Atomistic modelling of scattering data in the Collaborative Computational Project for Small Angle Scattering (CCP-SAS)

Scattering-based structural reconstruction by dimensional elevation

This study outlines a conceptually new approach for reconstructing the neutron scattering length density profile, Δρ(r), directly from small-angle neutron scattering (SANS) intensity profiles, I(Q). The method is built upon a universal operator A, fundamental to scattering processes, which relates I(Q) to Δρ(r) through the covariance matrix X ≡ Δρ(r)Δρ(r)†. In contrast to conventional SANS data analysis techniques, this approach eliminates the need to predefine a model of Δρ(r) in the regression process. This capability inherently addresses challenges often encountered in existing spectral inversion analysis, such as convergence to local minima due to incomplete analytical models, insufficient orthogonal basis vectors, or non-orthogonality among basis functions in model-free approaches. By extending spectral regression analysis from the vector space of I(Q) to the higher-dimensional space of AXA†, the PhaseLift framework imposes convexity on the regression process. This ensures the stable and computationally efficient reconstruction of the universal minimum Δρ(r) from I(Q). Numerical benchmarks and experimental validations confirm the reliability of this approach in tackling neutron scattering inverse problems. The method establishes a robust and flexible framework for advancing neutron scattering data analysis, with the potential to significantly enhance both the precision and efficiency of experiments across various scientific domains. It provides a solid foundation for further research into the interpretation and application of scattering data.

Dynamic self-assembled meso-structures formed across a wide concentration range in aqueous solutions of propranolol hydrochloride

HYPOTHESIS

Nanoscale characterisation of the self-associated species formed by amphiphilic pharmaceuticals in aqueous solution carries relevance across their entire journey from development through to manufacture - relevant, therefore, not only as regards formulation of the drug products as medicines, but also potentially relevant to their bioavailability, activity, and clinical side effects. Such knowledge and understanding, however, can only be fully secured by applying a range of experimental and theoretical methodologies.

EXPERIMENTS

Herein, we apply a synergistic combination of solubility, surface tension, SANS, NMR and UV spectroscopic studies, together with MD simulation and QM calculations, to investigate the meso-structures of propranolol hydrochloride aggregates in bulk aqueous solutions, at concentrations spanning 2.5 mM to > 200 mM. In addition, we explore the effects of adding NaCl to mimic the ionic strength of physiological fluids, and the differences between racemate and single enantiomer.

FINDINGS

There is a continuum of particle sizes shown to exist across the entire concentration range, with molecules joining and leaving on the nanosecond timescale, and with the distributions of aggregate sizes varying with drug and salt concentration. Given that propranolol is a highly prescribed (WHO essential) medicine, disfavouring aggregators from consideration in high-throughput screening for potential new drug candidates - as many have advocated - should thus be done cautiously.

The analysis of neutron reflectivity from Langmuir monolayers of lipids using molecular dynamics simulations: the role of lipid area

Biomolecular simulations are increasingly being used to generate detailed structural models to aid interpretation of neutron reflectometry (NR) data obtained from model biological membranes. Unlike globular systems, often studied by small-angle scattering, simulations of two-dimensional layers are sensitive to the simulation cell used which constrains the system laterally. We perform a careful analysis of NR data obtained from a monolayer of the lipid distearoylphosphatidylcholine at the air-water interface and show that the fit of number density profiles obtained from atomistic molecular dynamics simulation to the experimental data is very sensitive to the assumed area per lipid (APL). We propose a protocol for obtaining a realistic isotherm by combining the experimental surface pressure corresponding to a reflectometry measurement with an APL obtained from the simulation that best fits that data. Finally, we demonstrate how downstream interpretation of the experimental sample, derived from structural and dynamic properties of the atomistic model, depends strongly on the correct choice of simulation cell.

SEC-SAXS/MC Ensemble Structural Studies of the Microtubule Binding Protein Cdt1 Show Monomeric, Folded-Over Conformations

Cdt1 is a mixed folded protein critical for DNA replication licensing and it also has a "moonlighting" role at the kinetochore via direct binding to microtubules and the Ndc80 complex. However, it is unknown how the structure and conformations of Cdt1 could allow it to participate in these multiple, unique sets of protein complexes. While robust methods exist to study entirely folded or unfolded proteins, structure-function studies of combined, mixed folded/disordered proteins remain challenging. In this work, we employ orthogonal biophysical and computational techniques to provide structural characterization of mitosis-competent human Cdt1. Thermal stability analyses shows that both folded winged helix domains1 are unstable. CD and NMR show that the N-terminal and linker regions are intrinsically disordered. DLS shows that Cdt1 is monomeric and polydisperse, while SEC-MALS confirms that it is monomeric at high concentrations, but without any apparent inter-molecular self-association. SEC-SAXS enabled computational modeling of the protein structures. Using the program SASSIE, we performed rigid body Monte Carlo simulations to generate a conformational ensemble of structures. We observe that neither fully extended nor extremely compact Cdt1 conformations are consistent with SAXS. The best-fit models have the N-terminal and linker disordered regions extended into the solution and the two folded domains close to each other in apparent "folded over" conformations. We hypothesize the best-fit Cdt1 conformations could be consistent with a function as a scaffold protein that may be sterically blocked without binding partners. Our study also provides a template for combining experimental and computational techniques to study mixed-folded proteins.

The SCR-17 and SCR-18 glycans in human complement factor H enhance its regulatory function

Human complement factor H (CFH) plays a central role in regulating activated C3b to protect host cells. CFH contain 20 short complement regulator (SCR) domains and eight N-glycosylation sites. The N-terminal SCR domains mediate C3b degradation while the C-terminal CFH domains bind to host cell surfaces to protect these. Our earlier study of Pichia-generated CFH fragments indicated a self-association site at SCR-17/18 that comprises a dimerization site for human factor H. Two N-linked glycans are located on SCR-17 and SCR-18. Here, when we expressed SCR-17/18 without glycans in an Escherichia coli system, analytical ultracentrifugation showed that no dimers were now formed. To investigate this novel finding, full-length CFH and its C-terminal fragments were purified from human plasma and Pichia pastoris respectively, and their glycans were enzymatically removed using PNGase F. Using size-exclusion chromatography, mass spectrometry, and analytical ultracentrifugation, SCR-17/18 from Pichia showed notably less dimer formation without its glycans, confirming that the glycans are necessary for the formation of SCR-17/18 dimers. By surface plasmon resonance, affinity analyses interaction showed decreased binding of deglycosylated full-length CFH to immobilized C3b, showing that CFH glycosylation enhances the key CFH regulation of C3b. We conclude that our study revealed a significant new aspect of CFH regulation based on its glycosylation and its resulting dimerization.

SEB: a computational tool for symbolic derivation of the small-angle scattering from complex composite structures

Analysis of small-angle scattering (SAS) data requires intensive modeling to infer and characterize the structures present in a sample. This iterative improvement of models is a time-consuming process. Presented here is Scattering Equation Builder (SEB), a C++ library that derives exact analytic expressions for the form factors of complex composite structures. The user writes a small program that specifies how the sub-units should be linked to form a composite structure and calls SEB to obtain an expression for the form factor. SEB supports e.g. Gaussian polymer chains and loops, thin rods and circles, solid spheres, spherical shells and cylinders, and many different options for how these can be linked together. The formalism behind SEB is presented and simple case studies are given, such as block copolymers with different types of linkage, as well as more complex examples, such as a random walk model of 100 linked sub-units, dendrimers, polymers and rods attached to the surfaces of geometric objects, and finally the scattering from a linear chain of five stars, where each star is built up of four diblock copolymers. These examples illustrate how SEB can be used to develop complex models and hence reduce the cost of analyzing SAS data.

Using atomistic solution scattering modelling to elucidate the role of the Fc glycans in human IgG4

Human immunoglobulin G (IgG) exists as four subclasses IgG1-4, each of which has two Fab subunits joined by two hinges to a Fc subunit. IgG4 has the shortest hinge with 12 residues. The Fc subunit has two glycan chains, but the importance of glycosylation is not fully understood in IgG4. Here, to evaluate the stability and structure of non-glycosylated IgG4, we performed a multidisciplinary structural study of glycosylated and deglycosylated human IgG4 A33 for comparison with our similar study of human IgG1 A33. After deglycosylation, IgG4 was found to be monomeric by analytical ultracentrifugation; its sedimentation coefficient of 6.52 S was reduced by 0.27 S in reflection of its lower mass. X-ray and neutron solution scattering showed that the overall Guinier radius of gyration RG and its cross-sectional values after deglycosylation were almost unchanged. In the P(r) distance distribution curves, the two M1 and M2 peaks that monitor the two most common distances within IgG4 were unchanged following deglycosylation. Further insight from Monte Carlo simulations for glycosylated and deglycosylated IgG4 came from 111,382 and 117,135 possible structures respectively. Their comparison to the X-ray and neutron scattering curves identified several hundred best-fit models for both forms of IgG4. Principal component analyses showed that glycosylated and deglycosylated IgG4 exhibited different conformations from each other. Within the constraint of unchanged RG and M1-M2 values, the glycosylated IgG4 models showed more restricted Fc conformations compared to deglycosylated IgG4, but no other changes. Kratky plots supported this interpretation of greater disorder upon deglycosylation, also observed in IgG1. Overall, these more variable Fc conformations may demonstrate a generalisable impact of deglycosylation on Fc structures, but with no large conformational changes in IgG4 unlike those seen in IgG1.

SAXS/MC studies of the mixed-folded protein Cdt1 reveal monomeric, folded over conformations

Cdt1 is a protein critical for DNA replication licensing and is well-established to be a binding partner of the minichromosome maintenance (MCM) complex. Cdt1 has also been demonstrated to have an emerging, "moonlighting" role at the kinetochore via direct binding to microtubules and to the Ndc80 complex. However, it is not known how the structure and conformations of Cdt1 could allow for these multiple, completely unique sets of protein complexes. And while there exist multiple robust methods to study entirely folded or entirely unfolded proteins, structure-function studies of combined, mixed folded/disordered proteins remain challenging. It this work, we employ multiple orthogonal biophysical and computational techniques to provide a detailed structural characterization of human Cdt1 92-546. DSF and DSCD show both folded winged helix (WH) domains of Cdt1 are relatively unstable. CD and NMR show the N-terminal and the linker regions are intrinsically disordered. Using DLS and SEC-MALS, we show that Cdt1 is polydisperse, monomeric at high concentrations, and without any apparent inter-molecular self-association. SEC-SAXS of the monomer in solution enabled computational modeling of the protein in silico. Using the program SASSIE, we performed rigid body Monte Carlo simulations to generate a conformational ensemble. Using experimental SAXS data, we filtered for conformations which did and did not fit our data. We observe that neither fully extended nor extremely compact Cdt1 conformations are consistent with our SAXS data. The best fit models have the N-terminal and linker regions extended into solution and the two folded domains close to each other in apparent "folded over" conformations. The best fit Cdt1 conformations are consistent with a function as a scaffold protein which may be sterically blocked without the presence of binding partners. Our studies also provide a template for combining experimental and computational biophysical techniques to study mixed-folded proteins.

Insight into structural biophysics from solution X-ray scattering

The current challenges of structural biophysics include determining the structure of large self-assembled complexes, resolving the structure of ensembles of complex structures and their mass fraction, and unraveling the dynamic pathways and mechanisms leading to the formation of complex structures from their subunits. Modern synchrotron solution X-ray scattering data enable simultaneous high-spatial and high-temporal structural data required to address the current challenges of structural biophysics. These data are complementary to crystallography, NMR, and cryo-TEM data. However, the analysis of solution scattering data is challenging; hence many different analysis tools, listed in the SAS Portal (http://smallangle.org/), were developed. In this review, we start by briefly summarizing classical X-ray scattering analyses providing insight into fundamental structural and interaction parameters. We then describe recent developments, integrating simulations, theory, and advanced X-ray scattering modeling, providing unique insights into the structure, energetics, and dynamics of self-assembled complexes. The structural information is essential for understanding the underlying physical chemistry principles leading to self-assembled supramolecular architectures and computational structural refinement.

Visualization of Self-Assembly and Hydration of a β-Hairpin through Integrated Small and Wide-Angle Neutron Scattering

Fundamental understanding of the structure and assembly of nanoscale building blocks is crucial for the development of novel biomaterials with defined architectures and function. However, accessing self-consistent structural information across multiple length scales is challenging. This limits opportunities to exploit atomic scale interactions to achieve emergent macroscale properties. In this work we present an integrative small- and wide-angle neutron scattering approach coupled with computational modeling to reveal the multiscale structure of hierarchically self-assembled β hairpins in aqueous solution across 4 orders of magnitude in length scale from 0.1 Å to 300 nm. Our results demonstrate the power of this self-consistent cross-length scale approach and allows us to model both the large-scale self-assembly and small-scale hairpin hydration of the model β hairpin CLN025. Using this combination of techniques, we map the hydrophobic/hydrophilic character of this model self-assembled biomolecular surface with atomic resolution. These results have important implications for the multiscale investigation of aqueous peptides and proteins, for the prediction of ligand binding and molecular associations for drug design, and for understanding the self-assembly of peptides and proteins for functional biomaterials.

The solution structure of the heavy chain-only C5-Fc nanobody reveals exposed variable regions that are optimal for COVID-19 antigen interactions

Heavy chain-only antibodies can offer advantages of higher binding affinities, reduced sizes, and higher stabilities than conventional antibodies. To address the challenge of SARS-CoV-2 coronavirus, a llama-derived single-domain nanobody C5 was developed previously that has high COVID-19 virus neutralization potency. The fusion protein C5-Fc comprises two C5 domains attached to a glycosylated Fc region of a human IgG1 antibody and shows therapeutic efficacy in vivo. Here, we have characterized the solution arrangement of the molecule. Two 1443 Da N-linked glycans seen in the mass spectra of C5-Fc were removed and the glycosylated and deglycosylated structures were evaluated. Reduction of C5-Fc with 2-mercaptoethylamine indicated three interchain Cys-Cys disulfide bridges within the hinge. The X-ray and neutron Guinier RG values, which provide information about structural elongation, were similar at 4.1 to 4.2 nm for glycosylated and deglycosylated C5-Fc. To explain these RG values, atomistic scattering modeling based on Monte Carlo simulations resulted in 72,737 and 56,749 physically realistic trial X-ray and neutron structures, respectively. From these, the top 100 best-fit X-ray and neutron models were identified as representative asymmetric solution structures, similar to that of human IgG1, with good R-factors below 2.00%. Both C5 domains were solvent exposed, consistent with the functional effectiveness of C5-Fc. Greater disorder occurred in the Fc region after deglycosylation. Our results clarify the importance of variable and exposed C5 conformations in the therapeutic function of C5-Fc, while the glycans in the Fc region are key for conformational stability in C5-Fc.

Role of Domain-Domain Interactions on the Self-Association and Physical Stability of Monoclonal Antibodies: Effect of pH and Salt

Monoclonal antibodies (mAbs) make up a major class of biotherapeutics with a wide range of clinical applications. Their physical stability can be affected by various environmental factors. For instance, an acidic pH can be encountered during different stages of the mAb manufacturing process, including purification and storage. Therefore, understanding the behavior of flexible mAb molecules in acidic solution environments will benefit the development of stable mAb products. This study used small-angle X-ray scattering (SAXS) and complementary biophysical characterization techniques to investigate the conformational flexibility and protein-protein interactions (PPI) of a model mAb molecule under near-neutral and acidic conditions. The study also characterized the interactions between Fab and Fc fragments under the same buffer conditions to identify domain-domain interactions. The results suggest that solution pH significantly influences mAb flexibility and thus could help mAbs remain physically stable by maximizing local electrostatic repulsions when mAbs become crowded in solution. Under acidic buffer conditions, both Fab and Fc contribute to the repulsive PPI observed among the full mAb at a low ionic strength. However, as ionic strength increases, hydrophobic interactions lead to the self-association of Fc fragments and, subsequently, could affect the aggregation state of the mAb.

The solution structure of the unbound IgG Fc receptor CD64 resembles its crystal structure: Implications for function

FcγRI (CD64) is the only high-affinity Fcγ receptor found on monocytes, macrophages, eosinophils, neutrophils and dendritic cells. It binds immunoglobulin G (IgG) antibody-antigen complexes at its Fc region to trigger key immune responses. CD64 contains three immunoglobulin-fold extracellular domains (D1, D2 and D3) and a membrane-spanning region. Despite the importance of CD64, no solution structure for this is known to date. To investigate this, we used analytical ultracentrifugation, small-angle X-ray scattering, and atomistic modelling. Analytical ultracentrifugation revealed that CD64 was monomeric with a sedimentation coefficient s020,w of 2.53 S, together with some dimer. Small-angle X-ray scattering showed that its radius of gyration RG was 3.3-3.4 nm and increased at higher concentrations to indicate low dimerization. Monte Carlo modelling implemented in the SASSIE-web package generated 279,162 physically-realistic trial CD64 structures. From these, the scattering best-fit models at the lowest measured concentrations that minimised dimers revealed that the D1, D2 and D3 domains were structurally similar to those seen in three CD64 crystal structures, but showed previously unreported flexibility between D1, D2 and D3. Despite the limitations of the scattering data, the superimposition of the CD64 solution structures onto crystal structures of the IgG Fc-CD64 complex showed that the CD64 domains do not sterically clash with the IgG Fc region, i.e. the solution structure of CD64 was sufficiently compact to allow IgG to bind to its high-affinity Fcγ receptor. This improved understanding may result in novel approaches to inhibit CD64 function, and opens the way for the solution study of the full-length CD64-IgG complex.

AlphaFold-predicted protein structures and small-angle X-ray scattering: insights from an extended examination of selected data in the Small-Angle Scattering Biological Data Bank

By providing predicted protein structures from nearly all known protein sequences, the artificial intelligence program AlphaFold (AF) is having a major impact on structural biology. While a stunning accuracy has been achieved for many folding units, predicted unstructured regions and the arrangement of potentially flexible linkers connecting structured domains present challenges. Focusing on single-chain structures without prosthetic groups, an earlier comparison of features derived from small-angle X-ray scattering (SAXS) data taken from the Small-Angle Scattering Biological Data Bank (SASBDB) is extended to those calculated using the corresponding AF-predicted structures. Selected SASBDB entries were carefully examined to ensure that they represented data from monodisperse protein solutions and had sufficient statistical precision and q resolution for reliable structural evaluation. Three examples were identified where there is clear evidence that the single AF-predicted structure cannot account for the experimental SAXS data. Instead, excellent agreement is found with ensemble models generated by allowing for flexible linkers between high-confidence predicted structured domains. A pool of representative structures was generated using a Monte Carlo method that adjusts backbone dihedral allowed angles along potentially flexible regions. A fast ensemble modelling method was employed that optimizes the fit of pair distance distribution functions [P(r) versus r] and intensity profiles [I(q) versus q] computed from the pool to their experimental counterparts. These results highlight the complementarity between AF prediction, solution SAXS and molecular dynamics/conformational sampling for structural modelling of proteins having both structured and flexible regions.

Shape2SAS: a web application to simulate small-angle scattering data and pair distance distributions from user-defined shapes

Shape2SAS is a web application that allows researchers and students to build intuition about and understanding of small-angle scattering. It is available at https://somo.chem.utk.edu/shape2sas. The user defines a model of arbitrary shape by combining geometrical subunits, and Shape2SAS then calculates and displays the scattering intensity and the pair distance distribution, as well as a visualization of the user-defined shape. Simulated data with realistic noise are also generated. Here, it is demonstrated how Shape2SAS can calculate and display the different scattering patterns for various geometrical shapes, such as spheres and cylinders. It is also shown how the effect of structure factors can be visualized. Finally, it is indicated how multi-contrast particles can readily be generated, and how the calculated scattering may be used to validate and visualize analytical models generated in analysis software for fitting small-angle scattering data.

Beyond the US-SOMO-AF database: a new website for hydrodynamic, structural, and circular dichroism calculations on user-supplied structures

At the 25th International Analytical Ultracentrifugation Workshop and Symposium, we described the recent implementation of the UltraScan SOlution MOdeler AlphaFold (US-SOMO-AF) database, containing hydrodynamic, structural, CD calculations, and other ancillary information, performed on the entire AF v2 database of predicted protein structures, containing more than 1,000,000 entries. The scope of the US-SOMO-AF database was that of providing direct access to pre-calculated physicochemical parameters for rapid assessment against their experimentally determined counterparts to test the compatibility in solution of predicted AlphaFold structures. In the meantime, the AlphaFold consortium has extended its database of predicted structures to an astonishing > 200 million entries, making it quite impractical for their coverage in the US-SOMO-AF database. Therefore, we have created the US-SOMO-Web site, allowing the rapid calculations of all the properties, as present in the US-SOMO-AF database, on user-supplied PDB and mmCIF structures, as well as allowing direct processing of the latest AlphaFold models. Major features on the website are described, along with current limitations and potential future developments.

Neutron Reflectometry and Molecular Simulations Demonstrate HIV-1 Nef Homodimer Formation on Model Lipid Bilayers

The HIV-1 Nef protein plays a critical role in viral infectivity, high-titer replication in vivo, and immune escape of HIV-infected cells. Nef lacks intrinsic biochemical activity, functioning instead through interactions with diverse host cell signaling proteins and intracellular trafficking pathways. Previous studies have established an essential role for Nef homodimer formation at the plasma membrane for most if not all its functions. Here we combined neutron reflectometry of full-length myristoylated Nef bound to model lipid bilayers with molecular simulations based on previous X-ray crystal structures of Nef homodimers. This integrated approach provides direct evidence that Nef associates with the membrane as a homodimer with its structured core region displaced from the membrane for partner protein engagement. Parallel studies of a dimerization-defective mutant, Nef-L112D, demonstrate that the helical dimerization interface present in previous crystal structures stabilizes the membrane-bound dimer. X-ray crystallography of the Nef-L112D mutant in complex with the SH3 domain of the Nef-associated host cell kinase Hck revealed a monomeric 1:1 complex instead of the 2:2 dimer complex formed with wild-type Nef. Importantly, the crystal structure of the Nef-L112D core and SH3 interface are virtually identical to the wild-type complex, indicating that this mutation does not affect the overall Nef fold. These findings support the intrinsic capacity of Nef to homodimerize at lipid bilayers using structural features present in X-ray crystal structures of dimeric complexes.

2023 update of template tables for reporting biomolecular structural modelling of small-angle scattering data

In 2017, guidelines were published for reporting structural modelling of small-angle scattering (SAS) data from biomolecules in solution that exemplified best-practice documentation of experiments and analysis. Since then, there has been significant progress in SAS data and model archiving, and the IUCr journal editors announced that the IUCr biology journals will require the deposition of SAS data used in biomolecular structure solution into a public archive, as well as adherence to the 2017 reporting guidelines. In this context, the reporting template tables accompanying the 2017 publication guidelines have been reviewed with a focus on making them both easier to use and more general. With input from the SAS community via the IUCr Commission on SAS and attendees of the triennial 2022 SAS meeting (SAS2022, Campinas, Brazil), an updated reporting template table has been developed that includes standard descriptions for proteins, glycosylated proteins, DNA and RNA, with some reorganization of the data to improve readability and interpretation. In addition, a specialized template has been developed for reporting SAS contrast-variation (SAS-cv) data and models that incorporates the additional reporting requirements from the 2017 guidelines for these more complicated experiments. To demonstrate their utility, examples of reporting with these new templates are provided for a SAS study of a DNA-protein complex and a SAS-cv experiment on a protein complex. The examples demonstrate how the tabulated information promotes transparent reporting that, in combination with the recommended figures and additional information best presented in the main text, enables the reader of the work to readily draw their own conclusions regarding the quality of the data and the validity of the models presented.

A solution structure analysis reveals a bent collagen triple helix in the complement activation recognition molecule mannan-binding lectin

Collagen triple helices are critical in the function of mannan-binding lectin (MBL), an oligomeric recognition molecule in complement activation. The MBL collagen regions form complexes with the serine proteases MASP-1 and MASP-2 in order to activate complement, and mutations lead to common immunodeficiencies. To evaluate their structure-function properties, we studied the solution structures of four MBL-like collagen peptides. The thermal stability of the MBL collagen region was much reduced by the presence of a GQG interruption in the typical (X-Y-Gly)n repeat compared to controls. Experimental solution structural data were collected using analytical ultracentrifugation and small angle X-ray and neutron scattering. As controls, we included two standard Pro-Hyp-Gly collagen peptides (POG)10-13, as well as three more peptides with diverse (X-Y-Gly)n sequences that represented other collagen features. These data were quantitatively compared with atomistic linear collagen models derived from crystal structures and 12,000 conformations obtained from molecular dynamics simulations. All four MBL peptides were bent to varying degrees up to 85o in the best-fit molecular dynamics models. The best-fit benchmark peptides (POG)n were more linear but exhibited a degree of conformational flexibility. The remaining three peptides showed mostly linear solution structures. In conclusion, the collagen helix is not strictly linear, the degree of flexibility in the triple helix depends on its sequence, and the triple helix with the GQG interruption showed a pronounced bend. The bend in MBL GQG peptides resembles the bend in the collagen of complement C1q and may be key for lectin pathway activation.

Shape2SAS -- a web application to simulate small-angle scattering data and pair distance distributions from user-defined shapes

Shape2SAS is a web application that allows researchers and students to build intuition and understanding of small-angle scattering. It is available at https://somo.chem.utk.edu/shape2sas. The user defines a model of arbitrary shape by combining geometrical subunits, and Shape2SAS then calculates and displays the scattering intensity, the pair distance distribution as well as a visualization of the user-defined shape. Simulated data with realistic noise are also generated. We demonstrate how Shape2SAS can calculate and display the different scattering patterns for various geometrical shapes, such as spheres and cylinders. We also demonstrate how the effect of structure factors can be visualized. Finally, we show how multi-contrast particles can readily be generated, and how the calculated scattering may be used to validate and visualize analytical models generated in analysis software for fitting small-angle scattering data.

Reconstruction of 3D density from solution scattering

Ab initio modeling methods have proven to be powerful means of interpreting solution scattering data. In the absence of atomic models, or complementary to them, ab initio modeling approaches can be used for generating low-resolution particle envelopes using only solution scattering profiles. Recently, a new ab initio reconstruction algorithm has been introduced to the scientific community, called DENSS. DENSS is unique among ab initio modeling algorithms in that it solves the inverse scattering problem, i.e., the 1D scattering intensities are directly used to determine the 3D particle density. The reconstruction of particle density has several advantages over conventional uniform density modeling approaches, including the ability to reconstruct a much wider range of particle types and the ability to visualize low-resolution density fluctuations inside the particle envelope. In this chapter we will discuss the theory behind this new approach, how to use DENSS, and how to interpret the results. Several examples with experimental and simulated data will be provided.

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.

Computational methods for the analysis of solution small-angle X-ray scattering of biomolecules: ATSAS

The ATSAS software suite provides a comprehensive set of programs for the processing, analysis and modeling of small-angle scattering data, tailored for but not limited to data acquired on biological macromolecules. In this review the major components and developments in the ATSAS package are described, with a focus on user driven application. Data reduction, analysis and modeling approaches and strategies will be introduced and discussed. At the time of writing the latest package, ATSAS 3.1, is freely available for academic users at: https://www.embl-hamburg.de/biosaxs/software.html.

Elucidation of critical pH-dependent structural changes in Botulinum Neurotoxin E

Botulinum Neurotoxins (BoNT) are the most potent toxins currently known. However, they also have therapeutic applications for an increasing number of motor related conditions due to their specificity, and low diffusion into the system. Although the start- and end- points for the BoNT mechanism of action are well-studied, a critical step remains poorly understood. It is theorised that BoNTs undergo a pH-triggered conformational shift, activating the neurotoxin by priming it to form a transmembrane (TM) channel. To test this hypothesis, we combined molecular dynamics (MD) simulations and small-angle x-ray scattering (SAXS), revealing a new conformation of serotype E (BoNT/E). This conformation was exclusively observed in simulations below pH 5.5, as determined by principal component analysis (PCA), and its theoretical SAXS profile matched an experimental SAXS profile obtained at pH 4. Additionally, a localised secondary structural change was observed in MD simulations below pH 5.5, in a region previously identified as instrumental for membrane insertion for serotype A (BoNT/A). These changes were found at a critical pH value for BoNTs in vivo, and may be relevant for their therapeutic use.

Styrene-Maleic Acid Copolymer Nanodiscs to Determine the Shape of Membrane Proteins

Lipid nanodiscs can be used to solubilize functional membrane proteins (MPs) in nativelike environments. Thus, they are promising reagents that have been proven useful to characterize MPs. Both protein and non-protein molecular belts have shown promise to maintain the structural integrity of MPs in lipid nanodiscs. Small-angle neutron scattering (SANS) can be used to determine low-resolution structures of proteins in solution, which can be enhanced through the use of contrast variation methods. We present theoretical contrast variation SANS results for protein and styrene-maleic acid copolymer (SMA) belt 1,2-dimyristoyl-sn-glycero-3-phosphorylcholine (DMPC) nanodiscs with and without additional bound or transmembrane proteins. The predicted scattering properties are derived from atomistic molecular dynamics simulations to account for conformational fluctuations, and we determine deuterium-labeling conditions such that SANS intensity profiles only include contributions from the scattering of the MP of interest. We propose strategies to tune the neutron scattering length densities (SLDs) of the SMA and DMPC using selective deuterium labeling such that the SLD of the nanodisc becomes homogeneous and its scattering can essentially be eliminated in solvents containing an appropriate amount of D₂O. These finely tuned labeled polymer-based nanodiscs are expected to be useful to extract the size and molecular shape information of MPs using SANS-based contrast variation experiments, and they can be used with MPs of any molecular weight.

Membrane-bound KRAS approximates an entropic ensemble of configurations

KRAS4B is a membrane-anchored signaling protein and a primary target in cancer research. Predictions from molecular dynamics simulations that have previously shaped our mechanistic understanding of KRAS signaling disagree with recent experimental results from neutron reflectometry, NMR, and thermodynamic binding studies. To gain insight into these discrepancies, we compare this body of biophysical data to back-calculated experimental results from a series of molecular simulations that implement different subsets of molecular interactions. Our results show that KRAS4B approximates an entropic ensemble of configurations at model membranes containing 30% phosphatidylserine lipids, which is not significantly shaped by interactions between the globular G-domain of KRAS4B and the lipid membrane. These findings revise our understanding of KRAS signaling and promote a model in which the protein samples the accessible conformational space in a near-uniform manner while being available to bind to effector proteins.

Solution structures of human myeloma IgG3 antibody reveal extended Fab and Fc regions relative to the other IgG subclasses

Human immunoglobulin G subclass 3 (IgG3) possesses a uniquely long hinge region that separates its Fab antigen-binding and Fc receptor-binding regions. Owing to this hinge length, the molecular structure of full-length IgG3 remains elusive, and the role of the two conserved Fc glycosylation sites are unknown. To address these issues, we subjected glycosylated and deglycosylated human myeloma IgG3 to multidisciplinary solution structure studies. Using analytical ultracentrifugation, the elongated structure of IgG3 was determined from the reduced sedimentation coefficients s020,w of 5.82 to 6.29 S for both glycosylated and deglycosylated IgG3. X-ray and neutron scattering showed that the Guinier RG values were 6.95 nm for glycosylated IgG3 and were unchanged after deglycosylation, again indicating an elongated structure. The distance distribution function P(r) showed a maximum length of 25 to 28 nm and three distinct maxima. The molecular structure of IgG3 was determined using atomistic modeling based on molecular dynamics simulations of the IgG3 hinge and Monte Carlo simulations to identify physically realistic arrangements of the Fab and Fc regions. This resulted in libraries containing 135,135 and 73,905 glycosylated and deglycosylated IgG3 structures, respectively. Comparisons with the X-ray and neutron scattering curves gave 100 best-fit models for each form of IgG3 that accounted for the experimental scattering curves. These models revealed the first molecular structures for full-length IgG3. The structures exhibited relatively restricted Fab and Fc conformations joined by an extended semirigid hinge, which explains the potent effector functions of IgG3 relative to the other subclasses IgG1, IgG2, and IgG4.

Searching for Aquamelt Behavior among Silklike Biomimetics during Fibrillation under Flow

In this paper, we elucidate a generic mechanism behind strain-induced phase transition in aqueous solutions of silk-inspired biomimetics by atomistic molecular dynamics simulations. We show the results of modeling of homopeptides polyglycine Gly₃₀ and polyalanine Ala₃₀ and a heteropeptide (Gly-Ala-Gly-Ala-Gly-Ser)₅, i.e., the simplest and yet relevant sequences that could mimic the behavior of natural silk under stress conditions. First, we analyze hydrophobicities of the sequences by calculating the Gibbs free energy of hydration and inspecting the interchain hydrogen bonding and hydration by water. Second, the force-extension profiles are scanned and compared with the results for poly(ethylene oxide), the synthetic polymer for which the aquamelt behavior has been proved recently. Additionally, the conformational transitions of oligopeptides from coiled to extended states are characterized by a generalized order parameter and by the dependence of the solvent-accessible surface area of the chains on applied stretching. Fibrillation itself is surveyed using both the two-dimensional interchain pair correlation function and the SAXS/WAXS patterns for the aggregates formed under stress. These are compared with experimental data found in the literature on fibril structure of silk composite materials doped with oligoalanine peptides. Our results show that tensile stress introduced into aqueous oligopeptide solutions facilitates interchain interactions. The oligopeptides display both a greater resistance to extension as compared to poly(ethylene oxide) and a reduced ability for hydrogen bonding of the stretched chains between oligomers and with water. Fiber formation is proved for all simulated objects, but the most structured one is made of a heteropeptide (Gly-Ala-Gly-Ala-Gly-Ser)₅: For this sequence, we obtain the highest degree of the secondary structure motifs in the fiber. We conclude that this is the most promising candidate among considered sequences to find the aquamelt behavior in further experimental studies.

Manipulation of a cation-π sandwich reveals conformational flexibility in phenylalanine hydroxylase

Phenylalanine hydroxylase (PAH) is an allosteric enzyme that maintains phenylalanine (Phe) below neurotoxic levels; its failure results in phenylketonuria, an inborn error of amino acid metabolism. Wild type (WT) PAH equilibrates among resting-state (RS-PAH) and activated (A-PAH) conformations, whose equilibrium position depends upon allosteric Phe binding. The RS-PAH conformation of WT rat PAH (rPAH) contains a cation-π sandwich involving Phe80 that cannot exist in the A-PAH conformation. Phe80 variants F80A, F80D, F80L, and F80R were prepared and evaluated using native PAGE, size exclusion chromatography, ion exchange behavior, intrinsic protein fluorescence, enzyme kinetics, and limited proteolysis, each as a function of [Phe]. Like WT rPAH, F80A and F80D show allosteric activation by Phe while F80L and F80R are constitutively active. Maximal activity of all variants suggests relief of a rate-determining conformational change. Limited proteolysis of WT rPAH (minus Phe) reveals facile cleavage within a 4-helix bundle that is buried in the RS-PAH tetramer interface, reflecting dynamic dissociation of that tetramer. This cleavage is not seen for the Phe80 variants, which all show proteolytic hypersensitivity in a linker that repositions during the RS-PAH to A-PAH interchange. Hypersensitivity is corrected by addition of Phe such that all variants become like WT rPAH and achieve the A-PAH conformation. Thus, manipulation of Phe80 perturbs the conformational space sampled by PAH, increasing sampling of on-pathway intermediates in the RS-PAH and A-PAH interchange. The behavior of the Phe80 variants mimics that of disease-associated R68S and suggests a molecular basis for proteolytic susceptibility in PKU-associated human PAH variants.

Solution structure of deglycosylated human IgG1 shows the role of CH2 glycans in its conformation

The human immunoglobulin G (IgG) class is the most prevalent antibody in serum, with the IgG1 subclass being the most abundant. IgG1 is composed of two Fab regions connected to a Fc region through a 15-residue hinge peptide. Two glycan chains are conserved in the Fc region in IgG; however, their importance for the structure of intact IgG1 has remained unclear. Here, we subjected glycosylated and deglycosylated monoclonal human IgG1 (designated as A33) to a comparative multidisciplinary structural study of both forms. After deglycosylation using peptide:N-glycosidase F, analytical ultracentrifugation showed that IgG1 remained monomeric and the sedimentation coefficients s⁰_20,w of IgG1 decreased from 6.45 S by 0.16-0.27 S. This change was attributed to the reduction in mass after glycan removal. X-ray and neutron scattering revealed changes in the Guinier structural parameters after deglycosylation. Although the radius of gyration (R_G) was unchanged, the cross-sectional radius of gyration (R_XS-1) increased by 0.1 nm, and the commonly occurring distance peak M2 of the distance distribution curve P(r) increased by 0.4 nm. These changes revealed that the Fab-Fc separation in IgG1 was perturbed after deglycosylation. To explain these changes, atomistic scattering modeling based on Monte Carlo simulations resulted in 123,284 and 119,191 trial structures for glycosylated and deglycosylated IgG1 respectively. From these, 100 x-ray and neutron best-fit models were determined. For these, principal component analyses identified five groups of structural conformations that were different for glycosylated and deglycosylated IgG1. The Fc region in glycosylated IgG1 showed a restricted range of conformations relative to the Fab regions, whereas the Fc region in deglycosylated IgG1 showed a broader conformational spectrum. These more variable Fc conformations account for the loss of binding to the Fcγ receptor in deglycosylated IgG1.

ATSAS 3.0: expanded functionality and new tools for small-angle scattering data analysis

The ATSAS software suite encompasses a number of programs for the processing, visualization, analysis and modelling of small-angle scattering data, with a focus on the data measured from biological macromolecules. Here, new developments in the ATSAS 3.0 package are described. They include IMSIM, for simulating isotropic 2D scattering patterns; IMOP, to perform operations on 2D images and masks; DATRESAMPLE, a method for variance estimation of structural invariants through parametric resampling; DATFT, which computes the pair distance distribution function by a direct Fourier transform of the scattering data; PDDFFIT, to compute the scattering data from a pair distance distribution function, allowing comparison with the experimental data; a new module in DATMW for Bayesian consensus-based concentration-independent molecular weight estimation; DATMIF, an ab initio shape analysis method that optimizes the search model directly against the scattering data; DAMEMB, an application to set up the initial search volume for multiphase modelling of membrane proteins; ELLLIP, to perform quasi-atomistic modelling of liposomes with elliptical shapes; NMATOR, which models conformational changes in nucleic acid structures through normal mode analysis in torsion angle space; DAMMIX, which reconstructs the shape of an unknown intermediate in an evolving system; and LIPMIX and BILMIX, for modelling multilamellar and asymmetric lipid vesicles, respectively. In addition, technical updates were deployed to facilitate maintainability of the package, which include porting the PRIMUS graphical interface to Qt5, updating SASpy - a PyMOL plugin to run a subset of ATSAS tools - to be both Python 2 and 3 compatible, and adding utilities to facilitate mmCIF compatibility in future ATSAS releases. All these features are implemented in ATSAS 3.0, freely available for academic users at https://www.embl-hamburg.de/biosaxs/software.html.

A Dimerization Site at SCR-17/18 in Factor H Clarifies a New Mechanism for Complement Regulatory Control

Complement Factor H (CFH), with 20 short complement regulator (SCR) domains, regulates the alternative pathway of complement in part through the interaction of its C-terminal SCR-19 and SCR-20 domains with host cell-bound C3b and anionic oligosaccharides. In solution, CFH forms small amounts of oligomers, with one of its self-association sites being in the SCR-16/20 domains. In order to correlate CFH function with dimer formation and the occurrence of rare disease-associated variants in SCR-16/20, we identified the dimerization site in SCR-16/20. For this, we expressed, in Pichia pastoris, the five domains in SCR-16/20 and six fragments of this with one-three domains (SCR-19/20, SCR-18/20, SCR-17/18, SCR-16/18, SCR-17 and SCR-18). Size-exclusion chromatography suggested that SCR dimer formation occurred in several fragments. Dimer formation was clarified using analytical ultracentrifugation, where quantitative c(s) size distribution analyses showed that SCR-19/20 was monomeric, SCR-18/20 was slightly dimeric, SCR-16/20, SCR-16/18 and SCR-18 showed more dimer formation, and SCR-17 and SCR-17/18 were primarily dimeric with dissociation constants of ~5 µM. The combination of these results located the SCR-16/20 dimerization site at SCR-17 and SCR-18. X-ray solution scattering experiments and molecular modelling fits confirmed the dimer site to be at SCR-17/18, this dimer being a side-by-side association of the two domains. We propose that the self-association of CFH at SCR-17/18 enables higher concentrations of CFH to be achieved when SCR-19/20 are bound to host cell surfaces in order to protect these better during inflammation. Dimer formation at SCR-17/18 clarified the association of genetic variants throughout SCR-16/20 with renal disease.

Structural Characterization and Modeling of a Respiratory Syncytial Virus Fusion Glycoprotein Nanoparticle Vaccine in Solution

The respiratory syncytial virus (RSV) fusion (F) protein/polysorbate 80 (PS80) nanoparticle vaccine is the most clinically advanced vaccine for maternal immunization and protection of newborns against RSV infection. It is composed of a near-full-length RSV F glycoprotein, with an intact membrane domain, formulated into a stable nanoparticle with PS80 detergent. To understand the structural basis for the efficacy of the vaccine, a comprehensive study of its structure and hydrodynamic properties in solution was performed. Small-angle neutron scattering experiments indicate that the nanoparticle contains an average of 350 PS80 molecules, which form a cylindrical micellar core structure and five RSV F trimers that are arranged around the long axis of the PS80 core. All-atom models of full-length RSV F trimers were built from crystal structures of the soluble ectodomain and arranged around the long axis of the PS80 core, allowing for the generation of an ensemble of conformations that agree with small-angle neutron and X-ray scattering data as well as transmission electron microscopy (TEM) images. Furthermore, the hydrodynamic size of the RSV F nanoparticle was found to be modulated by the molar ratio of PS80 to protein, suggesting a mechanism for nanoparticle assembly involving addition of RSV F trimers to and growth along the long axis of the PS80 core. This study provides structural details of antigen presentation and conformation in the RSV F nanoparticle vaccine, helping to explain the induction of broad immunity and observed clinical efficacy. Small-angle scattering methods provide a general strategy to visualize surface glycoproteins from other pathogens and to structurally characterize nanoparticle vaccines.

The solution structure of the complement deregulator FHR5 reveals a compact dimer and provides new insights into CFHR5 nephropathy

The human complement Factor H-related 5 protein (FHR5) antagonizes the main circulating complement regulator Factor H, resulting in the deregulation of complement activation. FHR5 normally contains nine short complement regulator (SCR) domains, but a FHR5 mutant has been identified with a duplicated N-terminal SCR-1/2 domain pair that causes CFHR5 nephropathy. To understand how this duplication causes disease, we characterized the solution structure of native FHR5 by analytical ultracentrifugation and small-angle X-ray scattering. Sedimentation velocity and X-ray scattering indicated that FHR5 was dimeric, with a radius of gyration (Rg ) of 5.5 ± 0.2 nm and a maximum protein length of 20 nm for its 18 domains. This result indicated that FHR5 was even more compact than the main regulator Factor H, which showed an overall length of 26-29 nm for its 20 SCR domains. Atomistic modeling for FHR5 generated a library of 250,000 physically realistic trial arrangements of SCR domains for scattering curve fits. Only compact domain structures in this library fit well to the scattering data, and these structures readily accommodated the extra SCR-1/2 domain pair present in CFHR5 nephropathy. This model indicated that mutant FHR5 can form oligomers that possess additional binding sites for C3b in FHR5. We conclude that the deregulation of complement regulation by the FHR5 mutant can be rationalized by the enhanced binding of FHR5 oligomers to C3b deposited on host cell surfaces. Our FHR5 structures thus explained key features of the mechanism and pathology of CFHR5 nephropathy.

Flow-Induced Formation of Thin PEO Fibers in Water and Their Stability After the Strain Release

Recently, we have shown that a tensile stress applied to chains of poly(ethylene oxide) (PEO) in water reduces the solubility and leads to phase separation of PEO chains from water with the formation of a two-phase region. In this work, we further elucidate the generic mechanism behind strain-induced phase transitions in aqueous PEO solutions with concentrations of 50-60 wt % by performing all-atom molecular dynamics simulations. In particular, we study the stability of oriented PEO fibers after removing stretching forces. We found that the size of the PEO bundle increased with time, which is associated with the dissolution of PEO chains on the fiber surface due to the reformation of hydrogen bonds between the outer PEO molecules and water. For precise characterization of the fibers, the scattering patterns (small- and wide-angle X-ray spectra) for configurations taken at different relaxation times are calculated. The tendency of the oligomer chains to be peeled off from the surface of the bundle eventually might lead to a complete dissolution of the PEO fiber. We conclude that either entanglement constraints or a quick drying process are necessary to conserve the fiber structure in a quiescent state. The scattering results show that external strain induced a liquid-liquid phase separation first. On long time scales, this can be a precursor for crystallization of the fiber.

Observing Protein Degradation by the PAN-20S Proteasome by Time-Resolved Neutron Scattering

The proteasome is a key player of regulated protein degradation in all kingdoms of life. Although recent atomic structures have provided snapshots on a number of conformations, data on substrate states and populations during the active degradation process in solution remain scarce. Here, we use time-resolved small-angle neutron scattering of a deuterium-labeled GFPssrA substrate and an unlabeled archaeal PAN-20S system to obtain direct structural information on substrate states during ATP-driven unfolding and subsequent proteolysis in solution. We find that native GFPssrA structures are degraded in a biexponential process, which correlates strongly with ATP hydrolysis, the loss of fluorescence, and the buildup of small oligopeptide products. Our solution structural data support a model in which the substrate is directly translocated from PAN into the 20S proteolytic chamber, after a first, to our knowledge, successful unfolding process that represents a point of no return and thus prevents dissociation of the complex and the release of harmful, aggregation-prone products.

Targeting Intrinsically Disordered Proteins through Dynamic Interactions

Intrinsically disordered proteins (IDPs) are over-represented in major disease pathways and have attracted significant interest in understanding if and how they may be targeted using small molecules for therapeutic purposes. While most existing studies have focused on extending the traditional structure-centric drug design strategies and emphasized exploring pre-existing structure features of IDPs for specific binding, several examples have also emerged to suggest that small molecules could achieve specificity in binding IDPs and affect their function through dynamic and transient interactions. These dynamic interactions can modulate the disordered conformational ensemble and often lead to modest compaction to shield functionally important interaction sites. Much work remains to be done on further elucidation of the molecular basis of the dynamic small molecule-IDP interaction and determining how it can be exploited for targeting IDPs in practice. These efforts will rely critically on an integrated experimental and computational framework for disordered protein ensemble characterization. In particular, exciting advances have been made in recent years in enhanced sampling techniques, Graphic Processing Unit (GPU)-computing, and protein force field optimization, which have now allowed rigorous physics-based atomistic simulations to generate reliable structure ensembles for nontrivial IDPs of modest sizes. Such de novo atomistic simulations will play crucial roles in exploring the exciting opportunity of targeting IDPs through dynamic interactions.

Obtaining Tertiary Protein Structures by the ab Initio Interpretation of Small Angle X-ray Scattering Data

Small angle X-ray scattering (SAXS) is an important tool for investigating the structure of proteins in solution. We present a novel ab initio method representing polypeptide chains as discrete curves used to derive a meaningful three-dimensional model from only the primary sequence and SAXS data. High resolution structures were used to generate probability density functions for each common secondary structural element found in proteins, which are used to place realistic restraints on the model curve’s geometry. This is coupled with a novel explicit hydration shell model in order to derive physically meaningful three-dimensional models by optimizing against experimental SAXS data. The efficacy of this model is verified on an established benchmark protein set, and then it is used to predict the lysozyme structure using only its primary sequence and SAXS data. The method is used to generate a biologically plausible model of the coiled-coil component of the human synaptonemal complex central element protein.

Solution structure of macromolecules using small angle neutron scattering and molecular simulations

An introductory account of using molecular simulations to deduce solution structure of macromolecules using small angle neutron scattering data is presented for biologists. The presence of a liquid solution provides mobility to the molecules, making it difficult to pin down their structure. Here a simple introduction to molecular dynamics and Monte Carlo techniques is followed by a recipe to use the output of the simulations along with the scattering data in order to infer the structure of macromolecules when they are placed in a liquid solution. Some practical issues to be watched for are also highlighted.

Atomistic Modeling of Scattering Curves for Human IgG1/4 Reveals New Structure-Function Insights

Small angle x-ray and neutron scattering are techniques that give solution structures for large macromolecules. The creation of physically realistic atomistic models from known high-resolution structures to determine joint x-ray and neutron scattering best-fit structures offers a, to our knowledge, new method that significantly enhances the utility of scattering. To validate this approach, we determined scattering curves for two human antibody subclasses, immunoglobulin G (IgG) 1 and IgG4, on five different x-ray and neutron instruments to show that these were reproducible, then we modeled these by Monte Carlo simulations. The two antibodies have different hinge lengths that connect their antigen-binding Fab and effector-binding Fc regions. Starting from 231,492 and 190,437 acceptable conformations for IgG1 and IgG4, respectively, joint x-ray and neutron scattering curve fits gave low goodness-of-fit R factors for 28 IgG1 and 2748 IgG4 structures that satisfied the disulphide connectivity in their hinges. These joint best-fit structures showed that the best-fit IgG1 models had a greater separation between the centers of their Fab regions than those for IgG4, in agreement with their hinge lengths of 15 and 12 residues, respectively. The resulting asymmetric IgG1 solution structures resembled its crystal structure. Both symmetric and asymmetric solution structures were determined for IgG4. Docking simulations with our best-fit IgG4 structures showed greater steric clashes with its receptor to explain its weaker FcγRI receptor binding compared to our best-fit IgG1 structures with fewer clashes and stronger receptor binding. Compared to earlier approaches for fitting molecular antibody structures by solution scattering, we conclude that this joint fit approach based on x-ray and neutron scattering data, combined with Monte Carlo simulations, significantly improved our understanding of antibody solution structures. The atomistic nature of the output extended our understanding of known functional differences in Fc receptor binding between IgG1 and IgG4.

An ensemble of flexible conformations underlies mechanotransduction by the cadherin-catenin adhesion complex

Adherens junctions are specialized cell–cell adhesion complexes found in epithelial, endothelial, and neuronal tissues of multicellular organism. The cadherin–catenin complex is the core component of the adherens junction and transmits mechanical stress from cell to cell. This study reveals that the cadherin–catenin complex displays a wide spectrum of flexible structures, which suggests a dynamic mechanism for this complex in mechanotransduction for cell–cell adhesion.

The cadherin–catenin adhesion complex is the central component of the cell–cell adhesion adherens junctions that transmit mechanical stress from cell to cell. We have determined the nanoscale structure of the adherens junction complex formed by the α-catenin•β-catenin•epithelial cadherin cytoplasmic domain (ABE) using negative stain electron microscopy, small-angle X-ray scattering, and selective deuteration/small-angle neutron scattering. The ABE complex is highly pliable and displays a wide spectrum of flexible structures that are facilitated by protein-domain motions in α- and β-catenin. Moreover, the 107-residue intrinsically disordered N-terminal segment of β-catenin forms a flexible “tongue” that is inserted into α-catenin and participates in the assembly of the ABE complex. The unanticipated ensemble of flexible conformations of the ABE complex suggests a dynamic mechanism for sensitivity and reversibility when transducing mechanical signals, in addition to the catch/slip bond behavior displayed by the ABE complex under mechanical tension. Our results provide mechanistic insight into the structural dynamics for the cadherin–catenin adhesion complex in mechanotransduction.

Dynamic structure of the full-length scaffolding protein NHERF1 influences signaling complex assembly

The Na+/H+ exchange regulatory cofactor 1 (NHERF1) protein modulates the assembly and intracellular trafficking of several transmembrane G protein-coupled receptors (GPCRs) and ion transport proteins with the membrane-cytoskeleton adapter protein ezrin. Here, we applied solution NMR and small-angle neutron scattering (SANS) to structurally characterize full-length NHERF1 and disease-associated variants that are implicated in impaired phosphate homeostasis. Using NMR, we mapped the modular architecture of NHERF1, which is composed of two structurally-independent PDZ domains that are connected by a flexible, disordered linker. We observed that the ultra-long and disordered C-terminal tail of NHERF1 has a type 1 PDZ-binding motif that interacts weakly with the proximal, second PDZ domain to form a dynamically autoinhibited structure. Using ensemble-optimized analysis of SANS data, we extracted the molecular size distribution of structures from the extensive conformational space sampled by the flexible chain. Our results revealed that NHERF1 is a diffuse ensemble of variable PDZ domain configurations and a disordered C-terminal tail. The joint NMR/SANS data analyses of three disease variants (L110V, R153Q, and E225K) revealed significant differences in the local PDZ domain structures and in the global conformations compared with the WT protein. Furthermore, we show that the substitutions affect the affinity and kinetics of NHERF1 binding to ezrin and to a C-terminal peptide from G protein-coupled receptor kinase 6A (GRK6A). These findings provide important insight into the modulation of the intrinsic flexibility of NHERF1 by disease-associated point mutations that alter the dynamic assembly of signaling complexes.

BEES: Bayesian Ensemble Estimation from SAS

Many biomolecular complexes exist in a flexible ensemble of states in solution that is necessary to perform their biological function. Small-angle scattering (SAS) measurements are a popular method for characterizing these flexible molecules because of their relative ease of use and their ability to simultaneously probe the full ensemble of states. However, SAS data is typically low dimensional and difficult to interpret without the assistance of additional structural models. In theory, experimental SAS curves can be reconstituted from a linear combination of theoretical models, although this procedure carries a significant risk of overfitting the inherently low-dimensional SAS data. Previously, we developed a Bayesian-based method for fitting ensembles of model structures to experimental SAS data that rigorously avoids overfitting. However, we have found that these methods can be difficult to incorporate into typical SAS modeling workflows, especially for users that are not experts in computational modeling. To this end, we present the Bayesian Ensemble Estimation from SAS (BEES) program. Two forks of BEES are available, the primary one existing as a module for the SASSIE web server and a developmental version that is a stand-alone Python program. BEES allows users to exhaustively sample ensemble models constructed from a library of theoretical states and to interactively analyze and compare each model's performance. The fitting routine also allows for secondary data sets to be supplied, thereby simultaneously fitting models to both SAS data as well as orthogonal information. The flexible ensemble of K63-linked ubiquitin trimers is presented as an example of BEES' capabilities.

The solution structure of the human IgG2 subclass is distinct from those for human IgG1 and IgG4 providing an explanation for their discrete functions

Human IgG2 antibody displays distinct therapeutically-useful properties compared with the IgG1, IgG3, and IgG4 antibody subclasses. IgG2 is the second most abundant IgG subclass, being able to bind human FcγRII/FcγRIII but not to FcγRI or complement C1q. Structural information on IgG2 is limited by the absence of a full-length crystal structure for this. To this end, we determined the solution structure of human myeloma IgG2 by atomistic X-ray and neutron-scattering modeling. Analytical ultracentrifugation disclosed that IgG2 is monomeric with a sedimentation coefficient (s20, w0) of 7.2 S. IgG2 dimer formation was ≤5% and independent of the buffer conditions. Small-angle X-ray scattering in a range of NaCl concentrations and in light and heavy water revealed that the X-ray radius of gyration (Rg ) is 5.2-5.4 nm, after allowing for radiation damage at higher concentrations, and that the neutron Rg value of 5.0 nm remained unchanged in all conditions. The X-ray and neutron distance distribution curves (P(r)) revealed two peaks, M1 and M2, that were unchanged in different buffers. The creation of >123,000 physically-realistic atomistic models by Monte Carlo simulations for joint X-ray and neutron-scattering curve fits, constrained by the requirement of correct disulfide bridges in the hinge, resulted in the determination of symmetric Y-shaped IgG2 structures. These molecular structures were distinct from those for asymmetric IgG1 and asymmetric and symmetric IgG4 and were attributable to the four hinge disulfides. Our IgG2 structures rationalize the existence of the human IgG1, IgG2, and IgG4 subclasses and explain the receptor-binding functions of IgG2.

An introduction to classical molecular dynamics simulation for experimental scattering users

Classical molecular dynamics simulations are a common component of multi-modal analyses of scattering measurements, such as small-angle scattering and diffraction. Users of these experimental techniques often have no formal training in the theory and practice of molecular dynamics simulation, leading to the possibility of these simulations being treated as a 'black box' analysis technique. This article describes an open educational resource (OER) designed to introduce classical molecular dynamics to users of scattering methods. This resource is available as a series of interactive web pages, which can be easily accessed by students, and as an open-source software repository, which can be freely copied, modified and redistributed by educators. The topics covered in this OER include classical atomistic modelling, parameterizing interatomic potentials, molecular dynamics simulations, typical sources of error and some of the approaches to using simulations in the analysis of scattering data.

Integrating NMR, SAXS, and Atomistic Simulations: Structure and Dynamics of a Two-Domain Protein

Multidomain proteins with two or more independently folded functional domains are prevalent in nature. Whereas most multidomain proteins are linked linearly in sequence, roughly one-tenth possess domain insertions where a guest domain is implanted into a loop of a host domain, such that the two domains are connected by a pair of interdomain linkers. Here, we characterized the influence of the interdomain linkers on the structure and dynamics of a domain-insertion protein in which the guest LysM domain is inserted into a central loop of the host CVNH domain. Expanding upon our previous crystallographic and NMR studies, we applied SAXS in combination with NMR paramagnetic relaxation enhancement to construct a structural model of the overall two-domain system. Although the two domains have no fixed relative orientation, certain orientations were found to be preferred over others. We also assessed the accuracies of molecular mechanics force fields in modeling the structure and dynamics of tethered multidomain proteins by integrating our experimental results with microsecond-scale atomistic molecular dynamics simulations. In particular, our evaluation of two different combinations of the latest force fields and water models revealed that both combinations accurately reproduce certain structural and dynamical properties, but are inaccurate for others. Overall, our study illustrates the value of integrating experimental NMR and SAXS studies with long timescale atomistic simulations for characterizing structural ensembles of flexibly linked multidomain systems.

Neutron scattering in the biological sciences: progress and prospects

The scattering of neutrons can be used to provide information on the structure and dynamics of biological systems on multiple length and time scales. Pursuant to a National Science Foundation-funded workshop in February 2018, recent developments in this field are reviewed here, as well as future prospects that can be expected given recent advances in sources, instrumentation and computational power and methods. Crystallography, solution scattering, dynamics, membranes, labeling and imaging are examined. For the extraction of maximum information, the incorporation of judicious specific deuterium labeling, the integration of several types of experiment, and interpretation using high-performance computer simulation models are often found to be particularly powerful.

Two distinct conformations of factor H regulate discrete complement-binding functions in the fluid phase and at cell surfaces

Factor H (FH) is the major regulator of C3b in the alternative pathway of the complement system in immunity. FH comprises 20 short complement regulator (SCR) domains, including eight glycans, and its Y402H polymorphism predisposes those who carry it to age-related macular degeneration. To better understand FH complement binding and self-association, we have studied the solution structures of both the His-402 and Tyr-402 FH allotypes. Analytical ultracentrifugation revealed that up to 12% of both FH allotypes self-associate, and this was confirmed by small-angle X-ray scattering (SAXS), MS, and surface plasmon resonance analyses. SAXS showed that monomeric FH has a radius of gyration (Rg ) of 7.2-7.8 nm and a length of 25 nm. Starting from known structures for the SCR domains and glycans, the SAXS data were fitted using Monte Carlo methods to determine atomistic structures of monomeric FH. The analysis of 29,715 physically realistic but randomized FH conformations resulted in 100 similar best-fit FH structures for each allotype. Two distinct molecular structures resulted that showed either an extended N-terminal domain arrangement with a folded-back C terminus or an extended C terminus and a folded-back N terminus. These two structures are the most accurate to date for glycosylated full-length FH. To clarify FH functional roles in host protection, crystal structures for the FH complexes with C3b and C3dg revealed that the extended N-terminal conformation accounted for C3b fluid-phase regulation, the extended C-terminal conformation accounted for C3d binding, and both conformations accounted for bivalent FH binding to glycosaminoglycans on the target cell surface.

A methodology to calculate small-angle scattering profiles of macromolecular solutions from molecular simulations in the grand-canonical ensemble

The theoretical framework to evaluate small-angle scattering (SAS) profiles for multi-component macromolecular solutions is re-examined from the standpoint of molecular simulations in the grand-canonical ensemble, where the chemical potentials of all species in solution are fixed. This statistical mechanical ensemble resembles more closely scattering experiments, capturing concentration fluctuations that arise from the exchange of molecules between the scattering volume and the bulk solution. The resulting grand-canonical expression relates scattering intensities to the different intra- and intermolecular pair distribution functions, as well as to the distribution of molecular concentrations on the scattering volume. This formulation represents a generalized expression that encompasses most of the existing methods to evaluate SAS profiles from molecular simulations. The grand-canonical SAS methodology is probed for a series of different implicit-solvent, homogeneous systems at conditions ranging from dilute to concentrated. These systems consist of spherical colloids, dumbbell particles, and highly flexible polymer chains. Comparison of the resulting SAS curves against classical methodologies based on either theoretical approaches or canonical simulations (i.e., at a fixed number of molecules) shows equivalence between the different scattering intensities so long as interactions between molecules are net repulsive or weakly attractive. On the other hand, for strongly attractive interactions, grand-canonical SAS profiles deviate in the low- and intermediate-q range from those calculated in a canonical ensemble. Such differences are due to the distribution of molecules becoming asymmetric, which yields a higher contribution from configurations with molecular concentrations larger than the nominal value. Additionally, for flexible systems, explicit discrimination between intra- and inter-molecular SAS contributions permits the implementation of model-free, structural analysis such as Guinier's plots at high molecular concentrations, beyond what the traditional limits are for such analysis.

Biological small-angle neutron scattering: recent results and development

Small-angle neutron scattering (SANS) has increasingly been used by the structural biology community in recent years to obtain low-resolution information on solubilized biomacromolecular complexes in solution. In combination with deuterium labelling and solvent-contrast variation (H2O/D2O exchange), SANS provides unique information on individual components in large heterogeneous complexes that is perfectly complementary to the structural restraints provided by crystallography, nuclear magnetic resonance and electron microscopy. Typical systems studied include multi-protein or protein–DNA/RNA complexes and solubilized membrane proteins. The internal features of these systems are less accessible to the more broadly used small-angle X-ray scattering (SAXS) technique owing to a limited range of intra-complex and solvent electron-density variation. Here, the progress and developments of biological applications of SANS in the past decade are reviewed. The review covers scientific results from selected biological systems, including protein–protein complexes, protein–RNA/DNA complexes and membrane proteins. Moreover, an overview of recent developments in instruments, sample environment, deuterium labelling and software is presented. Finally, the perspectives for biological SANS in the context of integrated structural biology approaches are discussed.