Wide-angle X-ray Solution Scattering Research Articles

Predicting X-ray solution scattering from flexible macromolecules.

Wide-angle X-ray solution scattering (WAXS) patterns contain substantial information about the structure and dynamics of a protein. Solution scattering from a rigid protein can be predicted from atomic coordinate sets to within experimental error. However, structural fluctuations of proteins in solution can lead to significant changes in the observed intensities. The magnitude and form of these changes contain information about the nature and spatial extent of structural fluctuations in the protein. Molecular dynamics (MD) simulations based on a crystal structure and selected force field generate models for protein internal motions, and here we demonstrate that they can be used to predict the impact of structural fluctuations on solution scattering data. In cases where the observed and calculated intensities correspond, we can conclude that the X-ray scattering provides direct experimental validation of the structural and MD results. In cases where calculated and observed intensities are at odds, the inconsistencies can be used to determine the origins of these discrepancies. They may be because of overestimates or underestimates of structural fluctuations in MD simulations, under-sampling of the structural ensemble in the simulations, errors in the structural model, or a mismatch between the experimental conditions and the parameters used in carrying out the MD simulation.

Verifying Self-Consistency of Protein Structure and Dynamics through MD Simulation and WAXS

Molecular Dynamics (MD) simulations based on a crystal structure and selected force field represent a powerful approach to generate models for the internal motions of a protein in order to interpret the results of biological experiments and model the interactions between proteins and ligands. However, there are relatively few experimental probes that can be used to verify the results of MD, particularly with regard to slow, correlated motions of loops, folds or domains. Wide-angle X-ray solution scattering (WAXS) is sensitive to protein structure and dynamics including secondary, tertiary and quaternary structure and slow, correlated motions. Here, we present a method to utilize the crystal structure of a protein and its corresponding MD simulation to predict WAXS data from a protein. First, the WAXS pattern of a rigid protein is calculated using an explicit atom model of the hydration layer with the software package, XS. Second, MD trajectories are utilized to calculate a sigma-r plot (the standard deviation of interatomic distances averaged as a function of interatomic distance) which is subsequently combined with the results of the XS calculation to predict the scattering pattern of the dynamic protein. The difference between observed and calculated intensities is minimized by scaling the sigma-r plot with a single variable factor which provides a measure of the discrepancy between experimental and computational characterization of global dynamics. In examples presented here, we show that the correspondence between observed and calculated intensities are often excellent, providing direct experimental validation of the MD results. In other examples, we demonstrate how the approach can identify over or under-estimates of large scale motions in MD simulations that may arise from under-sampling of the structural ensemble or inappropriate choice of simulation parameters.

Characterizing Conformational Ensemble of H‐, K‐, and N‐Ras Using Accelerated Molecular Dynamics and Wide‐Angle X‐ray Solution Scattering (WAXS)

Ras GTPase is involved in cell‐signaling pathways that control cell proliferation, differentiation, and apoptosis. There are three main isoforms of Ras, H‐, K‐, and N‐Ras, which share about 95% sequence identity in their soluble domain. They have very similar three‐dimensional folds, however they have been suggested to display functional specificity. For example, in pancreatic cancer K‐Ras mutations occur at much higher frequency than either H‐ or N‐Ras, whereas in leukemia N‐Ras mutations play the dominant role. These isoforms have also been shown to follow distinct cellular processing pathways and localize to different subcellular compartments. In this study, we combine accelerated Molecular Dynamics (aMD) and wide‐angle X‐ray scattering (WAXS) methods to characterize the structural ensemble of Ras isoforms and measure their dynamic properties. Using aMD, we reduce the energetic barriers to enhance conformational sampling of these proteins. A representative subset of structures from aMD is then experimentally tested using WAXS patterns to quantify their relative population. Each isoform shows at least two major conformations, where one is characterized as a relaxed state and another one as a reactive state, based on their relative potential energy calculated from aMD. These conformations are unique for each of the isoform, where they differ primarily around the active site and regions away from the active site, including helix 3/loop 7. This study will provide significant insights into the conformational features of these small proteins that give rise to their functional specificity.Support or Funding InformationNSF MCB‐1244203

Wide‐angle X‐ray Solution Scattering Studies of Slow Correlated Motions in Proteins

Slow correlated motions in the submicrosecond to second range are particularly important for protein function but remain challenging to study. Wide‐angle x‐ray solution scattering (WAXS) generates information about the length scale of intramolecular motions difficult to obtain by other methods; is highly sensitive to these motions, being able to detect changes due to single amino acid replacements, ligand binding or alterations in solution conditions; and is sufficiently fast as to make practical the screening of hundreds of conditions/ligands/mutations to identify those that impact protein motions.Direct comparison of the results of WAXS and molecular dynamics (MD) is accomplished through introduction of the sigma‐r plot, a plot of the standard deviation of interatomic vector lengths as a function of that length ‐ derivable from WAXS data and MD trajectories. MD simulations generate extraordinary detail about protein trajectories; WAXS provides experimental measures of length scale of protein motion under a large number of conditions. Direct comparison of WAXS with MD will enable detailed molecular interpretations of WAXS data using the power of MD; while making possible the extrapolation of MD results to understand molecular behavior of a large number of mutants in multiple ligation states and solution conditions. Application of this approach to HIV protease provides new insights into the role of protein dynamics in its enzymatic function.

SAXS, WAXS, MD, Protein fluctuations and function

Conformational mobility is essential to many protein functions and design of therapies for a broad spectrum of human diseases depends on a deep understanding the linkage between protein structure, intramolecular motions and function. Methods for screening small molecules and mutations that alter fluctuations are essential for improved understanding of this linkage. To what extent do changes in intramolecular motions lead to changes in function? To address this question, we are using a combination of wide-angle x-ray solution scattering (WAXS) and molecular dynamics (MD) to generate novel insights into the magnitude, form and functional consequences of intramolecular motions of proteins in solution. WAXS has proven unexpectedly sensitive to the intramolecular motions of proteins in solution and can detect changes in flexibility generated by single amino acid replacements or binding of small molecule ligands. Here we formulate the effect of structural fluctuations on WAXS data in such a way as to make possible direct experimental assessment of the range of motion that proteins explore in solution. The approach differs from other strategies by treating it as an inverse source problem, deriving flexibility parameters directly from data rather than from an ensemble of structures generated to predict the data.

Wide-Angle X-Ray Solution Scattering for Protein-Ligand Binding: Multivariate Curve Resolution with Bayesian Confidence Intervals

A new way to use wide-angle x-ray solution scattering to study protein-ligand binding is presented. First, scattering patterns are measured at different protein and ligand concentrations. Multivariate curve resolution based on singular value decomposition and global analysis is applied to estimate the binding affinities and reference patterns (i.e., the scattering patterns of individual components). As validated by simulation, Bayesian confidence intervals provide accurate uncertainty estimates for the binding free energies and reference patterns. Experimental results from several protein-ligand systems demonstrate the feasibility of the approach, which promises to expand the role of wide-angle x-ray scattering as a quantitative biophysical tool.

WAXS Studies of the Structural Diversity of Hemoglobin in Solution

Specific ligation states of hemoglobin are, when crystallized, capable of taking on multiple quaternary structures. The relationship between these structures, captured in crystal lattices, and hemoglobin structure in solution remains uncertain. Wide-angle X-ray solution scattering (WAXS) is a sensitive probe of protein structure in solution that can distinguish among similar structures and has the potential to contribute to these issues. We used WAXS to assess the relationships among the structures of human and bovine hemoglobins in different liganded forms in solution. WAXS data readily distinguished among the various forms of hemoglobins. WAXS patterns confirm some of the relationships among hemoglobin structures that have been defined through crystallography and NMR and extend others. For instance, methemoglobin A in solution is, as expected, nearly indistinguishable from HbCO A. Interestingly, for bovine hemoglobin, the differences between deoxy-Hb, methemoglobin and HbCO are smaller than the corresponding differences in human hemoglobin. WAXS data were also used to assess the spatial extent of structural fluctuations of various hemoglobins in solution. Dynamics has been implicated in allosteric control of hemoglobin, and increased dynamics has been associated with lowered oxygen affinity. Consistent with that notion, WAXS patterns indicate that deoxy-Hb A exhibits substantially larger structural fluctuations than HbCO A. Comparisons between the observed WAXS patterns and those predicted on the basis of atomic coordinate sets suggest that the structures of Hb in different liganded forms exhibit clear differences from known crystal structures.

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.

SoftWAXS: a computational tool for modeling wide-angle X-ray solution scattering from biomolecules.

This paper describes a computational approach to estimating wide-angle X-ray solution scattering (WAXS) from proteins, which has been implemented in a computer program called SoftWAXS. The accuracy and efficiency of SoftWAXS are analyzed for analytically solvable model problems as well as for proteins. Key features of the approach include a numerical procedure for performing the required spherical averaging and explicit representation of the solute-solvent boundary and the surface of the hydration layer. These features allow the Fourier transform of the excluded volume and hydration layer to be computed directly and with high accuracy. This approach will allow future investigation of different treatments of the electron density in the hydration shell. Numerical results illustrate the differences between this approach to modeling the excluded volume and a widely used model that treats the excluded-volume function as a sum of Gaussians representing the individual atomic excluded volumes. Comparison of the results obtained here with those from explicit-solvent molecular dynamics clarifies shortcomings inherent to the representation of solvent as a time-averaged electron-density profile. In addition, an assessment is made of how the calculated scattering patterns depend on input parameters such as the solute-atom radii, the width of the hydration shell and the hydration-layer contrast. These results suggest that obtaining predictive calculations of high-resolution WAXS patterns may require sophisticated treatments of solvent.

Slow Correlated Movement of Structural Elements in Hemoglobin and Myoglobin

Structural fluctuations of proteins in solution are often reflections of functional movements and appear to follow low energy pathways that have evolved to accommodate conformational changes triggered, for instance, by binding to ligands or catalysis of reactions. The study of these fluctuations can provide substantial insight into protein function. The spatial extent and dynamics of intramolecular movements in proteins are highly dependent on the environment of the protein, being particularly sensitive to the concentration of proteins and other constituents in the solution. Consequently, studies as a function of protein concentration may provide further insight into the nature of these fluctuations than is possible when experiments are carried out at a single protein concentration. Wide-angle x-ray solution scattering (WAXS) and neutron spin echo spectroscopy (NSE) provide substantial information about the spatial extent and time scale, respectively, of structural fluctuations in solution. They are particularly well suited to the study of slow, correlated movements that are central to many protein functions, providing information complementary to that obtainable by x-ray crystallography and NMR. Using these approaches, we have characterized the spatial and temporal properties of hemoglobin and myoglobin across a wide range of environments. For these proteins, the spatial extent and dynamics of correlated movements both increase rapidly as protein concentration decreases below about 50 mg/ml. A combined analysis of WAXS and NSE data indicates that the slow correlated fluctuations in these molecules are dominated by movement of relatively rigid alpha helices within the subunits. These fluctuations are highly dependent on the ligation state of the molecules and are altered by mutations that impact the function of the molecules.

Characterization of Protein Fold by Wide-Angle X-ray Solution Scattering

Wide-angle X-ray solution scattering (WAXS) patterns contain substantial information about the three-dimensional structure of a protein. Although WAXS data have far less information than is required for determination of a full three-dimensional structure, the actual amount of information contained in a WAXS pattern has not been carefully quantified. Here we carry out an analysis of the amount of information that can be extracted from a WAXS pattern and demonstrate that it is adequate to estimate the secondary-structure content of a protein and to strongly limit its possible tertiary structures. WAXS patterns computed from the atomic coordinates of a set of 498 protein domains representing all of known fold space were used as the basis for constructing a multidimensional space of all corresponding WAXS patterns (‘WAXS space’). Within WAXS space, each scattering pattern is represented by a single vector. A principal components analysis was carried out to identify those directions in WAXS space that provide the greatest discrimination among patterns. The number of dimensions that provide significant discrimination among protein folds agrees well with the number of independent parameters estimated from a naïve Shannon sampling theorem approach. Estimates of the relative abundances of secondary structures were made using training/test sets derived from this data set. The average error in the estimate of α-helical content was 11%, and of β-sheet content was 9%. The distribution of proteins that are members of the four structure classes, α, β, α/β and α+β, are well separated in WAXS space when data extending to a spacing of 2.2 Å are used. Quantification of the information embedded within a WAXS pattern indicates that these data can be used as a powerful constraint in homology modeling of protein structures.

Computational challenges in wide-angle X-ray solution scattering (WAXS)

Computational challenges in wide-angle X-ray solution scattering (WAXS)

Wide-angle X-ray solution scattering as a probe of ligand-induced conformational changes in proteins.

A chemical genetics approach to functional analysis of gene products utilizes high-throughput target-based screens of compound libraries to identify ligands that modulate the activity of proteins of interest. Candidates are further screened using functional assays designed specifically for the protein--and function--of interest, suffering from the need to customize the assay to each protein. An alternative strategy is to utilize a probe to detect the structural changes that usually accompany binding of a functional ligand. Wide-angle X-ray scattering from proteins provides a means to identify a broad range of ligand-induced changes in secondary, tertiary, and quaternary structure. The speed and accuracy of data acquisition, combined with the label-free targets and binding conditions achievable, indicate that WAXS is well suited as a moderate-throughput assay in the detection and analysis of protein-ligand interactions.