Re-examining the spectra of macromolecules. Current practice of spectral quasi B-factor flattening

Electron scattering properties of biological macromolecules and their use for cryo-EM map sharpening

Resolution-dependent loss of contrast in cryo-EM maps may obscure features at high resolution that are critical for map interpretation. Post-processing of cryo-EM maps can improve the interpretability by adjusting the resolution-dependence of structure factor amplitudes through map sharpening. Traditionally this has been done by rescaling the relative contribution of low and high-resolution frequencies globally. More recently, the realisation that molecular motion and heterogeneity cause non-uniformity of resolution throughout the map has inspired the development of techniques that optimise sharpening locally. We previously developed LocScale, a method that utilises the radial structure factor from a refined atomic model as a restraint for local map sharpening. While this method has proved beneficial for the interpretation of cryo-EM maps, the dependence on the availability of (partial) model information limits its general applicability. Here, we review the basic assumptions of resolution-dependent contrast loss in cryo-EM maps and propose a route towards a robust alternative for local map sharpening that utilises information on expected scattering properties of biological macromolecules, but requires no detailed knowledge of the underlying molecular structure. We examine remaining challenges for implementation and discuss possible applications.

Image processing tools for the validation of CryoEM maps

The number of maps deposited in public databases (Electron Microscopy Data Bank, EMDB) determined by cryo-electron microscopy has quickly grown in recent years. With this rapid growth, it is critical to guarantee their quality. So far, map validation has primarily focused on the agreement between maps and models. From the image processing perspective, the validation has been mostly restricted to using two half-maps and the measurement of their internal consistency. In this article, we suggest that map validation can be taken much further from the point of view of image processing if 2D classes, particles, angles, coordinates, defoci, and micrographs are also provided. We present a progressive validation scheme that qualifies a result validation status from 0 to 5 and offers three optional qualifiers (A, W, and O) that can be added. The simplest validation state is 0, while the most complete would be 5AWO. This scheme has been implemented in a website https://biocomp.cnb.csic.es/EMValidationService/ to which reconstructed maps and their ESI can be uploaded.

Emerging Themes in CryoEM─Single Particle Analysis Image Processing

Cryo-electron microscopy (CryoEM) has become a vital technique in structural biology. It is an interdisciplinary field that takes advantage of advances in biochemistry, physics, and image processing, among other disciplines. Innovations in these three basic pillars have contributed to the boosting of CryoEM in the past decade. This work reviews the main contributions in image processing to the current reconstruction workflow of single particle analysis (SPA) by CryoEM. Our review emphasizes the time evolution of the algorithms across the different steps of the workflow differentiating between two groups of approaches: analytical methods and deep learning algorithms. We present an analysis of the current state of the art. Finally, we discuss the emerging problems and challenges still to be addressed in the evolution of CryoEM image processing methods in SPA.

On bias, variance, overfitting, gold standard and consensus in single-particle analysis by cryo-electron microscopy

Cryo-electron microscopy (cryoEM) has become a well established technique to elucidate the 3D structures of biological macromolecules. Projection images from thousands of macromolecules that are assumed to be structurally identical are combined into a single 3D map representing the Coulomb potential of the macromolecule under study. This article discusses possible caveats along the image-processing path and how to avoid them to obtain a reliable 3D structure. Some of these problems are very well known in the community. These may be referred to as sample-related (such as specimen denaturation at interfaces or non-uniform projection geometry leading to underrepresented projection directions). The rest are related to the algorithms used. While some have been discussed in depth in the literature, such as the use of an incorrect initial volume, others have received much less attention. However, they are fundamental in any data-analysis approach. Chiefly among them, instabilities in estimating many of the key parameters that are required for a correct 3D reconstruction that occur all along the processing workflow are referred to, which may significantly affect the reliability of the whole process. In the field, the term overfitting has been coined to refer to some particular kinds of artifacts. It is argued that overfitting is a statistical bias in key parameter-estimation steps in the 3D reconstruction process, including intrinsic algorithmic bias. It is also shown that common tools (Fourier shell correlation) and strategies (gold standard) that are normally used to detect or prevent overfitting do not fully protect against it. Alternatively, it is proposed that detecting the bias that leads to overfitting is much easier when addressed at the level of parameter estimation, rather than detecting it once the particle images have been combined into a 3D map. Comparing the results from multiple algorithms (or at least, independent executions of the same algorithm) can detect parameter bias. These multiple executions could then be averaged to give a lower variance estimate of the underlying parameters.

Advances in Xmipp for Cryo-Electron Microscopy: From Xmipp to Scipion

Xmipp is an open-source software package consisting of multiple programs for processing data originating from electron microscopy and electron tomography, designed and managed by the Biocomputing Unit of the Spanish National Center for Biotechnology, although with contributions from many other developers over the world. During its 25 years of existence, Xmipp underwent multiple changes and updates. While there were many publications related to new programs and functionality added to Xmipp, there is no single publication on the Xmipp as a package since 2013. In this article, we give an overview of the changes and new work since 2013, describe technologies and techniques used during the development, and take a peek at the future of the package.

Wilson statistics: derivation, generalization and applications to electron cryomicroscopy

The power spectrum of proteins at high frequencies is remarkably well described by the flat Wilson statistics. Wilson statistics therefore plays a significant role in X-ray crystallography and more recently in electron cryomicroscopy (cryo-EM). Specifically, modern computational methods for three-dimensional map sharpening and atomic modelling of macromolecules by single-particle cryo-EM are based on Wilson statistics. Here the first rigorous mathematical derivation of Wilson statistics is provided. The derivation pinpoints the regime of validity of Wilson statistics in terms of the size of the macromolecule. Moreover, the analysis naturally leads to generalizations of the statistics to covariance and higher-order spectra. These in turn provide a theoretical foundation for assumptions underlying the widespread Bayesian inference framework for three-dimensional refinement and for explaining the limitations of autocorrelation-based methods in cryo-EM.

Image Processing in Cryo-Electron Microscopy of Single Particles: The Power of Combining Methods

Cryo-electron microscopy has established as a mature structural biology technique to elucidate the three-dimensional structure of biological macromolecules. The Coulomb potential of the sample is imaged by an electron beam, and fast semi-conductor detectors produce movies of the sample under study. These movies have to be further processed by a whole pipeline of image-processing algorithms that produce the final structure of the macromolecule. In this chapter, we illustrate this whole processing pipeline putting in value the strength of "meta algorithms," which are the combination of several algorithms, each one with different mathematical rationale, in order to distinguish correctly from incorrectly estimated parameters. We show how this strategy leads to superior performance of the whole pipeline as well as more confident assessments about the reconstructed structures. The "meta algorithms" strategy is common to many fields and, in particular, it has provided excellent results in bioinformatics. We illustrate this combination using the workflow engine, Scipion.

DeepEMhancer: a deep learning solution for cryo-EM volume post-processing

Cryo-EM maps are valuable sources of information for protein structure modeling. However, due to the loss of contrast at high frequencies, they generally need to be post-processed to improve their interpretability. Most popular approaches, based on global B-factor correction, suffer from limitations. For instance, they ignore the heterogeneity in the map local quality that reconstructions tend to exhibit. Aiming to overcome these problems, we present DeepEMhancer, a deep learning approach designed to perform automatic post-processing of cryo-EM maps. Trained on a dataset of pairs of experimental maps and maps sharpened using their respective atomic models, DeepEMhancer has learned how to post-process experimental maps performing masking-like and sharpening-like operations in a single step. DeepEMhancer was evaluated on a testing set of 20 different experimental maps, showing its ability to reduce noise levels and obtain more detailed versions of the experimental maps. Additionally, we illustrated the benefits of DeepEMhancer on the structure of the SARS-CoV-2 RNA polymerase.

Sanchez-Garcia et al. present DeepEMhancer, a deep learning-based method that can automatically perform post-processing of raw cryo-electron microscopy density maps. The authors report that DeepEMhancer globally improves local quality of density maps, and may represent a useful tool for novel structures where PDB models are not readily available.

Identification of a Na+-Binding Site near the Oxygen-Evolving Complex of Spinach Photosystem II

The oxygen-evolving complex (OEC) of photosystem II (PSII) is an oxomanganese cluster composed of four redox-active Mn ions and one redox-inactive Ca²⁺ ion, with two nearby bound Cl^- ions. Sodium is a common counterion of both chloride and hydroxide anions, and a sodium-specific binding site has not been identified near the OEC. Here, we find that the oxygen-evolution activity of spinach PSII increases with Na⁺ concentration, particularly at high pH. A Na⁺-specific binding site next to the OEC, becomes available after deprotonation of the D1-H337 amino acid residue, is suggested by the analysis of two recently published PSII cryo-electron microscopy maps in combination with quantum mechanical calculations and multiconformation continuum electrostatics simulations.