Inferential optimization for simultaneous fitting of multiple components into a CryoEM map of their assembly

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.

DiffModeler: Large Macromolecular Structure Modeling in Low-Resolution Cryo-EM Maps Using Diffusion Model

Cryogenic electron microscopy (cryo-EM) has now been widely used for determining multi-chain protein complexes. However, modeling a complex structure is challenging particularly when the map resolution is low, typically in the intermediate resolution range of 5 to 10 Å. Within this resolution range, even accurate structure fitting is difficult, let alone de novo modeling. To address this challenge, here we present DiffModeler, a fully automated method for modeling protein complex structures. DiffModeler employs a diffusion model for backbone tracing and integrates AlphaFold2-predicted single-chain structures for structure fitting. Extensive testing on cryo-EM maps at intermediate resolutions demonstrates the exceptional accuracy of DiffModeler in structure modeling, achieving an average TM-Score of 0.92, surpassing existing methodologies significantly. Notably, DiffModeler successfully modeled a protein complex composed of 47 chains and 13,462 residues, achieving a high TM-Score of 0.94. Further benchmarking at low resolutions (10-20 Å confirms its versatility, demonstrating plausible performance. Moreover, when coupled with CryoREAD, DiffModeler excels in constructing protein-DNA/RNA complex structures for near-atomic resolution maps (0-5 Å), showcasing state-of-the-art performance with average TM-Scores of 0.88 and 0.91 across two datasets.

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.

Combining Electron Microscopy (EM) and Cross-Linking Mass Spectrometry (XL-MS) for Structural Characterization of Protein Complexes

Structural biology has recently witnessed the benefits of the combined use of two complementary techniques: electron microscopy (EM) and cross-linking mass spectrometry (XL-MS). EM (especially its cryogenic variant cryo-EM) has proven to be a very powerful tool for the structural determination of proteins and protein complexes, even at an atomic level. In a complementary way, XL-MS allows the precise characterization of particular interactions when residues are located in close proximity. When working from low-resolution, negative-staining images and less-defined regions of flexible domains (whose mapping is made possible by cryo-EM), XL-MS can provide critical information on specific amino acids, thus identifying interacting regions and helping to deduce the overall protein structure. The protocol described here is particularly well suited for the study of protein complexes whose intrinsically flexible or transient nature prevents their high-resolution characterization by any structural technique itself.

Integrative structural modeling of macromolecular complexes using Assembline

Integrative modeling enables structure determination of macromolecular complexes by combining data from multiple experimental sources such as X-ray crystallography, electron microscopy or cross-linking mass spectrometry. It is particularly useful for complexes not amenable to high-resolution electron microscopy-complexes that are flexible, heterogeneous or imaged in cells with cryo-electron tomography. We have recently developed an integrative modeling protocol that allowed us to model multi-megadalton complexes as large as the nuclear pore complex. Here, we describe the Assembline software package, which combines multiple programs and libraries with our own algorithms in a streamlined modeling pipeline. Assembline builds ensembles of models satisfying data from atomic structures or homology models, electron microscopy maps and other experimental data, and provides tools for their analysis. Compared with other methods, Assembline enables efficient sampling of conformational space through a multistep procedure, provides new modeling restraints and includes a unique configuration system for setting up the modeling project. Our protocol achieves exhaustive sampling in less than 100-1,000 CPU-hours even for complexes in the megadalton range. For larger complexes, resources available in institutional or public computer clusters are needed and sufficient to run the protocol. We also provide step-by-step instructions for preparing the input, running the core modeling steps and assessing modeling performance at any stage.

Bayesian metamodeling of complex biological systems across varying representations

Comprehensive modeling of a whole cell requires an integration of vast amounts of information on various aspects of the cell and its parts. To divide and conquer this task, we introduce Bayesian metamodeling, a general approach to modeling complex systems by integrating a collection of heterogeneous input models. Each input model can in principle be based on any type of data and can describe a different aspect of the modeled system using any mathematical representation, scale, and level of granularity. These input models are 1) converted to a standardized statistical representation relying on probabilistic graphical models, 2) coupled by modeling their mutual relations with the physical world, and 3) finally harmonized with respect to each other. To illustrate Bayesian metamodeling, we provide a proof-of-principle metamodel of glucose-stimulated insulin secretion by human pancreatic β-cells. The input models include a coarse-grained spatiotemporal simulation of insulin vesicle trafficking, docking, and exocytosis; a molecular network model of glucose-stimulated insulin secretion signaling; a network model of insulin metabolism; a structural model of glucagon-like peptide-1 receptor activation; a linear model of a pancreatic cell population; and ordinary differential equations for systemic postprandial insulin response. Metamodeling benefits from decentralized computing, while often producing a more accurate, precise, and complete model that contextualizes input models as well as resolves conflicting information. We anticipate Bayesian metamodeling will facilitate collaborative science by providing a framework for sharing expertise, resources, data, and models, as exemplified by the Pancreatic β-Cell Consortium.

Information-driven modeling of biomolecular complexes

Proteins play crucial roles in every cellular process by interacting with each other, nucleic acids, metabolites, and other molecules. The resulting assemblies can be very large and intricate and pose challenges to experimental methods. In the current era of integrative modeling, it is often only by a combination of various experimental techniques and computations that three-dimensional models of those molecular machines can be obtained. Among the various computational approaches available, molecular docking is often the method of choice when it comes to predicting three-dimensional structures of complexes. Docking can generate particularly accurate models when taking into account the available information on the complex of interest. We review here the use of experimental and bioinformatics data in protein-protein docking, describing recent software developments and highlighting applications for the modeling of antibody-antigen complexes and membrane protein complexes, and the use of evolutionary and shape information.

Fitting Low-Resolution Protein Structures into Cryo-EM Density Maps by Multiobjective Optimization of Global and Local Correlations

The rigid-body fitting of predicted structural models into cryo-electron microscopy (cryo-EM) density maps is a necessary procedure for density map-guided protein structure determination and prediction. We proposed a novel multiobjective optimization protocol, MOFIT, which performs a rigid-body density-map fitting based on particle swarm optimization (PSO). MOFIT was tested on a large set of 292 nonhomologous single-domain proteins. Starting from structural models predicted by I-TASSER, MOFIT achieved an average coordinate root-mean-square deviation of 2.46 Å, which was 1.57, 2.79, and 3.95 Å lower than three leading single-objective function-based methods, where the differences were statistically significant with p-values of 1.65 × 10^-6, 6.36 × 10^-8, and 6.44 × 10^-11 calculated using two-tail Student's t tests. Detailed analyses showed that the major advantages of MOFIT lie in the multiobjective protocol and the extensive PSO search simulations guided by the composite objective functions, which integrates complementary correlation coefficients from the global structure, local fragments, and individual residues with the cryo-EM density maps.

Methods for Molecular Modelling of Protein Complexes

Biological processes are often mediated by complexes formed between proteins and various biomolecules. The 3D structures of such protein-biomolecule complexes provide insights into the molecular mechanism of their action. The structure of these complexes can be predicted by various computational methods. Choosing an appropriate method for modelling depends on the category of biomolecule that a protein interacts with and the availability of structural information about the protein and its interacting partner. We intend for the contents of this chapter to serve as a guide as to what software would be the most appropriate for the type of data at hand and the kind of 3D complex structure required. Particularly, we have dealt with protein-small molecule ligand, protein-peptide, protein-protein, and protein-nucleic acid interactions.Most, if not all, model building protocols perform some sampling and scoring. Typically, several alternate conformations and configurations of the interactors are sampled. Each such sample is then scored for optimization. To boost the confidence in these predicted models, their assessment using other independent scoring schemes besides the inbuilt/default ones would prove to be helpful. This chapter also lists such software and serves as a guide to gauge the fidelity of modelled structures of biomolecular complexes.

From integrative structural biology to cell biology

Integrative modeling is an increasingly important tool in structural biology, providing structures by combining data from varied experimental methods and prior information. As a result, molecular architectures of large, heterogeneous, and dynamic systems, such as the ∼52-MDa Nuclear Pore Complex, can be mapped with useful accuracy, precision, and completeness. Key challenges in improving integrative modeling include expanding model representations, increasing the variety of input data and prior information, quantifying a match between input information and a model in a Bayesian fashion, inventing more efficient structural sampling, as well as developing better model validation, analysis, and visualization. In addition, two community-level challenges in integrative modeling are being addressed under the auspices of the Worldwide Protein Data Bank (wwPDB). First, the impact of integrative structures is maximized by PDB-Development, a prototype wwPDB repository for archiving, validating, visualizing, and disseminating integrative structures. Second, the scope of structural biology is expanded by linking the wwPDB resource for integrative structures with archives of data that have not been generally used for structure determination but are increasingly important for computing integrative structures, such as data from various types of mass spectrometry, spectroscopy, optical microscopy, proteomics, and genetics. To address the largest of modeling problems, a type of integrative modeling called metamodeling is being developed; metamodeling combines different types of input models as opposed to different types of data to compute an output model. Collectively, these developments will facilitate the structural biology mindset in cell biology and underpin spatiotemporal mapping of the entire cell.

The In Situ Structure of Parkinson's Disease-Linked LRRK2

Mutations in leucine-rich repeat kinase 2 (LRRK2) are the most frequent cause of familial Parkinson's disease. LRRK2 is a multi-domain protein containing a kinase and GTPase. Using correlative light and electron microscopy, in situ cryo-electron tomography, and subtomogram analysis, we reveal a 14-Å structure of LRRK2 bearing a pathogenic mutation that oligomerizes as a right-handed double helix around microtubules, which are left-handed. Using integrative modeling, we determine the architecture of LRRK2, showing that the GTPase and kinase are in close proximity, with the GTPase closer to the microtubule surface, whereas the kinase is exposed to the cytoplasm. We identify two oligomerization interfaces mediated by non-catalytic domains. Mutation of one of these abolishes LRRK2 microtubule-association. Our work demonstrates the power of cryo-electron tomography to generate models of previously unsolved structures in their cellular environment.

Principles for Integrative Structural Biology Studies

Integrative structure determination is a powerful approach to modeling the structures of biological systems based on data produced by multiple experimental and theoretical methods, with implications for our understanding of cellular biology and drug discovery. This Primer introduces the theory and methods of integrative approaches, emphasizing the kinds of data that can be effectively included in developing models and using the nuclear pore complex as an example to illustrate the practice and challenges involved. These guidelines are intended to aid the researcher in understanding and applying integrative structural methods to systems of their interest and thus take advantage of this rapidly evolving field.

Investigating eukaryotic cells with cryo-ET

The interior of eukaryotic cells is mysterious. How do the large communities of macromolecular machines interact with each other? How do the structures and positions of these nanoscopic entities respond to new stimuli? Questions like these can now be answered with the help of a method called electron cryotomography (cryo-ET). Cryo-ET will ultimately reveal the inner workings of a cell at the protein, secondary structure, and perhaps even side-chain levels. Combined with genetic or pharmacological perturbation, cryo-ET will allow us to answer previously unimaginable questions, such as how structure, biochemistry, and forces are related in situ. Because it bridges structural biology and cell biology, cryo-ET is indispensable for structural cell biology-the study of the 3-D macromolecular structure of cells. Here we discuss some of the key ideas, strategies, auxiliary techniques, and innovations that an aspiring structural cell biologist will consider when planning to ask bold questions.

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.

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.

SSEThread: Integrative threading of the DNA-PKcs sequence based on data from chemical cross-linking and hydrogen deuterium exchange

X-ray crystallography and electron microscopy maps resolved to 3-8 Å are generally sufficient for tracing the path of the polypeptide chain in space, while often insufficient for unambiguously registering the sequence on the path (i.e., threading). Frequently, however, additional information is available from other biophysical experiments, physical principles, statistical analyses, and other prior models. Here, we formulate an integrative approach for sequence assignment to a partial backbone model as an optimization problem, which requires three main components: the representation of the system, the scoring function, and the optimization method. The method is implemented in the open source Integrative Modeling Platform (IMP) (https://integrativemodeling.org), allowing a number of different terms in the scoring function. We apply this method to localizing the sequence assignment within a 199-residue disordered region of three structured and sequence unassigned helices in the DNA-PKcs crystallographic structure, using chemical crosslinks, hydrogen deuterium exchange, and sequence connectivity. The resulting ensemble of threading models provides two major solutions, one of which suggests that the crucial ABCDE cluster of phosphorylation sites cannot undergo intra-molecular autophosphorylation without a conformational rearrangement. The ensemble of solutions embodies the most accurate and precise sequence threading given the available information.

Archiving and disseminating integrative structure models

Limitations in the applicability, accuracy, and precision of individual structure characterization methods can sometimes be overcome via an integrative modeling approach that relies on information from all available sources, including all available experimental data and prior models. The open-source Integrative Modeling Platform (IMP) is one piece of software that implements all computational aspects of integrative modeling. To maximize the impact of integrative structures, the coordinates should be made publicly available, as is already the case for structures based on X-ray crystallography, NMR spectroscopy, and electron microscopy. Moreover, the associated experimental data and modeling protocols should also be archived, such that the original results can easily be reproduced. Finally, it is essential that the integrative structures are validated as part of their publication and deposition. A number of research groups have already developed software to implement integrative modeling and have generated a number of structures, prompting the formation of an Integrative/Hybrid Methods Task Force. Following the recommendations of this task force, the existing PDBx/mmCIF data representation used for atomic PDB structures has been extended to address the requirements for archiving integrative structural models. This IHM-dictionary adds a flexible model representation, including coarse graining, models in multiple states and/or related by time or other order, and multiple input experimental information sources. A prototype archiving system called PDB-Dev ( https://pdb-dev.wwpdb.org ) has also been created to archive integrative structural models, together with a Python library to facilitate handling of integrative models in PDBx/mmCIF format.

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.

Integrative Structure Modeling: Overview and Assessment

Integrative structure modeling computationally combines data from multiple sources of information with the aim of obtaining structural insights that are not revealed by any single approach alone. In the first part of this review, we survey the commonly used sources of structural information and the computational aspects of model building. Throughout the past decade, integrative modeling was applied to various biological systems, with a focus on large protein complexes. Recent progress in the field of cryo-electron microscopy (cryo-EM) has resolved many of these complexes to near-atomic resolution. In the second part of this review, we compare a range of published integrative models with their higher-resolution counterparts with the aim of critically assessing their accuracy. This comparison gives a favorable view of integrative modeling and demonstrates its ability to yield accurate and informative results. We discuss possible roles of integrative modeling in the new era of cryo-EM and highlight future challenges and directions.

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 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.

CryoEM-based hybrid modeling approaches for structure determination

Recent advances in cryo-electron microscopy (cryoEM) have dramatically improved the resolutions at which vitrified biological specimens can be studied, revealing new structural and mechanistic insights over a broad range of spatial scales. Bolstered by these advances, much effort has been directed toward the development of hybrid modeling methodologies for the construction and refinement of high-fidelity atomistic models from cryoEM data. In this brief review, we will survey the key elements of cryoEM-based hybrid modeling, providing an overview of available computational tools and strategies as well as several recent applications.

VirB8 homolog TraE from plasmid pKM101 forms a hexameric ring structure and interacts with the VirB6 homolog TraD

The overproduction and purification of membrane proteins are intrinsically difficult, making their analysis challenging. We purified the TraE membrane protein from a bacterial conjugation system that is involved in plasmid transfer. Our results suggest that this protein forms hexamers with a central pore, and we also show that it binds to the TraD protein. The structure of TraE is completely different from that of the previously characterized periplasmic domain. This has intriguing implications for the role of TraE and of its interaction partner TraD in substrate translocation across the bacterial cell envelope. This work makes an important contribution to understanding of the mechanism of plasmid transfer, contributing to the design of approaches to inhibit the spread of antibiotic resistance genes.

Type IV secretion systems (T4SSs) are multiprotein assemblies that translocate macromolecules across the cell envelope of bacteria. X-ray crystallographic and electron microscopy (EM) analyses have increasingly provided structural information on individual T4SS components and on the entire complex. As of now, relatively little information has been available on the exact localization of the inner membrane-bound T4SS components, notably the mostly periplasmic VirB8 protein and the very hydrophobic VirB6 protein. We show here that the membrane-bound, full-length version of the VirB8 homolog TraE from the plasmid pKM101 secretion system forms a high-molecular-mass complex that is distinct from the previously characterized periplasmic portion of the protein that forms dimers. Full-length TraE was extracted from the membranes with detergents, and analysis by size-exclusion chromatography, cross-linking, and size exclusion chromatography (SEC) multiangle light scattering (MALS) shows that it forms a high-molecular-mass complex. EM and small-angle X-ray scattering (SAXS) analysis demonstrate that full-length TraE forms a hexameric complex with a central pore. We also overproduced and purified the VirB6 homolog TraD and show by cross-linking, SEC, and EM that it binds to TraE. Our results suggest that TraE and TraD interact at the substrate translocation pore of the secretion system.

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

A new Gaussian mixture model (GMM) has been developed for better representations of both atomic models and electron microscopy 3D density maps. The standard GMM algorithm employs an EM algorithm to determine the parameters. It accepted a set of 3D points with weights, corresponding to voxel or atomic centers. Although the standard algorithm worked reasonably well; however, it had three problems. First, it ignored the size (voxel width or atomic radius) of the input, and thus it could lead to a GMM with a smaller spread than the input. Second, the algorithm had a singularity problem, as it sometimes stopped the iterative procedure due to a Gaussian function with almost zero variance. Third, a map with a large number of voxels required a long computation time for conversion to a GMM. To solve these problems, we have introduced a Gaussian-input GMM algorithm, which considers the input atoms or voxels as a set of Gaussian functions. The standard EM algorithm of GMM was extended to optimize the new GMM. The new GMM has identical radius of gyration to the input, and does not suddenly stop due to the singularity problem. For fast computation, we have introduced a down-sampled Gaussian functions (DSG) by merging neighboring voxels into an anisotropic Gaussian function. It provides a GMM with thousands of Gaussian functions in a short computation time. We also have introduced a DSG-input GMM: the Gaussian-input GMM with the DSG as the input. This new algorithm is much faster than the standard algorithm.

Assessing Exhaustiveness of Stochastic Sampling for Integrative Modeling of Macromolecular Structures

Modeling of macromolecular structures involves structural sampling guided by a scoring function, resulting in an ensemble of good-scoring models. By necessity, the sampling is often stochastic, and must be exhaustive at a precision sufficient for accurate modeling and assessment of model uncertainty. Therefore, the very first step in analyzing the ensemble is an estimation of the highest precision at which the sampling is exhaustive. Here, we present an objective and automated method for this task. As a proxy for sampling exhaustiveness, we evaluate whether two independently and stochastically generated sets of models are sufficiently similar. The protocol includes testing 1) convergence of the model score, 2) whether model scores for the two samples were drawn from the same parent distribution, 3) whether each structural cluster includes models from each sample proportionally to its size, and 4) whether there is sufficient structural similarity between the two model samples in each cluster. The evaluation also provides the sampling precision, defined as the smallest clustering threshold that satisfies the third, most stringent test. We validate the protocol with the aid of enumerated good-scoring models for five illustrative cases of binary protein complexes. Passing the proposed four tests is necessary, but not sufficient for thorough sampling. The protocol is general in nature and can be applied to the stochastic sampling of any set of models, not just structural models. In addition, the tests can be used to stop stochastic sampling as soon as exhaustiveness at desired precision is reached, thereby improving sampling efficiency; they may also help in selecting a model representation that is sufficiently detailed to be informative, yet also sufficiently coarse for sampling to be exhaustive.

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.

Integrative structure modeling with the Integrative Modeling Platform

Building models of a biological system that are consistent with the myriad data available is one of the key challenges in biology. Modeling the structure and dynamics of macromolecular assemblies, for example, can give insights into how biological systems work, evolved, might be controlled, and even designed. Integrative structure modeling casts the building of structural models as a computational optimization problem, for which information about the assembly is encoded into a scoring function that evaluates candidate models. Here, we describe our open source software suite for integrative structure modeling, Integrative Modeling Platform (https://integrativemodeling.org), and demonstrate its use.

Flexible Fitting of Atomic Models into Cryo-EM Density Maps Guided by Helix Correspondences

Although electron cryo-microscopy (cryo-EM) has recently achieved resolutions of better than 3 Å, at which point molecular modeling can be done directly from the density map, analysis and annotation of a cryo-EM density map still primarily rely on fitting atomic or homology models to the density map. In this article, we present, to our knowledge, a new method for flexible fitting of known or modeled protein structures into cryo-EM density maps. Unlike existing methods that are guided by local density gradients, our method is guided by correspondences between the α-helices in the density map and model, and does not require an initial rigid-body fitting step. Compared with current methods on both simulated and experimental density maps, our method not only achieves greater accuracy for proteins with large deformations but also runs as fast or faster than many of the other flexible fitting routines.

Flexible fitting to cryo-EM density map using ensemble molecular dynamics simulations

Flexible fitting is a computational algorithm to derive a new conformational model that conforms to low-resolution experimental data by transforming a known structure. A common application is against data from cryo-electron microscopy to obtain conformational models in new functional states. The conventional flexible fitting algorithms cannot derive correct structures in some cases due to the complexity of conformational transitions. In this study, we show the importance of conformational ensemble in the refinement process by performing multiple fittings trials using a variety of different force constants. Application to simulated maps of Ca²⁺ ATPase and diphtheria toxin as well as experimental data of release factor 2 revealed that for these systems, multiple conformations with similar agreement with the density map exist and a large number of fitting trials are necessary to generate good models. Clustering analysis can be an effective approach to avoid over-fitting models. In addition, we show that an automatic adjustment of the biasing force constants during the fitting process, implemented as replica-exchange scheme, can improve the success rate. © 2017 Wiley Periodicals, Inc.

Disentangling constraints using viability evolution principles in integrative modeling of macromolecular assemblies

Predicting the structure of large molecular assemblies remains a challenging task in structural biology when using integrative modeling approaches. One of the main issues stems from the treatment of heterogeneous experimental data used to predict the architecture of native complexes. We propose a new method, applied here for the first time to a set of symmetrical complexes, based on evolutionary computation that treats every available experimental input independently, bypassing the need to balance weight components assigned to aggregated fitness functions during optimization.

Computational Approaches for Revealing the Structure of Membrane Transporters: Case Study on Bilitranslocase

The structural and functional details of transmembrane proteins are vastly underexplored, mostly due to experimental difficulties regarding their solubility and stability. Currently, the majority of transmembrane protein structures are still unknown and this present a huge experimental and computational challenge. Nowadays, thanks to X-ray crystallography or NMR spectroscopy over 3000 structures of membrane proteins have been solved, among them only a few hundred unique ones. Due to the vast biological and pharmaceutical interest in the elucidation of the structure and the functional mechanisms of transmembrane proteins, several computational methods have been developed to overcome the experimental gap. If combined with experimental data the computational information enables rapid, low cost and successful predictions of the molecular structure of unsolved proteins. The reliability of the predictions depends on the availability and accuracy of experimental data associated with structural information. In this review, the following methods are proposed for in silico structure elucidation: sequence-dependent predictions of transmembrane regions, predictions of transmembrane helix–helix interactions, helix arrangements in membrane models, and testing their stability with molecular dynamics simulations. We also demonstrate the usage of the computational methods listed above by proposing a model for the molecular structure of the transmembrane protein bilitranslocase. Bilitranslocase is bilirubin membrane transporter, which shares similar tissue distribution and functional properties with some of the members of the Organic Anion Transporter family and is the only member classified in the Bilirubin Transporter Family. Regarding its unique properties, bilitranslocase is a potentially interesting drug target.

Portal protein functions akin to a DNA-sensor that couples genome-packaging to icosahedral capsid maturation

Tailed bacteriophages and herpesviruses assemble infectious particles via an empty precursor capsid (or ‘procapsid') built by multiple copies of coat and scaffolding protein and by one dodecameric portal protein. Genome packaging triggers rearrangement of the coat protein and release of scaffolding protein, resulting in dramatic procapsid lattice expansion. Here, we provide structural evidence that the portal protein of the bacteriophage P22 exists in two distinct dodecameric conformations: an asymmetric assembly in the procapsid (PC-portal) that is competent for high affinity binding to the large terminase packaging protein, and a symmetric ring in the mature virion (MV-portal) that has negligible affinity for the packaging motor. Modelling studies indicate the structure of PC-portal is incompatible with DNA coaxially spooled around the portal vertex, suggesting that newly packaged DNA triggers the switch from PC- to MV-conformation. Thus, we propose the signal for termination of ‘Headful Packaging' is a DNA-dependent symmetrization of portal protein.

Tailed bacteriophages assemble empty precursor capsids known as procapsids that are subsequently filled with viral DNA by a genome-packaging motor. Here the authors present a structure-based analysis that suggests the signal for termination of genome packaging is achieved through a DNA-dependent symmetrization of portal protein.

PRISM-EM: template interface-based modelling of multi-protein complexes guided by cryo-electron microscopy density maps

The structures of protein assemblies are important for elucidating cellular processes at the molecular level. Three-dimensional electron microscopy (3DEM) is a powerful method to identify the structures of assemblies, especially those that are challenging to study by crystallography. Here, a new approach, PRISM-EM, is reported to computationally generate plausible structural models using a procedure that combines crystallographic structures and density maps obtained from 3DEM. The predictions are validated against seven available structurally different crystallographic complexes. The models display mean deviations in the backbone of <5 Å. PRISM-EM was further tested on different benchmark sets; the accuracy was evaluated with respect to the structure of the complex, and the correlation with EM density maps and interface predictions were evaluated and compared with those obtained using other methods. PRISM-EM was then used to predict the structure of the ternary complex of the HIV-1 envelope glycoprotein trimer, the ligand CD4 and the neutralizing protein m36.

Metadynamic metainference: Enhanced sampling of the metainference ensemble using metadynamics

Accurate and precise structural ensembles of proteins and macromolecular complexes can be obtained with metainference, a recently proposed Bayesian inference method that integrates experimental information with prior knowledge and deals with all sources of errors in the data as well as with sample heterogeneity. The study of complex macromolecular systems, however, requires an extensive conformational sampling, which represents a separate challenge. To address such challenge and to exhaustively and efficiently generate structural ensembles we combine metainference with metadynamics and illustrate its application to the calculation of the free energy landscape of the alanine dipeptide.

Tools for Model Building and Optimization into Near-Atomic Resolution Electron Cryo-Microscopy Density Maps

Electron cryo-microscopy (cryoEM) has advanced dramatically to become a viable tool for high-resolution structural biology research. The ultimate outcome of a cryoEM study is an atomic model of a macromolecule or its complex with interacting partners. This chapter describes a variety of algorithms and software to build a de novo model based on the cryoEM 3D density map, to optimize the model with the best stereochemistry restraints and finally to validate the model with proper protocols. The full process of atomic structure determination from a cryoEM map is described. The tools outlined in this chapter should prove extremely valuable in revealing atomic interactions guided by cryoEM data.

Use of evolutionary information in the fitting of atomic level protein models in low resolution cryo-EM map of a protein assembly improves the accuracy of the fitting

Protein-protein interface residues, especially those at the core of the interface, exhibit higher conservation than residues in solvent exposed regions. Here, we explore the ability of this differential conservation to evaluate fittings of atomic models in low-resolution cryo-EM maps and select models from the ensemble of solutions that are often proposed by different model fitting techniques. As a prelude, using a non-redundant and high-resolution structural dataset involving 125 permanent and 95 transient complexes, we confirm that core interface residues are conserved significantly better than nearby non-interface residues and this result is used in the cryo-EM map analysis. From the analysis of inter-component interfaces in a set of fitted models associated with low-resolution cryo-EM maps of ribosomes, chaperones and proteasomes we note that a few poorly conserved residues occur at interfaces. Interestingly a few conserved residues are not in the interface, though they are close to the interface. These observations raise the potential requirement of refitting the models in the cryo-EM maps. We show that sampling an ensemble of models and selection of models with high residue conservation at the interface and in good agreement with the density helps in improving the accuracy of the fit. This study indicates that evolutionary information can serve as an additional input to improve and validate fitting of atomic models in cryo-EM density maps.

Two distinct trimeric conformations of natively membrane-anchored full-length herpes simplex virus 1 glycoprotein B

Many viruses are enveloped by a lipid bilayer acquired during assembly, which is typically studded with one or two types of glycoproteins. These viral surface proteins act as the primary interface between the virus and the host. Entry of enveloped viruses relies on specialized fusogen proteins to help merge the virus membrane with the host membrane. In the multicomponent herpesvirus fusion machinery, glycoprotein B (gB) acts as this fusogen. Although the structure of the gB ectodomain postfusion conformation has been determined, any other conformations (e.g., prefusion, intermediate conformations) have so far remained elusive, thus restricting efforts to develop antiviral treatments and prophylactic vaccines. Here, we have characterized the full-length herpes simplex virus 1 gB in a native membrane by displaying it on cell-derived vesicles and using electron cryotomography. Alongside the known postfusion conformation, a novel one was identified. Its structure, in the context of the membrane, was determined by subvolume averaging and found to be trimeric like the postfusion conformation, but appeared more condensed. Hierarchical constrained density-fitting of domains unexpectedly revealed the fusion loops in this conformation to be apart and pointing away from the anchoring membrane. This vital observation is a substantial step forward in understanding the complex herpesvirus fusion mechanism, and opens up new opportunities for more targeted intervention of herpesvirus entry.

Improving the Accuracy of Fitted Atomic Models in Cryo-EM Density Maps of Protein Assemblies Using Evolutionary Information from Aligned Homologous Proteins

Cryo-Electron Microscopy (cryo-EM) has become an important technique to obtain structural insights into large macromolecular assemblies. However the resolution of the density maps do not allow for its interpretation at atomic level. Hence they are combined with high resolution structures along with information from other experimental or bioinformatics techniques to obtain pseudo-atomic models. Here, we describe the use of evolutionary conservation of residues as obtained from protein structures and alignments of homologous proteins to detect errors in the fitting of atomic structures as well as improve accuracy of the protein-protein interfacial regions in the cryo-EM density maps.

γ-TEMPy: Simultaneous Fitting of Components in 3D-EM Maps of Their Assembly Using a Genetic Algorithm

We have developed a genetic algorithm for building macromolecular complexes using only a 3D-electron microscopy density map and the atomic structures of the relevant components. For efficient sampling the method uses map feature points calculated by vector quantization. The fitness function combines a mutual information score that quantifies the goodness of fit with a penalty score that helps to avoid clashes between components. Testing the method on ten assemblies (containing 3–8 protein components) and simulated density maps at 10, 15, and 20 Å resolution resulted in identification of the correct topology in 90%, 70%, and 60% of the cases, respectively. We further tested it on four assemblies with experimental maps at 7.2–23.5 Å resolution, showing the ability of the method to identify the correct topology in all cases. We have also demonstrated the importance of the map feature-point quality on assembly fitting in the lack of additional experimental information.

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γ-TEMPy uses a genetic algorithm to fit multiple components into 3D-EM density maps

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The fitness score is a combination of a Mutual Information score and a clash penalty

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Efficient sampling is aided by using map feature points from vector quantization

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Native topologies for assemblies containing up to eight components can be predicted

Numerical geometry of map and model assessment

We are describing best practices and assessment strategies for the atomic interpretation of cryo-electron microscopy (cryo-EM) maps. Multiscale numerical geometry strategies in the Situs package and in secondary structure detection software are currently evolving due to the recent increases in cryo-EM resolution. Criteria that aim to predict the accuracy of fitted atomic models at low (worse than 8Å) and medium (4-8 Å) resolutions remain challenging. However, a high level of confidence in atomic models can be achieved by combining such criteria. The observed errors are due to map-model discrepancies and due to the effect of imperfect global docking strategies. Extending the earlier motion capture approach developed for flexible fitting, we use simulated fiducials (pseudoatoms) at varying levels of coarse-graining to track the local drift of structural features. We compare three tracking approaches: naïve vector quantization, a smoothly deformable model, and a tessellation of the structure into rigid Voronoi cells, which are fitted using a multi-fragment refinement approach. The lowest error is an upper bound for the (small) discrepancy between the crystal structure and the EM map due to different conditions in their structure determination. When internal features such as secondary structures are visible in medium-resolution EM maps, it is possible to extend the idea of point-based fiducials to more complex geometric representations such as helical axes, strands, and skeletons. We propose quantitative strategies to assess map-model pairs when such secondary structure patterns are prominent.

Outcome of the First wwPDB Hybrid/Integrative Methods Task Force Workshop

Structures of biomolecular systems are increasingly computed by integrative modeling that relies on varied types of experimental data and theoretical information. We describe here the proceedings and conclusions from the first wwPDB Hybrid/Integrative Methods Task Force Workshop held at the European Bioinformatics Institute in Hinxton, UK, on October 6 and 7, 2014. At the workshop, experts in various experimental fields of structural biology, experts in integrative modeling and visualization, and experts in data archiving addressed a series of questions central to the future of structural biology. How should integrative models be represented? How should the data and integrative models be validated? What data should be archived? How should the data and models be archived? What information should accompany the publication of integrative models?

Conformational States of macromolecular assemblies explored by integrative structure calculation

A detailed description of macromolecular assemblies in multiple conformational states can be very valuable for understanding cellular processes. At present, structural determination of most assemblies in different biologically relevant conformations cannot be achieved by a single technique and thus requires an integrative approach that combines information from multiple sources. Different techniques require different computational methods to allow efficient and accurate data processing and analysis. Here, we summarize the latest advances and future challenges in computational methods that help the interpretation of data from two techniques—mass spectrometry and three-dimensional cryo-electron microscopy (with focus on alignment and classification of heterogeneous subtomograms from cryo-electron tomography). We evaluate how new developments in these two broad fields will lead to further integration with atomic structures to broaden our picture of the dynamic behavior of assemblies in their native environment.