Small-angle X-ray scattering (SAXS) is an increasingly common and useful technique for structural characterization of molecules in solution. A SAXS experiment determines the scattering intensity of a molecule as a function of spatial frequency, termed SAXS profile. SAXS profiles can be utilized in a variety of molecular modeling applications, such as comparing solution and crystal structures, structural characterization of flexible proteins, assembly of multi-protein complexes, and modeling of missing regions in the high-resolution structure. Here, we describe protocols for modeling atomic structures based on SAXS profiles. The first protocol is for comparing solution and crystal structures including modeling of missing regions and determination of the oligomeric state. The second protocol performs multi-state modeling by finding a set of conformations and their weights that fit the SAXS profile starting from a single-input structure. The third protocol is for protein-protein docking based on the SAXS profile of the complex. We describe the underlying software, followed by demonstrating their application on interleukin 33 (IL33) with its primary receptor ST2 and DNA ligase IV-XRCC4 complex.

AbstractRecent 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.

Integrative structural modeling uses multiple types of input information and proceeds in four stages: (i) gathering information, (ii) designing model representation and converting information into a scoring function, (iii) sampling good-scoring models, and (iv) analyzing models and information. In the first stage, uncertainty originates from data that are sparse, noisy, ambiguous, or derived from heterogeneous samples. In the second stage, uncertainty can originate from a representation that is too coarse for the available information or a scoring function that does not accurately capture the information. In the third stage, the major source of uncertainty is insufficient sampling. In the fourth stage, clustering, cross-validation, and other methods are used to estimate the precision and accuracy of the models and information.

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.

To obtain a structural model of a macromolecular assembly by single-particle EM, a large number of particle images need to be collected, aligned, clustered, averaged, and finally assembled via reconstruction into a 3D density map. This process is limited by the number and quality of the particle images, the accuracy of the initial model, and the compositional and conformational heterogeneity. Here, we describe a structure determination method that avoids the reconstruction procedure. The atomic structures of the individual complex components are assembled by optimizing a match against 2D EM class-average images, an excluded volume criterion, geometric complementarity, and optional restraints from proteomics and chemical cross-linking experiments. The optimization relies on a simulated annealing Monte Carlo search and a divide-and-conquer message-passing algorithm. Using simulated and experimentally determined EM class averages for 12 and 4 protein assemblies, respectively, we show that a few class averages can indeed result in accurate models for complexes of as many as five subunits. Thus, integrative structural biology can now benefit from the relative ease with which the EM class averages are determined.

Structural analysis of proteins and nucleic acids is complicated by their inherent flexibility, conferred, for example, by linkers between their contiguous domains. Therefore, the macromolecule needs to be represented by an ensemble of conformations instead of a single conformation. Determining this ensemble is challenging because the experimental data are a convoluted average of contributions from multiple conformations. As the number of the ensemble degrees of freedom generally greatly exceeds the number of independent observables, directly deconvolving experimental data into a representative ensemble is an ill-posed problem. Recent developments in sparse approximations and compressive sensing have demonstrated that useful information can be recovered from underdetermined (ill-posed) systems of linear equations by using sparsity regularization. Inspired by these advances, we designed the Sparse Ensemble Selection (SES) method for recovering multiple conformations from a limited number of observations. SES is more general and accurate than previously published minimum-ensemble methods, and we use it to obtain representative conformational ensembles of Lys48-linked diubiquitin, characterized by the residual dipolar coupling data measured at several pH conditions. These representative ensembles are validated against NMR chemical shift perturbation data and compared to maximum-entropy results. The SES method reproduced and quantified the previously observed pH dependence of the major conformation of Lys48-linked diubiquitin, and revealed lesser-populated conformations that are preorganized for binding known diubiquitin receptors, thus providing insights into possible mechanisms of receptor recognition by polyubiquitin. SES is applicable to any experimental observables that can be expressed as a weighted linear combination of data for individual states.

Motivation

Statistical potentials have been widely used for modeling whole proteins and their parts (e.g. sidechains and loops) as well as interactions between proteins, nucleic acids and small molecules. Here, we formulate the statistical potentials entirely within a statistical framework, avoiding questionable statistical mechanical assumptions and approximations, including a definition of the reference state.

Results

We derive a general Bayesian framework for inferring statistically optimized atomic potentials (SOAP) in which the reference state is replaced with data-driven 'recovery' functions. Moreover, we restrain the relative orientation between two covalent bonds instead of a simple distance between two atoms, in an effort to capture orientation-dependent interactions such as hydrogen bonds. To demonstrate this general approach, we computed statistical potentials for protein-protein docking (SOAP-PP) and loop modeling (SOAP-Loop). For docking, a near-native model is within the top 10 scoring models in 40% of the PatchDock benchmark cases, compared with 23 and 27% for the state-of-the-art ZDOCK and FireDock scoring functions, respectively. Similarly, for modeling 12-residue loops in the PLOP benchmark, the average main-chain root mean square deviation of the best scored conformations by SOAP-Loop is 1.5 Å, close to the average root mean square deviation of the best sampled conformations (1.2 Å) and significantly better than that selected by Rosetta (2.1 Å), DFIRE (2.3 Å), DOPE (2.5 Å) and PLOP scoring functions (3.0 Å). Our Bayesian framework may also result in more accurate statistical potentials for additional modeling applications, thus affording better leverage of the experimentally determined protein structures.

Availability and implementation

SOAP-PP and SOAP-Loop are available as part of MODELLER (http://salilab.org/modeller).

Passive acoustic monitoring has become an important data collection method, yielding massive datasets replete with biological, environmental and anthropogenic information. Automated signal detectors and classifiers are needed to identify events within these datasets, such as the presence of species-specific sounds or anthropogenic noise. These automated methods, however, are rarely a complete substitute for expert analyst review. The ability to visualize and annotate acoustic events efficiently can enhance scientific insights from large, previously intractable datasets. A MATLAB-based graphical user interface, called DetEdit, was developed to accelerate the editing and annotating of automated detections from extensive acoustic datasets. This tool is highly-configurable and multipurpose, with uses ranging from annotation and classification of individual signals or signal-clusters and evaluation of signal properties, to identification of false detections and false positive rate estimation. DetEdit allows users to step through acoustic events, displaying a range of signal features, including time series of received levels, long-term spectral averages, time intervals between detections, and scatter plots of peak frequency, RMS, and peak-to-peak received levels. Additionally, it displays either individual, or averaged sound pressure waveforms, and power spectra within each acoustic event. These views simultaneously provide analysts with signal-level detail and encounter-level context. DetEdit creates datasets of signal labels for further analyses, such as training classifiers and quantifying occurrence, abundances, or trends. Although designed for evaluating underwater-recorded odontocete echolocation click detections, DetEdit can be adapted to almost any stereotyped impulsive signal. Our software package complements available tools for the bioacoustic community and is provided open source at https://github.com/MarineBioAcousticsRC/DetEdit.

A set of software tools for building and distributing models of macromolecular assemblies uses an integrative structure modeling approach, which casts the building of models as a computational optimization problem where information is encoded into a scoring function used to evaluate candidate models.

Aberrant self-assembly, induced by structural misfolding of the prion proteins, leads to a number of neurodegenerative disorders. In particular, misfolding of the mostly α-helical cellular prion protein (PrP(C)) into a β-sheet-rich disease-causing isoform (PrP(Sc)) is the key molecular event in the formation of PrP(Sc) aggregates. The molecular mechanisms underlying the PrP(C)-to-PrP(Sc) conversion and subsequent aggregation remain to be elucidated. However, in persistently prion-infected cell-culture models, it was shown that treatment with monoclonal antibodies against defined regions of the prion protein (PrP) led to the clearing of PrP(Sc) in cultured cells. To gain more insight into this process, we characterized PrP-antibody complexes in solution using a fast protein liquid chromatography coupled with small-angle x-ray scattering (FPLC-SAXS) procedure. High-quality SAXS data were collected for full-length recombinant mouse PrP [denoted recPrP(23-230)] and N-terminally truncated recPrP(89-230), as well as their complexes with each of two Fab fragments (HuM-P and HuM-R1), which recognize N- and C-terminal epitopes of PrP, respectively. In-line measurements by fast protein liquid chromatography coupled with SAXS minimized data artifacts caused by a non-monodispersed sample, allowing structural analysis of PrP alone and in complex with Fab antibodies. The resulting structural models suggest two mechanisms for how these Fabs may prevent the conversion of PrP(C) into PrP(Sc).