Local analysis of strains and rotations for macromolecular electron microscopy maps.

Macromolecular complexes perform their physiological functions by local rearrangements of their constituents and biochemically interacting with their reaction partners. These rearrangements may involve local rotations and the induction of local strains causing different mechanical efforts and stretches at the different areas of the protein. The analysis of these local deformations may reveal important insight into the way proteins perform their tasks. In this paper we introduce a method to perform this kind of local analysis using Electron Microscopy volumes in a fully objective and automatic manner. For doing so, we exploit the continuous nature of the result of an elastic image registration using B-splines as its basis functions. We show that the results obtained by the new automatic method are consistent with previous observations on these macromolecules.

Scipion: A software framework toward integration, reproducibility and validation in 3D electron microscopy.

In the past few years, 3D electron microscopy (3DEM) has undergone a revolution in instrumentation and methodology. One of the central players in this wide-reaching change is the continuous development of image processing software. Here we present Scipion, a software framework for integrating several 3DEM software packages through a workflow-based approach. Scipion allows the execution of reusable, standardized, traceable and reproducible image-processing protocols. These protocols incorporate tools from different programs while providing full interoperability among them. Scipion is an open-source project that can be downloaded from http://scipion.cnb.csic.es.

A statistical approach to the initial volume problem in Single Particle Analysis by Electron Microscopy.

Cryo Electron Microscopy is a powerful Structural Biology technique, allowing the elucidation of the three-dimensional structure of biological macromolecules. In particular, the structural study of purified macromolecules -often referred as Single Particle Analysis(SPA)- is normally performed through an iterative process that needs a first estimation of the three-dimensional structure that is progressively refined using experimental data. It is well-known the local optimisation nature of this refinement, so that the initial choice of this first structure may substantially change the final result. Computational algorithms aiming to providing this first structure already exist. However, the question is far from settled and more robust algorithms are still needed so that the refinement process can be performed with sufficient guarantees. In this article we present a new algorithm that addresses the initial volume problem in SPA by setting it in a Weighted Least Squares framework and calculating the weights through a statistical approach based on the cumulative density function of different image similarity measures. We show that the new algorithm is significantly more robust than other state-of-the-art algorithms currently in use in the field. The algorithm is available as part of the software suite Xmipp (http://xmipp.cnb.csic.es) and Scipion (http://scipion.cnb.csic.es) under the name "Significant".

A pattern matching approach to the automatic selection of particles from low-contrast electron micrographs.

MOTIVATION: Structural information of macromolecular complexes provides key insights into the way they carry out their biological functions. Achieving high-resolution structural details with electron microscopy requires the identification of a large number (up to hundreds of thousands) of single particles from electron micrographs, which is a laborious task if it has to be manually done and constitutes a hurdle towards high-throughput. Automatic particle selection in micrographs is far from being settled and new and more robust algorithms are required to reduce the number of false positives and false negatives. RESULTS: In this article, we introduce an automatic particle picker that learns from the user the kind of particles he is interested in. Particle candidates are quickly and robustly classified as particles or non-particles. A number of new discriminative shape-related features as well as some statistical description of the image grey intensities are used to train two support vector machine classifiers. Experimental results demonstrate that the proposed method: (i) has a considerably low computational complexity and (ii) provides results better or comparable with previously reported methods at a fraction of their computing time. AVAILABILITY: The algorithm is fully implemented in the open-source Xmipp package and downloadable from http://xmipp.cnb.csic.es.

Particle quality assessment and sorting for automatic and semiautomatic particle-picking techniques.

Three-dimensional reconstruction of biological specimens using electron microscopy by single particle methodologies requires the identification and extraction of the imaged particles from the acquired micrographs. Automatic and semiautomatic particle selection approaches can localize these particles, minimizing the user interaction, but at the cost of selecting a non-negligible number of incorrect particles, which can corrupt the final three-dimensional reconstruction. In this work, we present a novel particle quality assessment and sorting method that can separate most erroneously picked particles from correct ones. The proposed method is based on multivariate statistical analysis of a particle set that has been picked previously using any automatic or manual approach. The new method uses different sets of particle descriptors, which are morphology-based, histogram-based and signal to noise analysis based. We have tested our proposed algorithm with experimental data obtaining very satisfactory results. The algorithm is freely available as a part of the Xmipp 3.0 package [http://xmipp.cnb.csic.es].

ENRICH: A fast method to improve the quality of flexible macromolecular reconstructions.

Cryo-electron microscopy using single particle analysis requires the computational averaging of thousands of projection images captured from identical macromolecules. However, macromolecules usually present some degree of flexibility showing different conformations. Computational approaches are then required to classify heterogeneous single particle images into homogeneous sets corresponding to different structural states. Nonetheless, sometimes the attainable resolution of reconstructions obtained from these smaller homogeneous sets is compromised because of reduced number of particles or lack of images at certain macromolecular orientations. In these situations, the current solution to improve map resolution is returning to the electron microscope and collect more data. In this work, we present a fast approach to partially overcome this limitation for heterogeneous data sets. Our method is based on deforming and then moving particles between different conformations using an optical flow approach. Particles are then merged into a unique conformation obtaining reconstructions with improved resolution, contrast and signal-to-noise ratio. We present experimental results that show clear improvements in the quality of obtained 3D maps, however, there are also limits to this approach, i.e., the method is restricted to small deformations and cannot determine local patterns of flexibility of small elements, such as secondary structures, which we discuss in the manuscript.

A review of resolution measures and related aspects in 3D Electron Microscopy.

Fourier Shell Correlation, Spectral Signal-to-Noise Ratio, Fourier Neighbour Correlation, and Differential Phase Residual are different measures that have been proposed over time to determine the spatial resolution achieved by a certain 3D reconstruction. Estimates of B-factors to describe the reduction in signal-to-noise ratio with increasing resolution is also a useful parameter. All these concepts are interrelated and different thresholds have been given for each one of them. However, the problem of resolution assessment in 3DEM is still far from settled and preferences are normally adopted in order to choose the "correct" threshold. In this paper we review the different concepts, their theoretical foundations and the derivation of their statistical distributions (the basis for establishing sensible thresholds). We provide theoretical justifications for some common practices in the field for which a formal justification was missing. We also analyze the relationship between SSNR and B-factors, the electron dose needed for achieving a given contrast and resolution, the number of images required, etc. Finally, we review the consequences for the number of particles needed to achieve a certain resolution and how to analyze the Signal-to-Noise Ratio for a sequence of imaging operations.

A fast iterative convolution weighting approach for gridding-based direct Fourier three-dimensional reconstruction with correction for the contrast transfer function.

We describe a fast and accurate method for the reconstruction of macromolecular complexes from a set of projections. Direct Fourier inversion (in which the Fourier Slice Theorem plays a central role) is a solution for dealing with this inverse problem. Unfortunately, the set of projections provides a non-equidistantly sampled version of the macromolecule Fourier transform in the single particle field (and, therefore, a direct Fourier inversion) may not be an optimal solution. In this paper, we introduce a gridding-based direct Fourier method for the three-dimensional reconstruction approach that uses a weighting technique to compute a uniform sampled Fourier transform. Moreover, the contrast transfer function of the microscope, which is a limiting factor in pursuing a high resolution reconstruction, is corrected by the algorithm. Parallelization of this algorithm, both on threads and on multiple CPU's, makes the process of three-dimensional reconstruction even faster. The experimental results show that our proposed gridding-based direct Fourier reconstruction is slightly more accurate than similar existing methods and presents a lower computational complexity both in terms of time and memory, thereby allowing its use on larger volumes. The algorithm is fully implemented in the open-source Xmipp package and is downloadable from http://xmipp.cnb.csic.es.

Cryo-EM and the elucidation of new macromolecular structures: Random Conical Tilt revisited.

Cryo-Electron Microscopy (cryo-EM) of macromolecular complexes is a fundamental structural biology technique which is expanding at a very fast pace. Key to its success in elucidating the three-dimensional structure of a macromolecular complex, especially of small and non-symmetric ones, is the ability to start from a low resolution map, which is subsequently refined with the actual images collected at the microscope. There are several methods to produce this first structure. Among them, Random Conical Tilt (RCT) plays a prominent role due to its unbiased nature (it can create an initial model based on experimental measurements). In this article, we revise the fundamental mathematical expressions supporting RCT, providing new expressions handling all key geometrical parameters without the need of intermediate operations, leading to improved automation and overall reliability, essential for the success of cryo-EM when analyzing new complexes. We show that the here proposed RCT workflow based on the new formulation performs very well in practical cases, requiring very few image pairs (as low as 13 image pairs in one of our examples) to obtain relevant 3D maps.