SAXS Merge: an automated statistical method to merge SAXS profiles using Gaussian processes

A round-robin approach provides a detailed assessment of biomolecular small-angle scattering data reproducibility and yields consensus curves for benchmarking

Through an expansive international effort that involved data collection on 12 small-angle X-ray scattering (SAXS) and four small-angle neutron scattering (SANS) instruments, 171 SAXS and 76 SANS measurements for five proteins (ribonuclease A, lysozyme, xylanase, urate oxidase and xylose isomerase) were acquired. From these data, the solvent-subtracted protein scattering profiles were shown to be reproducible, with the caveat that an additive constant adjustment was required to account for small errors in solvent subtraction. Further, the major features of the obtained consensus SAXS data over the q measurement range 0-1 Å-1 are consistent with theoretical prediction. The inherently lower statistical precision for SANS limited the reliably measured q-range to <0.5 Å-1, but within the limits of experimental uncertainties the major features of the consensus SANS data were also consistent with prediction for all five proteins measured in H2O and in D2O. Thus, a foundation set of consensus SAS profiles has been obtained for benchmarking scattering-profile prediction from atomic coordinates. Additionally, two sets of SAXS data measured at different facilities to q > 2.2 Å-1 showed good mutual agreement, affirming that this region has interpretable features for structural modelling. SAS measurements with inline size-exclusion chromatography (SEC) proved to be generally superior for eliminating sample heterogeneity, but with unavoidable sample dilution during column elution, while batch SAS data collected at higher concentrations and for longer times provided superior statistical precision. Careful merging of data measured using inline SEC and batch modes, or low- and high-concentration data from batch measurements, was successful in eliminating small amounts of aggregate or interparticle interference from the scattering while providing improved statistical precision overall for the benchmarking data set.

Automatic Bayesian Weighting for SAXS Data

Small-angle X-ray scattering (SAXS) experiments are important in structural biology because they are solution methods, and do not require crystallization of protein complexes. Structure determination from SAXS data, however, poses some difficulties. Computation of a SAXS profile from a protein model is expensive in CPU time. Hence, rather than directly refining against the data, most computational methods generate a large number of conformers and then filter the structures based on how well they satisfy the SAXS data. To address this issue in an efficient manner, we propose here a Bayesian model for SAXS data and use it to directly drive a Monte Carlo simulation. We show that the automatic weighting of SAXS data is the key to finding optimal structures efficiently. Another key problem with obtaining structures from SAXS data is that proteins are often flexible and the data represents an average over a structural ensemble. To address this issue, we first characterize the stability of the best model with extensive molecular dynamics simulations. We analyse the resulting trajectories further to characterize a dynamic structural ensemble satisfying the SAXS data. The combination of methods is applied to a tandem of domains from the protein PTPN4, which are connected by an unstructured linker. We show that the SAXS data contain information that supports and extends other experimental findings. We also show that the conformation obtained by the Bayesian analysis is stable, but that a minor conformation is present. We propose a mechanism in which the linker may maintain PTPN4 in an inhibited enzymatic state.

Structure-based screening of binding affinities via small-angle X-ray scattering

Protein-protein and protein-ligand interactions often involve conformational changes or structural rearrangements that can be quantified by solution small-angle X-ray scattering (SAXS). These scattering intensity measurements reveal structural details of the bound complex, the number of species involved and, additionally, the strength of interactions if carried out as a titration. Although a core part of structural biology workflows, SAXS-based titrations are not commonly used in drug discovery contexts. This is because prior knowledge of expected sample requirements, throughput and prediction accuracy is needed to develop reliable ligand screens. This study presents the use of the histidine-binding protein (26 kDa) and other periplasmic binding proteins to benchmark ligand screen performance. Sample concentrations and exposure times were varied across multiple screening trials at four beamlines to investigate the accuracy and precision of affinity prediction. The volatility ratio between titrated scattering curves and a common apo reference is found to most reliably capture the extent of structural and population changes. This obviates the need to explicitly model scattering intensities of bound complexes, which can be strongly ligand-dependent. Where the dissociation constant is within 102 of the protein concentration and the total exposure times exceed 20 s, the titration protocol presented at 0.5 mg ml-1 yields affinities comparable to isothermal titration calorimetry measurements. Estimated throughput ranges between 20 and 100 ligand titrations per day at current synchrotron beamlines, with the limiting step imposed by sample handling and cleaning procedures.

Archiving and disseminating integrative structure models

Limitations in the applicability, accuracy, and precision of individual structure characterization methods can sometimes be overcome via an integrative modeling approach that relies on information from all available sources, including all available experimental data and prior models. The open-source Integrative Modeling Platform (IMP) is one piece of software that implements all computational aspects of integrative modeling. To maximize the impact of integrative structures, the coordinates should be made publicly available, as is already the case for structures based on X-ray crystallography, NMR spectroscopy, and electron microscopy. Moreover, the associated experimental data and modeling protocols should also be archived, such that the original results can easily be reproduced. Finally, it is essential that the integrative structures are validated as part of their publication and deposition. A number of research groups have already developed software to implement integrative modeling and have generated a number of structures, prompting the formation of an Integrative/Hybrid Methods Task Force. Following the recommendations of this task force, the existing PDBx/mmCIF data representation used for atomic PDB structures has been extended to address the requirements for archiving integrative structural models. This IHM-dictionary adds a flexible model representation, including coarse graining, models in multiple states and/or related by time or other order, and multiple input experimental information sources. A prototype archiving system called PDB-Dev ( https://pdb-dev.wwpdb.org ) has also been created to archive integrative structural models, together with a Python library to facilitate handling of integrative models in PDBx/mmCIF format.

Mechanism of activating mutations and allosteric drug inhibition of the phosphatase SHP2

Protein tyrosine phosphatase SHP2 functions as a key regulator of cell cycle control, and activating mutations cause several cancers. Here, we dissect the energy landscape of wild-type SHP2 and the oncogenic mutation E76K. NMR spectroscopy and X-ray crystallography reveal that wild-type SHP2 exchanges between closed, inactive and open, active conformations. E76K mutation shifts this equilibrium toward the open state. The previously unknown open conformation is characterized, including the active-site WPD loop in the inward and outward conformations. Binding of the allosteric inhibitor SHP099 to E76K mutant, despite much weaker, results in an identical structure as the wild-type complex. A conformational selection to the closed state reduces drug affinity which, combined with E76K’s much higher activity, demands significantly greater SHP099 concentrations to restore wild-type  activity levels. The differences in structural ensembles and drug-binding kinetics of cancer-associated SHP2 forms may stimulate innovative ideas for developing more potent inhibitors for activated SHP2 mutants.

The protein tyrosine phosphatase SHP2 is a key regulator of cell cycle control. Here the authors combine NMR measurements and X-ray crystallography and show that wild-type SHP2 dynamically exchanges between a closed inactive conformation and an open activated form and that the oncogenic E76K mutation shifts the equilibrium to the open state, which is reversed by binding of the allosteric inhibitor SHP099.

Integrative structure modeling with the Integrative Modeling Platform

Building models of a biological system that are consistent with the myriad data available is one of the key challenges in biology. Modeling the structure and dynamics of macromolecular assemblies, for example, can give insights into how biological systems work, evolved, might be controlled, and even designed. Integrative structure modeling casts the building of structural models as a computational optimization problem, for which information about the assembly is encoded into a scoring function that evaluates candidate models. Here, we describe our open source software suite for integrative structure modeling, Integrative Modeling Platform (https://integrativemodeling.org), and demonstrate its use.

Reduction of small-angle scattering profiles to finite sets of structural invariants

This paper shows how small-angle scattering (SAS) curves can be decomposed in a simple sum using a set of invariant parameters called Kn which are related to the shape of the object of study. These Kn, together with a radius R, give a complete theoretical description of the SAS curve. Adding an overall constant, these parameters are easily fitted against experimental data giving a concise comprehensive description of the data. The pair distance distribution function is also entirely described by this invariant set and the Dmax parameter can be measured. In addition to the understanding they bring, these invariants can be used to reliably estimate structural moments beyond the radius of gyration, thereby rigorously expanding the actual set of model-free quantities one can extract from experimental SAS data, and possibly paving the way to designing new shape reconstruction strategies.

Determining Atomistic SAXS Models of Tri-Ubiquitin Chains from Bayesian Analysis of Accelerated Molecular Dynamics Simulations

Small-angle X-ray scattering (SAXS) has become an increasingly popular technique for characterizing the solution ensemble of flexible biomolecules. However, data resulting from SAXS is typically low-dimensional and is therefore difficult to interpret without additional structural knowledge. In theory, molecular dynamics (MD) trajectories can provide this information, but conventional simulations rarely sample the complete ensemble. Here, we demonstrate that accelerated MD simulations can be used to produce higher quality models in shorter time scales than standard simulations, and we present an iterative Bayesian Monte Carlo method that is able to identify multistate ensembles without overfitting. This methodology is applied to several ubiquitin trimers to demonstrate the effect of linkage type on the solution states of the signaling protein. We observe that the linkage site directly affects the solution flexibility of the trimer and theorize that this difference in plasticity contributes to their disparate roles in vivo.

Development of tools to automate quantitative analysis of radiation damage in SAXS experiments

Biological small-angle X-ray scattering (SAXS) is an increasingly popular technique used to obtain nanoscale structural information on macromolecules in solution. However, radiation damage to the samples limits the amount of useful data that can be collected from a single sample. In contrast to the extensive analytical resources available for macromolecular crystallography (MX), there are relatively few tools to quantitate radiation damage for SAXS, some of which require a significant level of manual characterization, with the potential of leading to conflicting results from different studies. Here, computational tools have been developed to automate and standardize radiation damage analysis for SAXS data. RADDOSE-3D, a dose calculation software utility originally written for MX experiments, has been extended to account for the cylindrical geometry of the capillary tube, the liquid composition of the sample and the attenuation of the beam by the capillary material to allow doses to be calculated for many SAXS experiments. Furthermore, a library has been written to visualize and explore the pairwise similarity of frames. The calculated dose for the frame at which three subsequent frames are determined to be dissimilar is defined as the radiation damage onset threshold (RDOT). Analysis of RDOTs has been used to compare the efficacy of radioprotectant compounds to extend the useful lifetime of SAXS samples. Comparison of the RDOTs shows that, for radioprotectant compounds at 5 and 10 mM concentration, glycerol is the most effective compound. However, at 1 and 2 mM concentrations, dithiothreitol (DTT) appears to be most effective. Our newly developed visualization library contains methods that highlight the unusual radiation damage results given by SAXS data collected using higher concentrations of DTT: these observations should pave the way to the development of more sophisticated frame merging strategies.

The dynamic duo: combining NMR and small angle scattering in structural biology

Structural biology provides essential information for elucidating molecular mechanisms that underlie biological function. Advances in hardware, sample preparation, experimental methods, and computational approaches now enable structural analysis of protein complexes with increasing complexity that more closely represent biologically entities in the cellular environment. Integrated multidisciplinary approaches are required to overcome limitations of individual methods and take advantage of complementary aspects provided by different structural biology techniques. Although X-ray crystallography remains the method of choice for structural analysis of large complexes, crystallization of flexible systems is often difficult and does typically not provide insights into conformational dynamics present in solution. Nuclear magnetic resonance spectroscopy (NMR) is well-suited to study dynamics at picosecond to second time scales, and to map binding interfaces even of large systems at residue resolution but suffers from poor sensitivity with increasing molecular weight. Small angle scattering (SAS) methods provide low resolution information in solution and can characterize dynamics and conformational equilibria complementary to crystallography and NMR. The combination of NMR, crystallography, and SAS is, thus, very useful for analysis of the structure and conformational dynamics of (large) protein complexes in solution. In high molecular weight systems, where NMR data are often sparse, SAS provides additional structural information and can differentiate between NMR-derived models. Scattering data can also validate the solution conformation of a crystal structure and indicate the presence of conformational equilibria. Here, we review current state-of-the-art approaches for combining NMR, crystallography, and SAS data to characterize protein complexes in solution.

SAXS Merge: an automated statistical method to merge SAXS profiles using Gaussian processes

Small-angle X-ray scattering (SAXS) is an experimental technique that allows structural information on biomolecules in solution to be gathered. High-quality SAXS profiles have typically been obtained by manual merging of scattering profiles from different concentrations and exposure times. This procedure is very subjective and results vary from user to user. Up to now, no robust automatic procedure has been published to perform this step, preventing the application of SAXS to high-throughput projects. Here, SAXS Merge, a fully automated statistical method for merging SAXS profiles using Gaussian processes, is presented. This method requires only the buffer-subtracted SAXS profiles in a specific order. At the heart of its formulation is non-linear interpolation using Gaussian processes, which provides a statement of the problem that accounts for correlation in the data.

Comparative Modeling of Drug Target Proteins☆

In this perspective, we begin by describing the comparative protein structure modeling technique and the accuracy of the corresponding models. We then discuss the significant role that comparative prediction plays in drug discovery. We focus on virtual ligand screening against comparative models and illustrate the state-of-the-art by a number of specific examples.