Gaussian-input Gaussian mixture model for representing density maps and atomic models

FP-Zernike: An Open-source Structural Database Construction Toolkit for Fast Structure Retrieval

The release of AlphaFold2 has sparked a rapid expansion in protein model databases. Efficient protein structure retrieval is crucial for the analysis of structure models, while measuring the similarity between structures is the key challenge in structural retrieval. Although existing structure alignment algorithms can address this challenge, they are often time-consuming. Currently, the state-of-the-art approach involves converting protein structures into three-dimensional (3D) Zernike descriptors and assessing similarity using Euclidean distance. However, the methods for computing 3D Zernike descriptors mainly rely on structural surfaces and are predominantly web-based, thus limiting their application in studying custom datasets. To overcome this limitation, we developed FP-Zernike, a user-friendly toolkit for computing different types of Zernike descriptors based on feature points. Users simply need to enter a single line of command to calculate the Zernike descriptors of all structures in customized datasets. FP-Zernike outperforms the leading method in terms of retrieval accuracy and binary classification accuracy across diverse benchmark datasets. In addition, we showed the application of FP-Zernike in the construction of the descriptor database and the protocol used for the Protein Data Bank (PDB) dataset to facilitate the local deployment of this tool for interested readers. Our demonstration contained 590,685 structures, and at this scale, our system required only 4-9 s to complete a retrieval. The experiments confirmed that it achieved the state-of-the-art accuracy level. FP-Zernike is an open-source toolkit, with the source code and related data accessible at https://ngdc.cncb.ac.cn/biocode/tools/BT007365/releases/0.1, as well as through a webserver at http://www.structbioinfo.cn/.

DEMO-EM2: assembling protein complex structures from cryo-EM maps through intertwined chain and domain fitting

The breakthrough in cryo-electron microscopy (cryo-EM) technology has led to an increasing number of density maps of biological macromolecules. However, constructing accurate protein complex atomic structures from cryo-EM maps remains a challenge. In this study, we extend our previously developed DEMO-EM to present DEMO-EM2, an automated method for constructing protein complex models from cryo-EM maps through an iterative assembly procedure intertwining chain- and domain-level matching and fitting for predicted chain models. The method was carefully evaluated on 27 cryo-electron tomography (cryo-ET) maps and 16 single-particle EM maps, where DEMO-EM2 models achieved an average TM-score of 0.92, outperforming those of state-of-the-art methods. The results demonstrate an efficient method that enables the rapid and reliable solution of challenging cryo-EM structure modeling problems.

Cryo-EM structure and B-factor refinement with ensemble representation

Cryo-EM experiments produce images of macromolecular assemblies that are combined to produce three-dimensional density maps. Typically, atomic models of the constituent molecules are fitted into these maps, followed by a density-guided refinement. We introduce TEMPy-ReFF, a method for atomic structure refinement in cryo-EM density maps. Our method represents atomic positions as components of a Gaussian mixture model, utilising their variances as B-factors, which are used to derive an ensemble description. Extensively tested on a substantial dataset of 229 cryo-EM maps from EMDB ranging in resolution from 2.1-4.9 Å with corresponding PDB and CERES atomic models, our results demonstrate that TEMPy-ReFF ensembles provide a superior representation of cryo-EM maps. On a single-model basis, it performs similarly to the CERES re-refinement protocol, although there are cases where it provides a better fit to the map. Furthermore, our method enables the creation of composite maps free of boundary artefacts. TEMPy-ReFF is useful for better interpretation of flexible structures, such as those involving RNA, DNA or ligands.

A robust normalized local filter to estimate compositional heterogeneity directly from cryo-EM maps

Cryo electron microscopy (cryo-EM) is used by biological research to visualize biomolecular complexes in 3D, but the heterogeneity of cryo-EM reconstructions is not easily estimated. Current processing paradigms nevertheless exert great effort to reduce flexibility and heterogeneity to improve the quality of the reconstruction. Clustering algorithms are typically employed to identify populations of data with reduced variability, but lack assessment of remaining heterogeneity. Here we develope a fast and simple algorithm based on spatial filtering to estimate the heterogeneity of a reconstruction. In the absence of flexibility, this estimate approximates macromolecular component occupancy. We show that our implementation can derive reasonable input parameters, that composition heterogeneity can be estimated based on contrast loss, and that the reconstruction can be modified accordingly to emulate altered constituent occupancy. This stands to benefit conventionally employed maximum-likelihood classification methods, whereas we here limit considerations to cryo-EM map interpretation, quantification, and particle-image signal subtraction.

Novel Artificial Intelligence-Based Approaches for Ab Initio Structure Determination and Atomic Model Building for Cryo-Electron Microscopy

Single particle cryo-electron microscopy (cryo-EM) has emerged as the prevailing method for near-atomic structure determination, shedding light on the important molecular mechanisms of biological macromolecules. However, the inherent dynamics and structural variability of biological complexes coupled with the large number of experimental images generated by a cryo-EM experiment make data processing nontrivial. In particular, ab initio reconstruction and atomic model building remain major bottlenecks that demand substantial computational resources and manual intervention. Approaches utilizing recent innovations in artificial intelligence (AI) technology, particularly deep learning, have the potential to overcome the limitations that cannot be adequately addressed by traditional image processing approaches. Here, we review newly proposed AI-based methods for ab initio volume generation, heterogeneous 3D reconstruction, and atomic model building. We highlight the advancements made by the implementation of AI methods, as well as discuss remaining limitations and areas for future development.

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.

Identification of hub proteins in cerebrospinal fluid as potential biomarkers of Alzheimer's disease by integrated bioinformatics

BACKGROUND

Alzheimer's disease (AD) is a heterogeneous neurodegenerative disease with complex pathophysiology. Therefore, the identification of novel effective fluid biomarkers is essential for Alzheimer's disease diagnosis and drug development. This study aimed to identify potential candidate hub proteins in cerebrospinal fluid for precise Alzheimer's disease diagnosis using bioinformatics methods.

METHODS

A total of 29 co-significant differentially expressed proteins were identified by differential protein expression analysis in four different cohorts. Functional enrichment analysis revealed that most of these proteins were enriched in pathways related to glycometabolism. Using the Least Absolute Shrinkage and Selection Operator (LASSO) and random forest feature selection methods, six hub proteins [14-3-3 protein zeta/delta (YWHAZ), SPARC-related modular calcium-binding protein 1 (SMOC1), aldolase A (ALDOA), pyruvate kinase isoenzyme type M2 (PKM), chitinase-3-like protein 1 (CHI3L1), and secreted phosphoprotein 1 (SPP1)] were identified.

RESULTS

These six hub proteins were upregulated in the cerebrospinal fluid of patients with Alzheimer's disease compared with cognitively unimpaired control individuals. Meanwhile, SMOC1, ALDOA, and PKM were specifically upregulated in the cerebrospinal fluid of patients with Alzheimer's disease but not in other neurodegenerative diseases. Build AD diagnostic models showed that a single hub protein or six hub proteins combination had an excellent ability to discriminate Alzheimer's disease.

CONCLUSIONS

In conclusion, our study suggests that these identified hub proteins, which are related to glycometabolism, may be potential biomarkers for further basic and clinical research in Alzheimer's disease.

A quantitative map of nuclear pore assembly reveals two distinct mechanisms

Understanding how the nuclear pore complex (NPC) is assembled is of fundamental importance to grasp the mechanisms behind its essential function and understand its role during the evolution of eukaryotes1-4. There are at least two NPC assembly pathways-one during the exit from mitosis and one during nuclear growth in interphase-but we currently lack a quantitative map of these events. Here we use fluorescence correlation spectroscopy calibrated live imaging of endogenously fluorescently tagged nucleoporins to map the changes in the composition and stoichiometry of seven major modules of the human NPC during its assembly in single dividing cells. This systematic quantitative map reveals that the two assembly pathways have distinct molecular mechanisms, in which the order of addition of two large structural components, the central ring complex and nuclear filaments are inverted. The dynamic stoichiometry data was integrated to create a spatiotemporal model of the NPC assembly pathway and predict the structures of postmitotic NPC assembly intermediates.

MarkovFit: Structure Fitting for Protein Complexes in Electron Microscopy Maps Using Markov Random Field

An increasing number of protein complex structures are determined by cryo-electron microscopy (cryo-EM). When individual protein structures have been determined and are available, an important task in structure modeling is to fit the individual structures into the density map. Here, we designed a method that fits the atomic structures of proteins in cryo-EM maps of medium to low resolutions using Markov random fields, which allows probabilistic evaluation of fitted models. The accuracy of our method, MarkovFit, performed better than existing methods on datasets of 31 simulated cryo-EM maps of resolution 10 Å , nine experimentally determined cryo-EM maps of resolution less than 4 Å , and 28 experimentally determined cryo-EM maps of resolution 6 to 20 Å .

Model building of protein complexes from intermediate-resolution cryo-EM maps with deep learning-guided automatic assembly

Advances in microscopy instruments and image processing algorithms have led to an increasing number of cryo-electron microscopy (cryo-EM) maps. However, building accurate models into intermediate-resolution EM maps remains challenging and labor-intensive. Here, we propose an automatic model building method of multi-chain protein complexes from intermediate-resolution cryo-EM maps, named EMBuild, by integrating AlphaFold structure prediction, FFT-based global fitting, domain-based semi-flexible refinement, and graph-based iterative assembling on the main-chain probability map predicted by a deep convolutional network. EMBuild is extensively evaluated on diverse test sets of 47 single-particle EM maps at 4.0-8.0 Å resolution and 16 subtomogram averaging maps of cryo-ET data at 3.7-9.3 Å resolution, and compared with state-of-the-art approaches. We demonstrate that EMBuild is able to build high-quality complex structures that are comparably accurate to the manually built PDB structures from the cryo-EM maps. These results demonstrate the accuracy and reliability of EMBuild in automatic model building.

Protein dynamics developments for the large scale and cryoEM: case study of ProDy 2.0

Cryo-electron microscopy (cryoEM) has become a well established technique with the potential to produce structures of large and dynamic supramolecular complexes that are not amenable to traditional approaches for studying structure and dynamics. The size and low resolution of such molecular systems often make structural modelling and molecular dynamics simulations challenging and computationally expensive. This, together with the growing wealth of structural data arising from cryoEM and other structural biology methods, has driven a trend in the computational biophysics community towards the development of new pipelines for analysing global dynamics using coarse-grained models and methods. At the centre of this trend has been a return to elastic network models, normal mode analysis (NMA) and ensemble analyses such as principal component analysis, and the growth of hybrid simulation methodologies that make use of them. Here, this field is reviewed with a focus on ProDy, the Python application programming interface for protein dynamics, which has been developed over the last decade. Two key developments in this area are highlighted: (i) ensemble NMA towards extracting and comparing the signature dynamics of homologous structures, aided by the recent SignDy pipeline, and (ii) pseudoatom fitting for more efficient global dynamics analyses of large and low-resolution supramolecular assemblies from cryoEM, revisited in the CryoDy pipeline. It is believed that such a renewal and extension of old models and methods in new pipelines will be critical for driving the field forward into the next cryoEM revolution.

Cryo-EM targets in CASP14

Structures of seven CASP14 targets were determined using cryo-electron microscopy (cryo-EM) technique with resolution between 2.1 and 3.8 Å. We provide an evaluation of the submitted models versus the experimental data (cryo-EM density maps) and experimental reference structures built into the maps. The accuracy of models is measured in terms of coordinate-to-density and coordinate-to-coordinate fit. A-posteriori refinement of the most accurate models in their corresponding cryo-EM density resulted in structures that are close to the reference structure, including some regions with better fit to the density. Regions that were found to be less "refineable" correlate well with regions of high diversity between the CASP models and low goodness-of-fit to density in the reference structure.

Reconstruction of Three-Dimensional Conformations of Bacterial ClpB from High-Speed Atomic-Force-Microscopy Images

ClpB belongs to the cellular disaggretase machinery involved in rescuing misfolded or aggregated proteins during heat or other cellular shocks. The function of this protein relies on the interconversion between different conformations in its native condition. A recent high-speed-atomic-force-microscopy (HS-AFM) experiment on ClpB from Thermus thermophilus shows four predominant conformational classes, namely, open, closed, spiral, and half-spiral. Analyses of AFM images provide only partial structural information regarding the molecular surface, and thus computational modeling of three-dimensional (3D) structures of these conformations should help interpret dynamical events related to ClpB functions. In this study, we reconstruct 3D models of ClpB from HS-AFM images in different conformational classes. We have applied our recently developed computational method based on a low-resolution representation of 3D structure using a Gaussian mixture model, combined with a Monte-Carlo sampling algorithm to optimize the agreement with target AFM images. After conformational sampling, we obtained models that reflect conformational variety embedded within the AFM images. From these reconstructed 3D models, we described, in terms of relative domain arrangement, the different types of ClpB oligomeric conformations observed by HS-AFM experiments. In particular, we highlighted the slippage of the monomeric components around the seam. This study demonstrates that such details of information, necessary for annotating the different conformational states involved in the ClpB function, can be obtained by combining HS-AFM images, even with limited resolution, and computational modeling.

Protocol for Retrieving Three-Dimensional Biological Shapes for a Few XFEL Single-Particle Diffraction Patterns

X-ray free-electron laser (XFEL) scattering promises to probe single biomolecular complexes without crystallization, enabling the study of biomolecular structures under near-physiological conditions at room temperature. However, such structural determination of biomolecules is extremely challenging thus far. In addition to the large numbers of diffraction patterns required, the orientation of each diffraction pattern needs to be accurately estimated and the missing phase information needs to be recovered for three-dimensional (3D) structure reconstruction. Given the current limitations to the amount and resolution of the data available from single-particle XFEL scattering experiments, we propose an alternative approach to find plausible 3D biological shapes from a limited number of diffraction patterns to serve as a starting point for further analyses. In our proposed strategy, small sets of input (e.g., five) XFEL diffraction patterns were matched against a library of diffraction patterns simulated from 1628 electron microscopy (EM) models to find potential matching 3D models that are consistent with the input diffraction patterns. This approach was tested for three example cases: EMD-3457 (Thermoplasma acidophilum 20S proteasome), EMD-5141 (Escherichia coli 70S ribosome complex), and EMD-5152 (budding yeast Nup84 complex). We observed that choosing the best strategy to define matching regions on the diffraction patterns is critical for identifying correctly matching diffraction patterns. While increasing the number of input diffraction patterns improved the matches in some cases, we found that the resulting matches are more dependent on the uniqueness or complexity of the shape as captured in the individual input diffraction patterns and the availability of a similar 3D biological shape in the search library. The protocol could be useful for finding candidate models for a limited amount of low-resolution data, even when insufficient for reconstruction, performing a quick exploration of new data upon collection, and the analysis of the conformational heterogeneity of the particle of interest as captured within the diffraction patterns.

Deep learning-based mixed-dimensional Gaussian mixture model for characterizing variability in cryo-EM

Structural flexibility and/or dynamic interactions with other molecules is a critical aspect of protein function. CryoEM provides direct visualization of individual macromolecules sampling different conformational and compositional states. While numerous methods are available for computational classification of discrete states, characterization of continuous conformational changes or large numbers of discrete state without human supervision remains challenging. Here we present e2gmm, a machine learning algorithm to determine a conformational landscape for proteins or complexes using a 3-D Gaussian mixture model mapped onto 2-D particle images in known orientations. Using a deep neural network architecture, e2gmm can automatically resolve the structural heterogeneity within the protein complex and map particles onto a small latent space describing conformational and compositional changes. This system presents a more intuitive and flexible representation than other manifold methods currently in use. We demonstrate this method on both simulated data as well as three biological systems, to explore compositional and conformational changes at a range of scales. The software is distributed as part of EMAN2.

Improving integrative 3D modeling into low- to medium-resolution electron microscopy structures with evolutionary couplings

Electron microscopy (EM) continues to provide near-atomic resolution structures for well-behaved proteins and protein complexes. Unfortunately, structures of some complexes are limited to low- to medium-resolution due to biochemical or conformational heterogeneity. Thus, the application of unbiased systematic methods for fitting individual structures into EM maps is important. A method that employs co-evolutionary information obtained solely from sequence data could prove invaluable for quick, confident localization of subunits within these structures. Here, we incorporate the co-evolution of intermolecular amino acids as a new type of distance restraint in the integrative modeling platform in order to build three-dimensional models of atomic structures into EM maps ranging from 10-14 Å in resolution. We validate this method using four complexes of known structure, where we highlight the conservation of intermolecular couplings despite dynamic conformational changes using the BAM complex. Finally, we use this method to assemble the subunits of the bacterial holo-translocon into a model that agrees with previous biochemical data. The use of evolutionary couplings in integrative modeling improves systematic, unbiased fitting of atomic models into medium- to low-resolution EM maps, providing additional information to integrative models lacking in spatial data.

Computational Protocol for Assessing the Optimal Pixel Size to Improve the Accuracy of Single-particle Cryo-electron Microscopy Maps

Cryo-electron microscopy (cryo-EM) single-particle analysis has come a long way in achieving atomic-level resolution when imaging biomolecules. To obtain the best possible three-dimensional (3D) structure in cryo-EM, many parameters have to be carefully considered. Here we address the often-overlooked parameter of the pixel size, which describes the magnification of the image produced by the experiment. While efforts are made to refine and validate this parameter in the analysis of cryo-EM experimental data, there is no systematic protocol in place. Since the pixel size parameter can have an impact on the resolution and accuracy of a cryo-EM map, and the atomic resolution 3D structure models derived from it, we propose a computational protocol to estimate the appropriate pixel size parameter. In our protocol, we fit and refine atomic structures against cryo-EM maps at multiple pixel sizes. The resulting fitted and refined structures are evaluated using the GOAP (generalized orientation-dependent, all-atom statistical potential) score, which we found to perform better than other commonly used functions, such as Molprobity and the correlation coefficient from refinement. Finally, we describe the efficacy of this protocol in retrieving appropriate pixel sizes for several examples; simulated data based on yeast elongation factor 2 and experimental data from Gro-EL chaperone, beta-galactosidase, and the TRPV1 ion channel.

Advances in Structure Modeling Methods for Cryo-Electron Microscopy Maps

Cryo-electron microscopy (cryo-EM) has now become a widely used technique for structure determination of macromolecular complexes. For modeling molecular structures from density maps of different resolutions, many algorithms have been developed. These algorithms can be categorized into rigid fitting, flexible fitting, and de novo modeling methods. It is also observed that machine learning (ML) techniques have been increasingly applied following the rapid progress of the ML field. Here, we review these different categories of macromolecule structure modeling methods and discuss their advances over time.

Small angle X-ray scattering-assisted protein structure prediction in CASP13 and emergence of solution structure differences

Small angle X-ray scattering (SAXS) measures comprehensive distance information on a protein's structure, which can constrain and guide computational structure prediction algorithms. Here, we evaluate structure predictions of 11 monomeric and oligomeric proteins for which SAXS data were collected and provided to predictors in the 13th round of the Critical Assessment of protein Structure Prediction (CASP13). The category for SAXS-assisted predictions made gains in certain areas for CASP13 compared to CASP12. Improvements included higher quality data with size exclusion chromatography-SAXS (SEC-SAXS) and better selection of targets and communication of results by CASP organizers. In several cases, we can track improvements in model accuracy with use of SAXS data. For hard multimeric targets where regular folding algorithms were unsuccessful, SAXS data helped predictors to build models better resembling the global shape of the target. For most models, however, no significant improvement in model accuracy at the domain level was registered from use of SAXS data, when rigorously comparing SAXS-assisted models to the best regular server predictions. To promote future progress in this category, we identify successes, challenges, and opportunities for improved strategies in prediction, assessment, and communication of SAXS data to predictors. An important observation is that, for many targets, SAXS data were inconsistent with crystal structures, suggesting that these proteins adopt different conformation(s) in solution. This CASP13 result, if representative of PDB structures and future CASP targets, may have substantive implications for the structure training databases used for machine learning, CASP, and use of prediction models for biology.

Preliminary results of computer-aided diagnosis for magnetic resonance imaging of solid breast lesions

PURPOSE

The present study aimed to determine suitable optimal classifiers and investigate the general applicability of computer-aided diagnosis (CAD) to compare magnetic resonance (MR)-CAD with MR imaging (MRI) in distinguishing benign from malignant solid breast masses.

METHODS

We analyzed a total of 251 patients (mean age: 44.8 ± 12.3 years; range: 21-81 years) with 274 breast masses (154 benign masses, 120 malignant masses) using a Gaussian mixture model and a random forest machine model for segmentation and classification.

RESULTS

The diagnostic performance of MRI alone and MRI plus CAD were compared with respect to sensitivity, specificity, and area under the curve (AUC), using receiver operating characteristic curve analysis. The discriminating power to detect malignancy using MR-CAD with an AUC of 0.955 (sensitivity was 95.8% and the specificity was 92.9%) was significantly higher than that of MRI alone with an AUC of 0.785 (sensitivity was 71.7% and the specificity was 85.7%).

CONCLUSION

CAD is feasible to differentiate breast lesions, and it can complement MRI, thereby making it easier to diagnose breast lesions and obviating the need for unnecessary biopsies.

Rigid-Body Fitting of Atomic Models on 3D Density Maps of Electron Microscopy

Cryo electron microscopy has revolutionarily evolved for the determination of the 3D structure of macromolecular complexes. The modeling procedures on the 3D density maps of electron microscopy are roughly classified into three categories: fitting, de novo modeling and refinement. The registered atomic models from the maps have mostly been hand-built and auto-refined. Several programs aiming at automatic modeling have also been developed using various kinds of molecular representations. Among these three classes of the modeling procedures, the rigid body fitting is reviewed here, because it is the most basic modeling process applied before the other steps. The fitting problems are classified as the fittings of single subunit or multiple subunits, and the fittings on global or local parts of maps. A higher resolution map enables more local fitting. Various molecular representations have been employed in the fitting programs. A point and digital image models are generally used to represent molecules, but new representations, such as the Gaussian mixture model, have been applied recently.