BCL::SAXS: GPU accelerated Debye method for computation of small angle X‐ray scattering profiles

Small angle X‐ray scattering (SAXS) is an experimental technique used for structural characterization of macromolecules in solution. Here, we introduce BCL::SAXS—an algorithm designed to replicate SAXS profiles from rigid protein models at different levels of detail. We first show our derivation of BCL::SAXS and compare our results with the experimental scattering profile of hen egg white lysozyme. Using this protein we show how to generate SAXS profiles representing: (1) complete models, (2) models with approximated side chain coordinates, and (3) models with approximated side chain and loop region coordinates. We evaluated the ability of SAXS profiles to identify a correct protein topology from a non‐redundant benchmark set of proteins. We find that complete SAXS profiles can be used to identify the correct protein by receiver operating characteristic (ROC) analysis with an area under the curve (AUC) > 99%. We show how our approximation of loop coordinates between secondary structure elements improves protein recognition by SAχS for protein models without loop regions and side chains. Agreement with SAXS data is a necessary but not sufficient condition for structure determination. We conclude that experimental SAXS data can be used as a filter to exclude protein models with large structural differences from the native. Proteins 2015; 83:1500–1512. © 2015 Wiley Periodicals, Inc.     

Integrative structural modeling with small angle X-ray scattering profiles

Recent technological advances enabled high-throughput collection of Small Angle X-ray Scattering (SAXS) profiles of biological macromolecules. Thus, computational methods for integrating SAXS profiles into structural modeling are needed more than ever. Here, we review specifically the use of SAXS profiles for the structural modeling of proteins, nucleic acids, and their complexes. First, the approaches for computing theoretical SAXS profiles from structures are presented. Second, computational methods for predicting protein structures, dynamics of proteins in solution, and assembly structures are covered. Third, we discuss the use of SAXS profiles in integrative structure modeling approaches that depend simultaneously on several data types.     

Small-angle X-ray scattering constraints and local geometry like secondary structures can construct a coarse-grained protein model at amino acid residue resolution

We have developed a new methodology that determines protein structures using small-angle X-ray scattering (SAXS) data. The current bottlenecks in determining the protein structures require a new strategy using the simple design of an experiment, and SAXS is suitable for this purpose in spite of its low information content. First we demonstrated that SAXS constraints work additively to NMR-derived information in calculating structures. Next, structure calculations for nine proteins taking different folds were performed using the SAXS constraints combined with the NMR-derived distance restraints for local geometry such as secondary structures or those for tertiary structure. The results show that the SAXS constraints complemented the tertiary-structural information for all the proteins, and that accuracy of the structures thus obtained with SAXS constraints and local geometrical restraints ranged from 1.85 to 4.33 Å. Based on these results, we were able to construct a coarse-grained protein model at amino acid residue resolution.     

EFAMIX,a tool to decompose inline chromatography SAXS data from partially overlapping components

Small‐angle X‐ray scattering (SAXS) is an established technique for structural analysis of biological macromolecules in solution. During the last decade, inline chromatography setups coupling SAXS with size exclusion (SEC‐SAXS) or ion exchange (IEC‐SAXS) have become popular in the community. These setups allow one to separate individual components in the sample and to record SAXS data from isolated fractions, which is extremely important for subsequent data interpretation, analysis, and structural modeling. However, in case of partially overlapping elution peaks, inline chromatography SAXS may still yield scattering profiles from mixtures of components. The deconvolution of these scattering data into the individual fractions is nontrivial and potentially ambiguous. We describe a cross‐platform computer program, EFAMIX, for restoring the scattering and concentration profiles of the components based on the evolving factor analysis (EFA). The efficiency of the program is demonstrated in a number of simulated and experimental SEC‐SAXS data sets. Sensitivity and limitations of the method are explored, and its applicability to IEC‐SAXS data is discussed. EFAMIX requires minimal user intervention and is available to academic users through the program package ATSAS as from release 3.1.     

Structural analysis of flexible proteins in solution by small angle X-ray scattering combined with crystallography

In the last few years, SAXS of biological materials has been rapidly evolving and promises to move structural analysis to a new level. Recent innovations in SAXS data analysis allow ab initio shape predictions of proteins in solution. Furthermore, experimental scattering data can be compared to calculated scattering curves from the growing data base of solved structures and also identify aggregation and unfolded proteins. Combining SAXS results with atomic resolution structures enables detailed characterizations in solution of mass, radius, conformations, assembly, and shape changes associated with protein folding and functions. SAXS can efficiently reveal the spatial organization of protein domains, including domains missing from or disordered in known crystal structures, and establish cofactor or substrate-induced conformational changes. For flexible domains or unstructured regions that are not amenable for study by many other structural techniques, SAXS provides a unique technology. Here, we present SAXS shape predictions for PCNA that accurately predict a trimeric ring assembly and for a full-length DNA repair glycosylase with a large unstructured region. These new results in combination with illustrative published data show how SAXS combined with high resolution crystal structures efficiently establishes architectures, assemblies, conformations, and unstructured regions for proteins and protein complexes in solution.     

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.     

Improving small-angle X-ray scattering data for structural analyses of the RNA world

Defining the shape, conformation, or assembly state of an RNA in solution often requires multiple investigative tools ranging from nucleotide analog interference mapping to X-ray crystallography. A key addition to this toolbox is small-angle X-ray scattering (SAXS). SAXS provides direct structural information regarding the size, shape, and flexibility of the particle in solution and has proven powerful for analyses of RNA structures with minimal requirements for sample concentration and volumes. In principle, SAXS can provide reliable data on small and large RNA molecules. In practice, SAXS investigations of RNA samples can show inconsistencies that suggest limitations in the SAXS experimental analyses or problems with the samples. Here, we show through investigations on the SAM-I riboswitch, the Group I intron P4-P6 domain, 30S ribosomal subunit from Sulfolobus solfataricus (30S), brome mosaic virus tRNA-like structure (BMV TLS), Thermotoga maritima asd lysine riboswitch, the recombinant tRNA^val, and yeast tRNA^phe that many problems with SAXS experiments on RNA samples derive from heterogeneity of the folded RNA. Furthermore, we propose and test a general approach to reducing these sample limitations for accurate SAXS analyses of RNA. Together our method and results show that SAXS with synchrotron radiation has great potential to provide accurate RNA shapes, conformations, and assembly states in solution that inform RNA biological functions in fundamental ways.     

Minireview: structural insights into early folding events using continuous-flow time-resolved small-angle X-ray scattering

Small-angle X-ray scattering (SAXS) is a powerful method for obtaining quantitative structural information on the size and shape of proteins, and it is increasingly used in kinetic studies of folding and association reactions. In this minireview, we discuss recent developments in using SAXS to obtain structural information on the unfolded ensemble and early folding intermediates of proteins using continuous-flow mixing devices. Interfacing of these micromachined devices to SAXS beamlines has allowed access to the microsecond time regime. The experimental constraints in implementation of turbulence and laminar flow-based mixers with SAXS detection and a comparison of the two approaches are presented. Current improvements and future prospects of microsecond time-resolved SAXS and the synergy with ab initio structure prediction and molecular dynamics simulations are discussed.     

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.     

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

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

Accurate flexible fitting of high-resolution protein structures to small-angle x-ray scattering data using a coarse-grained model with implicit hydration shell

Small-angle x-ray scattering (SAXS) is a powerful technique widely used to explore conformational states and transitions of biomolecular assemblies in solution. For accurate model reconstruction from SAXS data, one promising approach is to flexibly fit a known high-resolution protein structure to low-resolution SAXS data by computer simulations. This is a highly challenging task due to low information content in SAXS data. To meet this challenge, we have developed what we believe to be a novel method based on a coarse-grained (one-bead-per-residue) protein representation and a modified form of the elastic network model that allows large-scale conformational changes while maintaining pseudobonds and secondary structures. Our method optimizes a pseudoenergy that combines the modified elastic-network model energy with a SAXS-fitting score and a collision energy that penalizes steric collisions. Our method uses what we consider a new implicit hydration shell model that accounts for the contribution of hydration shell to SAXS data accurately without explicitly adding waters to the system. We have rigorously validated our method using five test cases with simulated SAXS data and three test cases with experimental SAXS data. Our method has successfully generated high-quality structural models with root mean-squared deviation of 1 ∼ 3 Å from the target structures.     

Reweighting of molecular simulations with explicit-solvent SAXS restraints elucidates ion-dependent RNA ensembles

Small-angle X-ray scattering (SAXS) experiments are increasingly used to probe RNA structure. A number of forward models that relate measured SAXS intensities and structural features, and that are suitable to model either explicit-solvent effects or solute dynamics, have been proposed in the past years. Here, we introduce an approach that integrates atomistic molecular dynamics simulations and SAXS experiments to reconstruct RNA structural ensembles while simultaneously accounting for both RNA conformational dynamics and explicit-solvent effects. Our protocol exploits SAXS pure-solute forward models and enhanced sampling methods to sample an heterogenous ensemble of structures, with no information towards the experiments provided on-the-fly. The generated structural ensemble is then reweighted through the maximum entropy principle so as to match reference SAXS experimental data at multiple ionic conditions. Importantly, accurate explicit-solvent forward models are used at this reweighting stage. We apply this framework to the GTPase-associated center, a relevant RNA molecule involved in protein translation, in order to elucidate its ion-dependent conformational ensembles. We show that (a) both solvent and dynamics are crucial to reproduce experimental SAXS data and (b) the resulting dynamical ensembles contain an ion-dependent fraction of extended structures.     

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.     

Small angle X-ray scattering studies and modeling of Eudistylia vancouverii chlorocruorin and Macrobdella decora hemoglobin

Annelids possess giant extracellular oxygen carriers that exhibit a hexagonal bilayer appearance and have molecular masses of approximately 3.5 MDa. By small angle x-ray scattering (SAXS), Eudistylia vancouverii chlorocruorin and Macrobdella decora hemoglobin were investigated in solution. On the basis of the experimental SAXS data, three-dimensional models were established in a two-step approach (trial and error and averaging). The main differences between the complexes concern the structure of their central part and the subunit architecture. Usage of our SAXS models as templates for automated model generation (program DAMMIN) led to refined models that fit perfectly the experimental data. Special attention was paid to the inhomogeneous density distribution observed within the complexes. DAMMIN models without a priori information could not reproducibly locate low-density areas. The usage of templates, however, improved the results considerably, in particular by applying electron microscopy-based templates. Biologically relevant information on the presence of low-density areas and hints for their presumable location could be drawn from SAXS and sophisticated modeling approaches. Provided that different models are analyzed carefully, this obviously opens a way to gain additional biologically relevant structural information from SAXS data.     

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.     

A review of multi-domain and flexible molecular chaperones studies by small-angle X-ray scattering

Intrinsic flexibility is closely related to protein function, and a plethora of important regulatory proteins have been found to be flexible, multi-domain or even intrinsically disordered. On the one hand, understanding such systems depends on how these proteins behave in solution. On the other, small-angle X-ray scattering (SAXS) is a technique that fulfills the requirements to study protein structure and dynamics relatively quickly with few experimental limitations. Molecular chaperones from Hsp70 and Hsp90 families are multi-domain proteins containing flexible and/or disordered regions that play central roles in cellular proteostasis. Here, we review the structure and function of these proteins by SAXS. Our general approach includes the use of SAXS data to determine size and shape parameters, as well as protein shape reconstruction and their validation by using accessory biophysical tools. Some remarkable examples are presented that exemplify the potential of the SAXS technique. Protein structure can be determined in solution even at limiting protein concentrations (for example, human mortalin, a mitochondrial Hsp70 chaperone). The protein organization, flexibility and function (for example, the J-protein co-chaperones), oligomeric status, domain organization, and flexibility (for the Hsp90 chaperone and the Hip and Hep1 co-chaperones) may also be determined. Lastly, the shape, structural conservation, and protein dynamics (for the Hsp90 chaperone and both p23 and Aha1 co-chaperones) may be studied by SAXS. We believe this review will enhance the application of the SAXS technique to the study of the molecular chaperones.     

Structural Characterization of Protein-Protein Complexes by Integrating Computational Docking with Small-angle Scattering Data

X-ray crystallography and NMR can provide detailed structural information of protein-protein complexes, but technical problems make their application challenging in the high-throughput regime. Other methods such as small-angle X-ray scattering (SAXS) are more promising for large-scale application, but at the cost of lower resolution, which is a problem that can be solved by complementing SAXS data with theoretical simulations. Here, we propose a novel strategy that combines SAXS data and accurate protein-protein docking simulations. The approach has been benchmarked on a large pool of known structures with synthetic SAXS data, and on three experimental examples. The combined approach (pyDockSAXS) provided a significantly better success rate (43% for the top 10 predictions) than either of the two methods alone. Further analysis of the influence of different docking parameters made it possible to increase the success rates for specific cases, and to define guidelines for improving the data-driven protein-protein docking protocols.     

Small angle X-ray scattering as a complementary tool for high-throughput structural studies

Structural crystallography and nuclear magnetic resonance (NMR) spectroscopy are the predominant techniques for understanding the biological world on a molecular level. Crystallography is constrained by the ability to form a crystal that diffracts well and NMR is constrained to smaller proteins. Although powerful techniques, they leave many soluble, purified structurally uncharacterized protein samples. Small angle X-ray scattering (SAXS) is a solution technique that provides data on the size and multiple conformations of a sample, and can be used to reconstruct a low-resolution molecular envelope of a macromolecule. In this study, SAXS has been used in a high-throughput manner on a subset of 28 proteins, where structural information is available from crystallographic and/or NMR techniques. These crystallographic and NMR structures were used to validate the accuracy of molecular envelopes reconstructed from SAXS data on a statistical level, to compare and highlight complementary structural information that SAXS provides, and to leverage biological information derived by crystallographers and spectroscopists from their structures. All the ab initio molecular envelopes calculated from the SAXS data agree well with the available structural information. SAXS is a powerful albeit low-resolution technique that can provide additional structural information in a high-throughput and complementary manner to improve the functional interpretation of high-resolution structures.     

Time resolved SAXS and RNA folding

Small angle X-ray scattering provides low resolution structural information about macromolecules in solution. When coupled with rapid mixing methods, SAXS reports time-dependent conformational changes of RNA induced by the addition of Mg(2+) to trigger folding. Thus time-resolved SAXS provides unique information about the global or overall structures of transient intermediates populated during folding. Notably, SAXS provides information about the earliest folding events, which can evade detection by other methods.     

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。