Structural analysis of intrinsically disordered proteins by small-angle X-ray scattering

Small-angle scattering of X-rays (SAXS) is an established method to study the overall structure and structural transitions of biological macromolecules in solution. For folded proteins, the technique provides three-dimensional low resolution structures ab initio or it can be used to drive rigid-body modeling. SAXS is also a powerful tool for the quantitative analysis of flexible systems, including intrinsically disordered proteins (IDPs), and is highly complementary to the high resolution methods of X-ray crystallography and NMR. Here we present the basic principles of SAXS and review the main approaches to the characterization of IDPs and flexible multidomain proteins using SAXS. Together with the standard approaches based on the analysis of overall parameters, a recently developed Ensemble Optimization Method (EOM) is now available. The latter method allows for the co-existence of multiple protein conformations in solution compatible with the scattering data. Analysis of the selected ensembles provides quantitative information about flexibility and also offers insights into structural features. Examples of the use of SAXS and combined approaches with NMR, X-ray crystallography, and computational methods to characterize completely or partially disordered proteins are presented.     

Integration of small-angle X-ray scattering data into structural modeling of proteins and their assemblies

A major challenge in structural biology is to determine the configuration of domains and proteins in multidomain proteins and assemblies, respectively. All available data should be considered to maximize the accuracy and precision of these models. Small-angle X-ray scattering (SAXS) efficiently provides low-resolution experimental data about the shapes of proteins and their assemblies. Thus, we integrated SAXS profiles into our software for modeling proteins and their assemblies by satisfaction of spatial restraints. Specifically, we modeled the quaternary structures of multidomain proteins with structurally defined rigid domains as well as quaternary structures of binary complexes of structurally defined rigid proteins. In addition to SAXS profiles and the component structures, we used stereochemical restraints and an atomic distance-dependent statistical potential. The scoring function is optimized by a biased Monte Carlo protocol, including quasi-Newton and simulated annealing schemes. The final prediction corresponds to the best scoring solution in the largest cluster of many independently calculated solutions. To quantify how well the quaternary structures are determined based on their SAXS profiles, we used a benchmark of 12 simulated examples as well as an experimental SAXS profile of the homotetramer d-xylose isomerase. Optimization of the SAXS-dependent scoring function generally results in accurate models if sufficiently precise approximations for the constituent rigid bodies are available; otherwise, the best scoring models can have significant errors. Thus, SAXS profiles can play a useful role in the structural characterization of proteins and assemblies if they are combined with additional data and used judiciously. Our integration of a SAXS profile into modeling by satisfaction of spatial restraints will facilitate further integration of different kinds of data for structure determination of proteins and their assemblies.     

Validation of macromolecular flexibility in solution by small-angle X-ray scattering (SAXS)

The dynamics of macromolecular conformations are critical to the action of cellular networks. Solution X-ray scattering studies, in combination with macromolecular X-ray crystallography (MX) and nuclear magnetic resonance (NMR), strive to determine complete and accurate states of macromolecules, providing novel insights describing allosteric mechanisms, supramolecular complexes, and dynamic molecular machines. This review addresses theoretical and practical concepts, concerns, and considerations for using these techniques in conjunction with computational methods to productively combine solution-scattering data with high-resolution structures. I discuss the principal means of direct identification of macromolecular flexibility from SAXS data followed by critical concerns about the methods used to calculate theoretical SAXS profiles from high-resolution structures. The SAXS profile is a direct interrogation of the thermodynamic ensemble and techniques such as, for example, minimal ensemble search (MES), enhance interpretation of SAXS experiments by describing the SAXS profiles as population-weighted thermodynamic ensembles. I discuss recent developments in computational techniques used for conformational sampling, and how these techniques provide a basis for assessing the level of the flexibility within a sample. Although these approaches sacrifice atomic detail, the knowledge gained from ensemble analysis is often appropriate for developing hypotheses and guiding biochemical experiments. Examples of the use of SAXS and combined approaches with X-ray crystallography, NMR, and computational methods to characterize dynamic assemblies are presented.     

Improving protein template recognition by using small-angle x-ray scattering profiles

Small-angle x-ray scattering (SAXS) is able to extract low-resolution protein shape information without requiring a specific crystal formation. However, it has found little use in atomic-level protein structure determination due to the uncertainty of residue-level structural assignment. We developed a new algorithm, SAXSTER, to couple the raw SAXS data with protein-fold-recognition algorithms and thus improve template-based protein-structure predictions. We designed nine different matching scoring functions of template and experimental SAXS profiles. The logarithm of the integrated correlation score showed the best template recognition ability and had the highest correlation with the true template modeling (TM)-score of the target structures. We tested the method in large-scale protein-fold-recognition experiments and achieved significant improvements in prioritizing the best template structures. When SAXSTER was applied to the proteins of asymmetric SAXS profile distributions, the average TM-score of the top-ranking templates increased by 18% after homologous templates were excluded, which corresponds to a p-value < 10⁻⁹ in Student's t-test. These data demonstrate a promising use of SAXS data to facilitate computational protein structure modeling, which is expected to work most efficiently for proteins of irregular global shape and/or multiple-domain protein complexes.     

小角X-射线散射法解析多结构域蛋白质或复合物的溶液结构

随着同步辐射装置的建设与发展及各种建模方法的产生与完善,小角X-射线散射（small angle X-ray scattering,SAXS）法已经逐渐成为结构生物学中的一种重要的工具。SAXS可以用于研究溶液中生物大分子的结构及构象变化,蛋白质的组装、折叠等动态过程。本文对SAXS的基本原理、常用的研究技术和建模方法及其应用进行了综述。     

On the Calculation of SAXS Profiles of Folded and Intrinsically Disordered Proteins from Computer Simulations

Solution techniques such as small-angle X-ray scattering (SAXS) play a central role in structural studies of intrinsically disordered proteins (IDPs); yet, due to low resolution, it is generally necessary to combine SAXS with additional experimental sources of data and to use molecular simulations. Computational methods for the calculation of theoretical SAXS intensity profiles can be separated into two groups, depending on whether the solvent is modeled implicitly as continuous electron density or considered explicitly. The former offers reduced computational cost but requires the definition of a number of free parameters to account for, for example, the excess density of the solvation layer. Overfitting can thus be an issue, particularly when the structural ensemble is unknown. Here, we investigate and show how small variations of the contrast of the hydration shell, δρ, severely affect the outcome, analysis and interpretation of computed SAXS profiles for folded and disordered proteins. For both the folded and disordered proteins studied here, using a default δρ may, in some cases, result in the calculation of non-representative SAXS profiles, leading to an overestimation of their size and a misinterpretation of their structural nature. The solvation layer of the different IDP simulations also impacts their size estimates differently, depending on the protein force field used. The same is not true for the folded protein simulations, suggesting differences in the solvation of the two classes of proteins, and indicating that different force fields optimized for IDPs may cause expansion of the polypeptide chain through different physical mechanisms.     

Genome-wide Membrane Protein Structure Prediction

Transmembrane proteins allow cells to extensively communicate with the external world in a very accurate and specific way. They form principal nodes in several signaling pathways and attract large interest in therapeutic intervention, as the majority pharmaceutical compounds target membrane proteins. Thus, according to the current genome annotation methods, a detailed structural/functional characterization at the protein level of each of the elements codified in the genome is also required. The extreme difficulty in obtaining high-resolution three-dimensional structures, calls for computational approaches. Here we review to which extent the efforts made in the last few years, combining the structural characterization of membrane proteins with protein bioinformatics techniques, could help describing membrane proteins at a genome-wide scale. In particular we analyze the use of comparative modeling techniques as a way of overcoming the lack of high-resolution three-dimensional structures in the human membrane proteome.     

Building Structural Models of a Whole Mycoplasma Cell

Building structural models of entire cells has been a long-standing cross-discipline challenge for the research community, as it requires an unprecedented level of integration between multiple sources of biological data and enhanced methods for computational modeling and visualization. Here, we present the first 3D structural models of an entire Mycoplasma genitalium (MG) cell, built using the CellPACK suite of computational modeling tools. Our model recapitulates the data described in recent whole-cell system biology simulations and provides a structural representation for all MG proteins, DNA and RNA molecules, obtained by combining experimental and homology-modeled structures and lattice-based models of the genome. We establish a framework for gathering, curating and evaluating these structures, exposing current weaknesses of modeling methods and the boundaries of MG structural knowledge, and visualization methods to explore functional characteristics of the genome and proteome. We compare two approaches for data gathering, a manually-curated workflow and an automated workflow that uses homologous structures, both of which are appropriate for the analysis of mesoscale properties such as crowding and volume occupancy. Analysis of model quality provides estimates of the regularization that will be required when these models are used as starting points for atomic molecular dynamics simulations.     

Characterization of Protein Flexibility Using Small-Angle X-Ray Scattering and Amplified Collective Motion Simulations

Large-scale flexibility within a multidomain protein often plays an important role in its biological function. Despite its inherent low resolution, small-angle x-ray scattering (SAXS) is well suited to investigate protein flexibility and determine, with the help of computational modeling, what kinds of protein conformations would coexist in solution. In this article, we develop a tool that combines SAXS data with a previously developed sampling technique called amplified collective motions (ACM) to elucidate structures of highly dynamic multidomain proteins in solution. We demonstrate the use of this tool in two proteins, bacteriophage T4 lysozyme and tandem WW domains of the formin-binding protein 21. The ACM simulations can sample the conformational space of proteins much more extensively than standard molecular dynamics (MD) simulations. Therefore, conformations generated by ACM are significantly better at reproducing the SAXS data than are those from MD simulations.     

Characterization of Protein Flexibility Using Small-Angle X-Ray Scattering and Amplified Collective Motion Simulations

Large-scale flexibility within a multidomain protein often plays an important role in its biological function. Despite its inherent low resolution, small-angle x-ray scattering (SAXS) is well suited to investigate protein flexibility and determine, with the help of computational modeling, what kinds of protein conformations would coexist in solution. In this article, we develop a tool that combines SAXS data with a previously developed sampling technique called amplified collective motions (ACM) to elucidate structures of highly dynamic multidomain proteins in solution. We demonstrate the use of this tool in two proteins, bacteriophage T4 lysozyme and tandem WW domains of the formin-binding protein 21. The ACM simulations can sample the conformational space of proteins much more extensively than standard molecular dynamics (MD) simulations. Therefore, conformations generated by ACM are significantly better at reproducing the SAXS data than are those from MD simulations.     

Effect of interdomain dynamics on the structure determination of modular proteins by small-angle scattering

Multidomain proteins in which consecutive globular regions are connected by linkers are prevalent in nature (Levitt in Proc Natl Acad Sci USA 106:11079–11084, 2009). Some members of this family have largely resisted structural characterization as a result of challenges associated with their inherent flexibility. Small-angle scattering (SAS) is often the method of choice for their structural study. An extensive set of simulated data for both flexible and rigid multidomain systems was analyzed and modeled using standard protocols. This study clearly shows that SAXS profiles obtained from highly flexible proteins can be wrongly interpreted as arising from a rigid structure. In this context, it would be important to identify features from the SAXS data or from the derived structural models that indicate interdomain motions to differentiate between these two scenarios. Features of SAXS data that identify flexible proteins are: (1) general attenuation of fine structure in the scattering profiles, which becomes more dramatic in Kratky representations, and (2) a reduced number of interdomain correlation peaks in p(r) functions that also present large D _max values and a smooth decrease to 0. When modeling this dynamically averaged SAXS data, the structures obtained present characteristic trends: (1) ab initio models display a decrease in resolution, and (2) rigid-body models present highly extended conformations with a lack of interdomain contacts. The ensemble optimization method represents an excellent strategy to identify interdomain motions unambiguously. This study provides information that should help researchers to select the best modeling strategy for the structural interpretation of SAS experiments of multidomain proteins.     

Novel computational biology methods and their applications to drug discovery

Computational biology methods are now firmly entrenched in the drug discovery process. These methods focus on modeling and simulations of biological systems to complement and direct conventional experimental approaches. Two important branches of computational biology include protein homology modeling and the computational biophysics method of molecular dynamics. Protein modeling methods attempt to accurately predict three-dimensional (3D) structures of uncrystallized proteins for subsequent structure-based drug design applications. Molecular dynamics methods aim to elucidate the molecular motions of the static representations of crystallized protein structures. In this review we highlight recent novel methodologies in the field of homology modeling and molecular dynamics. Selected drug discovery applications using these methods conclude the review.     

Integrative Structural Biology in the Era of Accurate Structure Prediction

Characterizing the three-dimensional structure of macromolecules is central to understanding their function. Traditionally, structures of proteins and their complexes have been determined using experimental techniques such as X-ray crystallography, NMR, or cryo-electron microscopy—applied individually or in an integrative manner. Meanwhile, however, computational methods for protein structure prediction have been improving their accuracy, gradually, then suddenly, with the breakthrough advance by AlphaFold2, whose models of monomeric proteins are often as accurate as experimental structures. This breakthrough foreshadows a new era of computational methods that can build accurate models for most monomeric proteins. Here, we envision how such accurate modeling methods can combine with experimental structural biology techniques, enhancing integrative structural biology. We highlight the challenges that arise when considering multiple structural conformations, protein complexes, and polymorphic assemblies. These challenges will motivate further developments, both in modeling programs and in methods to solve experimental structures, towards better and quicker investigation of structure–function relationships.     

SAXSDom: Modeling multidomain protein structures using small-angle X-ray scattering data

Many proteins are composed of several domains that pack together into a complex tertiary structure. Multidomain proteins can be challenging for protein structure modeling, particularly those for which templates can be found for individual domains but not for the entire sequence. In such cases, homology modeling can generate high quality models of the domains but not for the orientations between domains. Small-angle X-ray scattering (SAXS) reports the structural properties of entire proteins and has the potential for guiding homology modeling of multidomain proteins. In this article, we describe a novel multidomain protein assembly modeling method, SAXSDom that integrates experimental knowledge from SAXS with probabilistic Input-Output Hidden Markov model to assemble the structures of individual domains together. Four SAXS-based scoring functions were developed and tested, and the method was evaluated on multidomain proteins from two public datasets. Incorporation of SAXS information improved the accuracy of domain assembly for 40 out of 46 critical assessment of protein structure prediction multidomain protein targets and 45 out of 73 multidomain protein targets from the ab initio domain assembly dataset. The results demonstrate that SAXS data can provide useful information to improve the accuracy of domain-domain assembly. The source code and tool packages are available at https://github.com/jianlin-cheng/SAXSDom .     

Recognition of remotely related structural homologues using sequence profiles of aligned homologous protein structures

In order to bridge the gap between proteins with three-dimensional (3-D) structural information and those without 3-D structures, extensive experimental and computational efforts for structure recognition are being invested. One of the rapid and simple computational approaches for structure recognition makes use of sequence profiles with sensitive profile matching procedures to identify remotely related homologous families. While adopting this approach we used profiles that are generated from structure-based sequence alignment of homologous protein domains of known structures integrated with sequence homologues. We present an assessment of this fast and simple approach. About one year ago, using this approach, we had identified structural homologues for 315 sequence families, which were not known to have any 3-D structural information. The subsequent experimental structure determination for at least one of the members in 110 of 315 sequence families allowed a retrospective assessment of the correctness of structure recognition. We demonstrate that correct folds are detected with an accuracy of 96.4% (106/110). Most (81/106) of the associations are made correctly to the specific structural family. For 23/106, the structure associations are valid at the superfamily level. Thus, profiles of protein families of known structure when used with sensitive profile-based search procedure result in structure association of high confidence. Further assignment at the level of superfamily or family would provide clues to probable functions of new proteins. Importantly, the public availability of these profiles from us could enable one to perform genome wide structure assignment in a local machine in a fast and accurate manner.     

Recent developments in structural proteomics for protein structure determination

The major challenges in structural proteomics include identifying all the proteins on the genome-wide scale, determining their structure-function relationships, and outlining the precise three-dimensional structures of the proteins. Protein structures are typically determined by experimental approaches such as X-ray crystallography or nuclear magnetic resonance (NMR) spectroscopy. However, the knowledge of three-dimensional space by these techniques is still limited. Thus, computational methods such as comparative and de novo approaches and molecular dynamic simulations are intensively used as alternative tools to predict the three-dimensional structures and dynamic behavior of proteins. This review summarizes recent developments in structural proteomics for protein structure determination; including instrumental methods such as X-ray crystallography and NMR spectroscopy, and computational methods such as comparative and de novo structure prediction and molecular dynamics simulations.     

Recent breakthroughs in computational structural biology harnessing the power of sequences and structures

Recent advances in computational approaches and their integration into structural biology enable tackling increasingly complex questions. Here, we discuss several key areas, highlighting breakthroughs and remaining challenges. Theoretical modeling has provided tools to accurately predict and design protein structures on a scale currently difficult to achieve using experimental approaches. Molecular Dynamics simulations have become faster and more precise, delivering actionable information inaccessible by current experimental methods. Virtual screening workflows allow a high-throughput approach to discover ligands that bind and modulate protein function, while Machine Learning methods enable the design of proteins with new functionalities. Integrative structural biology combines several of these approaches, pushing the frontiers of structural and functional characterization to ever larger systems, advancing towards a complete understanding of the living cell. These breakthroughs will accelerate and significantly impact diverse areas of science.     

Structure- and sequence-based function prediction for non-homologous proteins

The structural genomics projects have been accumulating an increasing number of protein structures, many of which remain functionally unknown. In parallel effort to experimental methods, computational methods are expected to make a significant contribution for functional elucidation of such proteins. However, conventional computational methods that transfer functions from homologous proteins do not help much for these uncharacterized protein structures because they do not have apparent structural or sequence similarity with the known proteins. Here, we briefly review two avenues of computational function prediction methods, i.e. structure-based methods and sequence-based methods. The focus is on our recent developments of local structure-based and sequence-based methods, which can effectively extract function information from distantly related proteins. Two structure-based methods, Pocket-Surfer and Patch-Surfer, identify similar known ligand binding sites for pocket regions in a query protein without using global protein fold similarity information. Two sequence-based methods, protein function prediction and extended similarity group, make use of weakly similar sequences that are conventionally discarded in homology based function annotation. Combined together with experimental methods we hope that computational methods will make leading contribution in functional elucidation of the protein structures.     

Continuum electrostatic methods applied to pH-dependent properties of antibody-antigen association

Protein association events are a critical component of the functioning of biological systems. Antibody/antigen association, which involves extraordinarily specific interactions, has been a paradigm for the study of structural factors and intermolecular forces controlling protein-protein association. As new experimental approaches to the study of antibody/antigen affinity have become routine, and as more structures of complexes of antibodies and their antigens have become available, it has become possible to use computational approaches to study these interactions. Electrostatic interactions are known to play an important role in protein complex formation. In this review, we focus on the use of continuum electrostatic methods to compute pH-dependent properties of proteins and discuss the use of these methods in the study of antibody/antigen complexes.     

Determination of protein oligomeric structure from small‐angle X‐ray scattering

Small‐angle X‐ray scattering (SAXS) is useful for determining the oligomeric states and quaternary structures of proteins in solution. The average molecular mass in solution can be calculated directly from a single SAXS curve collected on an arbitrary scale from a sample of unknown protein concentration without the need for beamline calibration or protein standards. The quaternary structure in solution can be deduced by comparing the experimental SAXS curve to theoretical curves calculated from proposed models of the oligomer. This approach is especially robust when the crystal structure of the target protein is known, and the candidate oligomer models are derived from the crystal lattice. When SAXS data are obtained at multiple protein concentrations, this analysis can provide insight into dynamic self‐association equilibria. Herein, we summarize the computational methods that are used to determine protein molecular mass and quaternary structure from SAXS data. These methods are organized into a workflow and demonstrated with four case studies using experimental SAXS data from the published literature.