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 .     

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.     

Global rigid body modeling of macromolecular complexes against small-angle scattering data

New methods to automatically build models of macromolecular complexes from high-resolution structures or homology models of their subunits or domains against x-ray or neutron small-angle scattering data are presented. Depending on the complexity of the object, different approaches are employed for the global search of the optimum configuration of subunits fitting the experimental data. An exhaustive grid search is used for hetero- and homodimeric particles and for symmetric oligomers formed by identical subunits. For the assemblies or multidomain proteins containing more then one subunit/domain per asymmetric unit, heuristic algorithms based on simulated annealing are used. Fast computational algorithms based on spherical harmonics representation of scattering amplitudes are employed. The methods allow one to construct interconnected models without steric clashes, to account for the particle symmetry and to incorporate information from other methods, on distances between specific residues or nucleotides. For multidomain proteins, addition of missing linkers between the domains is possible. Simultaneous fitting of multiple scattering patterns from subcomplexes or deletion mutants is incorporated. The efficiency of the methods is illustrated by their application to complexes of different types in several simulated and practical examples. Limitations and possible ambiguity of rigid body modeling are discussed and simplified docking criteria are provided to rank multiple models. The methods described are implemented in publicly available computer programs running on major hardware platforms.     

Macromolecular docking restrained by a small angle X-ray scattering profile

While many structures of single protein components are becoming available, structural characterization of their complexes remains challenging. Methods for modeling assembly structures from individual components frequently suffer from large errors, due to protein flexibility and inaccurate scoring functions. However, when additional information is available, it may be possible to reduce the errors and compute near-native complex structures. One such type of information is a small angle X-ray scattering (SAXS) profile that can be collected in a high-throughput fashion from a small amount of sample in solution. Here, we present an efficient method for protein–protein docking with a SAXS profile (FoXSDock): generation of complex models by rigid global docking with PatchDock, filtering of the models based on the SAXS profile, clustering of the models, and refining the interface by flexible docking with FireDock. FoXSDock is benchmarked on 124 protein complexes with simulated SAXS profiles, as well as on 6 complexes with experimentally determined SAXS profiles. When induced fit is less than 1.5 Å interface C_α RMSD and the fraction residues of missing from the component structures is less than 3%, FoXSDock can find a model close to the native structure within the top 10 predictions in 77% of the cases; in comparison, docking alone succeeds in only 34% of the cases. Thus, the integrative approach significantly improves on molecular docking alone. The improvement arises from an increased resolution of rigid docking sampling and more accurate scoring.     

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.     

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.     

Determination of the Individual Roles of the Linker Residues in the Interdomain Motions of Calmodulin Using NMR Chemical Shifts

Many protein molecules are formed by two or more domains whose structures and dynamics are closely related to their biological functions. It is thus important to develop methods to determine the structural properties of these multidomain proteins. Here, we characterize the interdomain motions in the calcium-bound state of calmodulin (Ca^2 +-CaM) using NMR chemical shifts as replica-averaged structural restraints in molecular dynamics simulations. We find that the conformational fluctuations of the interdomain linker, which are largely responsible for the overall interdomain motions of CaM, can be well described by exploiting the information provided by chemical shifts. We thus identify 10 residues in the interdomain linker region that change their conformations upon substrate binding. Five of these residues (Met76, Lys77, Thr79, Asp80 and Ser81) are highly flexible and cover the range of conformations observed in the substrate-bound state, while the remaining five (Arg74, Lys75, Asp78, Glu82 and Glu83) are much more rigid and do not populate conformations typical of the substrate-bound form. The ensemble of conformations representing the Ca^2 +-CaM state obtained in this study is in good agreement with residual dipolar coupling, paramagnetic resonance enhancement, small-angle X-ray scattering and fluorescence resonance energy transfer measurements, which were not used as restraints in the calculations. These results provide initial evidence that chemical shifts can be used to characterize the conformational fluctuations of multidomain proteins.     

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.     

Integrating NMR,SAXS, and Atomistic Simulations: Structure and Dynamics of a Two-Domain Protein

Multidomain proteins with two or more independently folded functional domains are prevalent in nature. Whereas most multidomain proteins are linked linearly in sequence, roughly one-tenth possess domain insertions where a guest domain is implanted into a loop of a host domain, such that the two domains are connected by a pair of interdomain linkers. Here, we characterized the influence of the interdomain linkers on the structure and dynamics of a domain-insertion protein in which the guest LysM domain is inserted into a central loop of the host CVNH domain. Expanding upon our previous crystallographic and NMR studies, we applied SAXS in combination with NMR paramagnetic relaxation enhancement to construct a structural model of the overall two-domain system. Although the two domains have no fixed relative orientation, certain orientations were found to be preferred over others. We also assessed the accuracies of molecular mechanics force fields in modeling the structure and dynamics of tethered multidomain proteins by integrating our experimental results with microsecond-scale atomistic molecular dynamics simulations. In particular, our evaluation of two different combinations of the latest force fields and water models revealed that both combinations accurately reproduce certain structural and dynamical properties, but are inaccurate for others. Overall, our study illustrates the value of integrating experimental NMR and SAXS studies with long timescale atomistic simulations for characterizing structural ensembles of flexibly linked multidomain systems.     

Integrative modeling of protein-protein interactions with pyDock for the new docking challenges

The seventh CAPRI edition imposed new challenges to the modeling of protein-protein complexes, such as multimeric oligomerization, protein-peptide, and protein-oligosaccharide interactions. Many of the proposed targets needed the efficient integration of rigid-body docking, template-based modeling, flexible optimization, multiparametric scoring, and experimental restraints. This was especially relevant for the multimolecular assemblies proposed in the CASP12-CAPRI37 and CASP13-CAPRI46 joint rounds, which were described and evaluated elsewhere. Focusing on the purely CAPRI targets of this edition (rounds 38-45), we have participated in all 17 assessed targets (considering heteromeric and homomeric interfaces in T125 as two separate targets) both as predictors and as scorers, by using integrative modeling based on our docking and scoring approaches: pyDock, IRaPPA, and LightDock. In the protein-protein and protein-peptide targets, we have also participated with our webserver (pyDockWeb). On these 17 CAPRI targets, we submitted acceptable models (or better) within our top 10 models for 10 targets as predictors, 13 targets as scorers, and 4 targets as servers. In summary, our participation in this CAPRI edition confirmed the capabilities of pyDock for the scoring of docking models, increasingly used within the context of integrative modeling of protein interactions and multimeric assemblies.     

Low-resolution structures of proteins in solution retrieved from X-ray scattering with a genetic algorithm.

Small-angle x-ray solution scattering (SAXS) is analyzed with a new method to retrieve convergent model structures that fit the scattering profiles. An arbitrary hexagonal packing of several hundred beads containing the problem object is defined. Instead of attempting to compute the Debye formula for all of the possible mass distributions, a genetic algorithm is employed that efficiently searches the configurational space and evolves best-fit bead models. Models from different runs of the algorithm have similar or identical structures. The modeling resolution is increased by reducing the bead radius together with the search space in successive cycles of refinement. The method has been tested with protein SAXS (0.001 < S < 0.06 A(-1)) calculated from x-ray crystal structures, adding noise to the profiles. The models obtained closely approach the volumes and radii of gyration of the known structures, and faithfully reproduce the dimensions and shape of each of them. This includes finding the active site cavity of lysozyme, the bilobed structure of gamma-crystallin, two domains connected by a stalk in betab2-crystallin, and the horseshoe shape of pancreatic ribonuclease inhibitor. The low-resolution solution structure of lysozyme has been directly modeled from its experimental SAXS profile (0.003 < S < 0.03 A(-1)). The model describes lysozyme size and shape to the resolution of the measurement. The method may be applied to other proteins, to the analysis of domain movements, to the comparison of solution and crystal structures, as well as to large macromolecular assemblies.     

A simple genetic algorithm for the optimization of multidomain protein homology models driven by NMR residual dipolar coupling and small angle <Emphasis Type="Italic">X</Emphasis>-ray scattering data

Most proteins comprise several domains and/or participate in functional complexes. Owing to ongoing structural genomic projects, it is likely that it will soon be possible to predict, with reasonable accuracy, the conserved regions of most structural domains. Under these circumstances, it will be important to have methods, based on simple-to-acquire experimental data, that allow to build and refine structures of multi-domain proteins or of protein complexes from homology models of the individual domains/proteins. It has been recently shown that small angle X-ray scattering (SAXS) and NMR residual dipolar coupling (RDC) data can be combined to determine the architecture of such objects when the X-ray structures of the domains are known and can be considered as rigid objects. We developed a simple genetic algorithm to achieve the same goal, but by using homology models of the domains considered as deformable objects. We applied it to two model systems, an S1KH bi-domain of the NusA protein and the γS-crystallin protein. Despite its simplicity our algorithm is able to generate good solutions when driven by SAXS and RDC data.     

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.     

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.     

Ensemble modeling of protein disordered states: Experimental restraint contributions and validation

Disordered states of proteins include the biologically functional intrinsically disordered proteins and the unfolded states of normally folded proteins. In recent years, ensemble‐modeling strategies using various experimental measurements as restraints have emerged as powerful means for structurally characterizing disordered states. However, these methods are still in their infancy compared with the structural determination of folded proteins. Here, we have addressed several issues important to ensemble modeling using our ENSEMBLE methodology. First, we assessed how calculating ensembles containing different numbers of conformers affects their structural properties. We find that larger ensembles have very similar properties to smaller ensembles fit to the same experimental restraints, thus allowing a considerable speed improvement in our calculations. In addition, we analyzed the contributions of different experimental restraints to the structural properties of calculated ensembles, enabling us to make recommendations about the experimental measurements that should be made for optimal ensemble modeling. The effects of different restraints, most significantly from chemical shifts, paramagnetic relaxation enhancements and small‐angle X‐ray scattering, but also from other data, underscore the importance of utilizing multiple sources of experimental data. Finally, we validate our ENSEMBLE methodology using both cross‐validation and synthetic experimental restraints calculated from simulated ensembles. Our results suggest that secondary structure and molecular size distribution can generally be modeled very accurately, whereas the accuracy of calculated tertiary structure is dependent on the number of distance restraints used. Proteins 2012. © 2011 Wiley Periodicals, Inc.     

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.     

Quaternary structure built from subunits combining NMR and small-angle x-ray scattering data

A new principle in constructing molecular complexes from the known high-resolution domain structures joining data from NMR and small-angle x-ray scattering (SAXS) measurements is described. Structure of calmodulin in complex with trifluoperazine was built from N- and C-terminal domains oriented based on residual dipolar couplings measured by NMR in a dilute liquid crystal, and the overall shape of the complex was derived from SAXS data. The residual dipolar coupling data serves to reduce angular degrees of freedom, and the small-angle scattering data serves to confine the translational degrees of freedom. The complex built by this method was found to be consistent with the known crystal structure. The study demonstrates how approximate tertiary structures of modular proteins or quaternary structures composed of subunits can be assembled from high-resolution structures of domains or subunits using mutually complementary NMR and SAXS data.     

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.     

Accurate SAXS Profile Computation and its Assessment by Contrast Variation Experiments

A major challenge in structural biology is to characterize structures of proteins and their assemblies in solution. At low resolution, such a characterization may be achieved by small angle x-ray scattering (SAXS). Because SAXS analyses often require comparing profiles calculated from many atomic models against those determined by experiment, rapid and accurate profile computation from molecular structures is needed. We developed fast open-source x-ray scattering (FoXS) for profile computation. To match the experimental profile within the experimental noise, FoXS explicitly computes all interatomic distances and implicitly models the first hydration layer of the molecule. For assessing the accuracy of the modeled hydration layer, we performed contrast variation experiments for glucose isomerase and lysozyme, and found that FoXS can accurately represent density changes of this layer. The hydration layer model was also compared with a SAXS profile calculated for the explicit water molecules in the high-resolution structures of glucose isomerase and lysozyme. We tested FoXS on eleven protein, one DNA, and two RNA structures, revealing superior accuracy and speed versus CRYSOL, AquaSAXS, the Zernike polynomials-based method, and Fast-SAXS-pro. In addition, we demonstrated a significant correlation of the SAXS score with the accuracy of a structural model. Moreover, FoXS utility for analyzing heterogeneous samples was demonstrated for intrinsically flexible XLF-XRCC4 filaments and Ligase III-DNA complex. FoXS is extensively used as a standalone web server as a component of integrative structure determination by programs IMP, Chimera, and BILBOMD, as well as in other applications that require rapidly and accurately calculated SAXS profiles.