexts. Examples are provided from samples of cultured cells prepared by high-pressure freezing and freeze-substitution as well as by chemical fixation before epoxy resin embedding

Novel computational methods for in vitro and in situ cryo-electron microscopy

Over the past decade, advances in microscope hardware and image data processing algorithms have made cryo-electron microscopy (cryo-EM) a dominant technique for protein structure determination. Near-atomic resolution can now be obtained for many challenging in vitro samples using single-particle analysis (SPA), while sub-tomogram averaging (STA) can obtain sub-nanometer resolution for large protein complexes in a crowded cellular environment. Reaching high resolution requires large amounts of im-age data. Modern transmission electron microscopes (TEMs) automate the acquisition process and can acquire thousands of micrographs or hundreds of tomographic tilt se-ries over several days without intervention. In a first step, the data must be pre-processed: Micrographs acquired as movies are cor-rected for stage and beam-induced motion. For tilt series, additional alignment of all micrographs in 3D is performed using gold- or patch-based fiducials. Parameters of the contrast-transfer function (CTF) are estimated to enable its reversal during SPA refine-ment. Finally, individual protein particles must be located and extracted from the aligned micrographs. Current pre-processing algorithms, especially those for particle picking, are not robust enough to enable fully unsupervised operation. Thus, pre-processing is start-ed after data collection, and takes several days due to the amount of supervision re-quired. Pre-processing the data in parallel to acquisition with more robust algorithms would save time and allow to discover bad samples and microscope settings early on. Warp is a new software for cryo-EM data pre-processing. It implements new algorithms for motion correction, CTF estimation, tomogram reconstruction, as well as deep learn-ing-based approaches to particle picking and image denoising. The algorithms are more accurate and robust, enabling unsupervised operation. Warp integrates all pre-processing steps into a pipeline that is executed on-the-fly during data collection. Inte-grated with SPA tools, the pipeline can produce 2D and 3D classes less than an hour into data collection for favorable samples. Here I describe the implementation of the new algorithms, and evaluate them on various movie and tilt series data sets. I show that un-supervised pre-processing of a tilted influenza hemagglutinin trimer sample with Warp and refinement in cryoSPARC can improve previously published resolution from 3.9 Å to 3.2 Å. Warp’s algorithms operate in a reference-free manner to improve the image resolution at the pre-processing stage when no high-resolution maps are available for the particles yet. Once 3D maps have been refined, they can be used to go back to the raw data and perform reference-based refinement of sample motion and CTF in movies and tilt series. M is a new tool I developed to solve this task in a multi-particle framework. Instead of following the SPA assumption that every particle is single and independent, M models all particles in a field of view as parts of a large, physically connected multi-particle system. This allows M to optimize hyper-parameters of the system, such as sample motion and deformation, or higher-order aberrations in the CTF. Because M models these effects accurately and optimizes all hyper-parameters simultaneously with particle alignments, it can surpass previous reference-based frame and tilt series alignment tools. Here I de-scribe the implementation of M, evaluate it on several data sets, and demonstrate that the new algorithms achieve equally high resolution with movie and tilt series data of the same sample. Most strikingly, the combination of Warp, RELION and M can resolve 70S ribosomes bound to an antibiotic at 3.5 Å inside vitrified Mycoplasma pneumoniae cells, marking a major advance in resolution for in situ imaging