Determining pair distance distribution function from SAXS data using parametric functionals

Implications of size dispersion on X-ray scattering of crystalline nanoparticles: CeO2 as a case study

Controlling the shape and size dispersivity and crystallinity of nanoparticles (NPs) has been a challenge in identifying these parameters' role in the physical and chemical properties of NPs. The need for reliable quantitative tools for analyzing the dispersivity and crystallinity of NPs is a considerable problem in optimizing scalable synthesis routes capable of controlling NP properties. The most common tools are electron microscopy (EM) and X-ray scattering techniques. However, each technique has different susceptibility to these parameters, implying that more than one technique is necessary to characterize NP systems with maximum reliability. Wide-angle X-ray scattering (WAXS) is mandatory to access information on crystallinity. In contrast, EM or small-angle X-ray scattering (SAXS) is required to access information on whole NP sizes. EM provides average values on relatively small ensembles in contrast to the bulk values accessed by X-ray techniques. Besides the fact that the SAXS and WAXS techniques have different susceptibilities to size distributions, SAXS is easily affected by NP-NP interaction distances. Because of all the variables involved, there have yet to be proposed methodologies for cross-analyzing data from two techniques that can provide reliable quantitative results of dispersivity and crystallinity. In this work, a SAXS/WAXS-based methodology is proposed for simultaneously quantifying size distribution and degree of crystallinity of NPs. The most reliable easy-to-access size result for each technique is demonstrated by computer simulation. Strategies on how to compare these results and how to identify NP-NP interaction effects underneath the SAXS intensity curve are presented. Experimental results are shown for cubic-like CeO2 NPs. WAXS size results from two analytical procedures are compared, line-profile fitting of individual diffraction peaks in opposition to whole pattern fitting. The impact of shape dispersivity is also evaluated. Extension of the proposed methodology for cross-analyzing EM and WAXS data is possible.

Structural Rearrangement Followed by Entrapment of Subnanometer Building Blocks of Iron Oxyhydroxide in Aqueous Iron Chloride Solutions

Iron oxyhydroxide, a natural nanophase of iron found in the environment, plays a crucial role in regulating surface and groundwater composition. Recent research proposes that within the nonclassical prenucleation cluster growth model, subnanometer-sized clusters (olation clusters/Fe13 δ-Keggin oxolation clusters) might act as the prenucleation clusters (PNCs) of ferrihydrite or iron oxyhydroxide solid phase. However, these clusters are difficult to characterize as they are only observable momentarily in low-pH, high-Fe concentration solutions before agglomerating into extended solids, keeping the controversy over the true nature of the PNCs alive. In this study, we introduce large quantities of zinc acetate salt (ZA) into iron chloride solutions at the olation-oxolation boundary (3.6 mM Fe3+ at pH ∼2.6). Remarkably, this manipulation is found to alter the structural arrangement of these subnanometer clusters before blocking them in isolation for hours, even at pH 6, where extended iron oxyhydroxide phases typically precipitate. On the other hand, controlled addition of ZA allows partial unblocking, leading to anisotropic agglomeration into cylindrical rod-like structures. Experimental techniques such as synchrotron-based small-angle X-ray scattering, X-ray absorption spectroscopy, high-resolution transmission electron microscopy (TEM), and cryo-TEM, along with density functional theory (DFT) calculations, reveal the nature of the structural rearrangement and the crucial role of Zn2+ ions in cluster stabilization.

Solution Structures of Two Different FRP-OCP Complexes as Revealed via SEC-SANS

Photosynthetic organisms have established photoprotective mechanisms in order to dissipate excess light energy into heat, which is commonly known as non-photochemical quenching. Cyanobacteria utilize the orange carotenoid protein (OCP) as a high-light sensor and quencher to regulate the energy flow in the photosynthetic apparatus. Triggered by strong light, OCP undergoes conformational changes to form the active red state (OCPR). In many cyanobacteria, the back conversion of OCP to the dark-adapted state is assisted by the fluorescence recovery protein (FRP). However, the exact molecular events involving OCP and its interaction with FRP remain largely unraveled so far due to their metastability. Here, we use small-angle neutron scattering combined with size exclusion chromatography (SEC-SANS) to unravel the solution structures of FRP-OCP complexes using a compact mutant of OCP lacking the N-terminal extension (∆NTEOCPO) and wild-type FRP. The results are consistent with the simultaneous presence of stable 2:2 and 2:1 FRP-∆NTEOCPO complexes in solution, where the former complex type is observed for the first time. For both complex types, we provide ab initio low-resolution shape reconstructions and compare them to homology models based on available crystal structures. It is likely that both complexes represent intermediate states of the back conversion of OCP to its dark-adapted state in the presence of FRP, which are of transient nature in the photocycle of wild-type OCP. This study demonstrates the large potential of SEC-SANS in revealing the solution structures of protein complexes in polydisperse solutions that would otherwise be averaged, leading to unspecific results.

Mechanically Robust Cellulose-Based Piezoelectric Elastomer Formed by Slidable Polyrotaxane Cross-Linker

Cellulose has great potential in the field of piezoelectricity owing to its high crystallinity; however, it exhibits low processability and poor mechanical robustness. In this study, to enhance the applicability of cellulose-based piezoelectric materials, a robust cellulose-based piezoelectric elastomer with excellent piezoelectric properties was developed by cross-linking cellulose with polyrotaxane (PR). The effects of cross-linking on the mechanical properties and crystalline structures of the resulting elastomers were investigated. The ferroelectric and piezoelectric properties were evaluated from their polarization hysteresis loops and voltage generation characteristics. eHPC25PR75 exhibited 2.7 times higher toughness (20.4 MJ m-3) than eHPC100 (7.57 MJ m-3). It also shows a power density 4.2 times higher (1.34 μW cm-2) than eHPC100 (0.321 μW cm-2). As a result, eHPC25PR75 demonstrated piezosensitivity to mechanical vibrations in a variety of devices that require mechanical robustness. These results can inform the design and development of high-performance piezoelectric devices.

Interrogating Encapsulated Protein Structure within Metal-Organic Frameworks at Elevated Temperature

Encapsulating biomacromolecules within metal-organic frameworks (MOFs) can confer thermostability to entrapped guests. It has been hypothesized that the confinement of guest molecules within a rigid MOF scaffold results in heightened stability of the guests, but no direct evidence of this mechanism has been shown. Here, we present a novel analytical method using small-angle X-ray scattering (SAXS) to solve the structure of bovine serum albumin (BSA) while encapsulated within two zeolitic imidazolate frameworks (ZIF-67 and ZIF-8). Our approach comprises subtracting the scaled SAXS spectrum of the ZIF from that of the biocomposite BSA@ZIF to determine the radius of gyration of encapsulated BSA through Guinier, Kratky, and pair distance distribution function analyses. While native BSA exposed to 70 °C became denatured, in situ SAXS analysis showed that encapsulated BSA retained its size and folded state at 70 °C when encapsulated within a ZIF scaffold, suggesting that entrapment within MOF cavities inhibited protein unfolding and thus denaturation. This method of SAXS analysis not only provides insight into biomolecular stabilization in MOFs but may also offer a new approach to study the structure of other conformationally labile molecules in rigid matrices.

Modelling the 3D Structure of PEDOT:PSS Supramolecular Assembly in Aqueous Dispersion Based on SAXS with Synchrotron Light

In this work, we study the poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) structure in aqueous dispersion with small-angle X-ray scattering (SAXS). In-depth structure analysis is achieved based on a set of complementary and sophisticated algorithms, which provide not only shape and packing of chains but also 3D structure of the colloids. The structure information of the PEDOT chain was extracted from the well-known Guinier, Porod and pair distance distribution function (PDDF) analysis of the SAXS data, while the 3D modelling was achieved with the DAMMIF and DAMAVER programs in ATSAS software package. To the best of our knowledge, we first establish the 3D model of the PEDOT:PSS colloids’ structure that will help people to understand the supramolecular assembly in aqueous dispersion, which sheds light on the solution structure study of polymers that are widely used in daily life.

Small-angle X-ray microdiffraction from fibrils embedded in tissue thin sections

Small-angle X-ray scattering (SAXS) from fibrils embedded in a fixed, thin section of tissue includes contributions from the fibrils, the polymeric matrix surrounding the fibrils, other constituents of the tissue, and cross-terms due to the spatial correlation between fibrils and neighboring molecules. This complex mixture severely limits the amount of information that can be extracted from scattering studies. However, availability of micro- and nano-beams has made the measurement of scattering from very small volumes possible, which, in some cases, may be dominated by a single fibrillar constituent. In such cases, information about the predominant species may be accessible. Nevertheless, even in these cases, the correlations between the positions of fibrils and other constituents have a significant impact on the observed scattering. Here, strategies are proposed to extract partial information about fibril structure and tissue organization on the basis of SAXS from samples of this type. It is shown that the spatial correlation function of the fibril in the direction perpendicular to the fibril axis can be computed and contains information about the predominant fibril structure and the organization of the surrounding tissue matrix. This has significant advantages over approaches based on techniques developed for X-ray solution scattering. Examples of correlation calculations in different types of samples are given to demonstrate the information that can be obtained from these measurements.

Solution characterization of the dynamic conjugative entry exclusion protein TraG

The R100 plasmid and the secretion system it encodes are representative of F-like conjugative type IV secretion systems for the transmission of mobile DNA elements in gram-negative bacteria, serving as a major contributor to the spread of antibiotic resistance in bacterial pathogens. The TraG protein of F-like systems consists of a membrane-bound N-terminal domain and a periplasmic C-terminal domain, denoted TraG*. TraG* is essential in preventing redundant DNA transfer through a process termed entry exclusion. In the donor cell, it interacts with TraN to facilitate mating pair stabilization; however, if a mating pore forms between bacteria with identical plasmids, TraG* interacts with its cognate TraS in the inner membrane of the recipient bacterium to prevent redundant donor-donor conjugation. Structural studies of TraG* from the R100 plasmid have revealed the presence of a dynamic region between the N- and C-terminal domains of TraG. Thermofluor, circular dichroism, collision-induced unfolding-mass spectrometry, and size exclusion chromatography linked to multiangle light scattering and small angle x-ray scattering experiments indicated an N-terminal truncation mutant displayed higher stability and less disordered content relative to full-length TraG*. The 45 N-terminal residues of TraG* are hypothesized to serve as part of a flexible linker between the two independently functioning domains.

Extracting structural insights from soft X-ray scattering of biological assemblies

Resonant soft X-ray scattering (RSoXS), a technique that combines X-ray absorption spectroscopy and X-ray scattering, can probe the nano- and meso-scale structure of biological assemblies with chemical specificity. RSoXS experiments yield scattering data collected at several photon energies, for example across an elemental absorption edge of interest. Collecting a near-edge X-ray absorption fine structure (NEXAFS) spectrum complements RSoXS experiments and determines X-ray energies that are best suited for RSoXS measurements. The analysis of RSoXS data is similar in many ways to analysis of small angle X-ray scattering using hard X-rays, with an added dimension that includes an X-ray energy dependence. This chapter discusses procedures for predicting scattering contrast and thereby identifying energies suitable for RSoXS measurements using NEXAFS spectra, analyses of 2D RSoXS images through integration into 1D profiles, and strategies for elucidating the origin of RSoXS scattering features. It also discusses existing and potential methods for interpretation of RSoXS data to gain detailed structural insights into biological systems.

Magnetic-Core/Gold-Shell Nanoparticles for the Detection of Hydrophobic Chemical Contaminants

Magnetic-core/gold-shell nanoparticles (MAuNPs) are of interest for enabling rapid and portable detection of trace adulterants in complex media. Gold coating provides biocompatibility and facile functionalization, and a magnetic core affords analyte concentration and controlled deposition onto substrates for surface-enhanced Raman spectroscopy. Iron oxide cores were synthesized and coated with gold by reduction of HAuCl₄ by NH₂OH. MAuNPs were grafted with polyethylene glycol (PEG) and/or functionalized with 4-mercaptobenzoic acid (4-MBA) and examined using a variety of microscopic, spectroscopic, magnetometric, and scattering techniques. For MAuNPs grafted with both PEG and 4-MBA, the order in which they were grafted impacted not only the graft density of the individual ligands, but also the overall graft density. Significant Raman signal enhancement of the model analyte, 4-MBA, was observed. This enhancement demonstrates the functionality of MAuNPs in direct detection of trace contaminants. The magnetic deposition rate of MAuNPs in chloroform and water was explored. The presence of 4-MBA slowed the mass deposition rate, and it was postulated that the rate disparity originated from differing NP-substrate surface interactions. These findings emphasize the importance of ligand choice in reference to the medium, target analyte, and substrate material, as well as functionalization procedure in the design of similar sensing platforms.

Structural characterisation methods for supramolecular chemistry that go beyond crystallography

Supramolecular chemistry has grown rapidly over the past three decades, yet synthetic supramolecular chemists still face several challenges when it comes to characterising their compounds. In this review, we present an introduction to structural characterisation techniques commonly used for non-crystalline supramolecular molecules, e.g. nuclear magnetic and electron paramagnetic resonance spectroscopy (NMR and EPR), mass spectrometry (MS), ion mobility mass spectrometry (IM-MS), small-angle neutron and X-ray scattering (SANS and SAXS) as well as cryogenic transmission electron microscopy (cryo-TEM). We provide an overview of their fundamental concepts based on case studies from different fields of supramolecular chemistry, e.g. interlocked structures, molecular self-assembly and host-guest chemistry, while focussing on particular strengths and weaknesses of the discussed methods. Additionally, three multi-technique case studies are examined in detail to illustrate the benefits of using complementary techniques simultaneously.

SAS-cam: a program for automatic processing and analysis of small-angle scattering data

Small-angle X-ray scattering (SAXS) is a widely used method for investigating biological macromolecules in structural biology, providing information on macromolecular structures and dynamics in solution. Modern synchrotron SAXS beamlines are characterized as high-throughput, capable of collecting large volumes of data and thus demanding fast data processing for efficient beamline operations. This article presents a fully automated and high-throughput SAXS data analysis pipeline, SAS-cam, primarily based on the SASTBX package. Five modules are included in SAS-cam, encompassing the data analysis process from data reduction to model interpretation. The model parameters are extracted from SAXS profiles and stored in an HTML summary file, ready for online visualization using a web browser. SAS-cam can provide the user with the possibility of optimizing experimental parameters based on real-time feedback and it therefore significantly improves the efficiency of beam time. SAS-cam is installed on the BioSAXS beamline at the Shanghai Synchrotron Radiation Facility. The source code is available upon request.

Distance Distribution between Two Iodine Atoms Derived from Small-Angle X-ray Scattering Interferometry for Analyzing a Conformational Ensemble of Heavy Atom-Labeled Small Molecules

To obtain unbiased information about the dynamic conformational ensemble of a molecule in solution, one promising approach is small-angle X-ray scattering (SAXS). Conventionally, SAXS data are converted to a pair distribution function, which describes the distance distribution between all pairs of atoms within a molecule. If two strong X-ray scatterers are introduced and the background contributions from the other atoms are suppressed, then the distance distribution between the two scatterers provides spatial information about a flexible molecule. Gold nanocrystals can provide such information for distances of >50 Å. Here, we synthesized a chemical compound containing two iodine atoms attached to the ends of a flexible polyethylene glycol chain and used the relevant singly labeled and unlabeled compounds to suppress the background contribution. This is a feasibility demonstration to prove that the distance distribution in the range of 10-30 Å can be experimentally accessed by SAXS.

SAXSDom: Modeling multidomain protein structures using small-angle X-ray scattering data

Many proteins are composed of several domains that pack together into a complex tertiary structure. Multidomain proteins can be challenging for protein structure modeling, particularly those for which templates can be found for individual domains but not for the entire sequence. In such cases, homology modeling can generate high quality models of the domains but not for the orientations between domains. Small-angle X-ray scattering (SAXS) reports the structural properties of entire proteins and has the potential for guiding homology modeling of multidomain proteins. In this article, we describe a novel multidomain protein assembly modeling method, SAXSDom that integrates experimental knowledge from SAXS with probabilistic Input-Output Hidden Markov model to assemble the structures of individual domains together. Four SAXS-based scoring functions were developed and tested, and the method was evaluated on multidomain proteins from two public datasets. Incorporation of SAXS information improved the accuracy of domain assembly for 40 out of 46 critical assessment of protein structure prediction multidomain protein targets and 45 out of 73 multidomain protein targets from the ab initio domain assembly dataset. The results demonstrate that SAXS data can provide useful information to improve the accuracy of domain-domain assembly. The source code and tool packages are available at https://github.com/jianlin-cheng/SAXSDom.

Model Reconstruction from Small-Angle X-Ray Scattering Data Using Deep Learning Methods

Small-angle X-ray scattering (SAXS) method is widely used in investigating protein structures in solution, but high-quality 3D model reconstructions are challenging. We present a new algorithm based on a deep learning method for model reconstruction from SAXS data. An auto-encoder for protein 3D models was trained to compress 3D shape information into vectors of a 200-dimensional latent space, and the vectors are optimized using genetic algorithms to build 3D models that are consistent with the scattering data. The program has been tested with experimental SAXS data, demonstrating the capacity and robustness of accurate model reconstruction. Furthermore, the model size information can be optimized using this algorithm, enhancing the automation in model reconstruction directly from SAXS data. The program was implemented using Python with the TensorFlow framework, with source code and webserver available from http://liulab.csrc.ac.cn/decodeSAXS.

•

A convolutional neural network auto-encoder framework for 3D models is developed

•

The auto-encoder compresses protein shape information to 200 parameters

•

Accurate 3D models (both shape and radius) can be reconstructed from 1D SAXS data

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.

The crystal structure of a multidomain protease inhibitor (HAI-1) reveals the mechanism of its auto-inhibition

Hepatocyte growth factor activator inhibitor 1 (HAI-1) is a membrane-bound multidomain protein essential to the integrity of the basement membrane during placental development and is also important in maintaining postnatal homeostasis in many tissues. HAI-1 is a Kunitz-type serine protease inhibitor, and soluble fragments of HAI-1 with variable lengths have been identified in vivo The full-length extracellular portion of HAI-1 (sHAI-1) shows weaker inhibitory activity toward target proteases than the smaller fragments, suggesting auto-inhibition of HAI-1. However, this possible regulatory mechanism has not yet been evaluated. Here, we solved the crystal structure of sHAI-1 and determined the solution structure by small-angle X-ray scattering. These structural analyses revealed that, despite the presence of long linkers, sHAI-1 exists in a compact conformation in which sHAI-1 active sites in Kunitz domain 1 are sterically blocked by neighboring structural elements. We also found that in the presence of target proteases, sHAI-1 adopts an extended conformation that disables the auto-inhibition effect. Our results also reveal the roles of non-inhibitory domains of this multidomain protein and explain the low activity of the full-length protein. The structural insights gained here improve our understanding of the regulation of HAI-1 inhibitory activities and point to new approaches for better controlling these activities.

Analysis of RNA structure using small-angle X-ray scattering

In addition to their role in correctly attaching specific amino acids to cognate tRNAs, aminoacyl-tRNA synthetases (aaRS) have been found to possess many alternative functions and often bind to and act on other nucleic acids. In contrast to the well-defined 3D structure of tRNA, the structures of many of the other RNAs recognized by aaRSs have not been solved. Despite advances in the use of X-ray crystallography (XRC), nuclear magnetic resonance (NMR) spectroscopy and cryo-electron microscopy (cryo-EM) for structural characterization of biomolecules, significant challenges to solving RNA structures still exist. Recently, small-angle X-ray scattering (SAXS) has been increasingly employed to characterize the 3D structures of RNAs and RNA-protein complexes. SAXS is capable of providing low-resolution tertiary structure information under physiological conditions and with less intensive sample preparation and data analysis requirements than XRC, NMR and cryo-EM. In this article, we describe best practices involved in the process of RNA and RNA-protein sample preparation, SAXS data collection, data analysis, and structural model building.

Measurement of protein size in concentrated solutions by small angle X-ray scattering

By simulations on the distance distribution function (DDF) derived from small angle X-ray scattering (SAXS) theoretical data of a dense monodisperse system, we found a quantitative mathematical correlation between the apparent size of a spherically symmetric (or nearly spherically symmetric) homogenous particle and the concentration of the solution. SAXS experiments on protein solutions of human hemoglobin and horse myoglobin validated the correlation. This gives a new method to determine, from the SAXS DDF, the size of spherically symmetric (or nearly spherically symmetric) particles of a dense monodisperse system, specifically for protein solutions with interference effects.