Three-dimensional reconstruction with contrast transfer function correction from energy-filtered cryoelectron micrographs: procedure and application to the 70S Escherichia coli ribosome

Deep learning-assisted analysis of HRTEM images of crystalline nanoparticles

Accurate analysis of high-resolution transmission electron microscopy (HRTEM) images is important for the characterization and design of materials. However, conventional analyses rely mostly on manual procedures, which are time-consuming and lack accuracy, especially when the image contrast is low. Here, we propose an advanced analysis method for extracting crystal features from HRTEM images based on a 2D fast Fourier transform and U-Net based deep learning model. By using HRTEM images of iron oxide nanoparticles as examples, we show that our method is capable of providing information on the crystallinity profile, distribution of crystal planes, phases and defects automatically with high accuracy. In an era of data-driven technological development, we believe that deep learning based analysis tools will facilitate great progress in fundamental research on crystalline materials.

A review of the approaches used to solve sub-100 kDa membrane proteins by cryo-electron microscopy

Membrane proteins (MPs) are essential components of all biological membranes, contributing to key cellular functions that include signalling, molecular transport and energy metabolism. Consequently, MPs are important biomedical targets for therapeutics discovery. Despite hardware and software developments in cryo-electron microscopy, as well as MP sample preparation, MPs smaller than 100 kDa remain difficult to study structurally. Significant investment is required to overcome low levels of naturally abundant protein, MP hydrophobicity as well as conformational and compositional instability. Here we have reviewed the sample preparation approaches that have been taken to successfully express, purify and prepare small MPs for analysis by cryo-EM (those with a total solved molecular weight of under 100 kDa), as well as examining the differing approaches towards data processing and ultimately obtaining a structural solution. We highlight common challenges at each stage in the process as well as strategies that have been developed to overcome these issues. Finally, we discuss future directions and opportunities for the study of sub-100 kDa membrane proteins by cryo-EM.

Design of an ultrafast pulsed ponderomotive phase plate for cryo-electron tomography

Ponderomotive phase plates have shown that temporally consistent phase contrast is possible within electron microscopes via high-fluence static laser modes resonating in Fabry-Perot cavities. Here, we explore using pulsed laser beams as an alternative method of generating high fluences. We find through forward-stepping finite element models that picosecond or shorter interactions are required for meaningful fluences and phase shifts, with higher pulse energies and smaller beam waists leading to predicted higher fluences. An additional model based on quasi-classical assumptions is used to discover the shape of the phase plate by incorporating the oscillatory nature of the electric field. From these results, we find the transient nature of the laser pulses removes the influence of Kapitza-Dirac diffraction patterns that appear in the static resonator cases. We conclude by predicting that a total laser pulse energy of 8.7 μJ is enough to induce the required π/2 phase shift for Zernike-like phase microscopy.

Artificial Intelligence in Cryo-Electron Microscopy

Cryo-electron microscopy (cryo-EM) has become an unrivaled tool for determining the structure of macromolecular complexes. The biological function of macromolecular complexes is inextricably tied to the flexibility of these complexes. Single particle cryo-EM can reveal the conformational heterogeneity of a biochemically pure sample, leading to well-founded mechanistic hypotheses about the roles these complexes play in biology. However, the processing of increasingly large, complex datasets using traditional data processing strategies is exceedingly expensive in both user time and computational resources. Current innovations in data processing capitalize on artificial intelligence (AI) to improve the efficiency of data analysis and validation. Here, we review new tools that use AI to automate the data analysis steps of particle picking, 3D map reconstruction, and local resolution determination. We discuss how the application of AI moves the field forward, and what obstacles remain. We also introduce potential future applications of AI to use cryo-EM in understanding protein communities in cells.

Interconnecting solvent quality, transcription, and chromosome folding in Escherichia coli

All cells fold their genomes, including bacterial cells, where the chromosome is compacted into a domain-organized meshwork called the nucleoid. How compaction and domain organization arise is not fully understood. Here, we describe a method to estimate the average mesh size of the nucleoid in Escherichia coli. Using nucleoid mesh size and DNA concentration estimates, we find that the cytoplasm behaves as a poor solvent for the chromosome when the cell is considered as a simple semidilute polymer solution. Monte Carlo simulations suggest that a poor solvent leads to chromosome compaction and DNA density heterogeneity (i.e., domain formation) at physiological DNA concentration. Fluorescence microscopy reveals that the heterogeneous DNA density negatively correlates with ribosome density within the nucleoid, consistent with cryoelectron tomography data. Drug experiments, together with past observations, suggest the hypothesis that RNAs contribute to the poor solvent effects, connecting chromosome compaction and domain formation to transcription and intracellular organization.

CDAE: A Cascade of Denoising Autoencoders for Noise Reduction in the Clustering of Single-Particle Cryo-EM Images

As an emerging technology, cryo-electron microscopy (cryo-EM) has attracted more and more research interests from both structural biology and computer science, because many challenging computational tasks are involved in the processing of cryo-EM images. An important image processing step is to cluster the 2D cryo-EM images according to their projection angles, then the cluster mean images are used for the subsequent 3D reconstruction. However, cryo-EM images are quite noisy and denoising them is not easy, because the noise is a complicated mixture from samples and hardware. In this study, we design an effective cryo-EM image denoising model, CDAE, i.e., a cascade of denoising autoencoders. The new model comprises stacked blocks of deep neural networks to reduce noise in a progressive manner. Each block contains a convolutional autoencoder, pre-trained by simulated data of different SNRs and fine-tuned by target data set. We assess this new model on three simulated test sets and a real data set. CDAE achieves very competitive PSNR (peak signal-to-noise ratio) in the comparison of the state-of-the-art image denoising methods. Moreover, the denoised images have significantly enhanced clustering results compared to original image features or high-level abstraction features obtained by other deep neural networks. Both quantitative and visualized results demonstrate the good performance of CDAE for the noise reduction in clustering single-particle cryo-EM images.

Reliable cryo-EM resolution estimation with modified Fourier shell correlation

A modified Fourier shell correlation (mFSC) methodology is introduced that is aimed at addressing two fundamental problems that mar the use of the FSC: the strong influence of mask-induced artifacts on resolution estimation and the lack of assessment of FSC uncertainties stemming from the inability to determine the associated number of degrees of freedom. It is shown that by simply changing the order of the steps in which the FSC is computed, the correlations induced by masking of the input data can be eliminated. In addition, to further reduce artifacts, a smooth Gaussian window function is used to outline the regions of reciprocal space within which the mFSC is computed. Next, it is shown that the number of degrees of freedom (ndf) of the system is approximated well by combining the ndf associated with the Gaussian window in reciprocal space with further reduction of the ndf owing to the use of the mask in real space. It is demonstrated through the application of the mFSC to both single-particle and helical structures that the mFSC yields reliable, mask-induced artifact-free results as a result of the introduced modifications. Since the adverse effect of the mask is eliminated, it also becomes possible to compute robust local resolutions both per voxel of a 3D map as well as, in a newly developed approach, per functional subunit, segment or even larger secondary element of the studied complex.

Reducing bias and variance for CTF estimation in single particle cryo-EM

When using an electron microscope for imaging of particles embedded in vitreous ice, the recorded image, or micrograph, is a significantly degraded version of the tomographic projection of the sample. Apart from noise, the image is affected by the optical configuration of the microscope. This transformation is typically modeled as a convolution with a point spread function. The Fourier transform of this function, known as the contrast transfer function (CTF), is oscillatory, attenuating and amplifying different frequency bands, and sometimes flipping their signs. High-resolution reconstruction requires this CTF to be accounted for, but as its form depends on experimental parameters, it must first be estimated from the micrograph. We present a new method for CTF estimation based on multitaper techniques that reduce bias and variance in the estimate. We also use known properties of the CTF and the background power spectrum to further reduce the variance through background subtraction and steerable basis projection. We show that the resulting power spectrum estimates better capture the zero-crossings of the CTF and yield accurate CTF estimates on several experimental micrographs.

The ETFL formulation allows multi-omics integration in thermodynamics-compliant metabolism and expression models

Systems biology has long been interested in models capturing both metabolism and expression in a cell. We propose here an implementation of the metabolism and expression model formalism (ME-models), which we call ETFL, for Expression and Thermodynamics Flux models. ETFL is a hierarchical model formulation, from metabolism to RNA synthesis, that allows simulating thermodynamics-compliant intracellular fluxes as well as enzyme and mRNA concentration levels. ETFL formulates a mixed-integer linear problem (MILP) that enables both relative and absolute metabolite, protein, and mRNA concentration integration. ETFL is compatible with standard MILP solvers and does not require a non-linear solver, unlike the previous state of the art. It also accounts for growth-dependent parameters, such as relative protein or mRNA content. We present ETFL along with its validation using results obtained from a well-characterized E. coli model. We show that ETFL is able to reproduce proteome-limited growth. We also subject it to several analyses, including the prediction of feasible mRNA and enzyme concentrations and gene essentiality.

Accounting for the effects of genetic expression in genome-scale metabolic models is challenging. Here, the authors introduce a model formulation that efficiently simulates thermodynamic-compliant fluxes, enzyme and mRNA concentration levels, allowing omics integration and broad analysis of in silico cellular physiology.

Methods for merging data sets in electron cryo-microscopy

Recent developments have resulted in electron cryo-microscopy (cryo-EM) becoming a useful tool for the structure determination of biological macromolecules. For samples containing inherent flexibility, heterogeneity or preferred orientation, the collection of extensive cryo-EM data using several conditions and microscopes is often required. In such a scenario, merging cryo-EM data sets is advantageous because it allows improved three-dimensional reconstructions to be obtained. Since data sets are not always collected with the same pixel size, merging data can be challenging. Here, two methods to combine cryo-EM data are described. Both involve the calculation of a rescaling factor from independent data sets. The effects of errors in the scaling factor on the results of data merging are also estimated. The methods described here provide a guideline for cryo-EM users who wish to combine data sets from the same type of microscope and detector.

Joachim Frank's Binding with the Ribosome

With recent technological advancements, single-particle cryogenic electron microscopy (cryo-EM) is now the technique of choice to study structure and function of biological macromolecules at near-atomic resolution. Many single-particle EM reconstruction methods necessary for these advances were pioneered by Joachim Frank, and were optimized using the ribosome as a benchmark specimen. In doing so, he made several landmark contributions to the understanding of the structure and function of ribosomes. These include the first 3D visualization of ribosome-bound transfer RNAs, the first experimentally derived structures of the primary complexes formed during the bacterial translation elongation cycle, and the critical ribosomal conformational transitions required for translation. Over the years, his laboratory studied many important functional complexes of the ribosome from both eubacterial and eukaryotic systems, including ribosomes from pathogenic organisms. This article presents a brief account of the contributions made by Joachim Frank to the ribosome field.

Fast multiscale reconstruction for Cryo-EM

We present a multiscale reconstruction framework for single-particle analysis (SPA). The representation of three-dimensional (3D) objects with scaled basis functions permits the reconstruction of volumes at any desired scale in the real-space. This multiscale approach generates interesting opportunities in SPA for the stabilization of the initial volume problem or the 3D iterative refinement procedure. In particular, we show that reconstructions performed at coarse scale are more robust to angular errors and permit gains in computational speed. A key component of the proposed iterative scheme is its fast implementation. The costly step of reconstruction, which was previously hindering the use of advanced iterative methods in SPA, is formulated as a discrete convolution with a cost that does not depend on the number of projection directions. The inclusion of the contrast transfer function inside the imaging matrix is also done at no extra computational cost. By permitting full 3D regularization, the framework is by itself a robust alternative to direct methods for performing reconstruction in adverse imaging conditions (e.g., heavy noise, large angular misassignments, low number of projections). We present reconstructions obtained at different scales from a dataset of the 2015/2016 EMDataBank Map Challenge. The algorithm has been implemented in the Scipion package.

Single-Particle Reconstruction of Biological Molecules-Story in a Sample (Nobel Lecture)

Pictures tell a thousand words: The development of single-particle cryo-electron microscopy set the stage for high-resolution structure determination of biological molecules. In his Nobel lecture, J. Frank describes the ground-breaking discoveries that have enabled the development of cryo-EM. The method has taken biochemistry into a new era.

Defocus and magnification dependent variation of TEM image astigmatism

Daily alignment of the microscope is a prerequisite to reaching optimal lens conditions for high resolution imaging in cryo-EM. In this study, we have investigated how image astigmatism varies with the imaging conditions (e.g. defocus, magnification). We have found that the large change of defocus/magnification between visual correction of astigmatism and subsequent data collection tasks, or during data collection, will inevitably result in undesirable astigmatism in the final images. The dependence of astigmatism on the imaging conditions varies significantly from time to time, so that it cannot be reliably compensated by pre-calibration of the microscope. Based on these findings, we recommend that the same magnification and the median defocus of the intended defocus range for final data collection are used in the objective lens astigmatism correction task during microscope alignment and in the focus mode of the iterative low-dose imaging. It is also desirable to develop a fast, accurate method that can perform dynamic correction of the astigmatism for different intended defocuses during automated imaging. Our findings also suggest that the slope of astigmatism changes caused by varying defocuses can be used as a convenient measurement of objective lens rotation symmetry and potentially an acceptance test of new electron microscopes.

Guidelines for using Bsoft for high resolution reconstruction and validation of biomolecular structures from electron micrographs

Cryo-electron microscopy (cryoEM) is becoming popular as a tool to solve biomolecular structures with the recent availability of direct electron detectors allowing automated acquisition of high resolution data. The Bsoft software package, developed over 20 years for analyzing electron micrographs, offers a full workflow for validated single particle analysis with extensive functionality, enabling customization for specific cases. With the increasing use of cryoEM and its automation, proper validation of the results is a bigger concern. The three major validation approaches, independent data sets, resolution-limited processing, and coherence testing, can be incorporated into any Bsoft workflow. Here, the main workflow is divided into four phases: (i) micrograph preprocessing, (ii) particle picking, (iii) particle alignment and reconstruction, and (iv) interpretation. Each of these phases represents a conceptual unit that can be automated, followed by a check point to assess the results. The aim in the first three phases is to reconstruct one or more validated maps at the best resolution possible. Map interpretation then involves identification of components, segmentation, quantification, and modeling. The algorithms in Bsoft are well established, with future plans focused on ease of use, automation and institutionalizing validation.

A Survey of the Use of Iterative Reconstruction Algorithms in Electron Microscopy

One of the key steps in Electron Microscopy is the tomographic reconstruction of a three-dimensional (3D) map of the specimen being studied from a set of two-dimensional (2D) projections acquired at the microscope. This tomographic reconstruction may be performed with different reconstruction algorithms that can be grouped into several large families: direct Fourier inversion methods, back-projection methods, Radon methods, or iterative algorithms. In this review, we focus on the latter family of algorithms, explaining the mathematical rationale behind the different algorithms in this family as they have been introduced in the field of Electron Microscopy. We cover their use in Single Particle Analysis (SPA) as well as in Electron Tomography (ET).

Nucleoid and cytoplasmic localization of small RNAs in Escherichia coli

Bacterial small RNAs (sRNAs) regulate protein production by binding to mRNAs and altering their translation and degradation. sRNAs are smaller than most mRNAs but larger than many proteins. Therefore it is uncertain whether sRNAs can enter the nucleoid to target nascent mRNAs. Here, we investigate the intracellular localization of sRNAs transcribed from plasmids in Escherichia coli using RNA fluorescent in-situ hybridization. We found that sRNAs (GlmZ, OxyS, RyhB and SgrS) have equal preference for the nucleoid and cytoplasm, and no preferential localization at the cell membrane. We show using the gfp mRNA (encoding green fluorescent protein) that non-sRNAs can be engineered to have different proportions of nucleoid and cytoplasmic localization by altering their length and/or translation. The same localization as sRNAs was achieved by decreasing gfp mRNA length and translation, which suggests that sRNAs and other RNAs may enter the densely packed DNA of the nucleoid if they are sufficiently small. We also found that the Hfq protein, which binds sRNAs, minimally affects sRNA localization. Important implications of our findings for engineering synthetic circuits are: (i) sRNAs can potentially bind nascent mRNAs in the nucleoid, and (ii) localization patterns and distribution volumes of sRNAs can differ from some larger RNAs.

The advent of structural biology in situ by single particle cryo-electron tomography

Single particle tomography (SPT), also known as subtomogram averaging, is a powerful technique uniquely poised to address questions in structural biology that are not amenable to more traditional approaches like X-ray crystallography, nuclear magnetic resonance, and conventional cryoEM single particle analysis. Owing to its potential for in situ structural biology at subnanometer resolution, SPT has been gaining enormous momentum in the last five years and is becoming a prominent, widely used technique. This method can be applied to unambiguously determine the structures of macromolecular complexes that exhibit compositional and conformational heterogeneity, both in vitro and in situ. Here we review the development of SPT, highlighting its applications and identifying areas of ongoing development.

A resource dependent protein synthesis model for evaluating synthetic circuits

Reliable in silico design of synthetic gene networks necessitates novel approaches to model the process of protein synthesis under the influence of limited resources. We present such a novel protein synthesis model which originates from the Ribosome Flow Model and among other things describes the movement of RNA-polymerase and ribosomes on mRNA and DNA templates, respectively. By analyzing the convergence properties of this model based upon geometric considerations, we present additional insights into the dynamic mechanisms of the process of protein synthesis. Further, we demonstrate how this model can be used to evaluate the performance of synthetic gene circuits under different loading scenarios.

Real-time detection and single-pass minimization of TEM objective lens astigmatism

Minimization of the astigmatism of the objective lens is a critical daily instrument alignment task essential for high resolution TEM imaging. Fast and sensitive detection of astigmatism is needed to provide real-time feedback and adjust the stigmators to efficiently reduce astigmatism. Currently the method used by many microscopists is to visually examine the roundness of a diffractogram (Thon rings) and iteratively adjust the stigmators to make the Thon rings circular. This subjective method is limited by poor sensitivity and potentially biased by the astigmatism of human eyes. In this study, an s² power spectra based method, s²stigmator, was developed to allow fast and sensitive detection of the astigmatism in TEM live images. The "radar"-style display provides real-time feedback to guide the adjustment of the objective lens stigmators. Such unique capability allowed us to discover the mapping of the two stigmators to the astigmatism amplitude and angle, which led us to develop a single-pass tuning strategy capable of significantly quicker minimization of the objective lens astigmatism.

A guide to the 3D structure of the ryanodine receptor type 1 by cryoEM

Signal transduction by the ryanodine receptor (RyR) is essential in many excitable cells including all striated contractile cells and some types of neurons. While its transmembrane domain is a classic tetrameric, six-transmembrane cation channel, the cytoplasmic domain is uniquely large and complex, hosting a multiplicity of specialized domains. The overall outline and substructure readily recognizable by electron microscopy make RyR a geometrically well-behaved specimen. Hence, for the last two decades, the 3D structural study of the RyR has tracked closely the technological advances in electron microscopy, cryo-electron microscopy (cryoEM), and computerized 3D reconstruction. This review summarizes the progress in the structural determination of RyR by cryoEM and, bearing in mind the leap in resolution provided by the recent implementation of direct electron detection, analyzes the first near-atomic structures of RyR. These reveal a complex orchestration of domains controlling the channel's function, and help to understand how this could break down as a consequence of disease-causing mutations.

A primer to single-particle cryo-electron microscopy

Cryo-electron microscopy (cryo-EM) of single-particle specimens is used to determine the structure of proteins and macromolecular complexes without the need for crystals. Recent advances in detector technology and software algorithms now allow images of unprecedented quality to be recorded and structures to be determined at near-atomic resolution. However, compared with X-ray crystallography, cryo-EM is a young technique with distinct challenges. This primer explains the different steps and considerations involved in structure determination by single-particle cryo-EM to provide an overview for scientists wishing to understand more about this technique and the interpretation of data obtained with it, as well as a starting guide for new practitioners.

Do's and don'ts of cryo-electron microscopy: a primer on sample preparation and high quality data collection for macromolecular 3D reconstruction

Cryo-electron microscopy (cryoEM) entails flash-freezing a thin layer of sample on a support, and then visualizing the sample in its frozen hydrated state by transmission electron microscopy (TEM). This can be achieved with very low quantity of protein and in the buffer of choice, without the use of any stain, which is very useful to determine structure-function correlations of macromolecules. When combined with single-particle image processing, the technique has found widespread usefulness for 3D structural determination of purified macromolecules.

The protocol presented here explains how to perform cryoEM and examines the causes of most commonly encountered problems for rational troubleshooting; following all these steps should lead to acquisition of high quality cryoEM images. The technique requires access to the electron microscope instrument and to a vitrification device. Knowledge of the 3D reconstruction concepts and software is also needed for computerized image processing. Importantly, high quality results depend on finding the right purification conditions leading to a uniform population of structurally intact macromolecules.

The ability of cryoEM to visualize macromolecules combined with the versatility of single particle image processing has proven very successful for structural determination of large proteins and macromolecular machines in their near-native state, identification of their multiple components by 3D difference mapping, and creation of pseudo-atomic structures by docking of x-ray structures. The relentless development of cryoEM instrumentation and image processing techniques for the last 30 years has resulted in the possibility to generate de novo 3D reconstructions at atomic resolution level.

Rotationally invariant image representation for viewing direction classification in cryo-EM

We introduce a new rotationally invariant viewing angle classification method for identifying, among a large number of cryo-EM projection images, similar views without prior knowledge of the molecule. Our rotationally invariant features are based on the bispectrum. Each image is denoised and compressed using steerable principal component analysis (PCA) such that rotating an image is equivalent to phase shifting the expansion coefficients. Thus we are able to extend the theory of bispectrum of 1D periodic signals to 2D images. The randomized PCA algorithm is then used to efficiently reduce the dimensionality of the bispectrum coefficients, enabling fast computation of the similarity between any pair of images. The nearest neighbors provide an initial classification of similar viewing angles. In this way, rotational alignment is only performed for images with their nearest neighbors. The initial nearest neighbor classification and alignment are further improved by a new classification method called vector diffusion maps. Our pipeline for viewing angle classification and alignment is experimentally shown to be faster and more accurate than reference-free alignment with rotationally invariant K-means clustering, MSA/MRA 2D classification, and their modern approximations.

CTER-rapid estimation of CTF parameters with error assessment

In structural electron microscopy, the accurate estimation of the Contrast Transfer Function (CTF) parameters, particularly defocus and astigmatism, is of utmost importance for both initial evaluation of micrograph quality and for subsequent structure determination. Due to increases in the rate of data collection on modern microscopes equipped with new generation cameras, it is also important that the CTF estimation can be done rapidly and with minimal user intervention. Finally, in order to minimize the necessity for manual screening of the micrographs by a user it is necessary to provide an assessment of the errors of fitted parameters values. In this work we introduce CTER, a CTF parameters estimation method distinguished by its computational efficiency. The efficiency of the method makes it suitable for high-throughput EM data collection, and enables the use of a statistical resampling technique, bootstrap, that yields standard deviations of estimated defocus and astigmatism amplitude and angle, thus facilitating the automation of the process of screening out inferior micrograph data. Furthermore, CTER also outputs the spatial frequency limit imposed by reciprocal space aliasing of the discrete form of the CTF and the finite window size. We demonstrate the efficiency and accuracy of CTER using a data set collected on a 300kV Tecnai Polara (FEI) using the K2 Summit DED camera in super-resolution counting mode. Using CTER we obtained a structure of the 80S ribosome whose large subunit had a resolution of 4.03Å without, and 3.85Å with, inclusion of astigmatism parameters.

Nonequilibrium stochastic model for tRNA binding time statistics

Protein translation is one of the most important processes in cell life, but despite being well-understood biochemically, the implications of its intrinsic stochastic nature have not been fully elucidated. In this paper we develop a microscopic and stochastic model which describes a crucial step in protein translation, namely the binding of the tRNA to the ribosome. Our model explicitly takes into consideration tRNA recharging dynamics, spatial inhomogeneity, and stochastic fluctuations in the number of charged tRNAs around the ribosome. By analyzing this nonequilibrium system we are able to derive the statistical distribution of the times needed by the tRNAs to bind to the ribosome, and to show that it deviates from an exponential due to the coupling between the fluctuations of charged and uncharged populations of tRNA.

Atomic structure from large-area, low-dose exposures of materials: a new route to circumvent radiation damage

Beam-induced structural modifications are a major nuisance in the study of materials by high-resolution electron microscopy. Here, we introduce a new approach to circumvent the radiation damage problem by a statistical treatment of large, noisy, low-dose data sets of non-periodic configurations (e.g. defects) in the material. We distribute the dose over a mixture of different defect structures at random positions and with random orientations, and recover representative model images via a maximum likelihood search. We demonstrate reconstructions from simulated images at such low doses that the location of individual entities is not possible. The approach may open a route to study currently inaccessible beam-sensitive configurations.

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A new approach to circumvent radiation damage.

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Statistical treatment of large noisy data sets.

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Analysis of radiation sensitive material defects.

Critical importance of the correction of contrast transfer function for transmission electron microscopy-mediated structural biology

Background

Transmission electron microscopy (TEM) is an excellent tool for studying detailed biological structures. High-resolution structure determination is now routinely performed using advanced sample preparation techniques and image processing software. In particular, correction for contrast transfer function (CTF) is crucial for extracting high-resolution information from TEM image that is convoluted by imperfect imaging condition. Accurate determination of defocus, one of the major elements constituting the CTF, is mandatory for CTF correction.

Findings

To investigate the effect of correct estimation of image defocus and subsequent CTF correction, we tested arbitrary CTF imposition onto the images of two-dimensional crystals of Rous sarcoma virus capsid protein. The morphology of the crystal in calculated projection maps from incorrect CTF imposition was utterly distorted in comparison to an appropriately CTF-corrected image.

Conclusion

This result demonstrates critical importance of CTF correction for producing true representation of the specimen at high resolution.

Novel convergence-oriented approach for evaluation and optimization of workflow in single-particle two-dimensional averaging of electron microscope images

Three-dimensional (3D) protein structures facilitate the understanding of their biological functions and provide valuable information for developing medicines. Single-particle analysis (SPA) from electron microscopy (EM) is a structure determination method suitable for macromolecules. To achieve a high resolution using combinations of several SPA software packages, 'workflow' optimization and comparative evaluation by scoring results are essential. Two-dimensional (2D) averaging is a key step for 3D reconstruction. The integrated convergence-evaluation oriented system (IC-EOS) proposed here provides an effective tool for customizing 2D averaging. This assesses the behavior and characteristics of workflows and evaluates the convergence of iteration steps without human intervention. We chose five base measurements for quantifying convergence: resolution, variance, similarity, shift-distance and rotation-angle. Curve fitting to history graphs scored their stability. We call this score 'fluctuation'. The number of particle images discarded from the library and the number of classification groups were examined to see their effects on optimization levels and fluctuation of measurements, allowing the IC-EOS to select the most appropriate workflow for the target. A case study using a bacterial sodium channel and a simulation study using GroEL showed that resolution of 2D averaging improved with relatively stricter particle selection. With fewer groups, resolutions of class averages improved, but similarities between class-averages and their constituent particle images degraded. Fluctuation was useful for selecting adequate conditions, even when achieved values alone were not conclusive. The vote method, using fluctuation, was robust against noise and enabled a decision without exhaustive search trials. Thus, the IC-EOS is a step toward full automation of SPA.

Defocus estimation from stroboscopic cryo-electron microscopy data

Defocus estimation is an important step for improving the resolution of single particle reconstructions. It can be troublesome to estimate the defocus from low-dose cryo-electron microscopy (cryo-EM) data, particularly if there is not sufficient contrast present in the Fourier transform of the micrograph. Most existing approaches estimate the defocus from the presence of Thon rings within the power spectrum, employing image enhancement techniques to highlight these rings. In this paper, an approach to estimating the defocus from a stroboscopic image series is described. The image series is used to obtain two statistical metrics: figure of merit (FOM) and Q-factor. These metrics have been used to estimate the defoci from low-dose stroboscopic cryo-EM data consisting of a variable number of images.

Three-dimensional reconstruction of Heterocapsa circularisquama RNA virus by electron cryo-microscopy

Heterocapsa circularisquama RNA virus is a non-enveloped icosahedral ssRNA virus infectious to the harmful bloom-forming dinoflagellate, H. circularisquama, and which is assumed to be the major natural agent controlling the host population. The viral capsid is constructed from a single gene product. Electron cryo-microscopy revealed that the virus has a diameter of 34 nm and T = 3 symmetry. The 180 quasi-equivalent monomers have an unusual arrangement in that each monomer contributes to a 'bump' on the surface of the protein. Though the capsid protein probably has the classic 'jelly roll' β-sandwich fold, this is a new packing arrangement and is distantly related to the other positive-sense ssRNA virus capsid proteins. The handedness of the structure has been determined by a novel method involving high resolution scanning electron microscopy of the negatively stained viruses and secondary electron detection.

A fast algorithm for computing and correcting the CTF for tilted, thick specimens in TEM

Today, the resolution in phase-contrast cryo-electron tomography is for a significant part limited by the contrast transfer function (CTF) of the microscope. The CTF is a function of defocus and thus varies spatially as a result of the tilting of the specimen and the finite specimen thickness. Models that include spatial dependencies have not been adopted in daily practice because of their high computational complexity. Here we present an algorithm which reduces the processing time for computing the 'tilted' CTF by more than a factor 100. Our implementation of the full 3D CTF has a processing time on the order of a Radon transform of a full tilt-series. We derive and validate an expression for the damping envelope function describing the loss of resolution due to specimen thickness. Using simulations we quantify the effects of specimen thickness on the accuracy of various forward models. We study the influence of spatially varying CTF correction and subsequent tomographic reconstruction by simulation and present a new approach for space-variant phase-flipping. We show that our CTF correction strategies are successful in increasing the resolution after tomographic reconstruction.

An evolutionarily conserved mechanism for controlling the efficiency of protein translation

Recent years have seen intensive progress in measuring protein translation. However, the contributions of coding sequences to the efficiency of the process remain unclear. Here, we identify a universally conserved profile of translation efficiency along mRNAs computed based on adaptation between coding sequences and the tRNA pool. In this profile, the first approximately 30-50 codons are, on average, translated with a low efficiency. Additionally, in eukaryotes, the last approximately 50 codons show the highest efficiency over the full coding sequence. The profile accurately predicts position-dependent ribosomal density along yeast genes. These data suggest that translation speed and, as a consequence, ribosomal density are encoded by coding sequences and the tRNA pool. We suggest that the slow "ramp" at the beginning of mRNAs serves as a late stage of translation initiation, forming an optimal and robust means to reduce ribosomal traffic jams, thus minimizing the cost of protein expression.

A novel approximation method of CTF amplitude correction for 3D single particle reconstruction

The typical resolution of three-dimensional reconstruction by cryo-EM single particle analysis is now being pushed up to and beyond the nanometer scale. Correction of the contrast transfer function (CTF) of electron microscopic images is essential for achieving such a high resolution. Various correction methods exist and are employed in popular reconstruction software packages. Here, we present a novel approximation method that corrects the amplitude modulation introduced by the contrast transfer function by convoluting the images with a piecewise continuous function. Our new approach can easily be implemented and incorporated into other packages. The implemented method yielded higher resolution reconstructions with data sets from both highly symmetric and asymmetric structures. It is an efficient alternative correction method that allows quick convergence of the 3D reconstruction and has a high tolerance for noisy images, thus easing a bottleneck in practical reconstruction of macromolecules.

Fundamentals of three-dimensional reconstruction from projections

Three-dimensional (3D) reconstruction of an object mass density from the set of its 2D line projections lies at a core of both single-particle reconstruction technique and electron tomography. Both techniques utilize electron microscope to collect a set of projections of either multiple objects representing in principle the same macromolecular complex in an isolated form, or a subcellular structure isolated in situ. Therefore, the goal of macromolecular electron microscopy is to invert the projection transformation to recover the distribution of the mass density of the original object. The problem is interesting in that in its discrete form it is ill-posed and not invertible. Various algorithms have been proposed to cope with the practical difficulties of this inversion problem and their differ widely in terms of their robustness with respect to noise in the data, completeness of the collected projection dataset, errors in projections orientation parameters, abilities to efficiently handle large datasets, and other obstacles typically encountered in molecular electron microscopy. Here, we review the theoretical foundations of 3D reconstruction from line projections followed by an overview of reconstruction algorithms routinely used in practice of electron microscopy.

Image restoration in cryo-electron microscopy

Image restoration techniques are used to obtain, given experimental measurements, the best possible approximation of the original object within the limits imposed by instrumental conditions and noise level in the data. In molecular electron microscopy (EM), we are mainly interested in linear methods that preserve the respective relationships between mass densities within the restored map. Here, we describe the methodology of image restoration in structural EM, and more specifically, we will focus on the problem of the optimum recovery of Fourier amplitudes given electron microscope data collected under various defocus settings. We discuss in detail two classes of commonly used linear methods, the first of which consists of methods based on pseudoinverse restoration, and which is further subdivided into mean-square error, chi-square error, and constrained based restorations, where the methods in the latter two subclasses explicitly incorporates non-white distribution of noise in the data. The second class of methods is based on the Wiener filtration approach. We show that the Wiener filter-based methodology can be used to obtain a solution to the problem of amplitude correction (or "sharpening") of the EM map that makes it visually comparable to maps determined by X-ray crystallography, and thus amenable to comparative interpretation. Finally, we present a semiheuristic Wiener filter-based solution to the problem of image restoration given sets of heterogeneous solutions. We conclude the chapter with a discussion of image restoration protocols implemented in commonly used single particle software packages.

CTF determination and correction for low dose tomographic tilt series

The resolution of cryo-electron tomography can be limited by the first zero of the microscope's contrast transfer function (CTF). To achieve higher resolution, it is critical to determine the CTF and correct its phase inversions. However, the extremely low signal-to-noise ratio (SNR) and the defocus gradient in the projections of tilted specimens make this process challenging. Two programs, CTFPLOTTER and CTFPHASEFLIP, have been developed to address these issues. CTFPLOTTER obtains a 1D power spectrum by periodogram averaging and rotational averaging and it estimates the noise background with a novel approach, which uses images taken with no specimen. The background-subtracted 1D power spectra from image regions at different defocus values are then shifted to align their first zeros and averaged together. This averaging improves the SNR sufficiently that it becomes possible to determine the defocus for subsets of the tilt series rather than just the entire series. CTFPHASEFLIP corrects images line-by-line by inverting phases appropriately in thin strips of the image at nearly constant defocus. CTF correction by these methods is shown to improve the resolution of aligned, averaged particles extracted from tomograms. However, some restoration of Fourier amplitudes at high frequencies is important for seeing the benefits from CTF correction.

Single-particle reconstruction of biological macromolecules in electron microscopy--30 years

This essay gives the autho's personal account on the development of concepts underlying single-particle reconstruction, a technique in electron microscopy of macromolecular assemblies with a remarkable record of achievements as of late. The ribosome proved to be an ideal testing ground for the development of specimen preparation methods, cryo-EM techniques, and algorithms, with discoveries along the way as a rich reward. Increasingly, cryo-EM and single-particle reconstruction, in combination with classification techniques, is revealing dynamic information on functional molecular machines uninhibited by molecular contacts.

SPIDER image processing for single-particle reconstruction of biological macromolecules from electron micrographs

This protocol describes the reconstruction of biological molecules from the electron micrographs of single particles. Computation here is performed using the image-processing software SPIDER and can be managed using a graphical user interface, termed the SPIDER Reconstruction Engine. Two approaches are described to obtain an initial reconstruction: random-conical tilt and common lines. Once an existing model is available, reference-based alignment can be used, a procedure that can be iterated. Also described is supervised classification, a method to look for homogeneous subsets when multiple known conformations of the molecule may coexist.

Error analysis in the determination of the electron microscopical contrast transfer function parameters from experimental power Spectra

BACKGROUND

The transmission electron microscope is used to acquire structural information of macromolecular complexes. However, as any other imaging device, it introduces optical aberrations that must be corrected if high-resolution structural information is to be obtained. The set of all aberrations are usually modeled in Fourier space by the so-called Contrast Transfer Function (CTF). Before correcting for the CTF, we must first estimate it from the electron micrographs. This is usually done by estimating a number of parameters specifying a theoretical model of the CTF. This estimation is performed by minimizing some error measure between the theoretical Power Spectrum Density (PSD) and the experimentally observed PSD. The high noise present in the micrographs, the possible local minima of the error function for estimating the CTF parameters, and the cross-talking between CTF parameters may cause errors in the estimated CTF parameters.

RESULTS

In this paper, we explore the effect of these estimation errors on the theoretical CTF. For the CTF model proposed in 1 we show which are the most sensitive CTF parameters as well as the most sensitive background parameters. Moreover, we provide a methodology to reveal the internal structure of the CTF model (which parameters influence in which parameters) and to estimate the accuracy of each model parameter. Finally, we explore the effect of the variability in the detection of the CTF for CTF phase and amplitude correction.

CONCLUSION

We show that the estimation errors for the CTF detection methodology proposed in 1 does not show a significant deterioration of the CTF correction capabilities of subsequent algorithms. All together, the methodology described in this paper constitutes a powerful tool for the quantitative analysis of CTF models that can be applied to other models different from the one analyzed here.

Estimating contrast transfer function and associated parameters by constrained non-linear optimization

The three-dimensional reconstruction of macromolecules from two-dimensional single-particle electron images requires determination and correction of the contrast transfer function (CTF) and envelope function. A computational algorithm based on constrained non-linear optimization is developed to estimate the essential parameters in the CTF and envelope function model simultaneously and automatically. The application of this estimation method is demonstrated with focal series images of amorphous carbon film as well as images of ice-embedded icosahedral virus particles suspended across holes.

Electron digital imaging toward high-resolution structure analysis of biological macromolecules

Digital imaging has been applied to structure analysis of biological macromolecules in combination with electron energy filtering. Energy filtering can improve the image contrast of frozen-hydrated specimens, but needs a high-sensitivity imaging device instead of photographic film, because of a decrease in electrons after filtration. Here, a lens-coupled slow-scan charge-coupled device (SSCCD) camera with a post-column-type energy filter were examined to image bacterial flagellar filaments embedded in ice. We first measured the modulation transfer function of this camera and showed the remarkable improvement, compared to other fiber-coupled SSCCD cameras. The 3D structure calculated at approximately 7-angstroms resolution clearly resolves alpha-helices. Furthermore, filtered datasets recorded on the SSCCD camera with liquid-nitrogen and liquid-helium cooling were compared with the previous unfiltered one on film with liquid-helium cooling. This report describes the suitability of digital imaging with energy filtering for higher-resolution structure studies from its practical application.