Exploiting prior knowledge about biological macromolecules in cryo-EM structure determination

InstaMap: instant-NGP for cryo-EM density maps

Despite the parallels between problems in computer vision and cryo-electron microscopy (cryo-EM), many state-of-the-art approaches from computer vision have yet to be adapted for cryo-EM. Within the computer-vision research community, implicits such as neural radiance fields (NeRFs) have enabled the detailed reconstruction of 3D objects from few images at different camera-viewing angles. While other neural implicits, specifically density fields, have been used to map conformational heterogeneity from noisy cryo-EM projection images, most approaches represent volume with an implicit function in Fourier space, which has disadvantages compared with solving the problem in real space, complicating, for instance, masking, constraining physics or geometry, and assessing local resolution. In this work, we build on a recent development in neural implicits, a multi-resolution hash-encoding framework called instant-NGP, that we use to represent the scalar volume directly in real space and apply it to the cryo-EM density-map reconstruction problem (InstaMap). We demonstrate that for both synthetic and real data, InstaMap for homogeneous reconstruction achieves higher resolution at shorter training stages than five other real-spaced representations. We propose a solution to noise overfitting, demonstrate that InstaMap is both lightweight and fast to train, implement masking from a user-provided input mask and extend it to molecular-shape heterogeneity via bending space using a per-image vector field.

Efficient high-resolution refinement in cryo-EM with stochastic gradient descent

Electron cryomicroscopy (cryo-EM) is an imaging technique widely used in structural biology to determine the three-dimensional structure of biological molecules from noisy two-dimensional projections with unknown orientations. As the typical pipeline involves processing large amounts of data, efficient algorithms are crucial for fast and reliable results. The stochastic gradient descent (SGD) algorithm has been used to improve the speed of ab initio reconstruction, which results in a first, low-resolution estimation of the volume representing the molecule of interest, but has yet to be applied successfully in the high-resolution regime, where expectation-maximization algorithms achieve state-of-the-art results, at a high computational cost. In this article, we investigate the conditioning of the optimization problem and show that the large condition number prevents the successful application of gradient descent-based methods at high resolution. Our results include a theoretical analysis of the condition number of the optimization problem in a simplified setting where the individual projection directions are known, an algorithm based on computing a diagonal preconditioner using Hutchinson's diagonal estimator, and numerical experiments showing the improvement in the convergence speed when using the estimated preconditioner with SGD. The preconditioned SGD approach can potentially enable a simple and unified approach to ab initio reconstruction and high-resolution refinement with faster convergence speed and higher flexibility, and our results are a promising step in this direction.

Data-driven regularization lowers the size barrier of cryo-EM structure determination

Macromolecular structure determination by electron cryo-microscopy (cryo-EM) is limited by the alignment of noisy images of individual particles. Because smaller particles have weaker signals, alignment errors impose size limitations on its applicability. Here, we explore how image alignment is improved by the application of deep learning to exploit prior knowledge about biological macromolecular structures that would otherwise be difficult to express mathematically. We train a denoising convolutional neural network on pairs of half-set reconstructions from the electron microscopy data bank (EMDB) and use this denoiser as an alternative to a commonly used smoothness prior. We demonstrate that this approach, which we call Blush regularization, yields better reconstructions than do existing algorithms, in particular for data with low signal-to-noise ratios. The reconstruction of a protein-nucleic acid complex with a molecular weight of 40 kDa, which was previously intractable, illustrates that denoising neural networks will expand the applicability of cryo-EM structure determination for a wide range of biological macromolecules.

Confronting heterogeneity in cryogenic electron microscopy data: Innovative strategies and future perspectives with data-driven methods

The surge in the influx of data from cryogenic electron microscopy (cryo-EM) experiments has intensified the demand for robust algorithms capable of autonomously managing structurally heterogeneous datasets. This presents a wealth of exciting opportunities from a data science viewpoint, inspiring the development of numerous innovative, application-specific methods, many of which leverage contemporary data-driven techniques. However, addressing the challenges posed by heterogeneous datasets remains a paramount yet unresolved issue in the field. Here, we explore the subtleties of this challenge and the array of strategies devised to confront it. We pinpoint the shortcomings of existing methodologies and deliberate on prospective avenues for improvement. Specifically, our discussion focuses on strategies to mitigate model overfitting and manage data noise, as well as the effects of constraints, priors, and invariances on the optimization process.

Improvement of cryo-EM maps by simultaneous local and non-local deep learning

Cryo-EM has emerged as the most important technique for structure determination of macromolecular complexes. However, raw cryo-EM maps often exhibit loss of contrast at high resolution and heterogeneity over the entire map. As such, various post-processing methods have been proposed to improve cryo-EM maps. Nevertheless, it is still challenging to improve both the quality and interpretability of EM maps. Addressing the challenge, we present a three-dimensional Swin-Conv-UNet-based deep learning framework to improve cryo-EM maps, named EMReady, by not only implementing both local and non-local modeling modules in a multiscale UNet architecture but also simultaneously minimizing the local smooth L1 distance and maximizing the non-local structural similarity between processed experimental and simulated target maps in the loss function. EMReady was extensively evaluated on diverse test sets of 110 primary cryo-EM maps and 25 pairs of half-maps at 3.0-6.0 Å resolutions, and compared with five state-of-the-art map post-processing methods. It is shown that EMReady can not only robustly enhance the quality of cryo-EM maps in terms of map-model correlations, but also improve the interpretability of the maps in automatic de novo model building.

Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms

The number of noisy images required for molecular reconstruction in single-particle cryoelectron microscopy (cryo-EM) is governed by the autocorrelations of the observed, randomly oriented, noisy projection images. In this work, we consider the effect of imposing sparsity priors on the molecule. We use techniques from signal processing, optimization, and applied algebraic geometry to obtain theoretical and computational contributions for this challenging nonlinear inverse problem with sparsity constraints. We prove that molecular structures modeled as sums of Gaussians are uniquely determined by the second-order autocorrelation of their projection images, implying that the sample complexity is proportional to the square of the variance of the noise. This theory improves upon the nonsparse case, where the third-order autocorrelation is required for uniformly oriented particle images and the sample complexity scales with the cube of the noise variance. Furthermore, we build a computational framework to reconstruct molecular structures which are sparse in the wavelet basis. This method combines the sparse representation for the molecule with projection-based techniques used for phase retrieval in X-ray crystallography.

Deep learning for reconstructing protein structures from cryo-EM density maps: Recent advances and future directions

Cryo-Electron Microscopy (cryo-EM) has emerged as a key technology to determine the structure of proteins, particularly large protein complexes and assemblies in recent years. A key challenge in cryo-EM data analysis is to automatically reconstruct accurate protein structures from cryo-EM density maps. In this review, we briefly overview various deep learning methods for building protein structures from cryo-EM density maps, analyze their impact, and discuss the challenges of preparing high-quality data sets for training deep learning models. Looking into the future, more advanced deep learning models of effectively integrating cryo-EM data with other sources of complementary data such as protein sequences and AlphaFold-predicted structures need to be developed to further advance the field.

Toward Single Particle Reconstruction without Particle Picking: Breaking the Detection Limit

Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method to resolve biological macromolecules. In a cryo-EM experiment, the microscope produces images called micrographs. Projections of the molecule of interest are embedded in the micrographs at unknown locations, and under unknown viewing directions. Standard imaging techniques first locate these projections (detection) and then reconstruct the 3-D structure from them. Unfortunately, high noise levels hinder detection. When reliable detection is rendered impossible, the standard techniques fail. This is a problem, especially for small molecules. In this paper, we pursue a radically different approach: we contend that the structure could, in principle, be reconstructed directly from the micrographs, without intermediate detection. The aim is to bring small molecules within reach for cryo-EM. To this end, we design an autocorrelation analysis technique that allows one to go directly from the micrographs to the sought structures. This involves only one pass over the micrographs, allowing online, streaming processing for large experiments. We show numerical results and discuss challenges that lay ahead to turn this proof-of-concept into a complementary approach to state-of-the-art algorithms.

Higher resolution in cryo-EM by the combination of macromolecular prior knowledge and image-processing tools

Single-particle cryo-electron microscopy has become a powerful technique for the 3D structure determination of biological molecules. The last decade has seen an astonishing development of both hardware and software, and an exponential growth of new structures obtained at medium-high resolution. However, the knowledge accumulated in this field over the years has hardly been utilized as feedback in the reconstruction of new structures. In this context, this article explores the use of the deep-learning approach deepEMhancer as a regularizer in the RELION refinement process. deepEMhancer introduces prior information derived from macromolecular structures, and contributes to noise reduction and signal enhancement, as well as a higher degree of isotropy. These features have a direct effect on image alignment and reduction of overfitting during iterative refinement. The advantages of this combination are demonstrated for several membrane proteins, for which it is especially useful because of their high disorder and flexibility.

A molecular prior distribution for Bayesian inference based on Wilson statistics

BACKGROUND AND OBJECTIVE

Wilson statistics describe well the power spectrum of proteins at high frequencies. Therefore, it has found several applications in structural biology, e.g., it is the basis for sharpening steps used in cryogenic electron microscopy (cryo-EM). A recent paper gave the first rigorous proof of Wilson statistics based on a formalism of Wilson's original argument. This new analysis also leads to statistical estimates of the scattering potential of proteins that reveal a correlation between neighboring Fourier coefficients. Here we exploit these estimates to craft a novel prior that can be used for Bayesian inference of molecular structures.

METHODS

We describe the properties of the prior and the computation of its hyperparameters. We then evaluate the prior on two synthetic linear inverse problems, and compare against a popular prior in cryo-EM reconstruction at a range of SNRs.

RESULTS

We show that the new prior effectively suppresses noise and fills-in low SNR regions in the spectral domain. Furthermore, it improves the resolution of estimates on the problems considered for a wide range of SNR and produces Fourier Shell Correlation curves that are insensitive to masking effects.

CONCLUSIONS

We analyze the assumptions in the model, discuss relations to other regularization strategies, and postulate on potential implications for structure determination in cryo-EM.

Real space in cryo-EM: the future is local

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

New tools for automated cryo-EM single-particle analysis in RELION-4.0

We describe new tools for the processing of electron cryo-microscopy (cryo-EM) images in the fourth major release of the RELION software. In particular, we introduce VDAM, a variable-metric gradient descent algorithm with adaptive moments estimation, for image refinement; a convolutional neural network for unsupervised selection of 2D classes; and a flexible framework for the design and execution of multiple jobs in pre-defined workflows. In addition, we present a stand-alone utility called MDCatch that links the execution of jobs within this framework with metadata gathering during microscope data acquisition. The new tools are aimed at providing fast and robust procedures for unsupervised cryo-EM structure determination, with potential applications for on-the-fly processing and the development of flexible, high-throughput structure determination pipelines. We illustrate their potential on 12 publicly available cryo-EM data sets.

Detecting Protein Communities in Native Cell Extracts by Machine Learning: A Structural Biologist's Perspective

Native cell extracts hold great promise for understanding the molecular structure of ordered biological systems at high resolution. This is because higher-order biomolecular interactions, dubbed as protein communities, may be retained in their (near-)native state, in contrast to extensively purifying or artificially overexpressing the proteins of interest. The distinct machine-learning approaches are applied to discover protein-protein interactions within cell extracts, reconstruct dedicated biological networks, and report on protein community members from various organisms. Their validation is also important, e.g., by the cross-linking mass spectrometry or cell biology methods. In addition, the cell extracts are amenable to structural analysis by cryo-electron microscopy (cryo-EM), but due to their inherent complexity, sorting structural signatures of protein communities derived by cryo-EM comprises a formidable task. The application of image-processing workflows inspired by machine-learning techniques would provide improvements in distinguishing structural signatures, correlating proteomic and network data to structural signatures and subsequently reconstructed cryo-EM maps, and, ultimately, characterizing unidentified protein communities at high resolution. In this review article, we summarize recent literature in detecting protein communities from native cell extracts and identify the remaining challenges and opportunities. We argue that the progress in, and the integration of, machine learning, cryo-EM, and complementary structural proteomics approaches would provide the basis for a multi-scale molecular description of protein communities within native cell extracts.

Bayesian Inference: The Comprehensive Approach to Analyzing Single-Molecule Experiments

Biophysics experiments performed at single-molecule resolution provide exceptional insight into the structural details and dynamic behavior of biological systems. However, extracting this information from the corresponding experimental data unequivocally requires applying a biophysical model. In this review, we discuss how to use probability theory to apply these models to single-molecule data. Many current single-molecule data analysis methods apply parts of probability theory, sometimes unknowingly, and thus miss out on the full set of benefits provided by this self-consistent framework. The full application of probability theory involves a process called Bayesian inference that fully accounts for the uncertainties inherent to single-molecule experiments. Additionally, using Bayesian inference provides a scientifically rigorous method of incorporating information from multiple experiments into a single analysis and finding the best biophysical model for an experiment without the risk of overfitting the data. These benefits make the Bayesian approach ideal for analyzing any type of single-molecule experiment.