Multiple subunit fitting into a low-resolution density map of a macromolecular complex using a gaussian mixture model

Analyzing atomic force microscopy images of virus-like particles by expectation-maximization

Analysis of virus-like particles (VLPs) is an essential task in optimizing their implementation as vaccine antigens for virus-initiated diseases. Interrogating VLP collections for elasticity by probing with a rigid atomic force microscopy (AFM) tip is a potential method for determining VLP morphological changes. During VLP morphological change, it is not expected that all VLPs would be in the same state. This leads to the open question of whether VLPs may change in a continuous or stepwise fashion. For continuous change, the statistical distribution of observed VLP properties would be expected as a single distribution, while stepwise change would lead to a multimodal distribution of properties. This study presents the application of a Gaussian mixture model (GMM), fit by the Expectation-Maximization (EM) algorithm, to identify different states of VLP morphological change observed by AFM imaging.

Optimal 3D angular sampling with applications to cryo-EM problems

The goal of cryo-EM experiments in the biological sciences is to determine the atomic structure of a molecule and deduce insights into its functions and mechanisms. Despite improvements in instrumentation for data collection and new software algorithms, in most cases, individual atoms are not resolved. Model building of proteins, nucleic acids, or molecules in general, is feasible from the experimentally determined density maps at resolutions up to the range of 3-4 Angstroms. For lower-resolution maps or parts of maps, fitting smaller structures obtained by modelling or experimental techniques with higher resolution is a way to resolve the issue. In practice, we have an atomic structure, generate its density map at a given resolution, and translate/rotate the map within a region of interest in the experimental map, computing a measure-of-fit score with the corresponding areas of the experimental map. This procedure is computationally intensive since we work in 6D space. An optimal ordered list of rotations will reduce the angular error and help to find the best-fitting positions faster for a coarse global search or a local refinement. It can be used for adaptive approaches to stop fitting algorithms earlier once the desired accuracy has been achieved. We demonstrate how the performance of some fitting algorithms can be improved by grouping sets of rotations. We present an approach to generate more efficient 3D angular sampling, and provide the computer code to generate lists of optimal orientations for single and grouped rotations and the lists themselves.

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/.

The Molecular Architecture of the Nuclear Basket

The nuclear pore complex (NPC) is the sole mediator of nucleocytoplasmic transport. Despite great advances in understanding its conserved core architecture, the peripheral regions can exhibit considerable variation within and between species. One such structure is the cage-like nuclear basket. Despite its crucial roles in mRNA surveillance and chromatin organization, an architectural understanding has remained elusive. Using in-cell cryo-electron tomography and subtomogram analysis, we explored the NPC's structural variations and the nuclear basket across fungi (yeast; S. cerevisiae), mammals (mouse; M. musculus), and protozoa (T. gondii). Using integrative structural modeling, we computed a model of the basket in yeast and mammals that revealed how a hub of Nups in the nuclear ring binds to basket-forming Mlp/Tpr proteins: the coiled-coil domains of Mlp/Tpr form the struts of the basket, while their unstructured termini constitute the basket distal densities, which potentially serve as a docking site for mRNA preprocessing before nucleocytoplasmic transport.

Alignment of density maps in Wasserstein distance

In this article, we propose an algorithm for aligning three-dimensional objects when represented as density maps, motivated by applications in cryogenic electron microscopy. The algorithm is based on minimizing the 1-Wasserstein distance between the density maps after a rigid transformation. The induced loss function enjoys a more benign landscape than its Euclidean counterpart and Bayesian optimization is employed for computation. Numerical experiments show improved accuracy and efficiency over existing algorithms on the alignment of real protein molecules. In the context of aligning heterogeneous pairs, we illustrate a potential need for new distance functions.

Accurate global and local 3D alignment of cryo-EM density maps using local spatial structural features

Advances in cryo-electron microscopy (cryo-EM) imaging technologies have led to a rapidly increasing number of cryo-EM density maps. Alignment and comparison of density maps play a crucial role in interpreting structural information, such as conformational heterogeneity analysis using global alignment and atomic model assembly through local alignment. Here, we present a fast and accurate global and local cryo-EM density map alignment method called CryoAlign, that leverages local density feature descriptors to capture spatial structure similarities. CryoAlign is a feature-based cryo-EM map alignment tool, in which the employment of feature-based architecture enables the rapid establishment of point pair correspondences and robust estimation of alignment parameters. Extensive experimental evaluations demonstrate the superiority of CryoAlign over the existing methods in terms of both alignment accuracy and speed.

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.

Cryo-electron Microscopy and Molecular Modeling Methods to Characterize the Dynamics of Tau Bound to Microtubules

The electron microscopy metainference integrative structural biology method enables the combination of cryo-electron microscopy electron density maps with molecular modeling techniques such as molecular dynamics to unveil the atomistic biomolecular structural ensemble and the error in the map data in an efficient manner. Here we illustrate the electron microscopy metainference protocol and analysis used to elucidate the atomistic structural ensemble of the microtubule-associated protein tau bound to microtubules by using state-of-the-art molecular mechanic force field and the electron density map.

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.

Determination of the Structure and Dynamics of the Fuzzy Coat of an Amyloid Fibril of IAPP Using Cryo-Electron Microscopy

In recent years, major advances in cryo-electron microscopy (cryo-EM) have enabled the routine determination of complex biomolecular structures at atomistic resolution. An open challenge for this approach, however, concerns large systems that exhibit continuous dynamics. To address this problem, we developed the metadynamic electron microscopy metainference (MEMMI) method, which incorporates metadynamics, an enhanced conformational sampling approach, into the metainference method of integrative structural biology. MEMMI enables the simultaneous determination of the structure and dynamics of large heterogeneous systems by combining cryo-EM density maps with prior information through molecular dynamics, while at the same time modeling the different sources of error. To illustrate the method, we apply it to elucidate the dynamics of an amyloid fibril of the islet amyloid polypeptide (IAPP). The resulting conformational ensemble provides an accurate description of the structural variability of the disordered region of the amyloid fibril, known as fuzzy coat. The conformational ensemble also reveals that in nearly half of the structural core of this amyloid fibril, the side chains exhibit liquid-like dynamics despite the presence of the highly ordered network backbone of hydrogen bonds characteristic of the cross-β structure of amyloid fibrils.

CASP15 cryoEM protein and RNA targets: refinement and analysis using experimental maps

CASP assessments primarily rely on comparing predicted coordinates with experimental reference structures. However, errors in the reference structures can potentially reduce the accuracy of the assessment. This issue is particularly prominent in cryoEM-determined structures, and therefore, in the assessment of CASP15 cryoEM targets, we directly utilized density maps to evaluate the predictions. A method for ranking the quality of protein chain predictions based on rigid fitting to experimental density was found to correlate well with the CASP assessment scores. Overall, the evaluation against the density map indicated that the models are of high accuracy although local assessment of predicted side chains in a 1.52 Å resolution map showed that side-chains are sometimes poorly positioned. The top 136 predictions associated with 9 protein target reference structures were selected for refinement, in addition to the top 40 predictions for 11 RNA targets. To this end, we have developed an automated hierarchical refinement pipeline in cryoEM maps. For both proteins and RNA, the refinement of CASP15 predictions resulted in structures that are close to the reference target structure, including some regions with better fit to the density. This refinement was successful despite large conformational changes and secondary structure element movements often being required, suggesting that predictions from CASP-assessed methods could serve as a good starting point for building atomic models in cryoEM maps for both proteins and RNA. Loop modeling continued to pose a challenge for predictors with even short loops failing to be accurately modeled or refined at times. The lack of consensus amongst models suggests that modeling holds the potential for identifying more flexible regions within the structure.

Bayesian methods in integrative structure modeling

There is a growing interest in characterizing the structure and dynamics of large biomolecular assemblies and their interactions within the cellular environment. A diverse array of experimental techniques allows us to study biomolecular systems on a variety of length and time scales. These techniques range from imaging with light, X-rays or electrons, to spectroscopic methods, cross-linking mass spectrometry and functional genomics approaches, and are complemented by AI-assisted protein structure prediction methods. A challenge is to integrate all of these data into a model of the system and its functional dynamics. This review focuses on Bayesian approaches to integrative structure modeling. We sketch the principles of Bayesian inference, highlight recent applications to integrative modeling and conclude with a discussion of current challenges and future perspectives.

Protein dynamics by the combination of high-speed AFM and computational modeling

High-speed atomic force microscopy (HS-AFM) allows direct observation of biological molecules in dynamic action. However, HS-AFM has no atomic resolution. This article reviews recent progress of computational methods to infer high-resolution information, including the construction of 3D atomistic structures, from experimentally acquired resolution-limited HS-AFM images.

Guide for determination of protein structural ensembles by combining cryo-EM data with metadynamics

Metadynamics electron microscopy metaInference (MEMMI) is an integrative structural biology method that enables a rapid and accurate characterization of protein structural dynamics at the atomic level and the error in the cryo-EM experimental data, even in cases where conformations are separated by high energy barriers. It achieves this by incorporating (a) cryo-electron microscopy electron density maps with (b) metadynamic-enhanced-sampling molecular dynamics. Here, I showcase the setup and analysis protocol of MEMMI, used to discover the atomistic structural ensemble and error in the cryo-EM electron density map of the fuzzy coat of IAPP, a fibril implicated in type II diabetes.

History of Protein Data Bank Japan: standing at the beginning of the age of structural genomics

Prof. Haruki Nakamura, who is the former head of Protein Data Bank Japan (PDBj) and an expert in computational biology, retired from Osaka University at the end of March 2018. He founded PDBj at the Institute for Protein Research, together with other faculty members, researchers, engineers, and annotators in 2000, and subsequently established the worldwide Protein Data Bank (wwPDB) in 2003 to manage the core archive of the Protein Data Bank (PDB), collaborating with RCSB-PDB in the USA and PDBe in Europe. As the former head of PDBj and also an expert in structural bioinformatics, he has grown PDBj to become a well-known data center within the structural biology community and developed several related databases, tools and integrated with new technologies, such as the semantic web, as primary services offered by PDBj.

Predicting the structure of large protein complexes using AlphaFold and Monte Carlo tree search

AlphaFold can predict the structure of single- and multiple-chain proteins with very high accuracy. However, the accuracy decreases with the number of chains, and the available GPU memory limits the size of protein complexes which can be predicted. Here we show that one can predict the structure of large complexes starting from predictions of subcomponents. We assemble 91 out of 175 complexes with 10–30 chains from predicted subcomponents using Monte Carlo tree search, with a median TM-score of 0.51. There are 30 highly accurate complexes (TM-score ≥0.8, 33% of complete assemblies). We create a scoring function, mpDockQ, that can distinguish if assemblies are complete and predict their accuracy. We find that complexes containing symmetry are accurately assembled, while asymmetrical complexes remain challenging. The method is freely available and accesible as a Colab notebook https://colab.research.google.com/github/patrickbryant1/MoLPC/blob/master/MoLPC.ipynb.

The accuracy of AlphaFold decreases with the number of protein chains and the available GPU memory limits the size of protein complexes that can be predicted. Here, the authors show that complexes with 10–30 chains can be assembled from predicted subcomponents using Monte Carlo tree search.

A hybrid approach to study large conformational transitions of biomolecules from single particle XFEL diffraction data

X-ray free-electron laser (XFEL) is the latest generation of the X-ray source that could become an invaluable technique in structural biology. XFEL has ultrashort pulse duration, extreme peak brilliance, and high spatial coherence, which could enable the observation of the biological molecules in near nature state at room temperature without crystallization. However, for biological systems, due to their low diffraction power and complexity of sample delivery, experiments and data analysis are not straightforward, making it extremely challenging to reconstruct three-dimensional (3D) structures from single particle XFEL data. Given the current limitations to the amount and resolution of the data from such XFEL experiments, we propose a new hybrid approach for characterizing biomolecular conformational transitions by using a single 2D low-resolution XFEL diffraction pattern in combination with another known conformation. In our method, we represent the molecular structure with a coarse-grained model, the Gaussian mixture model, to describe large conformational transitions from low-resolution XFEL data. We obtain plausible 3D structural models that are consistent with the XFEL diffraction pattern by deforming an initial structural model to maximize the similarity between the target pattern and the simulated diffraction patterns from the candidate models. We tested the proposed algorithm on two biomolecules of different sizes with different complexities of conformational transitions, adenylate kinase, and elongation factor 2, using synthetic XFEL data. The results show that, with the proposed algorithm, we can successfully describe the conformational transitions by flexibly fitting the coarse-grained model of one conformation to become consistent with an XFEL diffraction pattern simulated from another conformation. In addition, we showed that the incident beam orientation has some effect on the accuracy of the 3D structure modeling and discussed the reasons for the inaccuracies for certain orientations. The proposed method could serve as an alternative approach for retrieving information on 3D conformational transitions from the XFEL diffraction patterns to interpret experimental data. Since the molecules are represented by Gaussian kernels and no atomic structure is needed in principle, such a method could also be used as a tool to seek initial models for 3D reconstruction algorithms.

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 Structural Modeling for Electron Microscopy Maps Using VESPER and MAINMAST

An increasing number of protein structures are determined by cryo-electron microscopy (cryo-EM) and stored in the Electron Microscopy Data Bank (EMDB). To interpret determined cryo-EM maps, several methods have been developed that model the tertiary structure of biomolecules, particularly proteins. Here we show how to use two such methods, VESPER and MAINMAST, which were developed in our group. VESPER is a method mainly for two purposes: fitting protein structure models into an EM map and aligning two EM maps locally or globally to capture their similarity. VESPER represents each EM map as a set of vectors pointing toward denser points. By considering matching the directions of vectors, in general, VESPER aligns maps better than conventional methods that only consider local densities of maps. MAINMAST is a de novo protein modeling tool designed for EM maps with resolution of 3-5 Å or better. MAINMAST builds a protein main chain directly from a density map by tracing dense points in an EM map and connecting them using a tree-graph structure. This article describes how to use these two tools using three illustrative modeling examples. © 2022 The Authors. Current Protocols published by Wiley Periodicals LLC. Basic Protocol 1: Protein structure model fitting using VESPER Alternate Protocol: Atomic model fitting using VESPER web server Basic Protocol 2: Protein de novo modeling using MAINMAST.

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

New computational biophysics pipelines for analysing the global dynamics of structural ensembles and large, dynamic complexes resolved by cryoEM are reviewed.

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.

Leveraging crosslinking mass spectrometry in structural and cell biology

Crosslinking mass spectrometry (crosslinking-MS) is a versatile tool providing structural insights into protein conformation and protein-protein interactions. Its medium-resolution residue-residue distance restraints have been used to validate protein structures proposed by other methods and have helped derive models of protein complexes by integrative structural biology approaches. The use of crosslinking-MS in integrative approaches is underpinned by progress in estimating error rates in crosslinking-MS data and in combining these data with other information. The flexible and high-throughput nature of crosslinking-MS has allowed it to complement the ongoing resolution revolution in electron microscopy by providing system-wide residue-residue distance restraints, especially for flexible regions or systems. Here, we review how crosslinking-MS information has been leveraged in structural model validation and integrative modeling. Crosslinking-MS has also been a key technology for cell biology studies and structural systems biology where, in conjunction with cryoelectron tomography, it can provide structural and mechanistic insights directly in situ.

Protein Data Bank Japan: Celebrating our 20th anniversary during a global pandemic as the Asian hub of three dimensional macromolecular structural data

Protein Data Bank Japan (PDBj), a founding member of the worldwide Protein Data Bank (wwPDB) has accepted, processed and distributed experimentally determined biological macromolecular structures for 20 years. During that time, we have continuously made major improvements to our query search interface of PDBj Mine 2, the BMRBj web interface, and EM Navigator for PDB/BMRB/EMDB entries. PDBj also serves PDB‐related secondary database data, original web‐based modeling services such as Homology modeling of complex structure (HOMCOS), visualization services and utility tools, which we have continuously enhanced and expanded throughout the years. In addition, we have recently developed several unique archives, BSM‐Arc for computational structure models, and XRDa for raw X‐ray diffraction images, both of which promote open science in the structural biology community. During the COVID‐19 pandemic, PDBj has also started to provide feature pages for COVID‐19 related entries across all available archives at PDBj from raw experimental data and PDB structural data to computationally predicted models, while also providing COVID‐19 outreach content for high school students and teachers.

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.

IMProv: A Resource for Cross-link-Driven Structure Modeling that Accommodates Protein Dynamics

Proteomics methodology has expanded to include protein structural analysis, primarily through cross-linking mass spectrometry (XL-MS) and hydrogen-deuterium exchange mass spectrometry (HX-MS). However, while the structural proteomics community has effective tools for primary data analysis, there is a need for structure modeling pipelines that are accessible to the proteomics specialist. Integrative structural biology requires the aggregation of multiple distinct types of data to generate models that satisfy all inputs. Here, we describe IMProv, an app in the Mass Spec Studio that combines XL-MS data with other structural data, such as cryo-EM densities and crystallographic structures, for integrative structure modeling on high-performance computing platforms. The resource provides an easily deployed bundle that includes the open-source Integrative Modeling Platform program (IMP) and its dependencies. IMProv also provides functionality to adjust cross-link distance restraints according to the underlying dynamics of cross-linked sites, as characterized by HX-MS. A dynamics-driven conditioning of restraint values can improve structure modeling precision, as illustrated by an integrative structure of the five-membered Polycomb Repressive Complex 2. IMProv is extensible to additional types of data.

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.

VESPER: global and local cryo-EM map alignment using local density vectors

An increasing number of density maps of biological macromolecules have been determined by cryo-electron microscopy (cryo-EM) and stored in the public database, EMDB. To interpret the structural information contained in EM density maps, alignment of maps is an essential step for structure modeling, comparison of maps, and for database search. Here, we developed VESPER, which captures the similarity of underlying molecular structures embedded in density maps by taking local gradient directions into consideration. Compared to existing methods, VESPER achieved substantially more accurate global and local alignment of maps as well as database retrieval.

TEMPy2: a Python library with improved 3D electron microscopy density-fitting and validation workflows

Structural determination of molecular complexes by cryo-EM requires large, often complex processing of the image data that are initially obtained. Here, TEMPy2, an update of the TEMPy package to process, optimize and assess cryo-EM maps and the structures fitted to them, is described. New optimization routines, comprehensive automated checks and workflows to perform these tasks are described.

Using Integrative Modeling Platform to compute, validate, and archive a model of a protein complex structure

Biology is advanced by producing structural models of biological systems, such as protein complexes. Some systems are recalcitrant to traditional structure determination methods. In such cases, it may still be possible to produce useful models by integrative structure determination that depends on simultaneous use of multiple types of data. An ensemble of models that are sufficiently consistent with the data is produced by a structural sampling method guided by a data-dependent scoring function. The variation in the ensemble of models quantified the uncertainty of the structure, generally resulting from the uncertainty in the input information and actual structural heterogeneity in the samples used to produce the data. Here, we describe how to generate, assess, and interpret ensembles of integrative structural models using our open source Integrative Modeling Platform program (https://integrativemodeling.org).

Real time structural search of the Protein Data Bank

Detection of protein structure similarity is a central challenge in structural bioinformatics. Comparisons are usually performed at the polypeptide chain level, however the functional form of a protein within the cell is often an oligomer. This fact, together with recent growth of oligomeric structures in the Protein Data Bank (PDB), demands more efficient approaches to oligomeric assembly alignment/retrieval. Traditional methods use atom level information, which can be complicated by the presence of topological permutations within a polypeptide chain and/or subunit rearrangements. These challenges can be overcome by comparing electron density volumes directly. But, brute force alignment of 3D data is a compute intensive search problem. We developed a 3D Zernike moment normalization procedure to orient electron density volumes and assess similarity with unprecedented speed. Similarity searching with this approach enables real-time retrieval of proteins/protein assemblies resembling a target, from PDB or user input, together with resulting alignments (http://shape.rcsb.org).

Hyper-Molecules: on the Representation and Recovery of Dynamical Structures for Applications in Flexible Macro-Molecules in Cryo-EM

Cryo-electron microscopy (cryo-EM), the subject of the 2017 Nobel Prize in Chemistry, is a technology for obtaining 3-D reconstructions of macromolecules from many noisy 2-D projections of instances of these macromolecules, whose orientations and positions are unknown. These molecules are not rigid objects, but flexible objects involved in dynamical processes. The different conformations are exhibited by different instances of the macromolecule observed in a cryo-EM experiment, each of which is recorded as a particle image. The range of conformations and the conformation of each particle are not known a priori; one of the great promises of cryo-EM is to map this conformation space. Remarkable progress has been made in reconstructing rigid molecules based on homogeneous samples of molecules in spite of the unknown orientation of each particle image and significant progress has been made in recovering a few distinct states from mixtures of rather distinct conformations, but more complex heterogeneous samples remain a major challenge. We introduce the "hyper-molecule" theoretical framework for modeling structures across different states of heterogeneous molecules, including continuums of states. The key idea behind this framework is representing heterogeneous macromolecules as high-dimensional objects, with the additional dimensions representing the conformation space. This idea is then refined to model properties such as localized heterogeneity. In addition, we introduce an algorithmic framework for reconstructing such heterogeneous objects from experimental data using a Bayesian formulation of the problem and Markov chain Monte Carlo (MCMC) algorithms to address the computational challenges in recovering these high dimensional hyper-molecules. We demonstrate these ideas in a preliminary prototype implementation, applied to synthetic data.

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.

Modelling structures in cryo-EM maps

Recent advances in structure determination of sub-cellular structures using cryo-electron microscopy and tomography have enabled us to understand their architecture in a more detailed manner and gain insight into their function. The choice of approach to use for atomic model building, fitting, refinement and validation in the 3D map resulting from these experiments depends primarily on the resolution of the map and the prior information on the corresponding model. Here, we survey some of such methods and approaches and highlight their uses in specific recent examples.

Reconstruction of low-resolution molecular structures from simulated atomic force microscopy images

BACKGROUND

Atomic Force Microscopy (AFM) is an experimental technique to study structure-function relationship of biomolecules. AFM provides images of biomolecules at nanometer resolution. High-speed AFM experiments produce a series of images following dynamics of biomolecules. To further understand biomolecular functions, information on three-dimensional (3D) structures is beneficial.

METHOD

We aim to recover 3D information from an AFM image by computational modeling. The AFM image includes only low-resolution representation of a molecule; therefore we represent the structures by a coarse grained model (Gaussian mixture model). Using Monte-Carlo sampling, candidate models are generated to increase similarity between AFM images simulated from the models and target AFM image.

RESULTS

The algorithm was tested on two proteins to model their conformational transitions. Using a simulated AFM image as reference, the algorithm can produce a low-resolution 3D model of the target molecule. Effect of molecular orientations captured in AFM images on the 3D modeling performance was also examined and it is shown that similar accuracy can be obtained for many orientations.

CONCLUSIONS

The proposed algorithm can generate 3D low-resolution protein models, from which conformational transitions observed in AFM images can be interpreted in more detail.

GENERAL SIGNIFICANCE

High-speed AFM experiments allow us to directly observe biomolecules in action, which provides insights on biomolecular function through dynamics. However, as only partial structural information can be obtained from AFM data, this new AFM based hybrid modeling method would be useful to retrieve 3D information of the entire biomolecule.

Gaussian Mixture Models for Probabilistic Classification of Breast Cancer

In the era of omics-driven research, it remains a common dilemma to stratify individual patients based on the molecular characteristics of their tumors. To improve molecular stratification of patients with breast cancer, we developed the Gaussian mixture model (GMM)-based classifier. This probabilistic classifier was built on mRNA expression data from more than 300 clinical samples of breast cancer and healthy tissue and was validated on datasets of ESR1, PGR, and ERBB2, which encode standard clinical markers and therapeutic targets. To demonstrate how a GMM approach could be exploited for multiclass classification using data from a candidate marker, we analyzed the insulin-like growth factor I receptor (IGF1R), a promising target, but a marker of uncertain importance in breast cancer. The GMM defined subclasses with downregulated (40%), unchanged (39%), upregulated (19%), and overexpressed (2%) IGF1R levels; inter- and intrapatient analyses of IGF1R transcript and protein levels supported these predictions. Overexpressed IGF1R was observed in a small percentage of tumors. Samples with unchanged and upregulated IGF1R were differentiated tumors, and downregulation of IGF1R correlated with poorly differentiated, high-risk hormone receptor-negative and HER2-positive tumors. A similar correlation was found in the independent cohort of carcinoma in situ, suggesting that loss or low expression of IGF1R is a marker of aggressiveness in subsets of preinvasive and invasive breast cancer. These results demonstrate the importance of probabilistic modeling that delves deeper into molecular data and aims to improve diagnostic classification, prognostic assessment, and treatment selection. SIGNIFICANCE: A GMM classifier demonstrates potential use for clinical validation of markers and determination of target populations, particularly when availability of specimens for marker development is low.

Simultaneous Determination of Protein Structure and Dynamics Using Cryo-Electron Microscopy

Cryo-electron microscopy is rapidly emerging as a powerful technique to determine the structures of complex macromolecular systems elusive to other techniques. Because many of these systems are highly dynamical, characterizing their movements is also a crucial step to unravel their biological functions. To achieve this goal, we report an integrative modeling approach to simultaneously determine structure and dynamics of macromolecular systems from cryo-electron microscopy density maps. By quantifying the level of noise in the data and dealing with their ensemble-averaged nature, this approach enables the integration of multiple sources of information to model ensembles of structures and infer their populations. We illustrate the method by characterizing structure and dynamics of the integral membrane receptor STRA6, thus providing insights into the mechanisms by which it interacts with retinol binding protein and translocates retinol across the membrane.

How low-resolution structural data predict the conformational changes of a protein: a study on data-driven molecular dynamics simulations

Parallel cascade selection molecular dynamics (PaCS-MD) is a conformational sampling method for generating transition pathways between a given reactant and a product. PaCS-MD repeats the following two steps: (1) selections of initial structures relevant to transitions and (2) their conformational resampling. When selecting the initial structures, several measures are utilized to identify their potential to undergo transitions. In the present study, low-resolution structural data obtained from small angle scattering (SAXS) and cryo-electron microscopy (EM) are adopted as the measures in PaCS-MD to promote the conformational transitions of proteins, which is defined as SAXS-/EM-driven targeted PaCS-MD. By selecting the essential structures that have high correlations with the low-resolution structural data, the SAXS-/EM-driven targeted PaCS-MD identifies a set of transition pathways between the reactant and the product. As a demonstration, the present method successfully predicted the open-closed transition pathway of the lysine-, arginine-, ornithine-binding protein with a ns-order simulation time, indicating that the data-driven PaCS-MD simulation might work to promote the conformational transitions of proteins efficiently.

Survey of the analysis of continuous conformational variability of biological macromolecules by electron microscopy

Single-particle analysis by electron microscopy is a well established technique for analyzing the three-dimensional structures of biological macromolecules. Besides its ability to produce high-resolution structures, it also provides insights into the dynamic behavior of the structures by elucidating their conformational variability. Here, the different image-processing methods currently available to study continuous conformational changes are reviewed.

Modeling Biological Complexes Using Integrative Modeling Platform

Integrative structure modeling provides 3D models of macromolecular systems that are based on information from multiple types of experiments, physical principles, statistical inferences, and prior structural models. Here, we provide a hands-on realistic example of integrative structure modeling of the quaternary structure of the actin, tropomyosin, and gelsolin protein assembly based on electron microscopy, solution X-ray scattering, and chemical crosslinking data for the complex as well as excluded volume, sequence connectivity, and rigid atomic X-ray structures of the individual subunits. We follow the general four-stage process for integrative modeling, including gathering the input information, converting the input information into a representation of the system and a scoring function, sampling alternative model configurations guided by the scoring function, and analyzing the results. The computational aspects of this approach are implemented in our open-source Integrative Modeling Platform (IMP), a comprehensive and extensible software package for integrative modeling ( https://integrativemodeling.org ). In particular, we rely on the Python Modeling Interface (PMI) module of IMP that provides facile mixing and matching of macromolecular representations, restraints based on different types of information, sampling algorithms, and analysis including validations of the input data and output models. Finally, we also outline how to deposit an integrative structure and corresponding experimental data into PDB-Dev, the nascent worldwide Protein Data Bank (wwPDB) resource for archiving and disseminating integrative structures ( https://pdb-dev.wwpdb.org ). The example application provides a starting point for a user interested in using IMP for integrative modeling of other biomolecular systems.

Bayesian inference of rotor ring stoichiometry from electron microscopy images of archaeal ATP synthase

The 'Bayesian inference of electron microscopy' (BioEM) framework makes it possible to determine the stoichiometry of protein complexes using 3D coarse-grained models and a relatively small number of cryo-electron microscopy images as input. We applied the method to determine the most probable rotor ring stoichiometry of the archaeal Na+ ATP synthase from Pyrococcus furiosus, a multisubunit complex able to produce ATP under extreme conditions. Archaeal ATP synthases consist of a catalytic A1 part and a membrane-embedded AO portion. The AO portion is composed of a rotor ring and the a-subunit. The rotor ring of P. furiosus ATP synthase is composed of 16-kDa c-subunits, each consisting of four helices forming a bundle, with only one Na+-binding site per bundle. This ring was proposed to be decameric from LILBID-MS analysis of the entire ATP synthase. By contrast, the BioEM posterior favors a c9 ring stoichiometry. With BioEM, we ranked coarse-grained models of the whole complex with different ring geometry, using 6400 unprocessed particle images of the A1AO complex collected in vitreous ice. BioEM makes it possible to probabilistically establish the domain stoichiometry using low-resolution information and comparably few particle images.

Bayesian Weighing of Electron Cryo-Microscopy Data for Integrative Structural Modeling

Cryo-electron microscopy (cryo-EM) has become a mainstream technique for determining the structures of complex biological systems. However, accurate integrative structural modeling has been hampered by the challenges in objectively weighing cryo-EM data against other sources of information due to the presence of random and systematic errors, as well as correlations, in the data. To address these challenges, we introduce a Bayesian scoring function that efficiently and accurately ranks alternative structural models of a macromolecular system based on their consistency with a cryo-EM density map as well as other experimental and prior information. The accuracy of this approach is benchmarked using complexes of known structure and illustrated in three applications: the structural determination of the GroEL/GroES, RNA polymerase II, and exosome complexes. The approach is implemented in the open-source Integrative Modeling Platform (http://integrativemodeling.org), thus enabling integrative structure determination by combining cryo-EM data with other sources of information.

Gaussian mixture model for coarse-grained modeling from XFEL

We explore the advantage of Gaussian mixture model (GMM) for interpretation of single particle diffraction patterns from X-ray free electron laser (XFEL) experiments. GMM approximates a biomolecular shape by the superposition of Gaussian distributions. As the Fourier transformation of GMM can be quickly performed, we can efficiently simulate XFEL diffraction patterns from approximated structure models. We report that the resolution that GMM can accurately reproduce is proportional to the cubic root of the number of Gaussians used in the modeling. This behavior can be attributed to the correspondence between the number of adjustable parameters in GMM and the amount of sampling points in diffraction space. Furthermore, GMMs can successfully be used to perform angular assignment and to detect conformational variation. These results demonstrate that GMMs serve as useful coarse-grained models for hybrid approach in XFEL single particle experiments.

Searching for 3D structural models from a library of biological shapes using a few 2D experimental images

Background

Advancements in biophysical experimental techniques have pushed the limits in terms of the types of phenomena that can be characterized, the amount of data that can be produced and the resolution at which we can visualize them. Single particle techniques such as Electron Microscopy (EM) and X-ray free electron laser (XFEL) scattering require a large number of 2D images collected to resolve three-dimensional (3D) structures. In this study, we propose a quick strategy to retrieve potential 3D shapes, as low-resolution models, from a few 2D experimental images by searching a library of 2D projection images generated from existing 3D structures.

Results

We developed the protocol to assemble a non-redundant set of 3D shapes for generating the 2D image library, and to retrieve potential match 3D shapes for query images, using EM data as a test. In our strategy, we disregard differences in volume size, giving previously unknown structures and conformations a greater number of 3D biological shapes as possible matches. We tested the strategy using images from three EM models as query images for searches against a library of 22750 2D projection images generated from 250 random EM models. We found that our ability to identify 3D shapes that match the query images depends on how complex the outline of the 2D shapes are and whether they are represented in the search image library.

Conclusions

Through our computational method, we are able to quickly retrieve a 3D shape from a few 2D projection images. Our approach has the potential for exploring other types of 2D single particle structural data such as from XFEL scattering experiments, for providing a tool to interpret low-resolution data that may be insufficient for 3D reconstruction, and for estimating the mixing of states or conformations that could exist in such experimental data.

Electronic supplementary material

The online version of this article (10.1186/s12859-018-2358-0) contains supplementary material, which is available to authorized users.

Advances in the Development of Shape Similarity Methods and Their Application in Drug Discovery

Molecular similarity is a key concept in drug discovery. It is based on the assumption that structurally similar molecules frequently have similar properties. Assessment of similarity between small molecules has been highly effective in the discovery and development of various drugs. Especially, two-dimensional (2D) similarity approaches have been quite popular due to their simplicity, accuracy and efficiency. Recently, the focus has been shifted toward the development of methods involving the representation and comparison of three-dimensional (3D) conformation of small molecules. Among the 3D similarity methods, evaluation of shape similarity is now gaining attention for its application not only in virtual screening but also in molecular target prediction, drug repurposing and scaffold hopping. A wide range of methods have been developed to describe molecular shape and to determine the shape similarity between small molecules. The most widely used methods include atom distance-based methods, surface-based approaches such as spherical harmonics and 3D Zernike descriptors, atom-centered Gaussian overlay based representations. Several of these methods demonstrated excellent virtual screening performance not only retrospectively but also prospectively. In addition to methods assessing the similarity between small molecules, shape similarity approaches have been developed to compare shapes of protein structures and binding pockets. Additionally, shape comparisons between atomic models and 3D density maps allowed the fitting of atomic models into cryo-electron microscopy maps. This review aims to summarize the methodological advances in shape similarity assessment highlighting advantages, disadvantages and their application in drug discovery.