CryoRes: Local Resolution Estimation of Cryo-EM Density Maps by Deep Learning.

Recent progress in cryo-EM research has ignited a revolution in biological macromolecule structure determination. Resolution is an essential parameter for quality assessment of a cryo-EM density map, and it is known that resolution varies in different regions of a map. Currently available methods for local resolution estimation require manual adjustment of parameters and in some cases necessitate acquisition or de novo generation of so-called "half maps". Here, we developed CryoRes, a deep-learning algorithm to estimate local resolution directly from a single final cryo-EM density map, specifically by learning resolution-aware patterns of density map voxels through supervised training on a large dataset comprising 1,174 experimental cryo-EM density maps. CryoRes significantly outperforms all of the state-of-the-art competing resolution estimation methods, achieving an average RMSE of 2.26 Å for local resolution estimation relative to the currently most reliable FSC-based method blocres, yet requiring only the single final map as input. Further, CryoRes is able to generate a molecular mask for each map, with accuracy 12.12% higher than the masks generated by ResMap. CryoRes is ultra-fast, fully automatic, parameter-free, applicable to cryo-EM subtomogram data, and freely available at https://cryores.zhanglab.net.

Analytic modeling of inhomogeneous-resolution maps in cryo-electron microscopy and crystallography.

Refinement of macromolecular atomic models versus experimental maps in crystallography and cryo-electron microscopy is a critical step in structure solution. For an appropriate comparison, model maps should mimic the imperfections in the experimental maps, mainly atomic disorder and limited resolution, which are often inhomogeneous over the molecular region. In the suggested method, these model maps are calculated as the sum of atomic contributions expressed through a specifically designed function describing a solitary spherical wave. Thanks to this function, atomic contributions are analytically expressed through their atomic displacement parameter and local resolution, a value now associated with each atom. Such a full analytic dependence of inhomogeneous-resolution map values on model parameters permits the refinement of all of these parameters together.

Making ripples in the comparison of calculated and experimental maps for real-space refinement and assessment by analytic modelling of local resolution.

Commentary is given on a paper [Urzhumtsev & Lunin (2022). IUCrJ, 9, 728-734] proposing a new method for the analytic modelling of inhomogeneous resolution in electrostatic potential volumes and electron density maps for improved real-space refinement.

Real space in cryo-EM: the future is local.

Cryo-EM images have extremely low signal-to-noise levels because biological macromolecules are highly radiation-sensitive, requiring low-dose imaging, and because the molecules are poor in contrast. Confident recovery of the signal requires the averaging of many images, the iterative optimization of parameters and the introduction of much prior information. Poor parameter estimates, overfitting and variations in signal strength and resolution across the resulting reconstructions remain frequent issues. Because biological samples are real-space phenomena, exhibiting local variations, real-space measures can be both more reliable and more appropriate than Fourier-space measures. Real-space measures can be calculated separately over each differing region of an image or volume. Real-space filters can be applied according to the local need. Powerful prior information, not available in Fourier space, can be introduced in real space. Priors can be applied in real space in ways that Fourier space precludes. The treatment of biological phenomena remains highly dependent on spatial frequency, however, which would normally be handled in Fourier space. We believe that measures and filters based around real-space operations on extracted frequency bands, i.e. a series of band-pass filtered real-space volumes, and over real-space densities of striding (sequentially increasing or decreasing) resolution through Fourier space are the best way to address this and will perform better than global Fourier-space-based approaches. Future developments in image processing within the field are generally expected to be based on a mixture of both rationally designed and deep-learning approaches, and to incorporate novel prior information from developments such as AlphaFold. Regardless of approach, it is clear that `locality', through real-space measures, filters and processing, will become central to image processing.

An atomic model for the human septin hexamer by cryo-EM.

In order to form functional filaments, human septins must assemble into hetero-oligomeric rod-like particles which polymerize end-to-end. The rules governing the assembly of these particles and the subsequent filaments are incompletely understood. Although crystallographic approaches have been successful in studying the separate components of the system, there has been difficulty in obtaining high resolution structures of the full particle. Here we report a first cryo-EM structure for a hexameric rod composed of human septins 2, 6 and 7 with a global resolution of ~3.6 Å and a local resolution of between ~3.0 Å and ~5.0 Å. By fitting the previously determined high-resolution crystal structures of the component subunits into the cryo-EM map, we are able to provide an essentially complete model for the particle. This exposes SEPT2 NC-interfaces at the termini of the hexamer and leaves internal cavities between the SEPT6-SEPT7 pairs. The floor of the cavity is formed by the two α0 helices including their polybasic regions. These are locked into place between the two subunits by interactions made with the α5 and α6 helices of the neighbouring monomer together with its polyacidic region. The cavity may serve to provide space allowing the subunits to move with respect to one another. The elongated particle shows a tendency to bend at its centre where two copies of SEPT7 form a homodimeric G-interface. Such bending is almost certainly related to the ability of septin filaments to recognize and even induce membrane curvature.

Spark-based parallel calculation of 3D fourier shell correlation for macromolecule structure local resolution estimation.

BACKGROUND: Resolution estimation is the main evaluation criteria for the reconstruction of macromolecular 3D structure in the field of cryoelectron microscopy (cryo-EM). At present, there are many methods to evaluate the 3D resolution for reconstructed macromolecular structures from Single Particle Analysis (SPA) in cryo-EM and subtomogram averaging (SA) in electron cryotomography (cryo-ET). As global methods, they measure the resolution of the structure as a whole, but they are inaccurate in detecting subtle local changes of reconstruction. In order to detect the subtle changes of reconstruction of SPA and SA, a few local resolution methods are proposed. The mainstream local resolution evaluation methods are based on local Fourier shell correlation (FSC), which is computationally intensive. However, the existing resolution evaluation methods are based on multi-threading implementation on a single computer with very poor scalability. RESULTS: This paper proposes a new fine-grained 3D array partition method by key-value format in Spark. Our method first converts 3D images to key-value data (K-V). Then the K-V data is used for 3D array partitioning and data exchange in parallel. So Spark-based distributed parallel computing framework can solve the above scalability problem. In this distributed computing framework, all 3D local FSC tasks are simultaneously calculated across multiple nodes in a computer cluster. Through the calculation of experimental data, 3D local resolution evaluation algorithm based on Spark fine-grained 3D array partition has a magnitude change in computing speed compared with the mainstream FSC algorithm under the condition that the accuracy remains unchanged, and has better fault tolerance and scalability. CONCLUSIONS: In this paper, we proposed a K-V format based fine-grained 3D array partition method in Spark to parallel calculating 3D FSC for getting a 3D local resolution density map. 3D local resolution density map evaluates the three-dimensional density maps reconstructed from single particle analysis and subtomogram averaging. Our proposed method can significantly increase the speed of the 3D local resolution evaluation, which is important for the efficient detection of subtle variations among reconstructed macromolecular structures.

Measurement of local resolution in electron tomography.

Resolution (global and local) is one of the most reported metrics of quality measurement in Single Particle Analysis (SPA). However, in electron tomography, the situation is different and its computation is not straightforward. Typically, resolution estimation is global and, therefore, reduces the assessment of a whole tomogram to a single number. However, it is known that tomogram quality is spatially variant. Still, up to our knowledge, a method to estimate local quality metrics in tomography is lacking. This work introduces MonoTomo, a method developed to estimate locally in a tomogram the highest reliable frequency component, expressed as a form of local resolution. The fundamentals lie in a local analysis of the density map via monogenic signals, which, in analogy to MonoRes, allows for local estimations. Results with experimental data show that the local resolution range that MonoTomo casts agrees with reported resolution values for experimental data sets, with the advantage of providing a local estimation. A range of applications of MonoTomo are suggested for further exploration.

Mitigating local over-fitting during single particle reconstruction with SIDESPLITTER.

Single particle analysis has become a key structural biology technique. Experimental images are extremely noisy, and during iterative refinement it is possible to stably incorporate noise into the reconstruction. Such "over-fitting" can lead to misinterpretation of the structure and flawed biological results. Several strategies are routinely used to prevent over-fitting, the most common being independent refinement of two sides of a split dataset. In this study, we show that over-fitting remains an issue within regions of low local signal-to-noise, despite independent refinement of half datasets. We propose a modification of the refinement process through the application of a local signal-to-noise filter: SIDESPLITTER. We show that our approach can reduce over-fitting for both idealised and experimental data while maintaining independence between the two sides of a split refinement. SIDESPLITTER refinement leads to improved density, and can also lead to improvement of the final resolution in extreme cases where datasets are prone to severe over-fitting, such as small membrane proteins.

Confidence maps: statistical inference of cryo-EM maps.

Confidence maps provide complementary information for interpreting cryo-EM densities as they indicate statistical significance with respect to background noise. They can be thresholded by specifying the expected false-discovery rate (FDR), and the displayed volume shows the parts of the map that have the corresponding level of significance. Here, the basic statistical concepts of confidence maps are reviewed and practical guidance is provided for their interpretation and usage inside the CCP-EM suite. Limitations of the approach are discussed and extensions towards other error criteria such as the family-wise error rate are presented. The observed map features can be rendered at a common isosurface threshold, which is particularly beneficial for the interpretation of weak and noisy densities. In the current article, a practical guide is provided to the recommended usage of confidence maps.

DeepRes: a new deep-learning- and aspect-based local resolution method for electron-microscopy maps.

In this article, a method is presented to estimate a new local quality measure for 3D cryoEM maps that adopts the form of a 'local resolution' type of information. The algorithm (DeepRes) is based on deep-learning 3D feature detection. DeepRes is fully automatic and parameter-free, and avoids the issues of most current methods, such as their insensitivity to enhancements owing to B-factor sharpening (unless the 3D mask is changed), among others, which is an issue that has been virtually neglected in the cryoEM field until now. In this way, DeepRes can be applied to any map, detecting subtle changes in local quality after applying enhancement processes such as isotropic filters or substantially more complex procedures, such as model-based local sharpening, non-model-based methods or denoising, that may be very difficult to follow using current methods. It performs as a human observer expects. The comparison with traditional local resolution indicators is also addressed.

Thresholding of cryo-EM density maps by false discovery rate control.

Cryo-EM now commonly generates close-to-atomic resolution as well as intermediate resolution maps from macromolecules observed in isolation and in situ. Interpreting these maps remains a challenging task owing to poor signal in the highest resolution shells and the necessity to select a threshold for density analysis. In order to facilitate this process, a statistical framework for the generation of confidence maps by multiple hypothesis testing and false discovery rate (FDR) control has been developed. In this way, three-dimensional confidence maps contain signal separated from background noise in the form of local detection rates of EM density values. It is demonstrated that confidence maps and FDR-based thresholding can be used for the interpretation of near-atomic resolution single-particle structures as well as lower resolution maps determined by subtomogram averaging. Confidence maps represent a conservative way of interpreting molecular structures owing to minimized noise. At the same time they provide a detection error with respect to background noise, which is associated with the density and is particularly beneficial for the interpretation of weaker cryo-EM densities in cases of conformational flexibility and lower occupancy of bound molecules and ions in the structure.

A Local Agreement Filtering Algorithm for Transmission EM Reconstructions.

We present LAFTER, an algorithm for de-noising single particle reconstructions from cryo-EM. Single particle analysis entails the reconstruction of high-resolution volumes from tens of thousands of particle images with low individual signal-to-noise. Imperfections in this process result in substantial variations in the local signal-to-noise ratio within the resulting reconstruction, complicating the interpretation of molecular structure. An effective local de-noising filter could therefore improve interpretability and maximise the amount of useful information obtained from cryo-EM maps. LAFTER is a local de-noising algorithm based on a pair of serial real-space filters. It compares independent half-set reconstructions to identify and retain shared features that have power greater than the noise. It is capable of recovering features across a wide range of signal-to-noise ratios, and we demonstrate recovery of the strongest features at Fourier shell correlation (FSC) values as low as 0.144 over a 2563-voxel cube. A fast and computationally efficient implementation of LAFTER is freely available. We also propose a new way to evaluate the effectiveness of real-space filters for noise suppression, based on the correspondence between two FSC curves: 1) the FSC between the filtered and unfiltered volumes, and 2) Cref, the FSC between the unfiltered volume and a hypothetical noiseless volume, which can readily be estimated from the FSC between two half-set reconstructions.

MonoRes: Automatic and Accurate Estimation of Local Resolution for Electron Microscopy Maps.

Since the beginning of electron microscopy, resolution has been a critical parameter. In this article, we propose a fully automatic, accurate method for determining the local resolution of a 3D map (MonoRes). The foundation of this algorithm is an extension of the concept of analytic signal, termed monogenic signal. The map is filtered at different frequencies and the amplitude of the monogenic signal is calculated, after which a criterion is applied to determine the resolution at each voxel. MonoRes is fully automatic without compulsory user parameters, with great accuracy in all tests, and is computationally more rapid than existing methods in the field. In addition, MonoRes offers the option of local filtering of the original map based on the calculated local resolution.

An N-terminal extension to the hepatitis B virus core protein forms a poorly ordered trimeric spike in assembled virus-like particles.

Virus-like particles composed of the core antigen of hepatitis B virus (HBcAg) have been shown to be an effective platform for the display of foreign epitopes in vaccine development. Heterologous sequences have been successfully inserted at both amino and carboxy termini as well as internally at the major immunodominant epitope. We used cryogenic electron microscopy (CryoEM) and three-dimensional image reconstruction to investigate the structure of VLPs assembled from an N-terminal extended HBcAg that contained a polyhistidine tag. The insert was seen to form a trimeric spike on the capsid surface that was poorly resolved, most likely owing to it being flexible. We hypothesise that the capacity of N-terminal inserts to form trimers may have application in the development of multivalent vaccines to trimeric antigens. Our analysis also highlights the value of tools for local resolution assessment in studies of partially disordered macromolecular assemblies by cryoEM.