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.     

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.     

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.     

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.     

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.     

Direct comparison of the crystal and solution structure of glucose/xylose isomerase from Streptomyces rubiginosus

Glucose isomerase (D-xylose ketol-isomerase, EC 5.3.1.5.) catalyses the isomerization reaction of glucose and xylose. The small angle X-ray scattering (SAXS) data of glucose/xylose isomerase from Streptomyces rubiginosus were recorded for protein solution using synchrotron radiation. The experimental data were compared with theoretical scattering calculated on the basis of the known crystal structure (PDB code: 1OAD). The radius of gyration measured by SAXS (R(G)=3.30 nm) was almost identical and the maximum dimension in the distance distribution function was by about 2.5 % lower than the corresponding values calculated on the basis of the crystal structure.     

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.     

Determining the Locations of Ions and Water around DNA from X-Ray Scattering Measurements

Nucleic acids carry a negative charge, attracting salt ions and water. Interactions with these components of the solvent drive DNA to condense, RNA to fold, and proteins to bind. To understand these biological processes, knowledge of solvent structure around the nucleic acids is critical. Yet, because they are often disordered, ions and water evade detection by x-ray crystallography and other high-resolution methods. Small-angle x-ray scattering (SAXS) is uniquely sensitive to the spatial correlations between solutes and the surrounding solvent. Thus, SAXS provides an experimental constraint to guide or test emerging solvation theories. However, the interpretation of SAXS profiles is nontrivial because of the difficulty in separating the scattering signals of each component: the macromolecule, ions, and hydration water. Here, we demonstrate methods for robustly deconvoluting these signals, facilitating a more straightforward comparison with theory. Using SAXS data collected on an absolute intensity scale for short DNA duplexes in solution with Na⁺, K⁺, Rb⁺, or Cs⁺ counterions, we mathematically decompose the scattering profiles into components (DNA, water, and ions) and validate the decomposition using anomalous scattering measurements. In addition, we generate a library of physically motivated ion atmosphere models and rank them by agreement with the scattering data. The best-fit models have relatively compact ion atmospheres when compared to predictions from the mean-field Poisson-Boltzmann theory of electrostatics. Thus, the x-ray scattering methods presented here provide a valuable measurement of the global structure of the ion atmosphere that can be used to test electrostatics theories that go beyond the mean-field approximation.     

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.     

Derivation of the small-angle x-ray scattering functions for local conformations of polypeptide chains in solution

The small-angle x-ray scattering (SAXS) functions are analytically derived for both the randomly coiled and helical local conformations of a polypeptide chain in solution. The resulting scattering functions for helices of various types are characterized by a maximum in the range of scattering-vector corresponding to Bragg spacings of 3-5 A, whereas the random-coil function has no maximum. This result is compatible with the extant SAXS data for partially neutralized poly(L-glutamic acid) and poly(L-lysine) in aqueous solutions. Comparison of the SAXS data with the calculated scattering functions shows that helical structures in both polypeptide chains are of the 3.6(13)-helix (alpha-helix) rather than 3.0(10)-type.     

Characterization of the solution structure of the M intermediate of photoactive yellow protein using high-angle solution x-ray scattering

It is widely accepted that PYP undergoes global structural changes during the formation of the biologically active intermediate PYP(M). High-angle solution x-ray scattering experiments were performed using PYP variants that lacked the N-terminal 6-, 15-, or 23-amino-acid residues (T6, T15, and T23, respectively) to clarify these structural changes. The scattering profile of the dark state of intact PYP exhibited two broad peaks in the high-angle region (0.3 A(-1) < Q < 0.8 A(-1)). The intensities and positions of the peaks were systematically changed as a result of the N-terminal truncations. These observations and the agreement between the observed scattering profiles and the calculated profiles based on the crystal structure confirm that the high-angle scattering profiles were caused by intramolecular interference and that the structure of the chromophore-binding domain was not affected by the N-terminal truncations. The profiles of the PYP(M) intermediates of the N-terminally truncated PYP variants were significantly different from the profiles of the dark states of these proteins, indicating that substantial conformational rearrangements occur within the chromophore-binding domain during the formation of PYP(M). By use of molecular fluctuation analysis, structural models of the chromophore-binding region of PYP(M) were constructed to reproduce the observed profile of T23. The structure obtained by averaging 51 potential models revealed the displacement of the loop connecting beta4 and beta5, and the deformation of the alpha4 helix. High-angle x-ray scattering with molecular fluctuation simulation allows us to derive the structural properties of the transient state of a protein in solution.     

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.     

On the interpretation and prediction of X-ray scattering profiles of biomolecules in solution

If solution scattering curves can be accurately predicted from structural models, measurements can provide useful tests of predictions of secondary and tertiary structure. We have developed a computational technique for the prediction and interpretation of x-ray scattering profiles of biomolecules in solution. The method employs a Monte Carlo procedure for the generation of length distribution functions and provides predictions to moderate resolution (～5 Å). In addition to facilitating the assignment and interpretation of features in a solution scattering profile, the method also allows the elucidation of the role of protein motion in shaping the final scattering curve. The effect of protein motion on a scattering profile is investigated by generating scattering curves from several consecutive 0.147 ps atomic coordinate frames from a molecular dynamics simulation of the motion of bovine pancreatic trypsin inhibitor (BPTI) [McCammon, J. A. & Karplus, M. (1980) Annu. Rev. Phys. Chem. 31 , 29–45]. The theoretical approach is applied to chicken egg white lysozyme and BPTI, and the overall features in the resulting theoretical scattering profiles match well with the experimental solution scattering curves recorded on film. It is apparent from this study that the scattering profile prediction technique in conjunction with other experimental methods may have value in testing ideas of conformational change based on crystallographic studies; investigations of this type would include a comparison of predicted scattering curves generated from a variety of crystallographic models with an actual scattering profile of the biomolecule in solution.     

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.     

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 Oxidation on the Structure of Human Low- and High-Density Lipoproteins

This work presents a controlled study of low-density lipoprotein (LDL) and high-density lipoprotein (HDL) structural changes due to in vitro oxidation with copper ions. The changes were studied by small-angle x-ray scattering (SAXS) and dynamic light scattering (DLS) techniques in the case of LDL and by SAXS, DLS, and Z-scan (ZS) techniques in the case of HDL. SAXS data were analyzed with a to our knowledge new deconvolution method. This method provides the electron density profile of the samples directly from the intensity scattering of the monomers. Results show that LDL particles oxidized for 18 h show significant structural changes when compared to nonoxidized particles. Changes were observed in the electrical density profile, in size polydispersity, and in the degree of flexibility of the APO-B protein on the particle. HDL optical results obtained with the ZS technique showed a decrease of the amplitude of the nonlinear optical signal as a function of oxidation time. In contrast to LDL results reported in the literature, the HDL ZS signal does not lead to a complete loss of nonlinear optical signal after 18 h of copper oxidation. Also, the SAXS results did not indicate significant structural changes due to oxidation of HDL particles, and DLS results showed that a small number of oligomers formed in the sample oxidized for 18 h. All experimental results for the HDL samples indicate that this lipoprotein is more resistant to the oxidation process than are LDL particles.     

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.     

An improved model for analyzing the small angle x-ray scattering of starch granules

The structure of starch was studied using small-angle x-ray scattering (SAXS). The scattering data was modeled by considering a finite stack of alternating lamellae that are allowed to fluctuate both along the layer repeat direction and along the transverse layer direction. Analysis in this way of the SAXS data from starch allowed fresh insights into the native structure of several starch species, particularly potato starch. The novel model presented in this work was able to capture the experimentally observed SAXS patterns much better than previous models, which did not incorporate transverse layer fluctuations.     

Equilibrium fluctuations in myoglobin and lysozyme

The angular dependencies of inelastic intensities of Rayleigh scattering of Moessbauer radiation were measured for myoglobin and lysozyme (in the hydration range h = 0.05-0.7). The data were fitted within the framework of model, when two types of intraglobular motions were taken into account: individual motions of small side-chain groups and cooperative motions of segments. The best agreement with the experiment at h > 0.05 was obtained when individual motions of small groups together with the cooperative motions of alpha-helices and beta-sheets for lysozyme, and alpha-helices for myoglobin were considered. At further hydration (h = 0.45), mean-square displacements (x2) of both types of motions strongly increase with the increase in hydration degree, while the motions with a large correlation radius (not less than macromolecule radius) remain nearly the same as for h = 0.05. The results of the study of the radial distribution function deduced by Fourier-transform from the diffuse x-ray measurements together with RSMR data allow one to conclude that the water during protein hydration competes with the intramolecular hydrogen bonds, loosens the protein and increases the internal dynamics. Concurrently, water arranges the ordering of macromolecule, which takes the native structure at h = 0.4-0.7. The analysis of auto and cross-correlation functions of bending fluctuations of alpha-helices in the large domain of lysozyme performed by molecular dynamics allows one to come to the final conclusion that it is the difference in the structural organization of myoglobin and lysozyme and not the presence of SS-bonds in lysozyme macromolecule that is responsible for different structural fluctuations in these proteins.     

UCSF Chimera, MODELLER, and IMP: an integrated modeling system

Structural modeling of macromolecular complexes greatly benefits from interactive visualization capabilities. Here we present the integration of several modeling tools into UCSF Chimera. These include comparative modeling by MODELLER, simultaneous fitting of multiple components into electron microscopy density maps by IMP MultiFit, computing of small-angle X-ray scattering profiles and fitting of the corresponding experimental profile by IMP FoXS, and assessment of amino acid sidechain conformations based on rotamer probabilities and local interactions by Chimera.