Unsupervised Cryo-EM Data Clustering through Adaptively Constrained K-Means Algorithm

Machine Learning for Structure Determination in Single-Particle Cryo-Electron Microscopy: A Systematic Review

Recently, single-particle cryo-electron microscopy (cryo-EM) has become an indispensable method for determining macromolecular structures at high resolution to deeply explore the relevant molecular mechanism. Its recent breakthrough is mainly because of the rapid advances in hardware and image processing algorithms, especially machine learning. As an essential support of single-particle cryo-EM, machine learning has powered many aspects of structure determination and greatly promoted its development. In this article, we provide a systematic review of the applications of machine learning in this field. Our review begins with a brief introduction of single-particle cryo-EM, followed by the specific tasks and challenges of its image processing. Then, focusing on the workflow of structure determination, we describe relevant machine learning algorithms and applications at different steps, including particle picking, 2-D clustering, 3-D reconstruction, and other steps. As different tasks exhibit distinct characteristics, we introduce the evaluation metrics for each task and summarize their dynamics of technology development. Finally, we discuss the open issues and potential trends in this promising field.

Structure, Dynamics and Function of the 26S Proteasome

The 26S proteasome is the most complex ATP-dependent protease machinery, of ~2.5 MDa mass, ubiquitously found in all eukaryotes. It selectively degrades ubiquitin-conjugated proteins and plays fundamentally indispensable roles in regulating almost all major aspects of cellular activities. To serve as the sole terminal "processor" for myriad ubiquitylation pathways, the proteasome evolved exceptional adaptability in dynamically organizing a large network of proteins, including ubiquitin receptors, shuttle factors, deubiquitinases, AAA-ATPase unfoldases, and ubiquitin ligases, to enable substrate selectivity and processing efficiency and to achieve regulation precision of a vast diversity of substrates. The inner working of the 26S proteasome is among the most sophisticated, enigmatic mechanisms of enzyme machinery in eukaryotic cells. Recent breakthroughs in three-dimensional atomic-level visualization of the 26S proteasome dynamics during polyubiquitylated substrate degradation elucidated an extensively detailed picture of its functional mechanisms, owing to progressive methodological advances associated with cryogenic electron microscopy (cryo-EM). Multiple sites of ubiquitin binding in the proteasome revealed a canonical mode of ubiquitin-dependent substrate engagement. The proteasome conformation in the act of substrate deubiquitylation provided insights into how the deubiquitylating activity of RPN11 is enhanced in the holoenzyme and is coupled to substrate translocation. Intriguingly, three principal modes of coordinated ATP hydrolysis in the heterohexameric AAA-ATPase motor  were discovered to regulate intermediate functional steps of the proteasome, including ubiquitin-substrate engagement, deubiquitylation, initiation of substrate translocation and processive substrate degradation. The atomic dissection of the innermost working of the 26S proteasome opens up a new era in our understanding of the ubiquitin-proteasome system and has far-reaching implications in health and disease.

AAA+ ATPases in Protein Degradation: Structures, Functions and Mechanisms

Adenosine triphosphatases (ATPases) associated with a variety of cellular activities (AAA+), the hexameric ring-shaped motor complexes located in all ATP-driven proteolytic machines, are involved in many cellular processes. Powered by cycles of ATP binding and hydrolysis, conformational changes in AAA+ ATPases can generate mechanical work that unfolds a substrate protein inside the central axial channel of ATPase ring for degradation. Three-dimensional visualizations of several AAA+ ATPase complexes in the act of substrate processing for protein degradation have been resolved at the atomic level thanks to recent technical advances in cryogenic electron microscopy (cryo-EM). Here, we summarize the resulting advances in structural and biochemical studies of AAA+ proteases in the process of proteolysis reactions, with an emphasis on cryo-EM structural analyses of the 26S proteasome, Cdc48/p97 and FtsH-like mitochondrial proteases. These studies reveal three highly conserved patterns in the structure–function relationship of AAA+ ATPase hexamers that were observed in the human 26S proteasome, thus suggesting common dynamic models of mechanochemical coupling during force generation and substrate translocation.

Robustness of signal detection in cryo-electron microscopy via a bi-objective-function approach

Background

The detection of weak signals and selection of single particles from low-contrast micrographs of frozen hydrated biomolecules by cryo-electron microscopy (cryo-EM) represents a major practical bottleneck in cryo-EM data analysis. Template-based particle picking by an objective function using fast local correlation (FLC) allows computational extraction of a large number of candidate particles from micrographs. Another independent objective function based on maximum likelihood estimates (MLE) can be used to align the images and verify the presence of a signal in the selected particles. Despite the widespread applications of the two objective functions, an optimal combination of their utilities has not been exploited. Here we propose a bi-objective function (BOF) approach that combines both FLC and MLE and explore the potential advantages and limitations of BOF in signal detection from cryo-EM data.

Results

The robustness of the BOF strategy in particle selection and verification was systematically examined with both simulated and experimental cryo-EM data. We investigated how the performance of the BOF approach is quantitatively affected by the signal-to-noise ratio (SNR) of cryo-EM data and by the choice of initialization for FLC and MLE. We quantitatively pinpointed the critical SNR (~ 0.005), at which the BOF approach starts losing its ability to select and verify particles reliably. We found that the use of a Gaussian model to initialize the MLE suppresses the adverse effects of reference dependency in the FLC function used for template-matching.

Conclusion

The BOF approach, which combines two distinct objective functions, provides a sensitive way to verify particles for downstream cryo-EM structure analysis. Importantly, reference dependency of the FLC does not necessarily transfer to the MLE, enabling the robust detection of weak signals. Our insights into the numerical behavior of the BOF approach can be used to improve automation efficiency in the cryo-EM data processing pipeline for high-resolution structural determination.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2714-8) contains supplementary material, which is available to authorized users.

Clustering cryo-EM images of helical protein polymers for helical reconstructions

Helical protein polymers are often dynamic and complex assemblies, with many conformations and flexible domains possible within the helical assembly. During cryo-electron microscopy reconstruction, classification of the image data into homogeneous subsets is a critical step for achieving high resolution, resolving different conformations and elucidating functional mechanisms. Hence, methods aimed at improving the homogeneity of these datasets are becoming increasingly important. In this paper, we introduce a new algorithm that uses results from 2D image classification to sort 2D classes into groups of similar helical polymers. We show that our approach is able to distinguish helical polymers that differ in conformation, composition, and helical symmetry. Our results on test and experimental cases - actin filaments and amyloid fibrils - illustrate how our approach can be useful to improve the homogeneity of a data set. This method is exclusively applicable to helical polymers and other limitations are discussed.