Fuzzy sets-based classification of electron microscopy images of biological macromolecules with an application to ribosomal particles

Machine Learning for Structure Determination in Single-Particle Cryo-Electron Microscopy: A Systematic Review

Recently, single-particle cryo-electron microscopy (cryo-EM) has become an indispensable method for determining macromolecular structures at high resolution to deeply explore the relevant molecular mechanism. Its recent breakthrough is mainly because of the rapid advances in hardware and image processing algorithms, especially machine learning. As an essential support of single-particle cryo-EM, machine learning has powered many aspects of structure determination and greatly promoted its development. In this article, we provide a systematic review of the applications of machine learning in this field. Our review begins with a brief introduction of single-particle cryo-EM, followed by the specific tasks and challenges of its image processing. Then, focusing on the workflow of structure determination, we describe relevant machine learning algorithms and applications at different steps, including particle picking, 2-D clustering, 3-D reconstruction, and other steps. As different tasks exhibit distinct characteristics, we introduce the evaluation metrics for each task and summarize their dynamics of technology development. Finally, we discuss the open issues and potential trends in this promising field.

Probabilistic principal component analysis with expectation maximization (PPCA-EM) facilitates volume classification and estimates the missing data

We have developed a new method for classifying 3D reconstructions with missing data obtained by electron microscopy techniques. The method is based on principal component analysis (PCA) combined with expectation maximization. The missing data, together with the principal components, are treated as hidden variables that are estimated by maximizing a likelihood function. PCA in 3D is similar to PCA for 2D image analysis. A lower dimensional subspace of significant features is selected, into which the data are projected, and if desired, subsequently classified. In addition, our new algorithm estimates the missing data for each individual volume within the lower dimensional subspace. Application to both a large model data set and cryo-electron microscopy experimental data demonstrates the good performance of the algorithm and illustrates its potential for studying macromolecular assemblies with continuous conformational variations.

Automation in single-particle electron microscopy connecting the pieces

Throughout the history of single-particle electron microscopy (EM), automated technologies have seen varying degrees of emphasis and development, usually depending upon the contemporary demands of the field. We are currently faced with increasingly sophisticated devices for specimen preparation, vast increases in the size of collected data sets, comprehensive algorithms for image processing, sophisticated tools for quality assessment, and an influx of interested scientists from outside the field who might lack the skills of experienced microscopists. This situation places automated techniques in high demand. In this chapter, we provide a generic definition of and discuss some of the most important advances in automated approaches to specimen preparation, grid handling, robotic screening, microscope calibrations, data acquisition, image processing, and computational infrastructure. Each section describes the general problem and then provides examples of how that problem has been addressed through automation, highlighting available processing packages, and sometimes describing the particular approach at the National Resource for Automated Molecular Microscopy (NRAMM). We contrast the more familiar manual procedures with automated approaches, emphasizing breakthroughs as well as current limitations. Finally, we speculate on future directions and improvements in automated technologies. Our overall goal is to present automation as more than simply a tool to save time. Rather, we aim to illustrate that automation is a comprehensive and versatile strategy that can deliver biological information on an unprecedented scale beyond the scope available with classical manual approaches.

Modeling experimental image formation for likelihood-based classification of electron microscopy data

The coexistence of multiple distinct structural states often obstructs the application of three-dimensional cryo-electron microscopy to large macromolecular complexes. Maximum likelihood approaches are emerging as robust tools for solving the image classification problems that are posed by such samples. Here, we propose a statistical data model that allows for a description of the experimental image formation within the formulation of 2D and 3D maximum-likelihood refinement. The proposed approach comprises a formulation of the probability calculations in Fourier space, including a spatial frequency-dependent noise model and a description of defocus-dependent imaging effects. The Expectation-Maximization-like algorithms presented are generally applicable to the alignment and classification of structurally heterogeneous projection data. Their effectiveness is demonstrated with various examples, including 2D classification of top views of the archaeal helicase MCM and 3D classification of 70S E. coli ribosome and Simian Virus 40 large T-antigen projections.

XMIPP: a new generation of an open-source image processing package for electron microscopy

X-windows based microscopy image processing package (Xmipp) is a specialized suit of image processing programs, primarily aimed at obtaining the 3D reconstruction of biological specimens from large sets of projection images acquired by transmission electron microscopy. This public-domain software package was introduced to the electron microscopy field eight years ago, and since then it has changed drastically. New methodologies for the analysis of single-particle projection images have been added to classification, contrast transfer function correction, angular assignment, 3D reconstruction, reconstruction of crystals, etc. In addition, the package has been extended with functionalities for 2D crystal and electron tomography data. Furthermore, its current implementation in C++, with a highly modular design of well-documented data structures and functions, offers a convenient environment for the development of novel algorithms. In this paper, we present a general overview of a new generation of Xmipp that has been re-engineered to maximize flexibility and modularity, potentially facilitating its integration in future standardization efforts in the field. Moreover, by focusing on those developments that distinguish Xmipp from other packages available, we illustrate its added value to the electron microscopy community.

Topology representing network enables highly accurate classification of protein images taken by cryo electron-microscope without masking

In single-particle analysis, a three-dimensional (3-D) structure of a protein is constructed using electron microscopy (EM). As these images are very noisy in general, the primary process of this 3-D reconstruction is the classification of images according to their Euler angles, the images in each classified group then being averaged to reduce the noise level. In our newly developed strategy of classification, we introduce a topology representing network (TRN) method. It is a modified method of a growing neural gas network (GNG). In this system, a network structure is automatically determined in response to the images input through a growing process. After learning without a masking procedure, the GNG creates clear averages of the inputs as unit coordinates in multi-dimensional space, which are then utilized for classification. In the process, connections are automatically created between highly related units and their positions are shifted where the inputs are distributed in multi-dimensional space. Consequently, several separated groups of connected units are formed. Although the interrelationship of units in this space are not easily understood, we succeeded in solving this problem by converting the unit positions into two-dimensional (2-D) space, and by further optimizing the unit positions with the simulated annealing (SA) method. In the optimized 2-D map, visualization of the connections of units provided rich information about clustering. As demonstrated here, this method is clearly superior to both the multi-variate statistical analysis (MSA) and the self-organizing map (SOM) as a classification method and provides a first reliable classification method which can be used without masking for very noisy images.

A novel neural network technique for analysis and classification of EM single-particle images

We propose a novel self-organizing neural network for the unsupervised classification of electron microscopy (EM) images of biological macromolecules. The radical novelty of the algorithm lies in its rigorous mathematical formulation that, starting from a large set of possibly very noisy input data, finds a set of "representative" data items, organized onto an ordered output map, such that the probability density of this set of representative items resembles at its possible best the probability density of the input data. In a way, it summarizes large amounts of information into a concise description that rigorously keeps the basic pattern of the input data distribution. In this application to the field of three-dimensional EM of single particles, two different data sets have been used; one comprised 2458 rotational power spectra of individual negative stain images of the G40P helicase of Bacillus subtilis bacteriophage SPP1, and the other contained 2822 cryoelectron images of SV40 large T-antigen. Our experimental results prove that this technique is indeed very successful, providing the user with the capability of exploring complex patterns in a succinct, informative, and objective manner. The above facts, together with the consideration that the integration of this new algorithm with commonly used software packages is immediate, prompt us to propose it as a valuable new tool in the analysis of large collections of noisy data.

Mapping and fuzzy classification of macromolecular images using self-organizing neural networks

In this work the effectiveness of the fuzzy kohonen clustering network (FKCN) in the unsupervised classification of electron microscopic images of biological macromolecules is studied. The algorithm combines Kohonen's self-organizing feature maps (SOFM) and Fuzzy c-means (FCM) in order to obtain a powerful clustering technique with the best properties inherited from both. Exploratory data analysis using SOFM is also presented as a step previous to final clustering. Two different data sets obtained from the G40P helicase from B. Subtilis bacteriophage SPP1 have been used for testing the proposed method, one composed of 2458 rotational power spectra of individual images and the other composed by 338 images from the same macromolecule. Results of FKCN are compared with self-organizing feature maps (SOFM) and manual classification. Experimental results prove that this new technique is suitable for working with large, high-dimensional and noisy data sets and, thus, it is proposed to be used as a classification tool in electron microscopy.

Medical image analysis with fuzzy models

This paper updates several recent surveys on the use of fuzzy models for segmentation and edge detection in medical image data. Our survey is divided into methods based on supervised and unsupervised learning (that is, on whether there are or are not labelled data available for supervising the computations), and is organized first and foremost by groups (that we know of!) that are active in this area. Our review is aimed more towards 'who is doing it' rather than 'how good it is'. This is partially dictated by the fact that direct comparisons of supervised and unsupervised methods is somewhat akin to comparing apples and oranges. There is a further subdivision into methods for two- and three-dimensional data and/or problems. We do not cover methods based on neural-like networks or fuzzy reasoning systems. These topics are covered in a recently published companion survey by keller et al.

Pattern recognition and classification of images of biological macromolecules using artificial neural networks

The goal of this work was to analyze an image data set and to detect the structural variability within this set. Two algorithms for pattern recognition based on neural networks are presented, one that performs an unsupervised classification (the self-organizing map) and the other a supervised classification (the learning vector quantization). The approach has a direct impact in current strategies for structural determination from electron microscopic images of biological macromolecules. In this work we performed a classification of both aligned but heterogeneous image data sets as well as basically homogeneous but otherwise rotationally misaligned image populations, in the latter case completely avoiding the typical reference dependency of correlation-based alignment methods. A number of examples on chaperonins are presented. The approach is computationally fast and robust with respect to noise. Programs are available through ftp.

The molecular chaperone TF55. Assessment of symmetry

TF55-like factor from Sulfolobus solfataricus was purified to homogeneity and analyzed by electron microscopy and image analysis to determine the symmetries of these particles. Three different procedures were used to analyze the electron micrographs: (1) fuzzy-set based classification of the particles according to their rotational power spectra; (2) multivariate statistical analysis based on singular value decomposition; (3) circular harmonic analysis. Averages obtained from the three methods show unequivocally that the TF55-like complex presents a 9-fold symmetry.

Three-dimensional reconstruction of single particles negatively stained or in vitreous ice

The random-conical reconstruction method has been highly successful in three-dimensional imaging of macromolecules under low-dose conditions. This article summarizes the different steps of this technique as applied to molecules prepared with negative staining or vitreous ice, and sketches out the current directions of development. We anticipate that by using new instrumental developments, transfer function correction and computational refinement techniques, a resolution in the range of 7-10 A could ultimately be achieved.

Detection, classification and 3D reconstruction of biological macromolecules on hypercube computers

In this work we present results of the mapping on hypercube computers of some of the key steps involved in the procedure for 3D structural determination from transmission electron microscopy images. The goal is the introduction of parallel processing tools in the field of electron microscopy image processing. We show how the rich topology of the hypercube, combined with an efficient programming strategy, allows for order-of-magnitude increase in computational capacity for such time-consuming tasks as calculation of multidimensional FFT's, cross-correlation coefficients, fuzzy partitioning functionals and the filtered back-projection 3D reconstruction method.

Covering events in eigenimages of biomolecules

Multivariate statistical analysis of a large set of micrographs of biological macromolecules involves the computation of eigenimages representing principal features, on the basis of which similar views of the complexes can be grouped. It is not generally clear what these eigenimages represent physically and which ones should be used in the classification process. In this paper, hierarchical maximum entropy discretisation and event covering are used to (1) detect statistically significant relationships in the eigenimages, (2) select the most relevant eigenimages for classifying biomolecular projections, and (3) build a prototype of the biomolecular complex under study.

Visualization of transport-related configurations of the nuclear pore transporter

The transport of macromolecules between the cytoplasm and nucleus of the cell is mediated by the nuclear pore complex (NPC). In this study, details of the central transporter assembly within NPCs have been examined by cryoelectron microscopy, image processing, and classification analysis. The NPC transporter in isolated amphibian nuclei appears to adopt a minimum of four transport-related configurations including: (a) a putative closed form with a 90-100 A diameter central pore, (b) a docked form with material aligned over the pore, (c) an open form with substrates apparently caught "in transit," and (d) an open form with an enlarged pore. This data confirms previous observations on NPC transporters labeled with nucleoplasmin-gold (Akey, C.W., and D.S. Goldfarb. 1989. J. Cell Biol. 109:971-982) and allows a working model of the central NPC transporter to be proposed. The model is comprised of two supramolecular irislike assemblies which open asynchronously to provide an expanded pore for translocation while maintaining transport fidelity.

Three-dimensional reconstruction of the sevenfolded form of Bacillus subtilis Gro EL Chaperonin

Bacillus subtilis grown at 42 degrees C produces a major form of Gro EL-like chaperonin that has been analyzed by electron microscopy. Most of the views show a clear sevenfold symmetry when studied by rotational analysis. The particles were classified into defined families by multivariate analysis and supervised fuzzy-set classification methods, and those belonging to a sevenfold family were averaged to produce a two-dimensional representative projection. These selected particles were then used, when titled by 55 degrees in the microscope goniometer stage, as the starting projections for a three-dimensional reconstruction protocol based on the random conical tilt series method. The resulting reconstruction shows the Gro EL-like chaperonin from B. subtilis as a cylindrical body with seven well defined lobules arranged almost parallel to the longitudinal axis of the particle. There is a channel that is placed along this axis and appears fully open in both sides. The geometry of the channel is polar and presents differences in both faces of the particle.