Hybrid methods for macromolecular structure determination: experiment with expectations

Identifying protein conformational states in the Protein Data Bank: Toward unlocking the potential of integrative dynamics studies

Studying protein dynamics and conformational heterogeneity is crucial for understanding biomolecular systems and treating disease. Despite the deposition of over 215 000 macromolecular structures in the Protein Data Bank and the advent of AI-based structure prediction tools such as AlphaFold2, RoseTTAFold, and ESMFold, static representations are typically produced, which fail to fully capture macromolecular motion. Here, we discuss the importance of integrating experimental structures with computational clustering to explore the conformational landscapes that manifest protein function. We describe the method developed by the Protein Data Bank in Europe - Knowledge Base to identify distinct conformational states, demonstrate the resource's primary use cases, through examples, and discuss the need for further efforts to annotate protein conformations with functional information. Such initiatives will be crucial in unlocking the potential of protein dynamics data, expediting drug discovery research, and deepening our understanding of macromolecular mechanisms.

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.

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.

Integrating cryo-EM and NMR data

Single-particle cryo-electron microscopy (cryo-EM) is increasingly used as a technique to determine the atomic structure of challenging biological systems. Recent advances in microscope engineering, electron detection, and image processing have allowed the structural determination of bigger and more flexible targets than possible with the complementary techniques X-ray crystallography and NMR spectroscopy. However, there exist many biological targets for which atomic resolution cannot be currently achieved with cryo-EM, making unambiguous determination of the protein structure impossible. Although determining the structure of large biological systems using solely NMR is often difficult, highly complementary experimental atomic-level data for each molecule can be derived from the spectra, and used in combination with cryo-EM data. We review here strategies with which both techniques can be synergistically combined, in order to reach detail and understanding unattainable by each technique acting alone; and the types of biological systems for which such an approach would be desirable.

Bayesian-Maximum-Entropy Reweighting of IDP Ensembles Based on NMR Chemical Shifts

Bayesian and Maximum Entropy approaches allow for a statistically sound and systematic fitting of experimental and computational data. Unfortunately, assessing the relative confidence in these two types of data remains difficult as several steps add unknown error. Here we propose the use of a validation-set method to determine the balance, and thus the amount of fitting. We apply the method to synthetic NMR chemical shift data of an intrinsically disordered protein. We show that the method gives consistent results even when other methods to assess the amount of fitting cannot be applied. Finally, we also describe how the errors in the chemical shift predictor can lead to an incorrect fitting and how using secondary chemical shifts could alleviate this problem.

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.

Producing Hfq/Sm Proteins and sRNAs for Structural and Biophysical Studies of Ribonucleoprotein Assembly

Hfq is a bacterial RNA-binding protein that plays key roles in the post-transcriptional regulation of gene expression. Like other Sm proteins, Hfq assembles into toroidal discs that bind RNAs with varying affinities and degrees of sequence specificity. By simultaneously binding to a regulatory small RNA (sRNA) and an mRNA target, Hfq hexamers facilitate productive RNA∙∙∙RNA interactions; the generic nature of this chaperone-like functionality makes Hfq a hub in many sRNA-based regulatory networks. That Hfq is crucial in diverse cellular pathways-including stress response, quorum sensing, and biofilm formation-has motivated genetic and "RNAomic" studies of its function and physiology (in vivo), as well as biochemical and structural analyses of Hfq∙∙∙RNA interactions (in vitro). Indeed, crystallographic and biophysical studies first established Hfq as a member of the phylogenetically conserved Sm superfamily. Crystallography and other biophysical methodologies enable the RNA-binding properties of Hfq to be elucidated in atomic detail, but such approaches have stringent sample requirements, viz.: reconstituting and characterizing an Hfq·RNA complex requires ample quantities of well-behaved (sufficient purity, homogeneity) specimens of Hfq and RNA (sRNA, mRNA fragments, short oligoribonucleotides, or even single nucleotides). The production of such materials is covered in this chapter, with a particular focus on recombinant Hfq proteins for crystallization experiments.

2DHybrid Analysis

We have developed an approach termed '2D hybrid analysis' for building three-dimensional (3D) structures from electron microscopy (EM) images of biological molecules. The key advantage is that it is applicable to flexible molecules, which are difficult to analyze by the approach in which 3DEM maps are reconstructed. In the proposed approach, a large number of atomic models with different conformations are first built by computer simulation. Then, simulated EM images are produced from each atomic model. Finally, these images are compared with an experimental EM image to identify the best-fitting atomic model. Two kinds of models are used to simulate the EM images: the negative-stain model and the simple projection model. Although the former is more realistic, the latter permits faster computation. We applied this approach to the averaged EM images of integrin. Although many of these were reproduced well by the best-fitting atomic models, others did not closely resemble any of the simulated EM images. However, the latter group were well reproduced by averaging multiple simulated EM images originating from atomic models with rather different conformations or orientations. This indicated that our approach is capable of detecting mixtures of conformations in the averaged EM images, which should assist in their correct interpretation.

Inferring Structural Ensembles of Flexible and Dynamic Macromolecules Using Bayesian, Maximum Entropy, and Minimal-Ensemble Refinement Methods

The flexible and dynamic nature of biomolecules and biomolecular complexes is essential for many cellular functions in living organisms but poses a challenge for experimental methods to determine high-resolution structural models. To meet this challenge, experiments are combined with molecular simulations. The latter propose models for structural ensembles, and the experimental data can be used to steer these simulations and to select ensembles that most likely underlie the experimental data. Here, we explain in detail how the "Bayesian Inference Of ENsembles" (BioEn) method can be used to refine such ensembles using a wide range of experimental data. The "Ensemble Refinement of SAXS" (EROS) method is a special case of BioEn, inspired by the Gull-Daniell formulation of maximum entropy image processing and focused originally on X-ray solution scattering experiments (SAXS) and then extended to integrative structural modeling. We also briefly sketch the "minimum ensemble method," a maximum-parsimony refinement method that seeks to represent an ensemble with a minimal number of representative structures.

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.

Likelihood-based structural analysis of electron microscopy images

Likelihood-based analysis of single-particle electron microscopy images has contributed much to the recent improvements in resolution. By treating particle orientations and classes probabilistically, uncertainties in the reconstruction process are explicitly accounted for, and the risk of bias towards the initial model is diminished. As a result, the quality and reliability of the reconstructions have greatly improved at manageable computational cost. Likelihood-based analysis of electron microscopy images also offers a route to direct coordinate refinement for dynamic systems, as an alternative to 3D density reconstruction. Here, we review recent developments in the algorithms used for reconstructions of high-resolution maps, and in the integrative framework of combining likelihood methods with simulations to address conformational variability in cryo-electron microscopy.

Bayesian refinement of protein structures and ensembles against SAXS data using molecular dynamics

Small-angle X-ray scattering is an increasingly popular technique used to detect protein structures and ensembles in solution. However, the refinement of structures and ensembles against SAXS data is often ambiguous due to the low information content of SAXS data, unknown systematic errors, and unknown scattering contributions from the solvent. We offer a solution to such problems by combining Bayesian inference with all-atom molecular dynamics simulations and explicit-solvent SAXS calculations. The Bayesian formulation correctly weights the SAXS data versus prior physical knowledge, it quantifies the precision or ambiguity of fitted structures and ensembles, and it accounts for unknown systematic errors due to poor buffer matching. The method further provides a probabilistic criterion for identifying the number of states required to explain the SAXS data. The method is validated by refining ensembles of a periplasmic binding protein against calculated SAXS curves. Subsequently, we derive the solution ensembles of the eukaryotic chaperone heat shock protein 90 (Hsp90) against experimental SAXS data. We find that the SAXS data of the apo state of Hsp90 is compatible with a single wide-open conformation, whereas the SAXS data of Hsp90 bound to ATP or to an ATP-analogue strongly suggest heterogenous ensembles of a closed and a wide-open state.

2D hybrid analysis: Approach for building three-dimensional atomic model by electron microscopy image matching

In this study, we develop an approach termed “2D hybrid analysis” for building atomic models by image matching from electron microscopy (EM) images of biological molecules. The key advantage is that it is applicable to flexible molecules, which are difficult to analyze by 3DEM approach. In the proposed approach, first, a lot of atomic models with different conformations are built by computer simulation. Then, simulated EM images are built from each atomic model. Finally, they are compared with the experimental EM image. Two kinds of models are used as simulated EM images: the negative stain model and the simple projection model. Although the former is more realistic, the latter is adopted to perform faster computations. The use of the negative stain model enables decomposition of the averaged EM images into multiple projection images, each of which originated from a different conformation or orientation. We apply this approach to the EM images of integrin to obtain the distribution of the conformations, from which the pathway of the conformational change of the protein is deduced.

Bayesian Modeling of Biomolecular Assemblies with Cryo-EM Maps

A growing array of experimental techniques allows us to characterize the three-dimensional structure of large biological assemblies at increasingly higher resolution. In addition to X-ray crystallography and nuclear magnetic resonance in solution, new structure determination methods such cryo-electron microscopy (cryo-EM), crosslinking/mass spectrometry and solid-state NMR have emerged. Often it is not sufficient to use a single experimental method, but complementary data need to be collected by using multiple techniques. The integration of all datasets can only be achieved by computational means. This article describes Inferential structure determination, a Bayesian approach to integrative modeling of biomolecular complexes with hybrid structural data. I will introduce probabilistic models for cryo-EM maps and outline Markov chain Monte Carlo algorithms for sampling model structures from the posterior distribution. I will focus on rigid and flexible modeling with cryo-EM data and discuss some of the computational challenges of Bayesian inference in the context of biomolecular modeling.

Defining Low-Dimensional Projections to Guide Protein Conformational Sampling

Exploring the conformational space of proteins is critical to characterize their functions. Numerous methods have been proposed to sample a protein's conformational space, including techniques developed in the field of robotics and known as sampling-based motion-planning algorithms (or sampling-based planners). However, these algorithms suffer from the curse of dimensionality when applied to large proteins. Many sampling-based planners attempt to mitigate this issue by keeping track of sampling density to guide conformational sampling toward unexplored regions of the conformational space. This is often done using low-dimensional projections as an indirect way to reduce the dimensionality of the exploration problem. However, how to choose an appropriate projection and how much it influences the planner's performance are still poorly understood issues. In this article, we introduce two methodologies defining low-dimensional projections that can be used by sampling-based planners for protein conformational sampling. The first method leverages information about a protein's flexibility to construct projections that can efficiently guide conformational sampling, when expert knowledge is available. The second method builds similar projections automatically, without expert intervention. We evaluate the projections produced by both methodologies on two conformational search problems involving three middle-size proteins. Our experiments demonstrate that (i) defining projections based on expert knowledge can benefit conformational sampling and (ii) automatically constructing such projections is a reasonable alternative.

Deriving Structural Information from Experimentally Measured Data on Biomolecules

During the past half century, the number and accuracy of experimental techniques that can deliver values of observables for biomolecular systems have been steadily increasing. The conversion of a measured value Q^exp of an observable quantity Q into structural information is, however, a task beset with theoretical and practical problems: 1) insufficient or inaccurate values of Q^exp , 2) inaccuracies in the function Q(r→) used to relate the quantity Q to structure r→ , 3) how to account for the averaging inherent in the measurement of Q^exp , 4) how to handle the possible multiple-valuedness of the inverse r→(Q) of the function Q(r→) , to mention a few. These apply to a variety of observable quantities Q and measurement techniques such as X-ray and neutron diffraction, small-angle and wide-angle X-ray scattering, free-electron laser imaging, cryo-electron microscopy, nuclear magnetic resonance, electron paramagnetic resonance, infrared and Raman spectroscopy, circular dichroism, Förster resonance energy transfer, atomic force microscopy and ion-mobility mass spectrometry. The process of deriving structural information from measured data is reviewed with an eye to non-experts and newcomers in the field using examples from the literature of the effect of the various choices and approximations involved in the process. A list of choices to be avoided is provided.

Bayesian ensemble refinement by replica simulations and reweighting

We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be characterized by integrating a wide range of experimental data, including measurements of ensemble-averaged observables. We start from a Bayesian formulation in which the posterior is a functional that ranks different configuration space distributions. By maximizing this posterior, we derive an optimal Bayesian ensemble distribution. For discrete configurations, this optimal distribution is identical to that obtained by the maximum entropy "ensemble refinement of SAXS" (EROS) formulation. Bayesian replica ensemble refinement enhances the sampling of relevant configurations by imposing restraints on averages of observables in coupled replica molecular dynamics simulations. We show that the strength of the restraints should scale linearly with the number of replicas to ensure convergence to the optimal Bayesian result in the limit of infinitely many replicas. In the "Bayesian inference of ensembles" method, we combine the replica and EROS approaches to accelerate the convergence. An adaptive algorithm can be used to sample directly from the optimal ensemble, without replicas. We discuss the incorporation of single-molecule measurements and dynamic observables such as relaxation parameters. The theoretical analysis of different Bayesian ensemble refinement approaches provides a basis for practical applications and a starting point for further investigations.

Identifying and Visualizing Macromolecular Flexibility in Structural Biology

Structural biology comprises a variety of tools to obtain atomic resolution data for the investigation of macromolecules. Conventional structural methodologies including crystallography, NMR and electron microscopy often do not provide sufficient details concerning flexibility and dynamics, even though these aspects are critical for the physiological functions of the systems under investigation. However, the increasing complexity of the molecules studied by structural biology (including large macromolecular assemblies, integral membrane proteins, intrinsically disordered systems, and folding intermediates) continuously demands in-depth analyses of the roles of flexibility and conformational specificity involved in interactions with ligands and inhibitors. The intrinsic difficulties in capturing often subtle but critical molecular motions in biological systems have restrained the investigation of flexible molecules into a small niche of structural biology. Introduction of massive technological developments over the recent years, which include time-resolved studies, solution X-ray scattering, and new detectors for cryo-electron microscopy, have pushed the limits of structural investigation of flexible systems far beyond traditional approaches of NMR analysis. By integrating these modern methods with powerful biophysical and computational approaches such as generation of ensembles of molecular models and selective particle picking in electron microscopy, more feasible investigations of dynamic systems are now possible. Using some prominent examples from recent literature, we review how current structural biology methods can contribute useful data to accurately visualize flexibility in macromolecular structures and understand its important roles in regulation of biological processes.

Computational Methodologies for Real-Space Structural Refinement of Large Macromolecular Complexes

The rise of the computer as a powerful tool for model building and refinement has revolutionized the field of structure determination for large biomolecular systems. Despite the wide availability of robust experimental methods capable of resolving structural details across a range of spatiotemporal resolutions, computational hybrid methods have the unique ability to integrate the diverse data from multimodal techniques such as X-ray crystallography and electron microscopy into consistent, fully atomistic structures. Here, commonly employed strategies for computational real-space structural refinement are reviewed, and their specific applications are illustrated for several large macromolecular complexes: ribosome, virus capsids, chemosensory array, and photosynthetic chromatophore. The increasingly important role of computational methods in large-scale structural refinement, along with current and future challenges, is discussed.

High resolution single particle refinement in EMAN2.1

EMAN2.1 is a complete image processing suite for quantitative analysis of grayscale images, with a primary focus on transmission electron microscopy, with complete workflows for performing high resolution single particle reconstruction, 2-D and 3-D heterogeneity analysis, random conical tilt reconstruction and subtomogram averaging, among other tasks. In this manuscript we provide the first detailed description of the high resolution single particle analysis pipeline and the philosophy behind its approach to the reconstruction problem. High resolution refinement is a fully automated process, and involves an advanced set of heuristics to select optimal algorithms for each specific refinement task. A gold standard FSC is produced automatically as part of refinement, providing a robust resolution estimate for the final map, and this is used to optimally filter the final CTF phase and amplitude corrected structure. Additional methods are in-place to reduce model bias during refinement, and to permit cross-validation using other computational methods.

X-ray crystallography over the past decade for novel drug discovery - where are we heading next?

INTRODUCTION

Macromolecular X-ray crystallography has been the primary methodology for determining the three-dimensional structures of proteins, nucleic acids and viruses. Structural information has paved the way for structure-guided drug discovery and laid the foundations for structural bioinformatics. However, X-ray crystallography still has a few fundamental limitations, some of which may be overcome and complemented using emerging methods and technologies in other areas of structural biology.

AREAS COVERED

This review describes how structural knowledge gained from X-ray crystallography has been used to advance other biophysical methods for structure determination (and vice versa). This article also covers current practices for integrating data generated by other biochemical and biophysical methods with those obtained from X-ray crystallography. Finally, the authors articulate their vision about how a combination of structural and biochemical/biophysical methods may improve our understanding of biological processes and interactions.

EXPERT OPINION

X-ray crystallography has been, and will continue to serve as, the central source of experimental structural biology data used in the discovery of new drugs. However, other structural biology techniques are useful not only to overcome the major limitation of X-ray crystallography, but also to provide complementary structural data that is useful in drug discovery. The use of recent advancements in biochemical, spectroscopy and bioinformatics methods may revolutionize drug discovery, albeit only when these data are combined and analyzed with effective data management systems. Accurate and complete data management is crucial for developing experimental procedures that are robust and reproducible.

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?