A Monte Carlo framework for missing wedge restoration and noise removal in cryo-electron tomography

Missing Wedge Completion via Unsupervised Learning with Coordinate Networks

Cryogenic electron tomography (cryoET) is a powerful tool in structural biology, enabling detailed 3D imaging of biological specimens at a resolution of nanometers. Despite its potential, cryoET faces challenges such as the missing wedge problem, which limits reconstruction quality due to incomplete data collection angles. Recently, supervised deep learning methods leveraging convolutional neural networks (CNNs) have considerably addressed this issue; however, their pretraining requirements render them susceptible to inaccuracies and artifacts, particularly when representative training data is scarce. To overcome these limitations, we introduce a proof-of-concept unsupervised learning approach using coordinate networks (CNs) that optimizes network weights directly against input projections. This eliminates the need for pretraining, reducing reconstruction runtime by 3-20× compared to supervised methods. Our in silico results show improved shape completion and reduction of missing wedge artifacts, assessed through several voxel-based image quality metrics in real space and a novel directional Fourier Shell Correlation (FSC) metric. Our study illuminates benefits and considerations of both supervised and unsupervised approaches, guiding the development of improved reconstruction strategies.

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.

A method for restoring signals and revealing individual macromolecule states in cryo-ET, REST

Cryo-electron tomography (cryo-ET) is widely used to explore the 3D density of biomacromolecules. However, the heavy noise and missing wedge effect prevent directly visualizing and analyzing the 3D reconstructions. Here, we introduced REST, a deep learning strategy-based method to establish the relationship between low-quality and high-quality density and transfer the knowledge to restore signals in cryo-ET. Test results on the simulated and real cryo-ET datasets show that REST performs well in denoising and compensating the missing wedge information. The application in dynamic nucleosomes, presenting either in the form of individual particles or in the context of cryo-FIB nuclei section, indicates that REST has the capability to reveal different conformations of target macromolecules without subtomogram averaging. Moreover, REST noticeably improves the reliability of particle picking. These advantages enable REST to be a powerful tool for the straightforward interpretation of target macromolecules by visual inspection of the density and of a broad range of other applications in cryo-ET, such as segmentation, particle picking, and subtomogram averaging.

Cryo-electron tomography related radiation-damage parameters for individual-molecule 3D structure determination

To understand the dynamic structure-function relationship of soft- and biomolecules, the determination of the three-dimensional (3D) structure of each individual molecule (nonaveraged structure) in its native state is sought-after. Cryo-electron tomography (cryo-ET) is a unique tool for imaging an individual object from a series of tilted views. However, due to radiation damage from the incident electron beam, the tolerable electron dose limits image contrast and the signal-to-noise ratio (SNR) of the data, preventing the 3D structure determination of individual molecules, especially at high-resolution. Although recently developed technologies and techniques, such as the direct electron detector, phase plate, and computational algorithms, can partially improve image contrast/SNR at the same electron dose, the high-resolution structure, such as tertiary structure of individual molecules, has not yet been resolved. Here, we review the cryo-electron microscopy (cryo-EM) and cryo-ET experimental parameters to discuss how these parameters affect the extent of radiation damage. This discussion can guide us in optimizing the experimental strategy to increase the imaging dose or improve image SNR without increasing the radiation damage. With a higher dose, a higher image contrast/SNR can be achieved, which is crucial for individual-molecule 3D structure. With 3D structures determined from an ensemble of individual molecules in different conformations, the molecular mechanism through their biochemical reactions, such as self-folding or synthesis, can be elucidated in a straightforward manner.

Structure Detection in Three-Dimensional Cellular Cryoelectron Tomograms by Reconstructing Two-Dimensional Annotated Tilt Series

The revolutionary technique cryoelectron tomography (cryo-ET) enables imaging of cellular structure and organization in a near-native environment at submolecular resolution, which is vital to subsequent data analysis and modeling. The conventional structure detection process first reconstructs the three-dimensional (3D) tomogram from a series of two-dimensional (2D) projections and then directly detects subcellular components found within the tomogram. However, this process is challenging due to potential structural information loss during the tomographic reconstruction and the limited scope of existing methods since most major state-of-the-art object detection methods are designed for 2D rather than 3D images. Therefore, in this article, as an alternative approach to complement the conventional process, we propose a novel 2D-to-3D framework that detects structures within 2D projection images before reconstructing the results back to 3D. We implemented the proposed framework as three specific algorithms for three individual tasks: semantic segmentation, edge detection, and object localization. As experimental validation of the 2D-to-3D framework for cryo-ET data, we applied the algorithms to the segmentation of mitochondrial calcium phosphate granules, detection of spherical edges, and localization of mitochondria. Quantitative and qualitative results show better performance for prediction tasks of segmentation on the 2D projections and promising performance on object localization and edge detection, paving the way for future studies in the exploration of cryo-ET for in situ structural biology.

HEMNMA-3D: Cryo Electron Tomography Method Based on Normal Mode Analysis to Study Continuous Conformational Variability of Macromolecular Complexes

Cryogenic electron tomography (cryo-ET) allows structural determination of biomolecules in their native environment (in situ). Its potential of providing information on the dynamics of macromolecular complexes in cells is still largely unexploited, due to the challenges of the data analysis. The crowded cell environment and continuous conformational changes of complexes make difficult disentangling the data heterogeneity. We present HEMNMA-3D, which is, to the best of our knowledge, the first method for analyzing cryo electron subtomograms in terms of continuous conformational changes of complexes. HEMNMA-3D uses a combination of elastic and rigid-body 3D-to-3D iterative alignments of a flexible 3D reference (atomic structure or electron microscopy density map) to match the conformation, orientation, and position of the complex in each subtomogram. The elastic matching combines molecular mechanics simulation (Normal Mode Analysis of the 3D reference) and experimental, subtomogram data analysis. The rigid-body alignment includes compensation for the missing wedge, due to the limited tilt angle of cryo-ET. The conformational parameters (amplitudes of normal modes) of the complexes in subtomograms obtained through the alignment are processed to visualize the distribution of conformations in a space of lower dimension (typically, 2D or 3D) referred to as space of conformations. This allows a visually interpretable insight into the dynamics of the complexes, by calculating 3D averages of subtomograms with similar conformations from selected (densest) regions and by recording movies of the 3D reference's displacement along selected trajectories through the densest regions. We describe HEMNMA-3D and show its validation using synthetic datasets. We apply HEMNMA-3D to an experimental dataset describing in situ nucleosome conformational variability. HEMNMA-3D software is available freely (open-source) as part of ContinuousFlex plugin of Scipion V3.0 (http://scipion.i2pc.es).

Novel nonlinear reconstruction method with grey-level quantisation units for electron tomography

We report a new computed tomography reconstruction method, named quantisation units reconstruction technique (QURT), applicable to electron and other fields of tomography. Conventional electron tomography methods such as filtered back projection, weighted back projection, simultaneous iterative reconstructed technique, etc. suffer from the 'missing wedge' problem due to the limited tilt-angle range. QURT demonstrates improvements to solve this problem by recovering a structural image blurred due to the missing wedge and substantially reconstructs the structure even if the number of projection images is small. QURT reconstructs a cross-section image by arranging grey-level quantisation units (QU pieces) in three-dimensional image space via unique discrete processing. Its viability is confirmed by model simulations and experimental results. An important difference from recently developed methods such as discrete algebraic reconstruction technique (DART), total variation regularisation-DART, and compressed sensing is that prior knowledge of the conditions regarding the specimen or the expected cross-section image is not necessary.

The promise and the challenges of cryo-electron tomography

Structural biologists have traditionally approached cellular complexity in a reductionist manner in which the cellular molecular components are fractionated and purified before being studied individually. This 'divide and conquer' approach has been highly successful. However, awareness has grown in recent years that biological functions can rarely be attributed to individual macromolecules. Most cellular functions arise from their concerted action, and there is thus a need for methods enabling structural studies performed in situ, ideally in unperturbed cellular environments. Cryo-electron tomography (Cryo-ET) combines the power of 3D molecular-level imaging with the best structural preservation that is physically possible to achieve. Thus, it has a unique potential to reveal the supramolecular architecture or 'molecular sociology' of cells and to discover the unexpected. Here, we review state-of-the-art Cryo-ET workflows, provide examples of biological applications, and discuss what is needed to realize the full potential of Cryo-ET.

Three-dimensional deconvolution processing for STEM cryotomography

The complex environment of biological cells and tissues has motivated development of three-dimensional (3D) imaging in both light and electron microscopies. To this end, one of the primary tools in fluorescence microscopy is that of computational deconvolution. Wide-field fluorescence images are often corrupted by haze due to out-of-focus light, i.e., to cross-talk between different object planes as represented in the 3D image. Using prior understanding of the image formation mechanism, it is possible to suppress the cross-talk and reassign the unfocused light to its proper source post facto. Electron tomography based on tilted projections also exhibits a cross-talk between distant planes due to the discrete angular sampling and limited tilt range. By use of a suitably synthesized 3D point spread function, we show here that deconvolution leads to similar improvements in volume data reconstructed from cryoscanning transmission electron tomography (CSTET), namely a dramatic in-plane noise reduction and improved representation of features in the axial dimension. Contrast enhancement is demonstrated first with colloidal gold particles and then in representative cryotomograms of intact cells. Deconvolution of CSTET data collected from the periphery of an intact nucleus revealed partially condensed, extended structures in interphase chromatin.