Image formation modeling in cryo-electron microscopy

Improved Denoising of Cryo-Electron Microscopy Micrographs with Simulation-Aware Pretraining

Cryo-electron microscopy (cryo-EM) has emerged as a potent technique for determining the structure and functionality of biological macromolecules. However, limited by the physical imaging conditions, such as low electron beam dose, micrographs in cryo-EM typically contend with an extremely low signal-to-noise ratio (SNR), impeding the efficiency and efficacy of subsequent analyses. Therefore, there is a growing demand for an efficient denoising algorithm designed for cryo-EM micrographs, aiming to enhance the quality of macromolecular analysis. However, owing to the absence of a comprehensive and well-defined dataset with ground truth images, supervised image denoising methods exhibit limited generalization when applied to experimental micrographs. To tackle this challenge, we introduce a simulation-aware image denoising (SaID) pretrained model designed to enhance the SNR of cryo-EM micrographs where the training is solely based on an accurately simulated dataset. First, we propose a parameter calibration algorithm for simulated dataset generation, aiming to align simulation parameters with those of experimental micrographs. Second, leveraging the accurately simulated dataset, we propose to train a deep general denoising model that can well generalize to real experimental cryo-EM micrographs. Comprehensive experimental results demonstrate that our pretrained denoising model achieves excellent denoising performance on experimental cryo-EM micrographs, significantly streamlining downstream analysis.

Electron videography of a lipid-protein tango

Biological phenomena, from enzymatic catalysis to synaptic transmission, originate in the structural transformations of biomolecules and biomolecular assemblies in liquid water. However, directly imaging these nanoscopic dynamics without probes or labels has been a fundamental methodological challenge. Here, we developed an approach for "electron videography"-combining liquid phase electron microscopy with molecular modeling-with which we filmed the nanoscale structural fluctuations of individual, suspended, and unlabeled membrane protein nanodiscs in liquid. Systematic comparisons with biochemical data and simulation indicate the graphene encapsulation involved can afford sufficiently reduced effects of the illuminating electron beam for these observations to yield quantitative fingerprints of nanoscale lipid-protein interactions. Our results suggest that lipid-protein interactions delineate dynamically modified membrane domains across unexpectedly long ranges. Moreover, they contribute to the molecular mechanics of the nanodisc as a whole in a manner specific to the protein within. Overall, this work illustrates an experimental approach to film, quantify, and understand biomolecular dynamics at the nanometer scale.

Simulations of dislocation contrast in dark-field X-ray microscopy

Dark-field X-ray microscopy (DFXM) is a full-field imaging technique that non-destructively maps the structure and local strain inside deeply embedded crystalline elements in three dimensions. In DFXM, an objective lens is placed along the diffracted beam to generate a magnified projection image of the local diffracted volume. This work explores contrast methods and optimizes the DFXM setup specifically for the case of mapping dislocations. Forward projections of detector images are generated using two complementary simulation tools based on geometrical optics and wavefront propagation, respectively. Weak and strong beam contrast and the mapping of strain components are studied. The feasibility of observing dislocations in a wall is elucidated as a function of the distance between neighbouring dislocations and the spatial resolution. Dislocation studies should be feasible with energy band widths of 10-2, of relevance for fourth-generation synchrotron and X-ray free-electron laser sources.

Cryo-forum: A framework for orientation recovery with uncertainty measure with the application in cryo-EM image analysis

In single-particle cryo-electron microscopy (cryo-EM), efficient determination of orientation parameters for particle images poses a significant challenge yet is crucial for reconstructing 3D structures. This task is complicated by the high noise levels in the datasets, which often include outliers, necessitating several time-consuming 2D clean-up processes. Recently, solutions based on deep learning have emerged, offering a more streamlined approach to the traditionally laborious task of orientation estimation. These solutions employ amortized inference, eliminating the need to estimate parameters individually for each image. However, these methods frequently overlook the presence of outliers and may not adequately concentrate on the components used within the network. This paper introduces a novel method using a 10-dimensional feature vector for orientation representation, extracting orientations as unit quaternions with an accompanying uncertainty metric. Furthermore, we propose a unique loss function that considers the pairwise distances between orientations, thereby enhancing the accuracy of our method. Finally, we also comprehensively evaluate the design choices in constructing the encoder network, a topic that has not received sufficient attention in the literature. Our numerical analysis demonstrates that our methodology effectively recovers orientations from 2D cryo-EM images in an end-to-end manner. Notably, the inclusion of uncertainty quantification allows for direct clean-up of the dataset at the 3D level. Lastly, we package our proposed methods into a user-friendly software suite named cryo-forum, designed for easy access by developers.

Computational models of amorphous ice for accurate simulation of cryo-EM images of biological samples

Simulations of cryo-electron microscopy (cryo-EM) images of biological samples can be used to produce test datasets to support the development of instrumentation, methods, and software, as well as to assess data acquisition and analysis strategies. To be useful, these simulations need to be based on physically realistic models which include large volumes of amorphous ice. The gold standard model for EM image simulation is a physical atom-based ice model produced using molecular dynamics simulations. Although practical for small sample volumes; for simulation of cryo-EM data from large sample volumes, this can be too computationally expensive. We have evaluated a Gaussian Random Field (GRF) ice model which is shown to be more computationally efficient for large sample volumes. The simulated EM images are compared with the gold standard atom-based ice model approach and shown to be directly comparable. Comparison with experimentally acquired data shows the Gaussian random field ice model produces realistic simulations. The software required has been implemented in the Parakeet software package and the underlying atomic models are available online for use by the wider community.

Virus structures revealed by advanced cryoelectron microscopy methods

Before the resolution revolution, cryoelectron microscopy (cryo-EM) single-particle analysis (SPA) already achieved resolutions beyond 4 Å for certain icosahedral viruses, enabling ab initio atomic model building of these viruses. As the only samples that achieved such high resolution at that time, cryo-EM method development was closely intertwined with the improvement of reconstructions of symmetrical viruses. Viral morphology exhibits significant diversity, ranging from small to large, uniform to non-uniform, and from containing single symmetry to multiple symmetries. Furthermore, viruses undergo conformational changes during their life cycle. Several methods, such as asymmetric reconstruction, Ewald sphere correction, cryoelectron tomography (cryo-ET), and sub-tomogram averaging (STA), have been developed and applied to determine virus structures in vivo and in vitro. This review outlines current advanced cryo-EM methods for high-resolution structure determination of viruses and summarizes accomplishments obtained with these approaches. Moreover, persisting challenges in comprehending virus structures are discussed and we propose potential solutions.

Computational methods for in situ structural studies with cryogenic electron tomography

Cryo-electron tomography (cryo-ET) plays a critical role in imaging microorganisms in situ in terms of further analyzing the working mechanisms of viruses and drug exploitation, among others. A data processing workflow for cryo-ET has been developed to reconstruct three-dimensional density maps and further build atomic models from a tilt series of two-dimensional projections. Low signal-to-noise ratio (SNR) and missing wedge are two major factors that make the reconstruction procedure challenging. Because only few near-atomic resolution structures have been reconstructed in cryo-ET, there is still much room to design new approaches to improve universal reconstruction resolutions. This review summarizes classical mathematical models and deep learning methods among general reconstruction steps. Moreover, we also discuss current limitations and prospects. This review can provide software and methods for each step of the entire procedure from tilt series by cryo-ET to 3D atomic structures. In addition, it can also help more experts in various fields comprehend a recent research trend in cryo-ET. Furthermore, we hope that more researchers can collaborate in developing computational methods and mathematical models for high-resolution three-dimensional structures from cryo-ET datasets.

Alternative Forward Models for Imaging Thick Specimens in Transmission Electron Microscopy

I have investigated two different forward models for image formation in transmission electron microscopy of thick specimens, the 3DCtf model, which introduces a defocus gradient in the linear approximation, and the multislice model. An important result is that the 3DCtf model does not seem to be compatible with the multislice image formation model. A second very useful finding is that the exit wave in the multislice model has an imaginary part, which, in first-order approximation, is a pure projection of the specimen and is not affected by the defocus gradient. The defocus gradient only comes into play in real valued and higher-order imaginary terms. If the multislice model is closer to reality than the 3DCtf-model, then the best way to retrieve the specimen projection for thicker specimens should be a procedure for retrieving the exit wave's imaginary term, for example using images recorded at different defocus values.

Cryogenic electron ptychographic single particle analysis with wide bandwidth information transfer

Advances in cryogenic transmission electron microscopy have revolutionised the determination of many macromolecular structures at atomic or near-atomic resolution. This method is based on conventional defocused phase contrast imaging. However, it has limitations of weaker contrast for small biological molecules embedded in vitreous ice, in comparison with cryo-ptychography, which shows increased contrast. Here we report a single-particle analysis based on the use of ptychographic reconstruction data, demonstrating that three dimensional reconstructions with a wide information transfer bandwidth can be recovered by Fourier domain synthesis. Our work suggests future applications in otherwise challenging single particle analyses, including small macromolecules and heterogeneous or flexible particles. In addition structure determination in situ within cells without the requirement for protein purification and expression may be possible.

A strategy combining denoising and cryo-EM single particle analysis

In cryogenic electron microscopy (cryo-EM) single particle analysis (SPA), high-resolution three-dimensional structures of biological macromolecules are determined by iteratively aligning and averaging a large number of two-dimensional projections of molecules. Since the correlation measures are sensitive to the signal-to-noise ratio, various parameter estimation steps in SPA will be disturbed by the high-intensity noise in cryo-EM. However, denoising algorithms tend to damage high frequencies and suppress mid- and high-frequency contrast of micrographs, which exactly the precise parameter estimation relies on, therefore, limiting their application in SPA. In this study, we suggest combining a cryo-EM image processing pipeline with denoising and maximizing the signal's contribution in various parameter estimation steps. To solve the inherent flaws of denoising algorithms, we design an algorithm named MScale to correct the amplitude distortion caused by denoising and propose a new orientation determination strategy to compensate for the high-frequency loss. In the experiments on several real datasets, the denoised particles are successfully applied in the class assignment estimation and orientation determination tasks, ultimately enhancing the quality of biomacromolecule reconstruction. The case study on classification indicates that our strategy not only improves the resolution of difficult classes (up to 5 Å) but also resolves an additional class. In the case study on orientation determination, our strategy improves the resolution of the final reconstructed density map by 0.34 Å compared with conventional strategy. The code is available at https://github.com/zhanghui186/Mscale.

Deep generative modeling for volume reconstruction in cryo-electron microscopy

Advances in cryo-electron microscopy (cryo-EM) for high-resolution imaging of biomolecules in solution have provided new challenges and opportunities for algorithm development for 3D reconstruction. Next-generation volume reconstruction algorithms that combine generative modelling with end-to-end unsupervised deep learning techniques have shown promise, but many technical and theoretical hurdles remain, especially when applied to experimental cryo-EM images. In light of the proliferation of such methods, we propose here a critical review of recent advances in the field of deep generative modelling for cryo-EM reconstruction. The present review aims to (i) provide a unified statistical framework using terminology familiar to machine learning researchers with no specific background in cryo-EM, (ii) review the current methods in this framework, and (iii) outline outstanding bottlenecks and avenues for improvements in the field.

MEPSi: A tool for simulating tomograms of membrane-embedded proteins

The throughput and fidelity of cryogenic cellular electron tomography (cryo-ET) is constantly increasing through advances in cryogenic electron microscope hardware, direct electron detection devices, and powerful image processing algorithms. However, the need for careful optimization of sample preparations and for access to expensive, high-end equipment, make cryo-ET a costly and time-consuming technique. Generally, only after the last step of the cryo-ET workflow, when reconstructed tomograms are available, it becomes clear whether the chosen imaging parameters were suitable for a specific type of sample in order to answer a specific biological question. Tools for a-priory assessment of the feasibility of samples to answer biological questions and how to optimize imaging parameters to do so would be a major advantage. Here we describe MEPSi (Membrane Embedded Protein Simulator), a simulation tool aimed at rapid and convenient evaluation and optimization of cryo-ET data acquisition parameters for studies of transmembrane proteins in their native environment. We demonstrate the utility of MEPSi by showing how to detangle the influence of different data collection parameters and different orientations in respect to tilt axis and electron beam for two examples: (1) simulated plasma membranes with embedded single-pass transmembrane αIIbβ3 integrin receptors and (2) simulated virus membranes with embedded SARS-CoV-2 spike proteins.

CryoAI: Amortized Inference of Poses for Ab Initio Reconstruction of 3D Molecular Volumes from Real Cryo-EM Images

Cryo-electron microscopy (cryo-EM) has become a tool of fundamental importance in structural biology, helping us understand the basic building blocks of life. The algorithmic challenge of cryo-EM is to jointly estimate the unknown 3D poses and the 3D electron scattering potential of a biomolecule from millions of extremely noisy 2D images. Existing reconstruction algorithms, however, cannot easily keep pace with the rapidly growing size of cryo-EM datasets due to their high computational and memory cost. We introduce cryoAI, an ab initio reconstruction algorithm for homogeneous conformations that uses direct gradient-based optimization of particle poses and the electron scattering potential from single-particle cryo-EM data. CryoAI combines a learned encoder that predicts the poses of each particle image with a physics-based decoder to aggregate each particle image into an implicit representation of the scattering potential volume. This volume is stored in the Fourier domain for computational efficiency and leverages a modern coordinate network architecture for memory efficiency. Combined with a symmetrized loss function, this framework achieves results of a quality on par with state-of-the-art cryo-EM solvers for both simulated and experimental data, one order of magnitude faster for large datasets and with significantly lower memory requirements than existing methods.

Ab-initio contrast estimation and denoising of cryo-EM images

BACKGROUND AND OBJECTIVE

The contrast of cryo-EM images varies from one to another, primarily due to the uneven thickness of the ice layer. This contrast variation can affect the quality of 2-D class averaging, 3-D ab-initio modeling, and 3-D heterogeneity analysis. Contrast estimation is currently performed during 3-D iterative refinement. As a result, the estimates are not available at the earlier computational stages of class averaging and ab-initio modeling. This paper aims to solve the contrast estimation problem directly from the picked particle images in the ab-initio stage, without estimating the 3-D volume, image rotations, or class averages.

METHODS

The key observation underlying our analysis is that the 2-D covariance matrix of the raw images is related to the covariance of the underlying clean images, the noise variance, and the contrast variability between images. We show that the contrast variability can be derived from the 2-D covariance matrix and we apply the existing Covariance Wiener Filtering (CWF) framework to estimate it. We also demonstrate a modification of CWF to estimate the contrast of individual images.

RESULTS

Our method improves the contrast estimation by a large margin, compared to the previous CWF method. Its estimation accuracy is often comparable to that of an oracle that knows the ground truth covariance of the clean images. The more accurate contrast estimation also improves the quality of image restoration as demonstrated in both synthetic and experimental datasets.

CONCLUSIONS

This paper proposes an effective method for contrast estimation directly from noisy images without using any 3-D volume information. It enables contrast correction in the earlier stage of single particle analysis, and may improve the accuracy of downstream processing.

MeasureIce: accessible on-the-fly measurement of ice thickness in cryo-electron microscopy

Ice thickness is arguably one of the most important factors limiting the resolution of protein structures determined by cryo-electron microscopy (cryo-EM). The amorphous atomic structure of the ice that stabilizes and protects biological samples in cryo-EM grids also imprints some additional noise in cryo-EM images. Ice that is too thick jeopardizes the success of particle picking and reconstruction of the biomolecule in the worst case and, at best, deteriorates eventual map resolution. Minimizing the thickness of the ice layer and thus the magnitude of its noise contribution is thus imperative in cryo-EM grid preparation. In this paper we introduce MeasureIce, a simple, easy to use ice thickness measurement tool for screening and selecting acquisition areas of cryo-EM grids. We show that it is possible to simulate thickness-image intensity look-up tables, also usable in SerialEM and Leginon, using elementary scattering physics and thereby adapt the tool to any microscope without time consuming experimental calibration. We benchmark our approach using two alternative techniques: the “ice channel” technique and tilt-series tomography. We also demonstrate the utility of ice thickness measurement for selecting holes in gold grids containing an Equine apoferritin sample, achieving a 1.88 Ångstrom resolution in subsequent refinement of the atomic map.

MeasureIce is an ice thickness measurement tool for screening and selecting acquisition areas of cryo-EM grids.

Quantitative Cryo-Electron Tomography

The three-dimensional organization of biomolecules important for the functioning of all living systems can be determined by cryo-electron tomography imaging under native biological contexts. Cryo-electron tomography is continually expanding and evolving, and the development of new methods that use the latest technology for sample thinning is enabling the visualization of ever larger and more complex biological systems, allowing imaging across scales. Quantitative cryo-electron tomography possesses the capability of visualizing the impact of molecular and environmental perturbations in subcellular structure and function to understand fundamental biological processes. This review provides an overview of current hardware and software developments that allow quantitative cryo-electron tomography studies and their limitations and how overcoming them may allow us to unleash the full power of cryo-electron tomography.

OUP accepted manuscript

Motivation

Cryo-electron microscopy (cryo-EM) is a widely used technology for ultrastructure determination, which constructs the 3D structures of protein and macromolecular complex from a set of 2D micrographs. However, limited by the electron beam dose, the micrographs in cryo-EM generally suffer from the extremely low signal-to-noise ratio (SNR), which hampers the efficiency and effectiveness of downstream analysis. Especially, the noise in cryo-EM is not simple additive or multiplicative noise whose statistical characteristics are quite different from the ones in natural image, extremely shackling the performance of conventional denoising methods.

Results

Here, we introduce the Noise-Transfer2Clean (NT2C), a denoising deep neural network (DNN) for cryo-EM to enhance image contrast and restore specimen signal, whose main idea is to improve the denoising performance by correctly learning the noise distribution of cryo-EM images and transferring the statistical nature of noise into the denoiser. Especially, to cope with the complex noise model in cryo-EM, we design a contrast-guided noise and signal re-weighted algorithm to achieve clean-noisy data synthesis and data augmentation, making our method authentically achieve signal restoration based on noise’s true properties. Our work verifies the feasibility of denoising based on mining the complex cryo-EM noise patterns directly from the noise patches. Comprehensive experimental results on simulated datasets and real datasets show that NT2C achieved a notable improvement in image denoising, especially in background noise removal, compared with the commonly used methods. Moreover, a case study on the real dataset demonstrates that NT2C can greatly alleviate the obstacles caused by the SNR to particle picking and simplify the identifying of particles.

Availabilityand implementation

The code is available at https://github.com/Lihongjia-ict/NoiseTransfer2Clean/.

Supplementary information

Supplementary data are available at Bioinformatics online.

A cryogenic, coincident fluorescence, electron, and ion beam microscope

Cryogenic electron tomography (cryo-ET) combined with subtomogram averaging, allows in situ visualization and structure determination of macromolecular complexes at subnanometre resolution. Cryogenic focused ion beam (cryo-FIB) micromachining is used to prepare a thin lamella-shaped sample out of a frozen-hydrated cell for cryo-ET imaging, but standard cryo-FIB fabrication is blind to the precise location of the structure or proteins of interest. Fluorescence-guided focused ion beam (FIB) milling at target locations requires multiple sample transfers prone to contamination, and relocation and registration accuracy is often insufficient for 3D targeting. Here, we present in situ fluorescence microscopy-guided FIB fabrication of a frozen-hydrated lamella to address this problem: we built a coincident three-beam cryogenic correlative microscope by retrofitting a compact cryogenic microcooler, custom positioning stage, and an inverted widefield fluorescence microscope (FM) on an existing FIB scanning electron microscope. We show FM controlled targeting at every milling step in the lamella fabrication process, validated with transmission electron microscope tomogram reconstructions of the target regions. The ability to check the lamella during and after the milling process results in a higher success rate in the fabrication process and will increase the throughput of fabrication for lamellae suitable for high-resolution imaging.

Cryo-TEM simulations of amorphous radiation-sensitive samples using multislice wave propagation

Image simulation plays a central role in the development and practice of high-resolution electron microscopy, including transmission electron microscopy of frozen-hydrated specimens (cryo-EM). Simulating images with contrast that matches the contrast observed in experimental images remains challenging, especially for amorphous samples. Current state-of-the-art simulators apply post hoc scaling to approximate empirical solvent contrast, attenuated image intensity due to specimen thickness and amplitude contrast. This practice fails for images that require spatially variable scaling, e.g. simulations of a crowded or cellular environment. Modeling both the signal and the noise accurately is necessary to simulate images of biological specimens with contrast that is correct on an absolute scale. The 'frozen plasmon' method is introduced to explicitly model spatially variable inelastic scattering processes in cryo-EM specimens. This approach produces amplitude contrast that depends on the atomic composition of the specimen, reproduces the total inelastic mean free path as observed experimentally and allows for the incorporation of radiation damage in the simulation. These improvements are quantified using the matched filter concept to compare simulation and experiment. The frozen plasmon method, in combination with a new mathematical formulation for accurately sampling the tabulated atomic scattering potentials onto a Cartesian grid, is implemented in the open-source software package cisTEM.

A novel constrained reconstruction model towards high-resolution subtomogram averaging

MOTIVATION

Electron tomography (ET) offers a unique capacity to image biological structures in situ. However, the resolution of ET reconstructed tomograms is not comparable to that of the single-particle cryo-EM. If many copies of the object of interest are present in the tomograms, their structures can be reconstructed in the tomogram, picked, aligned and averaged to increase the signal-to-noise ratio and improve the resolution, which is known as the subtomogram averaging. To date, the resolution improvement of the subtomogram averaging is still limited because each reconstructed subtomogram is of low reconstruction quality due to the missing wedge issue.

RESULTS

In this article, we propose a novel computational model, the constrained reconstruction model (CRM), to better recover the information from the multiple subtomograms and compensate for the missing wedge issue in each of them. CRM is supposed to produce a refined reconstruction in the final turn of subtomogram averaging after alignment, instead of directly taking the average. We first formulate the averaging method and our CRM as linear systems, and prove that the solution space of CRM is no larger, and in practice much smaller, than that of the averaging method. We then propose a sparse Kaczmarz algorithm to solve the formulated CRM, and further extend the solution to the simultaneous algebraic reconstruction technique (SART). Experimental results demonstrate that CRM can significantly alleviate the missing wedge issue and improve the final reconstruction quality. In addition, our model is robust to the number of images in each tilt series, the tilt range and the noise level.

AVAILABILITY AND IMPLEMENTATION

The codes of CRM-SIRT and CRM-SART are available at https://github.com/icthrm/CRM.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Gold nanoparticles and tilt pairs to assess protein flexibility by cryo-electron microscopy

A computational method was developed to recover the three-dimensional coordinates of gold nanoparticles specifically attached to a protein complex from tilt-pair images collected by electron microscopy. The program was tested on a simulated dataset and applied to a real dataset comprising tilt-pair images recorded by cryo electron microscopy of RNA polymerase II in a complex with four gold-labeled single-chain antibody fragments. The positions of the gold nanoparticles were determined, and comparison of the coordinates among the tetrameric particles revealed the range of motion within the protein complexes.

A streamlined workflow for automated cryo focused ion beam milling

Cryo-electron tomography (cryo-ET) is an emerging technique to study the cellular architecture and the structure of proteins at high resolution in situ. Most biological specimens are too thick to be directly investigated and are therefore thinned by milling with a focused ion beam under cryogenic conditions (cryo-FIB). This procedure is prone to contaminations, which makes it a tedious process, often leading to suboptimal results. Here, we present new hardware that overcomes the current limitations. We developed a new glove box and a high vacuum cryo transfer system and installed a stage heater, a cryo-shield and a cryo-shutter in the FIB milling microscope. This reduces the ice contamination during the transfer and milling process and simplifies the handling of the sample. In addition, we tested a new software application that automates the key milling steps. Together, these improvements allow for high-quality, high-throughput cryo-FIB milling. This paves the way for new types of experiments, which have been previously considered infeasible.

[Progress in filters for denoising cryo-electron microscopy images]

Cryo-electron microscopy (cryo-EM) imaging has the unique potential to bridge the gap between cellular and molecular biology. Therefore, cryo-EM three-dimensional (3D) reconstruction has been rapidly developed in recent several years and applied widely in life science research to reveal the structures of large macromolecular assemblies and cellular complexes, which is critical to understanding their functions at all scales. Although the technical breakthrough in recent years, for example, the introduction of the direct detection device (DDD) camera and the development of cryo-EM software tools, made the three cryo-EM pioneers share the 2017 Nobel Prize, several bottleneck problems still exist that hamper the further increase of the resolution of single-particle reconstruction and hold back the application of in situ subnanometer structure determination by cryo-tomography. Radiation damage is still the key limiting factor in cryo-EM. In order to minimize the radiation damage and preserve as much resolution as possible, the imaging conditions of a low dose and weak contrast make cryo-EM images extremely noisy with very low signal-to-noise ratios (SNR), generally about 0.1. The high noise will obscure the fine details in cryo-EM images or reconstructed maps. Thus, a method to reduce the level of noise and improve the resolution has become an important issue. In this paper, we systematically reviewed and compared some robust filters in the cryo-EM field of two aspects, single-particle analysis (SPA) and cryo-electron tomography (cryo-ET), and especially studied their applications, such as, 3D reconstruction, visualization, structural analysis, and interpretation. Conventional approaches to noise reduction in cryo-EM imaging include the use of Gaussian, median, and bilateral filters, among other means. A Gaussian filter selects an appropriate filter kernel to conduct spatial convolution with a noisy image. Although noise with larger standard deviations in cryo-EM images can be suppressed and satisfactory performance is achieved in certain cases, this filter also blurs the images and over-smooths small-scale image features. This is especially detrimental when precise quantitative information needs to be extracted. Unlike a Gaussian filter, a median filter is based on the order statistics of the image and selects the median intensity in a window of the adjacent pixels to denoise the image. Although this filter is robust to outliers, it suffers from aliasing problems that possibly result in incorrect information for cryo-EM structure interpretation. A bilateral filter is a nonlinear filter that performs spatial weighted averaging and is more selective in the pixels allowing to contribute to the weighted sum, excluding the high frequency noise from the smoothing process. Thus, this filter can be used to smooth out noise while maintaining the edge details, which is similar to an anisotropic diffusion filter, and distinct from a Gaussian filter but its utility will be limited when the SNR of a cryo-EM image is very low. Generally, spatial filtering methods have the disadvantage of losing image resolution when reducing noise. A wavelet transform can exploit the wavelet's natural ability to separate a signal from noise at multiple image scales to allow for joint resolution in both the spatial and frequency domains, and thus has the potential to outperform existing methods. The modified wavelet shrinkage filter we developed can offer a remarkable improvement in image quality with a good compromise between detail preservation and noise smoothing. We expect that our review study on different filters can provide benefits to cryo-EM applications and the interpretation of biological structures.

Demonstration of electron diffraction from membrane protein crystals grown in a lipidic mesophase after lamella preparation by focused ion beam milling at cryogenic temperatures

Electron crystallography of sub-micrometre-sized 3D protein crystals has emerged recently as a valuable field of structural biology. In meso crystallization methods, utilizing lipidic mesophases, particularly lipidic cubic phases (LCPs), can produce high-quality 3D crystals of membrane proteins (MPs). A major step towards realizing 3D electron crystallography of MP crystals, grown in meso, is to demonstrate electron diffraction from such crystals. The first task is to remove the viscous and sticky lipidic matrix that surrounds the crystals without damaging the crystals. Additionally, the crystals have to be thin enough to let electrons traverse them without significant multiple scattering. In the present work, the concept that focused ion beam milling at cryogenic temperatures (cryo-FIB milling) can be used to remove excess host lipidic mesophase matrix is experimentally verified, and then the crystals are thinned to a thickness suitable for electron diffraction. In this study, bacteriorhodopsin (BR) crystals grown in a lipidic cubic mesophase of monoolein were used as a model system. LCP from a part of a hexagon-shaped plate-like BR crystal (∼10 µm in thickness and ∼70 µm in the longest dimension), which was flash-frozen in liquid nitro-gen, was milled away with a gallium FIB under cryogenic conditions, and a part of the crystal itself was thinned into a ∼210 nm-thick lamella with the ion beam. The frozen sample was then transferred into an electron cryo-microscope, and a nanovolume of ∼1400 × 1400 × 210 nm of the BR lamella was exposed to 200 kV electrons at a fluence of ∼0.06 e Å-2. The resulting electron diffraction peaks were detected beyond 2.7 Å resolution (with an average peak height to background ratio of >2) by a CMOS-based Ceta 16M camera. The results demonstrate that cryo-FIB milling produces high-quality lamellae from crystals grown in lipidic mesophases and pave the way for 3D electron crystallography on crystals grown or embedded in highly viscous media.

Assessing the JEOL CRYO ARM 300 for high-throughput automated single-particle cryo-EM in a multiuser environment

Single-particle cryo-EM has become an indispensable structural biology method. It requires regular access to high-resolution electron cryogenic microscopes. To fully utilize the capacity of the expensive high-resolution instruments, the time used for data acquisition and the rate of data collection have to be maximized. This in turn requires high stability and high uptime of the instrument. One of the first 300 kV JEOL CRYO ARM 300 microscopes has been installed at the cryo-EM facility BECM at VIB-VUB, Brussels, where the microscope is used for continuous data collection on multiple projects. Here, the suitability and performance of the microscope is assessed for high-throughput single-particle data collection. In particular, the properties of the illumination system, the stage stability and ice contamination rates are reported. The microscope was benchmarked using mouse heavy-chain apoferritin which was reconstructed to a resolution of 1.9 Å. Finally, uptime and throughput statistics of the instrument accumulated during the first six months of the facility operation in user access mode are reported.

Liquid-Phase Electron Microscopy for Soft Matter Science and Biology

Innovations in liquid-phase electron microscopy (LP-EM) have made it possible to perform experiments at the optimized conditions needed to examine soft matter. The main obstacle is conducting experiments in such a way that electron beam radiation can be used to obtain answers for scientific questions without changing the structure and (bio)chemical processes in the sample due to the influence of the radiation. By overcoming these experimental difficulties at least partially, LP-EM has evolved into a new microscopy method with nanometer spatial resolution and sub-second temporal resolution for analysis of soft matter in materials science and biology. Both experimental design and applications of LP-EM for soft matter materials science and biological research are reviewed, and a perspective of possible future directions is given.

Could Egg White Lysozyme be Solved by Single Particle Cryo-EM?

The combination of high-end cryogenic transmission electron microscopes (cryo-EM), direct electron detectors, and advanced image algorithms allows researchers to obtain the 3D structures of much smaller macromolecules than years ago. However, there are still major challenges for the single-particle cryo-EM method to achieve routine structure determinations for macromolecules much smaller than 100 kDa, which are the majority of all plant and animal proteins. These challenges include sample characteristics such as sample heterogeneity, beam damage, ice layer thickness, stability, and quality, as well as hardware limitations such as detector performance, beam, and phase plate quality. Here, single particle data sets were simulated for samples that were ideal in terms of homogeneity, distribution, and stability, but with realistic parameters for ice layer, dose, detector performance, and beam characteristics. Reference data were calculated for human apo-ferritin using identical parameters reported for an experimental data set downloaded from EMPIAR. Processing of the simulated data set resulted in a value of 1.86 Å from 20 214 particles, similar to a 2 Å density map obtained from 29 224 particles selected from real micrographs. Simulated data sets were then generated for a 14 kDa protein, hen egg white lysozyme (HEWL), with and without an ideal phase plate (PP). Whereas we could not obtain a high-resolution 3D reconstruction of HEWL for the data set without PP, the one with PP resulted in a 2.78 Å resolution density map from 225 751 particles. Our simulator and simulations could help in pushing the size limits of cryo-EM.

Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes

Single-particle electron cryomicroscopy is an essential tool for high-resolution 3D reconstruction of proteins and other biological macromolecules. An important challenge in cryo-EM is the reconstruction of non-rigid molecules with parts that move and deform. Traditional reconstruction methods fail in these cases, resulting in smeared reconstructions of the moving parts. This poses a major obstacle for structural biologists, who need high-resolution reconstructions of entire macromolecules, moving parts included. To address this challenge, we present a new method for the reconstruction of macromolecules exhibiting continuous heterogeneity. The proposed method uses projection images from multiple viewing directions to construct a graph Laplacian through which the manifold of three-dimensional conformations is analyzed. The 3D molecular structures are then expanded in a basis of Laplacian eigenvectors, using a novel generalized tomographic reconstruction algorithm to compute the expansion coefficients. These coefficients, which we name spectral volumes, provide a high-resolution visualization of the molecular dynamics. We provide a theoretical analysis and evaluate the method empirically on several simulated data sets.

Low-energy in-line electron holographic imaging of vitreous ice-embedded small biomolecules using a modified scanning electron microscope

Cryo-electron microscopy (cryo-EM) has become the method of choice in the field of structural biology, owing to its unique ability to deduce structures of vitreous ice-embedded, hydrated biomolecules over a wide range of structural resolutions. As cryo-transmission electron microscopes (cryo-TEM) become increasingly specialised for high, near-atomic resolution studies, operational complexity and associated costs serve as significant barriers to widespread usability and adoptability. To facilitate the expansion and accessibility of the cryo-EM method, an efficient, user-friendly means of imaging vitreous ice-embedded biomolecules has been called for. In this study, we present a solution to this issue by integrating cryo-EM capabilities into a commercial scanning electron microscope (SEM). Utilising the principle of low-energy in-line electron holography, our newly developed hybrid microscope permits low-to-moderate resolution imaging of vitreous ice-embedded biomolecules without the need for any form of sample staining or chemical fixation. Operating at 20 kV, the microscope takes advantage of the ease-of-use of SEM-based imaging and phase contrast imaging of low-energy electron holography. This study represents the first reported successful application of low-energy in-line electron holographic imaging to vitreous ice-embedded small biomolecules, the effectiveness of which is demonstrated here with three morphologically distinct specimens.

AuTom-dualx: a toolkit for fully automatic fiducial marker-based alignment of dual-axis tilt series with simultaneous reconstruction

Motivation

Dual-axis electron tomography is an important 3 D macro-molecular structure reconstruction technology, which can reduce artifacts and suppress the effect of missing wedge. However, the fully automatic data process for dual-axis electron tomography still remains a challenge due to three difficulties: (i) how to track the mass of fiducial markers automatically; (ii) how to integrate the information from the two different tilt series; and (iii) how to cope with the inconsistency between the two different tilt series.

Results

Here we develop a toolkit for fully automatic alignment of dual-axis electron tomography, with a simultaneous reconstruction procedure. The proposed toolkit and its workflow carries out the following solutions: (i) fully automatic detection and tracking of fiducial markers under large-field datasets; (ii) automatic combination of two different tilt series and global calibration of projection parameters; and (iii) inconsistency correction based on distortion correction parameters and the consequently simultaneous reconstruction. With all of these features, the presented toolkit can achieve accurate alignment and reconstruction simultaneously and conveniently under a single global coordinate system.

Availability and implementation

The toolkit AuTom-dualx (alignment module dualxmauto and reconstruction module volrec_mltm) are accessible for general application at http://ear.ict.ac.cn, and the key source code is freely available under request.

Supplementary information

Supplementary data are available at Bioinformatics online.

Real-time cryo-electron microscopy data preprocessing with Warp

The acquisition of cryo-electron microscopy (cryo-EM) data from biological specimens must be tightly coupled to data preprocessing to ensure the best data quality and microscope usage. Here we describe Warp, a software that automates all preprocessing steps of cryo-EM data acquisition and enables real-time evaluation. Warp corrects micrographs for global and local motion, estimates the local defocus and monitors key parameters for each recorded micrograph or tomographic tilt series in real time. The software further includes deep-learning-based models for accurate particle picking and image denoising. The output from Warp can be fed into established programs for particle classification and 3D-map refinement. Our benchmarks show improvement in the nominal resolution, which went from 3.9 Å to 3.2 Å, of a published cryo-EM data set for influenza virus hemagglutinin. Warp is easy to install from http://github.com/cramerlab/warp and computationally inexpensive, and has an intuitive, streamlined user interface.

Analysis of depth-sectioning STEM for thick samples and 3D imaging

We derive a model that describes 3D volume imaging in depth-sectioning STEM that is valid for all STEM techniques under three well-defined conditions: linearity, undisturbed probe and elastic scattering. The resulting undisturbed probe model generalizes the widely used idea that the undisturbed probe intensity in three dimensions can be used as the point spread function for depth-sectioning ADF-STEM to all STEM techniques including (A)BF- and iDPC-STEM. The model provides closed expressions for depth-sectioning STEM, which follow directly from the 2D expressions for thin samples, and thereby enables analysis of the 3D resolution. Using the model we explore the consequences of the resulting 3D contrast transfer function (CTF) for the z-resolution at different length scales and illustrate this with experiments. We investigate the validity and limitations of the model using multi-slice simulations showing that it is valid and quantitatively accurate for relatively thick amorphous samples but not for crystalline samples in zone-axis due to channeling. We compare depth-sectioning in iDPC- and ADF-STEM and show that iDPC-STEM can extract information from deeper into the sample, all the way till the bottom of the sample, thereby effectively allowing a thickness measurement. Also the difference in optimal focus conditions between iDPC- and ADF-STEM is explained. Finally, we propose practical criteria for deciding whether a sample is thin or thick.

Iterative Bayesian denoising based on variance stabilization using Contourlet Transform with Sharp Frequency Localization: application to EFTEM images

Background

Due to the presence of high noise level in tomographic series of energy filtered transmission electron microscopy (EFTEM) images, alignment and 3D reconstruction steps become so difficult. To improve the alignment process which will in turn allow a more accurate and better three dimensional tomography reconstructions, a preprocessing step should be applied to the EFTEM data series.

Results

Experiments with real EFTEM data series at low SNR, show the feasibility and the accuracy of the proposed denoising approach being competitive with the best existing methods for Poisson image denoising. The effectiveness of the proposed denoising approach is thanks to the use of a nonparametric Bayesian estimation in the Contourlet Transform with Sharp Frequency Localization Domain (CTSD) and variance stabilizing transformation (VST). Furthermore, the optimal inverse Anscome transformation to obtain the final estimate of the denoised images, has allowed an accurate tomography reconstruction.

Conclusion

The proposed approach provides qualitative information on the 3D distribution of individual chemical elements on the considered sample.

PIXER: an automated particle-selection method based on segmentation using a deep neural network

BACKGROUND

Cryo-electron microscopy (cryo-EM) has become a widely used tool for determining the structures of proteins and macromolecular complexes. To acquire the input for single-particle cryo-EM reconstruction, researchers must select hundreds of thousands of particles from micrographs. As the signal-to-noise ratio (SNR) of micrographs is extremely low, the performance of automated particle-selection methods is still unable to meet research requirements. To free researchers from this laborious work and to acquire a large number of high-quality particles, we propose an automated particle-selection method (PIXER) based on the idea of segmentation using a deep neural network.

RESULTS

First, to accommodate low-SNR conditions, we convert micrographs into probability density maps using a segmentation network. These probability density maps indicate the likelihood that each pixel of a micrograph is part of a particle instead of just background noise. Particles selected from density maps have a more robust signal than do those directly selected from the original noisy micrographs. Second, at present, there is no segmentation-training dataset for cryo-EM. To enable our plan, we present an automated method to generate a training dataset for segmentation using real-world data. Third, we propose a grid-based, local-maximum method to locate the particles from the probability density maps. We tested our method on simulated and real-world experimental datasets and compared PIXER with the mainstream methods RELION, DeepEM and DeepPicker to demonstrate its performance. The results indicate that, as a fully automated method, PIXER can acquire results as good as the semi-automated methods RELION and DeepEM.

CONCLUSION

To our knowledge, our work is the first to address the particle-selection problem using the segmentation network concept. As a fully automated particle-selection method, PIXER can free researchers from laborious particle-selection work. Based on the results of experiments, PIXER can acquire accurate results under low-SNR conditions within minutes.

Advances in image processing for single-particle analysis by electron cryomicroscopy and challenges ahead

Electron cryomicroscopy (cryoEM) is essential for the study and functional understanding of non-crystalline macromolecules such as proteins. These molecules cannot be imaged using X-ray crystallography or other popular methods. CryoEM has been successfully used to visualize macromolecular complexes such as ribosomes, viruses, and ion channels. Determination of structural models of these at various conformational states leads to insight on how these molecules function. Recent advances in imaging technology have given cryoEM a scientific rebirth. As a result of these technological advances image processing and analysis have yielded molecular structures at atomic resolution. Nevertheless there continue to be challenges in image processing, and in this article we will touch on the most essential in order to derive an accurate three-dimensional model from noisy projection images. Traditional approaches, such as k-means clustering for class averaging, will be provided as background. We will then highlight new approaches for each image processing subproblem, including a 3D reconstruction method for asymmetric molecules using just two projection images and deep learning algorithms for automated particle picking.

Routine determination of ice thickness for cryo-EM grids

Recent advances in instrumentation and automation have made cryo-EM a popular method for producing near-atomic resolution structures of a variety of proteins and complexes. Sample preparation is still a limiting factor in collecting high quality data. Thickness of the vitreous ice in which the particles are embedded is one of the many variables that need to be optimized for collection of the highest quality data. Here we present two methods, using either an energy filter or scattering outside the objective aperture, to measure ice thickness for potentially every image collected. Unlike geometrical or tomographic methods, these can be implemented directly in the single particle collection workflow without interrupting or significantly slowing down data collection. We describe the methods as implemented into the Leginon/Appion data collection workflow, along with some examples from test cases. Routine monitoring of ice thickness should prove helpful for optimizing sample preparation, data collection, and data processing.

A methodology using Gaussian-based density map approximation to assess sets of cryo-electron microscopy density maps

This article presents a methodology to assess a set of density maps, as used in the Blind Assessment Phase of the 2015/2016 Map Challenge (EMDataBank Validation Challenges). The synthetic and experimental cryo-electron microscopy (cryo-EM) density maps obtained by different single particle analysis protocols and by different participants, submitted in the Challenge Phase for assessment, were analyzed with this methodology and the obtained results are presented and discussed here. The goal of using such a methodology was to blindly identify the density maps with globally similar structural information, meaning the maps with the structural information mostly "reproduced" by different protocols. To this end, the density maps are "coarsened" using Gaussian-based approximations, with the same input approximation parameters for all maps of the target biological complex. The approximated maps are then represented in a common reduced-dimension (here, 3D) space of their correlation-coefficient-based distances, in which close maps mean similar maps. The distance analysis allows identifying maps with the most "reproduced" structural information by different protocols. The obtained results are also discussed taking into account the detailed information about the protocols that has been released after the end of the Blind Assessment Phase.

Map Challenge assessment: Fair comparison of single particle cryoEM reconstructions

Cryo-electron microscopy (cryoEM) is capable of achieving near-atomic resolution of biomolecular structures due to recent advances in hardware. Despite the long history of image processing software development for cryoEM, uncertainty about best practices and validation remains. The Map Challenge was therefore designed to test the current state of single particle reconstruction. As the first such challenge, the participants were given the freedom to analyze the cases in whichever way they wanted. Therefore, the maps submitted feature different sizes, sampling and orientations, making assessment non-trivial. To be fair, I developed a method to pose all maps in each case in the same configuration with minimal interpolation. I assessed the quality of these maps by visual inspection and Fourier shell correlation (FSC). Comparing the even-odd FSC with an FSC calculated against a reference structure analysis, I concluded that the quality of the maps related more to the user than to other factors, such as the software package used. Poor quality maps suffer either from lack of data or poor choices made by the user. Some maps appear significantly better than a reference or consensus of other maps, indicating overfitting. Best practices to avoid problems include an understanding of the effects of reference map modifications on particle image alignment, and generating appropriate masks. Ultimately, none of the issues revealed in the Map Challenge is insurmountable, as underscored by the excellent quality of reconstructions achieved by a significant number of participants.

Single particle reconstruction and validation using Bsoft for the map challenge

The Bsoft package is aimed at processing electron micrographs for the determination of the three-dimensional structures of biological specimens. Recent advances in hardware allow us to solve structures to near atomic resolution using single particle analysis (SPA). The Map Challenge offered me an opportunity to test the ability of Bsoft to produce reconstructions from cryo-electron micrographs at the best resolution. I also wanted to understand what needed to be done to work towards full automation with validation. Here, I present two cases for the Map Challenge using Bsoft: ß-galactosidase and GroEL. I processed two independent subsets in each case with resolution-limited alignment. In both cases the reconstructions approached the expected resolution within a few iterations of alignment. I further validated the results by coherency-testing: i.e., that the reconstructions from real particles give better resolutions than reconstructions from the same number of aligned noise images. The key operations requiring attention for full automation are: particle picking, faster accurate alignment, proper mask generation, appropriate map sharpening, and understanding the amount of data needed to reach a desired resolution.

Structural Variability from Noisy Tomographic Projections

In cryo-electron microscopy, the three-dimensional (3D) electric potentials of an ensemble of molecules are projected along arbitrary viewing directions to yield noisy two-dimensional images. The volume maps representing these potentials typically exhibit a great deal of structural variability, which is described by their 3D covariance matrix. Typically, this covariance matrix is approximately low rank and can be used to cluster the volumes or estimate the intrinsic geometry of the conformation space. We formulate the estimation of this covariance matrix as a linear inverse problem, yielding a consistent least-squares estimator. For n images of size N-by-N pixels, we propose an algorithm for calculating this covariance estimator with computational complexity O ( n N 4 + κ N 6 log N ) , where the condition number κ is empirically in the range 10-200. Its efficiency relies on the observation that the normal equations are equivalent to a deconvolution problem in six dimensions. This is then solved by the conjugate gradient method with an appropriate circulant preconditioner. The result is the first computationally efficient algorithm for consistent estimation of the 3D covariance from noisy projections. It also compares favorably in runtime with respect to previously proposed nonconsistent estimators. Motivated by the recent success of eigenvalue shrinkage procedures for high-dimensional covariance matrix estimation, we incorporate a shrinkage procedure that improves accuracy at lower signal-to-noise ratios. We evaluate our methods on simulated datasets and achieve classification results comparable to state-of-the-art methods in shorter running time. We also present results on clustering volumes in an experimental dataset, illustrating the power of the proposed algorithm for practical determination of structural variability.

Quantification and optimization of ADF-STEM image contrast for beam-sensitive materials

Many functional materials are difficult to analyse by scanning transmission electron microscopy (STEM) on account of their beam sensitivity and low contrast between different phases. The problem becomes even more severe when thick specimens need to be investigated, a situation that is common for materials that are ordered from the nanometre to micrometre length scales or when performing dynamic experiments in a TEM liquid cell. Here we report a method to optimize annular dark-field (ADF) STEM imaging conditions and detector geometries for a thick and beam-sensitive low-contrast specimen using the example of a carbon nanotube/polymer nanocomposite. We carried out Monte Carlo simulations as well as quantitative ADF-STEM imaging experiments to predict and verify optimum contrast conditions. The presented method is general, can be easily adapted to other beam-sensitive and/or low-contrast materials, as shown for a polymer vesicle within a TEM liquid cell, and can act as an expert guide on whether an experiment is feasible and to determine the best imaging conditions.

Water without windows: Evaluating the performance of open cell transmission electron microscopy under saturated water vapor conditions, and assessing its potential for microscopy of hydrated biological specimens

We have performed open cell transmission electron microscopy experiments through pure water vapor in the saturation pressure regime (>0.6 kPa), in a modern microscope capable of sub-Å resolution. We have systematically studied achievable pressure levels, stability and gas purity, effective thickness of the water vapor column and associated electron scattering processes, and the effect of gas pressure on electron optical resolution and image contrast. For example, for 1.3 kPa pure water vapor and 300kV electrons, we report pressure stability of ± 20 Pa over tens of minutes, effective thickness of 0.57 inelastic mean free paths, lattice resolution of 0.14 nm on a reference Au specimen, and no significant degradation in contrast or stability of a biological specimen (M13 virus, with 6 nm body diameter). We have also done some brief experiments to confirm feasibility of loading specimens into an in situ water vapor ambient without exposure to intermediate desiccating conditions. Finally, we have also checked if water experiments had any discernible impact on the microscope performance, and report pertinent vacuum and electron optical data, for reference purposes.

Low-dose cryo electron ptychography via non-convex Bayesian optimization

Electron ptychography has seen a recent surge of interest for phase sensitive imaging at atomic or near-atomic resolution. However, applications are so far mainly limited to radiation-hard samples, because the required doses are too high for imaging biological samples at high resolution. We propose the use of non-convex Bayesian optimization to overcome this problem, and show via numerical simulations that the dose required for successful reconstruction can be reduced by two orders of magnitude compared to previous experiments. As an important application we suggest to use this method for imaging single biological macromolecules at cryogenic temperatures and demonstrate 2D single-particle reconstructions from simulated data with a resolution up to 5.4 Å at a dose of 20e⁻/Ų. When averaging over only 30 low-dose datasets, a 2D resolution around 3.5 Å is possible for macromolecular complexes even below 100 kDa. With its independence from the microscope transfer function, direct recovery of phase contrast, and better scaling of signal-to-noise ratio, low-dose cryo electron ptychography may become a promising alternative to Zernike phase-contrast microscopy.

Antibody-Based Affinity Cryoelectron Microscopy at 2.6-Å Resolution

The affinity cryoelectron microscopy (cryo-EM) approach has been explored in recent years to simplify and/or improve the sample preparation for cryo-EM, which can bring previously challenging specimens such as those of low abundance and/or unpurified ones within reach of the cryo-EM technique. Despite the demonstrated successes for solving structures to low to intermediate resolutions, the lack of near-atomic structures using this approach has led to a common perception of affinity cryo-EM as a niche technique incapable of reaching high resolutions. Here, we report a ∼2.6-Å structure solved using the antibody-based affinity grid approach with low-concentration Tulane virus purified from a low-yield cell-culture system that has been challenging to standard cryo-EM grid preparation. Quantitative analyses of the structure indicate data and reconstruction quality comparable with the conventional grid preparation method using samples at high concentration.

Factor Analysis for Spectral Estimation

Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model where a signal is given by a random linear combination of fixed, yet unknown, stochastic sources. Given multiple such signals, we estimate the subspace spanned by the power spectra of these fixed sources. Projecting individual power spectrum estimates onto this subspace increases estimation accuracy. We provide accuracy guarantees for this method and demonstrate it on simulated and experimental data from cryo-electron microscopy.

Multi-pass transmission electron microscopy

Feynman once asked physicists to build better electron microscopes to be able to watch biology at work. While electron microscopes can now provide atomic resolution, electron beam induced specimen damage precludes high resolution imaging of sensitive materials, such as single proteins or polymers. Here, we use simulations to show that an electron microscope based on a multi-pass measurement protocol enables imaging of single proteins, without averaging structures over multiple images. While we demonstrate the method for particular imaging targets, the approach is broadly applicable and is expected to improve resolution and sensitivity for a range of electron microscopy imaging modalities, including, for example, scanning and spectroscopic techniques. The approach implements a quantum mechanically optimal strategy which under idealized conditions can be considered interaction-free.

Single-protein detection in crowded molecular environments in cryo-EM images

We present an approach to study macromolecular assemblies by detecting component proteins' characteristic high-resolution projection patterns, calculated from their known 3D structures, in single electron cryo-micrographs. Our method detects single apoferritin molecules in vitreous ice with high specificity and determines their orientation and location precisely. Simulations show that high spatial-frequency information and-in the presence of protein background-a whitening filter are essential for optimal detection, in particular for images taken far from focus. Experimentally, we could detect small viral RNA polymerase molecules, distributed randomly among binding locations, inside rotavirus particles. Based on the currently attainable image quality, we estimate a threshold for detection that is 150 kDa in ice and 300 kDa in 100 nm thick samples of dense biological material.

SHAPE BASED IMAGE RECONSTRUCTION USING LINEARIZED DEFORMATIONS

We introduce a reconstruction framework that can account for shape related a priori information in ill-posed linear inverse problems in imaging. It is a variational scheme that uses a shape functional defined using deformable templates machinery from shape theory. As proof of concept, we apply the proposed shape based reconstruction to 2D tomography with very sparse measurements, and demonstrate strong empirical results.

Site-Specific Preparation of Intact Solid-Liquid Interfaces by Label-Free In Situ Localization and Cryo-Focused Ion Beam Lift-Out

Scanning transmission electron microscopy (STEM) allows atomic scale characterization of solid-solid interfaces, but has seen limited applications to solid-liquid interfaces due to the volatility of liquids in the microscope vacuum. Although cryo-electron microscopy is routinely used to characterize hydrated samples stabilized by rapid freezing, sample thinning is required to access the internal interfaces of thicker specimens. Here, we adapt cryo-focused ion beam (FIB) "lift-out," a technique recently developed for biological specimens, to prepare intact internal solid-liquid interfaces for high-resolution structural and chemical analysis by cryo-STEM. To guide the milling process we introduce a label-free in situ method of localizing subsurface structures in suitable materials by energy dispersive X-ray spectroscopy (EDX). Monte Carlo simulations are performed to evaluate the depth-probing capability of the technique, and show good qualitative agreement with experiment. We also detail procedures to produce homogeneously thin lamellae, which enable nanoscale structural, elemental, and chemical analysis of intact solid-liquid interfaces by analytical cryo-STEM. This work demonstrates the potential of cryo-FIB lift-out and cryo-STEM for understanding physical and chemical processes at solid-liquid interfaces.