A rapid coarse residue-based computational method for x-ray solution scattering characterization of protein folds and multiple conformational states of large protein complexes

MARTINI bead form factors for the analysis of time-resolved X-ray scattering of proteins

Time-resolved small- and wide-angle X-ray scattering (SAXS and WAXS) methods probe the structural dynamics of proteins in solution. Although technologically advanced, these methods are in many cases limited by data interpretation. The calculation of X-ray scattering profiles is computationally demanding and poses a bottleneck for all SAXS/WAXS-assisted structural refinement and, in particular, for the analysis of time-resolved data. A way of speeding up these calculations is to represent biomolecules as collections of coarse-grained scatterers. Here, such coarse-graining schemes are presented and discussed and their accuracies examined. It is demonstrated that scattering factors coincident with the popular MARTINI coarse-graining scheme produce reliable difference scattering in the range 0 < q < 0.75 Å-1. The findings are promising for future attempts at X-ray scattering data analysis, and may help to bridge the gap between time-resolved experiments and their interpretation.

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.

Two practical Java software tools for small-angle X-ray scattering analysis of biomolecules

Small-angle X-ray scattering has established itself as a common technique in structural biology research. Here, two novel Java applications to aid modelling of three-dimensional macromolecular structures based on small-angle scattering data are described.MolScatis an application that computes small-angle scattering intensities from user-provided three-dimensional models. The program can fit the theoretical scattering intensities to experimental X-ray scattering data.SAFIRis a program for interactive rigid-body modelling into low-resolution shapes restored from small-angle scattering data. The program has been designed with an emphasis on ease of use and intuitive handling. An embedded version ofMolScatis used to enable quick evaluation of the fit between the model and experimental scattering data.SAFIRalso provides options to refine macromolecular complexes with optional user-specified restraints against scattering data by means of a Monte Carlo approach.

Protein conformational populations and functionally relevant substates

Functioning proteins do not remain fixed in a unique structure, but instead they sample a range of conformations facilitated by motions within the protein. Even in the native state, a protein exists as a collection of interconverting conformations driven by thermodynamic fluctuations. Motions on the fast time scale allow a protein to sample conformations in the nearby area of its conformational landscape, while motions on slower time scales give it access to conformations in distal areas of the landscape. Emerging evidence indicates that protein landscapes contain conformational substates with dynamic and structural features that support the designated function of the protein. Nuclear magnetic resonance (NMR) experiments provide information about conformational ensembles of proteins. X-ray crystallography allows researchers to identify the most populated states along the landscape, and computational simulations give atom-level information about the conformational substates of different proteins. This ability to characterize and obtain quantitative information about the conformational substates and the populations of proteins within them is allowing researchers to better understand the relationship between protein structure and dynamics and the mechanisms of protein function. In this Account, we discuss recent developments and challenges in the characterization of functionally relevant conformational populations and substates of proteins. In some enzymes, the sampling of functionally relevant conformational substates is connected to promoting the overall mechanism of catalysis. For example, the conformational landscape of the enzyme dihydrofolate reductase has multiple substates, which facilitate the binding and the release of the cofactor and substrate and catalyze the hydride transfer. For the enzyme cyclophilin A, computational simulations reveal that the long time scale conformational fluctuations enable the enzyme to access conformational substates that allow it to attain the transition state, therefore promoting the reaction mechanism. In the long term, this emerging view of proteins with conformational substates has broad implications for improving our understanding of enzymes, enzyme engineering, and better drug design. Researchers have already used photoactivation to modulate protein conformations as a strategy to develop a hypercatalytic enzyme. In addition, the alteration of the conformational substates through binding of ligands at locations other than the active site provides the basis for the design of new medicines through allosteric modulation.

Rapid and accurate calculation of small-angle scattering profiles using the golden ratio

Calculating the scattering intensity of anN-atom system is a numerically exhaustingO(N2) task. A simple approximation technique that scales linearly with the number of atoms is presented. Using an exact expression for the scattering intensityI(q) at a given wavevectorq, the rotationally averaged intensityI(q) is computed by evaluatingI(q) in several scattering directions. The orientations of theqvectors are taken from a quasi-uniform spherical grid generated by the golden ratio. Using various biomolecules as examples, this technique is compared with an established multipole expansion method. For a given level of speed, the technique is more accurate than the multipole expansion for anisotropically shaped molecules, while comparable in accuracy for globular shapes. The processing time scales sub-linearly inNwhen the atoms are identical and lie on a lattice. The procedure is easily implemented and should accelerate the analysis of small-angle scattering data.

Fast-SAXS-pro: a unified approach to computing SAXS profiles of DNA, RNA, protein, and their complexes

A generalized method, termed Fast-SAXS-pro, for computing small angle x-ray scattering (SAXS) profiles of proteins, nucleic acids, and their complexes is presented. First, effective coarse-grained structure factors of DNA nucleotides are derived using a simplified two-particle-per-nucleotide representation. Second, SAXS data of a 18-bp double-stranded DNA are measured and used for the calibration of the scattering contribution from excess electron density in the DNA solvation layer. Additional test on a 25-bp DNA duplex validates this SAXS computational method and suggests that DNA has a different contribution from its hydration surface to the total scattering compared to RNA and protein. To account for such a difference, a sigmoidal function is implemented for the treatment of non-uniform electron density across the surface of a protein/nucleic-acid complex. This treatment allows differential scattering from the solvation layer surrounding protein/nucleic-acid complexes. Finally, the applications of this Fast-SAXS-pro method are demonstrated for protein/DNA and protein/RNA complexes.

Atomic-resolution structural information from scattering experiments on macromolecules in solution

The pair-distance distribution function (PDDF) contains all structural information probed in an elastic scattering experiment of macromolecular solutions. However, in small-angle x-ray scattering (SAXS) or small-angle neutron scattering (SANS) experiments only their Fourier transform is measured over a restricted range of scattering angles. We therefore developed a mathematically simple and computationally efficient method to calculate the PDDFs as well as accurate scattering intensities from molecular dynamics simulations. The calculated solution scattering intensities are in excellent agreement with SAXS and wide-angle x-ray scattering (WAXS) experiments for a series of proteins. The corresponding PDDFs are remarkably rich in features reporting on the detailed protein structure. Using an inverse Fourier transform method, most of these features can be recovered if scattering intensities are measured up to a momentum transfer of q≈2-3Å(-1). Our results establish that high-precision solution scattering experiments utilizing x-ray free-electron lasers and third generation synchrotron sources can resolve subnanometer structural detail, well beyond size, shape, and fold.

Assembling a xylanase-lichenase chimera through all-atom molecular dynamics simulations

Multifunctional enzyme engineering can improve enzyme cocktails for emerging biofuel technology. Molecular dynamics through structure-based models (SB) is an effective tool for assessing the tridimensional arrangement of chimeric enzymes as well as for inferring the functional practicability before experimental validation. This study describes the computational design of a bifunctional xylanase-lichenase chimera (XylLich) using the xynA and bglS genes from Bacillus subtilis. In silico analysis of the average solvent accessible surface area (SAS) and the root mean square fluctuation (RMSF) predicted a fully functional chimera, with minor fluctuations and variations along the polypeptide chains. Afterwards, the chimeric enzyme was built by fusing the xynA and bglS genes. XylLich was evaluated through small-angle X-ray scattering (SAXS) experiments, resulting in scattering curves with a very accurate fit to the theoretical protein model. The chimera preserved the biochemical characteristics of the parental enzymes, with the exception of a slight variation in the temperature of operation and the catalytic efficiency (kcat/Km). The absence of substantial shifts in the catalytic mode of operation was also verified. Furthermore, the production of chimeric enzymes could be more profitable than producing a single enzyme separately, based on comparing the recombinant protein production yield and the hydrolytic activity achieved for XylLich with that of the parental enzymes.

Allosteric activation transitions in enzymes and biomolecular motors: insights from atomistic and coarse-grained simulations

The chemical step in enzymes is usually preceded by a kinetically distinct activation step that involves large-scale conformational transitions. In "simple" enzymes this step corresponds to the closure of the active site; in more complex enzymes, such as biomolecular motors, the activation step is more complex and may involve interactions with other biomolecules. These activation transitions are essential to the function of enzymes and perturbations in the scale and/or rate of these transitions are implicated in various serious human diseases; incorporating key flexibilities into engineered enzymes is also considered a major remaining challenge in rational enzyme design. Therefore it is important to understand the underlying mechanism of these transitions. This is a significant challenge to both experimental and computational studies because of the allosteric and multi-scale nature of such transitions. Using our recent studies of two enzyme systems, myosin and adenylate kinase (AK), we discuss how atomistic and coarse-grained simulations can be used to provide insights into the mechanism of activation transitions in realistic systems. Collectively, the results suggest that although many allosteric transitions can be viewed as domain displacements mediated by flexible hinges, there are additional complexities and various deviations. For example, although our studies do not find any evidence for "cracking" in AK, our results do underline the contribution of intra-domain properties (e.g., dihedral flexibility) to the rate of the transition. The study of mechanochemical coupling in myosin highlights that local changes important to chemistry require stabilization from more extensive structural changes; in this sense, more global structural transitions are needed to activate the chemistry in the active site. These discussions further emphasize the importance of better understanding factors that control the degree of co-operativity for allosteric transitions, again hinting at the intimate connection between protein stability and functional flexibility. Finally, a number of topics of considerable future interest are briefly discussed.

Sample preparation, data collection, and preliminary data analysis in biomolecular solution X-ray scattering

In addition to the classic methods of structural biology--X-ray crystallography and NMR--solution X-ray scattering (SAXS) is playing an increasingly important role in structural investigation of biological macromolecules. However, the simultaneous ease of SAXS data collection and sophistication of its data analysis tools can present challenges to the investigator. Any sample, whether pure or contaminated, whether monodisperse or polydisperse, will yield scattering data, and it is up to the user to ensure the absence of artifacts and to choose a proper structural modeling strategy. This unit discusses experimental aspects of X-ray solution scattering, including sample preparation and data collection, as well as the steps in data processing and preliminary analysis required to ensure the absence of artifacts. The goal is to summarize everything than can go wrong with SAXS data measurement so the user can have confidence in the data before undertaking structural modeling.

A hierarchical algorithm for fast Debye summation with applications to small angle scattering

Debye summation, which involves the summation of sinc functions of distances between all pair of atoms in three-dimensional space, arises in computations performed in crystallography, small/wide angle X-ray scattering (SAXS/WAXS), and small angle neutron scattering (SANS). Direct evaluation of Debye summation has quadratic complexity, which results in computational bottleneck when determining crystal properties, or running structure refinement protocols that involve SAXS or SANS, even for moderately sized molecules. We present a fast approximation algorithm that efficiently computes the summation to any prescribed accuracy ε in linear time. The algorithm is similar to the fast multipole method (FMM), and is based on a hierarchical spatial decomposition of the molecule coupled with local harmonic expansions and translation of these expansions. An even more efficient implementation is possible when the scattering profile is all that is required, as in small angle scattering reconstruction (SAS) of macromolecules. We examine the relationship of the proposed algorithm to existing approximate methods for profile computations, and show that these methods may result in inaccurate profile computations, unless an error-bound derived in this article is used. Our theoretical and computational results show orders of magnitude improvement in computation complexity over existing methods, while maintaining prescribed accuracy.

Substrate-specific reorganization of the conformational ensemble of CSK implicates novel modes of kinase function

Protein kinases use ATP as a phosphoryl donor for the posttranslational modification of signaling targets. It is generally thought that the binding of this nucleotide induces conformational changes leading to closed, more compact forms of the kinase domain that ideally orient active-site residues for efficient catalysis. The kinase domain is oftentimes flanked by additional ligand binding domains that up- or down-regulate catalytic function. C-terminal Src kinase (Csk) is a multidomain tyrosine kinase that is up-regulated by N-terminal SH2 and SH3 domains. Although the X-ray structure of Csk suggests the enzyme is compact, X-ray scattering studies indicate that the enzyme possesses both compact and open conformational forms in solution. Here, we investigated whether interactions with the ATP analog AMP-PNP and ADP can shift the conformational ensemble of Csk in solution using a combination of small angle x-ray scattering and molecular dynamics simulations. We find that binding of AMP-PNP shifts the ensemble towards more extended rather than more compact conformations. Binding of ADP further shifts the ensemble towards extended conformations, including highly extended conformations not adopted by the apo protein, nor by the AMP-PNP bound protein. These ensembles indicate that any compaction of the kinase domain induced by nucleotide binding does not extend to the overall multi-domain architecture. Instead, assembly of an ATP-bound kinase domain generates further extended forms of Csk that may have relevance for kinase scaffolding and Src regulation in the cell.

The Src protein kinases are integral members of numerous signaling pathways involved in cellular growth and differentiation. The master regulator of the Src family is the protein kinase Csk, which adds a phosphate to the C-terminal tail, inhibiting Src Kinase function. Proper regulation of these signaling pathways by Csk is essential as unregulated activity in these pathways is correlated with the development of various cancers and autoimmune diseases. Understanding the nature of the mechanism and structure of Csk may lead to therapeutics and a better understanding of Src signaling pathways. Conformational changes associated with nucleotide binding and release have been shown to regulate the efficiency of Src down-regulation by Csk. To obtain insights into the nature of these nucleotide-induced structural changes, we examined the conformation of Csk in solution while bound to the ATP analog AMP-PNP and product ADP using a combination of small angle x-ray scattering and molecular dynamics. Surprisingly, both nucleotides induce extended conformations of Csk compared to the apo-enzyme, suggesting a novel mode of function. Further understanding of this mode of function may aid in the design of cancer therapeutics that act by regulating Src signaling pathways by modulating the function of Csk.

How random are intrinsically disordered proteins? A small angle scattering perspective

While the crucial role of intrinsically disordered proteins (IDPs) in the cell cycle is now recognized, deciphering their molecular mode of action at the structural level still remains highly challenging and requires a combination of many biophysical approaches. Among them, small angle X-ray scattering (SAXS) has been extremely successful in the last decade and has become an indispensable technique for addressing many of the fundamental questions regarding the activities of IDPs. After introducing some experimental issues specific to IDPs and in relation to the latest technical developments, this article presents the interest of the theory of polymer physics to evaluate the flexibility of fully disordered proteins. The different strategies to obtain 3-dimensional models of IDPs, free in solution and associated in a complex, are then reviewed. Indeed, recent computational advances have made it possible to readily extract maximum information from the scattering curve with a special emphasis on highly flexible systems, such as multidomain proteins and IDPs. Furthermore, integrated computational approaches now enable the generation of ensembles of conformers to translate the unique flexible characteristics of IDPs by taking into consideration the constraints of more and more various complementary experiment. In particular, a combination of SAXS with high-resolution techniques, such as x-ray crystallography and NMR, allows us to provide reliable models and to gain unique structural insights about the protein over multiple structural scales. The latest neutron scattering experiments also promise new advances in the study of the conformational changes of macromolecules involving more complex systems.

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.

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.

Large-scale motions in the adenylate kinase solution ensemble: coarse-grained simulations and comparison with solution X-ray scattering

While coarse-grained (CG) simulations provide an efficient approach to identify small- and large-scale motions important to protein conformational transitions, coupling with appropriate experimental validation is essential. Here, by comparing small-angle X-ray scattering (SAXS) predictions from CG simulation ensembles of adenylate kinase (AK) with a range of energetic parameters, we demonstrate that AK is flexible in solution in the absence of ligand and that a small population of the closed form exists without ligand. In addition, by analyzing variation of scattering patterns within CG simulation ensembles, we reveal that rigid-body motion of the LID domain corresponds to a dominant scattering feature. Thus, we have developed a novel approach for three-dimensional structural interpretation of SAXS data. Finally, we demonstrate that the agreement between predicted and experimental SAXS can be improved by increasing the simulation temperature or by computationally mutating selected residues to glycine, both of which perturb LID rigid-body flexibility.

Determining RNA three-dimensional structures using low-resolution data

Knowing the 3-D structure of an RNA is fundamental to understand its biological function. Nowadays X-ray crystallography and NMR spectroscopy are systematically applied to newly discovered RNAs. However, the application of these high-resolution techniques is not always possible, and thus scientists must turn to lower resolution alternatives. Here, we introduce a pipeline to systematically generate atomic resolution 3-D structures that are consistent with low-resolution data sets. We compare and evaluate the discriminative power of a number of low-resolution experimental techniques to reproduce the structure of the Escherichia coli tRNA(VAL) and P4-P6 domain of the Tetrahymena thermophila group I intron. We test single and combinations of the most accessible low-resolution techniques, i.e. hydroxyl radical footprinting (OH), methidiumpropyl-EDTA (MPE), multiplexed hydroxyl radical cleavage (MOHCA), and small-angle X-ray scattering (SAXS). We show that OH-derived constraints are accurate to discriminate structures at the atomic level, whereas EDTA-based constraints apply to global shape determination. We provide a guide for choosing which experimental techniques or combination of thereof is best in which context. The pipeline represents an important step towards high-throughput low-resolution RNA structure determination.

Multi-wavelength anomalous diffraction using medium-angle X-ray solution scattering (MADMAX)

Proteins are dynamic molecules whose function in virtually all biological processes requires conformational motion. Direct experimental probes of protein structure in solution are needed to characterize these motions. Anomalous scattering from proteins in solution has the potential to act as a precise molecular ruler to determine the positions of specific chemical groups or atoms within proteins under conditions in which structural changes can take place free from the constraints of crystal contacts. In solution, anomalous diffraction has two components: a set of cross-terms that depend on the relative location of the anomalous centers and the rest of the protein, and a set of pure anomalous terms that depend on the distances between the anomalous centers. The cross-terms are demonstrated here to be observable and to provide direct information about the distance between the anomalous center and the center of mass of the protein. The second set of terms appears immeasurably small in the context of current experimental capabilities. Here, we outline the theory underlying anomalous scattering from proteins in solution, predict the anomalous differences expected on the basis of atomic coordinate sets, and demonstrate the measurement of anomalous differences at the iron edge for solutions of myoglobin and hemoglobin.

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.

Modeling the hydration layer around proteins: applications to small- and wide-angle x-ray scattering

Small-/wide-angle x-ray scattering (SWAXS) experiments can aid in determining the structures of proteins and protein complexes, but success requires accurate computational treatment of solvation. We compare two methods by which to calculate SWAXS patterns. The first approach uses all-atom explicit-solvent molecular dynamics (MD) simulations. The second, far less computationally expensive method involves prediction of the hydration density around a protein using our new HyPred solvation model, which is applied without the need for additional MD simulations. The SWAXS patterns obtained from the HyPred model compare well to both experimental data and the patterns predicted by the MD simulations. Both approaches exhibit advantages over existing methods for analyzing SWAXS data. The close correspondence between calculated and observed SWAXS patterns provides strong experimental support for the description of hydration implicit in the HyPred model.

DADIMODO: a program for refining the structure of multidomain proteins and complexes against small-angle scattering data and NMR-derived restraints

DADIMODOis a program for refining atomic models of multidomain proteins or complexes against small-angle X-ray scattering data. Interdomain distance and orientational restraints, such as those derived from NMR measurements, can be included in the optimization process. While domain structures are mainly kept rigid, flexible regions can be user defined. Stepwise generic conformational changes, specified by the user, are applied cyclically in a stochastic optimization algorithm that performs a search in the protein conformation space. The convergence for this genetic algorithm is driven by an adaptable selection pressure. The algorithmic structure guarantees that a physically acceptable full atomic model of the structure is present at all stages of the optimization. A graphical user interface ensures user-friendly handling.

AquaSAXS: a web server for computation and fitting of SAXS profiles with non-uniformally hydrated atomic models

Small Angle X-ray Scattering (SAXS) techniques are becoming more and more useful for structural biologists and biochemists, thanks to better access to dedicated synchrotron beamlines, better detectors and the relative easiness of sample preparation. The ability to compute the theoretical SAXS profile of a given structural model, and to compare this profile with the measured scattering intensity, yields crucial structural informations about the macromolecule under study and/or its complexes in solution. An important contribution to the profile, besides the macromolecule itself and its solvent-excluded volume, is the excess density due to the hydration layer. AquaSAXS takes advantage of recently developed methods, such as AquaSol, that give the equilibrium solvent density map around macromolecules, to compute an accurate SAXS/WAXS profile of a given structure and to compare it to the experimental one. Here, we describe the interface architecture and capabilities of the AquaSAXS web server (http://lorentz.dynstr.pasteur.fr/aquasaxs.php).

Macromolecular assembly of polycystin-2 intracytosolic C-terminal domain

Mutations in PKD2 are responsible for approximately 15% of the autosomal dominant polycystic kidney disease cases. This gene encodes polycystin-2, a calcium-permeable cation channel whose C-terminal intracytosolic tail (PC2t) plays an important role in its interaction with a number of different proteins. In the present study, we have comprehensively evaluated the macromolecular assembly of PC2t homooligomer using a series of biophysical and biochemical analyses. Our studies, based on a new delimitation of PC2t, have revealed that it is capable of assembling as a homotetramer independently of any other portion of the molecule. Our data support this tetrameric arrangement in the presence and absence of calcium. Molecular dynamics simulations performed with a modified all-atoms structure-based model supported the PC2t tetrameric assembly, as well as how different populations are disposed in solution. The simulations demonstrated, indeed, that the best-scored structures are the ones compatible with a fourfold oligomeric state. These findings clarify the structural properties of PC2t domain and strongly support a homotetramer assembly of PC2.

Effects of ionic strength on SAXS data for proteins revealed by molecular dynamics simulations

The combination of small-angle X-ray solution scattering (SAXS) experiments and molecular dynamics (MD) simulations is now becoming a powerful tool to study protein conformations in solution at an atomic resolution. In this study, we investigated effects of ionic strength on SAXS data theoretically by using MD simulations of hen egg white lysozyme at various NaCl concentrations from 0 to 1 M. The calculated SAXS excess intensities showed a significant dependence on ion concentration, which originates from the different solvent density distributions in the presence and absence of ions. The addition of ions induced a slow convergence of the SAXS data, and a ∼20 ns simulation is required to obtain convergence of the SAXS data with the presence of ions whereas only a 0.2 ns simulation is sufficient in the absence of ions. To circumvent the problem of the slow convergence in the presence of ions, we developed a novel method that reproduces the SAXS excess intensities with the presence of ions from short MD trajectories in pure water. By applying this method to SAXS data for the open and closed forms of transferrin at 1 M ion concentration, the correct form could be identified by simply using short MD simulations of the protein in pure water for 0.2 ns.

SAXS ensemble refinement of ESCRT-III CHMP3 conformational transitions

We developed and implemented an ensemble-refinement method to study dynamic biomolecular assemblies with intrinsically disordered segments. Data from small angle X-ray scattering (SAXS) experiments and from coarse-grained molecular simulations were combined by using a maximum-entropy approach. The method was applied to CHMP3 of ESCRT-III, a protein with multiple helical domains separated by flexible linkers. Based on recent SAXS data by Lata et al. (J. Mol. Biol. 378, 818, 2008), we constructed ensembles of CHMP3 at low- and high-salt concentration to characterize its closed autoinhibited state and open active state. At low salt, helix α(5) is bound to the tip of helices α(1) and α(2), in excellent agreement with a recent crystal structure. Helix α(6) remains free in solution and does not appear to be part of the autoinhibitory complex. The simulation-based ensemble refinement is general and effectively increases the resolution of SAXS beyond shape information to atomically detailed structures.

EROS: Better than SAXS!

Revealing the three-dimensional organization of large dynamic protein complexes in solution is challenging. To tackle this problem, Różycki and colleagues (2011) design a method combining small angle X-ray scattering (SAXS) data with the results of computer simulations. Their study offers new insights into the conformational transition induced by salt that occurs in an endosome-associated ESCRT-III CHMP3 domain.

Improved fitting of solution X-ray scattering data to macromolecular structures and structural ensembles by explicit water modeling

A new procedure, AXES, is introduced for fitting small-angle X-ray scattering (SAXS) data to macromolecular structures and ensembles of structures. By using explicit water models to account for the effect of solvent, and by restricting the adjustable fitting parameters to those that dominate experimental uncertainties, including sample/buffer rescaling, detector dark current, and, within a narrow range, hydration layer density, superior fits between experimental high resolution structures and SAXS data are obtained. AXES results are found to be more discriminating than standard Crysol fitting of SAXS data when evaluating poorly or incorrectly modeled protein structures. AXES results for ensembles of structures previously generated for ubiquitin show improved fits over fitting of the individual members of these ensembles, indicating these ensembles capture the dynamic behavior of proteins in solution.

RNA structure determination using SAXS data

Exploiting the experimental information from small-angle X-ray solution scattering (SAXS) in conjunction with structure prediction algorithms can be advantageous in the case of ribonucleic acids (RNA), where global restraints on the 3D fold are often lacking. Traditional usage of SAXS data often starts by attempting to reconstruct the molecular shape ab initio, which is subsequently used to assess the quality of a model. Here, an alternative strategy is explored whereby the models from a very large decoy set are directly sorted according to their fit to the SAXS data. For rapid computation of SAXS patterns, the method developed here makes use of a coarse-grained representation of RNA. It also accounts for the explicit treatment of the contribution to the scattering of water molecules and ions surrounding the RNA. The method, called Fast-SAXS-RNA, is first calibrated using a tRNA (tRNA-val) and then tested on the P4-P6 fragment of group I intron (P4-P6). Fast-SAXS-RNA is then used as a filter for decoy models generated by the MC-Fold and MC-Sym pipeline, a suite of RNA 3D all-atom structure algorithms that encode and exploit RNA 3D architectural principles. The ability of Fast-SAXS-RNA to discriminate native folds is tested against three widely used RNA molecules in molecular modeling benchmarks: the tRNA, the P4-P6, and a synthetic hairpin suspected to assemble into a homodimer. For each molecule, a large pool of decoys are generated, scored, and ranked using Fast-SAXS-RNA. The method is able to identify low-rmsd models among top ranking structures, for both tRNA and P4-P6. For the hairpin, the approach correctly identifies the dimeric state as the solution structure over the monomeric state and alternative secondary structures. The method offers a powerful strategy for recognizing native RNA conformations as well as multimeric assemblies and alternative secondary structures, thus enabling high-throughput RNA structure determination using SAXS data.

Structure modeling from small angle X-ray scattering data with elastic network normal mode analysis

Computational algorithms to construct structural models from SAXS experimental data are reviewed. SAXS data provides a wealth of information to study the structure and dynamics of biological molecules, however it does not provide atomic details of structures. Thus combining the low-resolution data with already known X-ray structure is a common approach to study conformational transitions of biological molecules. This review provides a survey of SAXS modeling approaches. In addition, we will discuss theoretical backgrounds and performance of our approach, in which elastic network normal mode analysis is used to predict reasonable conformational transitions from known X-ray structures, and find alternative conformations that are consistent with SAXS data.

Proteins at work: a combined small angle X-RAY scattering and theoretical determination of the multiple structures involved on the protein kinase functional landscape

C-terminal Src kinase (Csk) phosphorylates and down-regulates the Src family tyrosine kinases (SFKs). Crystallographic studies of Csk found an unusual arrangement of the SH2 and SH3 regulatory domains about the kinase core, forming a compact structure. However, recent structural studies of mutant Csk in the presence of an inhibitor indicate that the enzyme accesses an expanded structure. To investigate whether wt-Csk may also access open conformations we applied small angle x-ray scattering (SAXS). We find wt-Csk frequently occupies an extended conformation where the regulatory domains are removed from the kinase core. In addition, all-atom structure-based simulations indicate Csk occupies two free energy basins. These basins correspond to ensembles of distinct global conformations of Csk: a compact structure and an extended structure. The transitions between these structures are entropically driven and accessible via thermal fluctuations that break local interactions. We further characterized the ensemble by generating theoretical scattering curves for mixed populations of conformations from both basins and compared the predicted scattering curves to the experimental profile. This population-combination analysis is more consistent with the experimental data than any rigid model. It suggests that Csk adopts a broad ensemble of conformations in solution, populating extended conformations not observed in the crystal structure that may play an important role in the regulation of Csk. The methodology developed here is broadly applicable to biological macromolecules and will provide useful information about what ensembles of conformations are consistent with the experimental data as well as the ubiquitous dynamic reversible assembly processes inherent in biology.

Multidomain assembled states of Hck tyrosine kinase in solution

An approach combining small-angle X-ray solution scattering (SAXS) data with coarse-grained (CG) simulations is developed to characterize the assembly states of Hck, a member of the Src-family kinases, under various conditions in solution. First, a basis set comprising a small number of assembly states is generated from extensive CG simulations. Second, a theoretical SAXS profile for each state in the basis set is computed by using the Fast-SAXS method. Finally, the relative population of the different assembly states is determined via a Bayesian-based Monte Carlo procedure seeking to optimize the theoretical scattering profiles against experimental SAXS data. The study establishes the concept of basis-set supported SAXS (BSS-SAXS) reconstruction combining computational and experimental techniques. Here, BSS-SAXS reconstruction is used to reveal the structural organization of Hck in solution and the different shifts in the equilibrium population of assembly states upon the binding of different signaling peptides.

Small-angle X-ray and neutron scattering as a tool for structural systems biology

Small-angle scattering (SAS) of X-rays and neutrons reveals low-resolution structures of biological macromolecules in solution. With the recent experimental and methodological advances, SAS became a unique tool for characterising biological systems. The method covers an extremely broad range of molecule sizes (from a few kDa to hundreds of MDa) and experimental conditions (temperature, pH, salinity, ligand addition, etc.), which is of primary importance for a systemic approach in structural biology. The method provides unique information about the overall structure and conformational changes of native individual proteins, functional complexes, flexible macromolecules and hierarchical systems. New developments in small-angle X-ray and neutron scattering studies of biological macromolecules in solution are briefly reviewed, with a special emphasis on technical and methodological approaches useful for structural systems biology. Possibilities of synergistic use of the method with other techniques are considered.

Normal Mode Flexible Fitting of High-Resolution Structures of Biological Molecules Toward SAXS Data

We present a method to reconstruct a three-dimensional protein structure from an atomic pair distribution function derived from the scattering intensity profile from SAXS data by flexibly fitting known x-ray structures. This method uses a linear combination of low-frequency normal modes from an elastic network description of the molecule in an iterative manner to deform the structure to conform optimally to the target pair distribution function derived from SAXS data. For computational efficiency, the protein and water molecules included in the protein first hydration shell are coarse-grained. In this paper, we demonstrate the validity of our coarse-graining approach to study SAXS data. Illustrative results of our flexible fitting studies on simulated SAXS data from five different proteins are presented.

Structural characterization of proteins and complexes using small-angle X-ray solution scattering

Small-angle scattering of X-rays (SAXS) is an established method for the low-resolution structural characterization of biological macromolecules in solution. The technique provides three-dimensional low-resolution structures, using ab initio and rigid body modeling, and allow one to assess the oligomeric state of proteins and protein complexes. In addition, SAXS is a powerful tool for structure validation and the quantitative analysis of flexible systems, and is highly complementary to the high resolution methods of X-ray crystallography and NMR. At present, SAXS analysis methods have reached an advanced state, allowing for automated and rapid characterization of protein solutions in terms of low-resolution models, quaternary structure and oligomeric composition. In this communication, main approaches to the characterization of proteins and protein complexes using SAXS are reviewed. The tools for the analysis of proteins in solution are presented, and the impact that these tools have made in modern structural biology is discussed.

FoXS: a web server for rapid computation and fitting of SAXS profiles

Small angle X-ray scattering (SAXS) is an increasingly common technique for low-resolution structural characterization of molecules in solution. SAXS experiment determines the scattering intensity of a molecule as a function of spatial frequency, termed SAXS profile. SAXS profiles can contribute to many applications, such as comparing a conformation in solution with the corresponding X-ray structure, modeling a flexible or multi-modular protein, and assembling a macromolecular complex from its subunits. These applications require rapid computation of a SAXS profile from a molecular structure. FoXS (Fast X-Ray Scattering) is a rapid method for computing a SAXS profile of a given structure and for matching of the computed and experimental profiles. Here, we describe the interface and capabilities of the FoXS web server (http://salilab.org/foxs).

Characterization of proteins with wide-angle X-ray solution scattering (WAXS)

X-ray solution scattering in both the small-angle (SAXS) and wide-angle (WAXS) regimes is making an increasing impact on our understanding of biomolecular complexes. The accurate calculation of WAXS patterns from atomic coordinates has positioned the approach for rapid growth and integration with existing Structural Genomics efforts. WAXS data are sensitive to small structural changes in proteins; useful for calculation of the pair-distribution function at relatively high resolution; provides a means to characterize the breadth of the structural ensemble in solution; and can be used to identify proteins with similar folds. WAXS data are often used to test structural models, identify structural similarities and characterize structural changes. WAXS is highly complementary to crystallography and NMR. It holds great potential for the testing of structural models of proteins; identification of proteins that may exhibit novel folds; characterization of unfolded or natively disordered proteins; and detection of structural changes associated with protein function.