Computational Reverse Engineering Analysis of the Scattering Experiment Method for Interpretation of 2D Small-Angle Scattering Profiles (CREASE-2D)

Small-angle scattering (SAS) is a widely used characterization technique that provides structural information in soft materials at varying length scales (nanometers to microns). The output of an SAS measurement is the scattered intensity I(q) as a function of q, the scattered wavevector with respect to the incident wave; the latter is represented by its magnitude |q| ≡ q (in inverse distance units) and azimuthal angle θ. While isotropic structural arrangement can be interpreted by analysis of the azimuthally averaged one-dimensional (1D) scattering profile, to understand anisotropic arrangements, one has to interpret the two-dimensional (2D) scattering profile, I(q, θ). Manual interpretation of such 2D profiles usually involves fitting of approximate analytical models to azimuthally averaged sections of the 2D profile. In this paper, we present a new method called CREASE-2D that interprets, without any azimuthal averaging, the entire 2D scattering profile, I(q, θ), and outputs the relevant structural features. CREASE-2D is an extension of the "computational reverse engineering analysis for scattering experiments" (CREASE) method that has been used successfully to analyze 1D SAS profiles for a variety of soft materials. CREASE-2D goes beyond CREASE by enabling analysis of 2D scattering profiles, which is far more challenging to interpret than the azimuthally averaged 1D profiles. The CREASE-2D workflow identifies the structural features whose computed I(q, θ) profiles, calculated using a surrogate XGBoost machine learning model, match the input experimental I(q, θ). We expect that this CREASE-2D method will be a valuable tool for materials' researchers who need direct interpretation of the 2D scattering profiles in contrast to analyzing azimuthally averaged 1D I(q) vs q profiles that can lose important information related to structural anisotropy.

Simple Scattering: Lipid nanoparticle structural data repository

Lipid nanoparticles (LNPs) are being intensively researched and developed to leverage their ability to safely and effectively deliver therapeutics. To achieve optimal therapeutic delivery, a comprehensive understanding of the relationship between formulation, structure, and efficacy is critical. However, the vast chemical space involved in the production of LNPs and the resulting structural complexity make the structure to function relationship challenging to assess and predict. New components and formulation procedures, which provide new opportunities for the use of LNPs, would be best identified and optimized using high-throughput characterization methods. Recently, a high-throughput workflow, consisting of automated mixing, small-angle X-ray scattering (SAXS), and cellular assays, demonstrated a link between formulation, internal structure, and efficacy for a library of LNPs. As SAXS data can be rapidly collected, the stage is set for the collection of thousands of SAXS profiles from a myriad of LNP formulations. In addition, correlated LNP small-angle neutron scattering (SANS) datasets, where components are systematically deuterated for additional contrast inside, provide complementary structural information. The centralization of SAXS and SANS datasets from LNPs, with appropriate, standardized metadata describing formulation parameters, into a data repository will provide valuable guidance for the formulation of LNPs with desired properties. To this end, we introduce Simple Scattering, an easy-to-use, open data repository for storing and sharing groups of correlated scattering profiles obtained from LNP screening experiments. Here, we discuss the current state of the repository, including limitations and upcoming changes, and our vision towards future usage in developing our collective knowledge base of LNPs.

Synthesis and Characterization of Ultra-Small Gold Nanoparticles in the Ionic Liquid 1-Ethyl-3-methylimidazolium Dicyanamide, [Emim][DCA]

We report on gold clusters with around 62 gold atoms and a diameter of 1.15±0.10 nm. Dispersions of the clusters are long-term stable for two years at ambient conditions. The synthesis was performed by mixing tetrachloroauric acid (HAuCl4  ⋅ 3 H2 O) with the ionic liquid 1-ethyl-3-methylimidazolium dicyanamide ([Emim][DCA]) at temperatures of 20 to 80 °C. Characterization was performed with small-angle X-ray scattering (SAXS), UV-Vis spectroscopy, and MALDI-TOF mass spectrometry. A three-stage model is proposed for the formation of the clusters, in which cluster growth from gold nuclei takes place according to the Lifshitz-Slyozov-Wagner (LSW) model followed by oriented attachment to form colloidal stable clusters.

BioXTAS RAW 2: new developments for a free open-source program for small-angle scattering data reduction and analysis

BioXTAS RAW is a free open-source program for reduction, analysis and modelling of biological small-angle scattering data. Here, the new developments in RAW version 2 are described. These include improved data reduction using pyFAI; updated automated Guinier fitting and D max finding algorithms; automated series (e.g. size-exclusion chromatography coupled small-angle X-ray scattering or SEC-SAXS) buffer- and sample-region finding algorithms; linear and integral baseline correction for series; deconvolution of series data using regularized alternating least squares (REGALS); creation of electron-density reconstructions using electron density via solution scattering (DENSS); a comparison window showing residuals, ratios and statistical comparisons between profiles; and generation of PDF reports with summary plots and tables for all analysis. Furthermore, there is now a RAW API, which can be used without the graphical user interface (GUI), providing full access to all of the functionality found in the GUI. In addition to these new capabilities, RAW has undergone significant technical updates, such as adding Python 3 compatibility, and has entirely new documentation available both online and in the program.

Computation of X-ray and Neutron Scattering Patterns to Benchmark Atomistic Simulations against Experiments

Molecular Dynamics simulations study material structure and dynamics at the atomic level. X-ray and neutron scattering experiments probe exactly the same time- and length scales as the simulations. In order to benchmark simulations against measured scattering data, a program is required that computes scattering patterns from simulations with good single-core performance and support for parallelization. In this work, the existing program Sassena is used as a potent solution to this requirement for a range of scattering methods, covering pico- to nanosecond dynamics, as well as the structure from some Ångströms to hundreds of nanometers. In the case of nanometer-level structures, the finite size of the simulation box, which is referred to as the finite size effect, has to be factored into the computations for which a method is described and implemented into Sassena. Additionally, the single-core and parallelization performance of Sassena is investigated, and several improvements are introduced.

Form factor of helical structures and twisted fibres

A general formalism is presented for the isotropically averaged single-chain scattering function (form factor) of single, double, triple and higher-order helices, as well as twisted fibres consisting of concentric layers of strands. Form factors for double and triple helices with differently sized grooves have also been derived. The formulas include the longitudinal and transverse interference over the pitch and radius of the helices, respectively. The results may be useful for the analysis of small-angle scattering data of (bio)macromolecules or molecular assemblies exhibiting a helical arrangement.

Tailoring the Self-Assembly of Steviol Glycoside Nanocarriers with Steroidal Amphiphiles

Bile salts are biosurfactants that can induce structure transformations in supramolecular nanoassemblies with conventional surfactants owing to their unique, planar amphiphilic character and the rigidity of their hydrophobic steroid skeleton. However, structural information about the association of bile salts and amphiphilic glycosides is lacking. In this work, we investigated the micelle structure of two anionic di- and trihydroxy bile salts [sodium deoxycholate (SDC) and sodium cholate (SC)] and a conventional anionic surfactant [sodium dodecyl sulfate (SDS)] in mixtures with a nonionic steviol glycoside [α-glucosyl stevia (Stevia-G)] and studied their potential as a nanocarrier system for two poorly water-soluble drugs (clotrimazole and ketoconazole). Decreased critical micelle concentrations determined from surface tension measurements demonstrate synergistic interactions between Stevia-G and SDS/SDC/SC in a decreasing order. Small-angle X-ray and neutron scattering, interpreted by a core-shell ellipsoid model, indicate that SDS and bile salts act differently on the mixed micelle structure. Compared with SDS/Stevia-G, bile salt/Stevia-G had a core-shell structure more similar to that of pure Stevia-G micelles. SDC and SDS had an increasing and decreasing influence, respectively, on the available molecular surface area in mixtures with Stevia-G on the micelle core but a similar influence on the micelle shell solvation number relative to that of their pure micellar structures. The number of bile salt hydroxyl groups was influential in determining the micelle stoichiometry: an increasing number of hydroxyl groups corresponded to decreasing bile salt aggregation numbers and a smaller hydrophobic micellar core. The core volume was the most important structural factor in explaining the drug solubilization capacity of the nanocarrier systems. Therefore, bile salt-steviol glycoside mixed micellar assemblies exhibit structure control mechanisms allowing the fine-tuning of their interior hydrophobic domains important for nanocarrier applications toward solubilization of poorly water-soluble drugs.

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.

I-Shaped Dimers of a Plant Chloroplast FOF1-ATP Synthase in Response to Changes in Ionic Strength

F-type ATP synthases play a key role in oxidative and photophosphorylation processes generating adenosine triphosphate (ATP) for most biochemical reactions in living organisms. In contrast to the mitochondrial F_OF₁-ATP synthases, those of chloroplasts are known to be mostly monomers with approx. 15% fraction of oligomers interacting presumably non-specifically in a thylakoid membrane. To shed light on the nature of this difference we studied interactions of the chloroplast ATP synthases using small-angle X-ray scattering (SAXS) method. Here, we report evidence of I-shaped dimerization of solubilized F_OF₁-ATP synthases from spinach chloroplasts at different ionic strengths. The structural data were obtained by SAXS and demonstrated dimerization in response to ionic strength. The best model describing SAXS data was two ATP-synthases connected through F₁/F₁' parts, presumably via their δ-subunits, forming "I" shape dimers. Such I-shaped dimers might possibly connect the neighboring lamellae in thylakoid stacks assuming that the F_OF₁ monomers comprising such dimers are embedded in parallel opposing stacked thylakoid membrane areas. If this type of dimerization exists in nature, it might be one of the pathways of inhibition of chloroplast F_OF₁-ATP synthase for preventing ATP hydrolysis in the dark, when ionic strength in plant chloroplasts is rising. Together with a redox switch inserted into a γ-subunit of chloroplast F_OF₁ and lateral oligomerization, an I-shaped dimerization might comprise a subtle regulatory process of ATP synthesis and stabilize the structure of thylakoid stacks in chloroplasts.

Stability of Nanopeptides: Structure and Molecular Exchange of Self-assembled Peptide Fibers

Often nanostructures formed by self-assembly of small molecules based on hydrophobic interactions are rather unstable, causing morphological changes or even dissolution when exposed to changes in aqueous media. In contrast, peptides offer precise control of the nanostructure through a range of molecular interactions where physical stability can be engineered in and, to a certain extent, decoupled from size via rational design. Here, we investigate a family of peptides that form beta-sheet nanofibers and demonstrate a remarkable physical stability even after attachment of poly(ethylene glycol). We employed small-angle neutron/X-ray scattering, circular dichroism spectroscopy, and molecular dynamics simulation techniques to investigate the detailed nanostructure, stability, and molecular exchange. The results for the most stable sequence did not reveal any structural alterations or unimer exchange for temperatures up to 85 °C in the biologically relevant pH range. Only under severe mechanical perturbation (i.e., tip sonication) would the fibers break up, which is reflected in a very high activation barrier for unimer exchange of ∼320 kJ/mol extracted from simulations. The results give important insight into the relation between molecular structure and stability of peptide nanostructure that is important for, e.g., biomedical applications.

A reactor for time-resolved X-ray studies of nucleation and growth during solvothermal synthesis

Understanding the nucleation and growth mechanisms of nanocrystals under hydro- and solvothermal conditions is key to tailoring functional nanomaterials. High-energy and high-flux synchrotron radiation is ideal for characterization by powder X-ray diffraction and X-ray total scattering in real time. Different versions of batch-type cell reactors have been employed in this work, exploiting the robustness of polyimide-coated fused quartz tubes with an inner diameter of 0.7 mm, as they can withstand pressures up to 250 bar and temperatures up to 723 K for several hours. Reported here are recent developments of the in situ setups available for general users on the P21.1 beamline at PETRA III and the DanMAX beamline at MAX IV to study nucleation and growth phenomena in solvothermal synthesis. It is shown that data suitable for both reciprocal-space Rietveld refinement and direct-space pair distribution function refinement can be obtained on a timescale of 4 ms.

Computational Reverse-Engineering Analysis for Scattering Experiments for Form Factor and Structure Factor Determination ("P(q) and S(q) CREASE")

In this paper, we present an open-source machine learning (ML)-accelerated computational method to analyze small-angle scattering profiles [I(q) vs q] from concentrated macromolecular solutions to simultaneously obtain the form factor P(q) (e.g., dimensions of a micelle) and the structure factor S(q) (e.g., spatial arrangement of the micelles) without relying on analytical models. This method builds on our recent work on Computational Reverse-Engineering Analysis for Scattering Experiments (CREASE) that has either been applied to obtain P(q) from dilute macromolecular solutions (where S(q) ∼1) or to obtain S(q) from concentrated particle solutions when P(q) is known (e.g., sphere form factor). This paper's newly developed CREASE that calculates P(q) and S(q), termed as "P(q) and S(q) CREASE", is validated by taking as input I(q) vs q from in silico structures of known polydisperse core(A)-shell(B) micelles in solutions at varying concentrations and micelle-micelle aggregation. We demonstrate how "P(q) and S(q) CREASE" performs if given two or three of the relevant scattering profiles-I _total(q), I _A(q), and I _B(q)-as inputs; this demonstration is meant to guide experimentalists who may choose to do small-angle X-ray scattering (for total scattering from the micelles) and/or small-angle neutron scattering with appropriate contrast matching to get scattering solely from one or the other component (A or B). After validation of "P(q) and S(q) CREASE" on in silico structures, we present our results analyzing small-angle neutron scattering profiles from a solution of core-shell type surfactant-coated nanoparticles with varying extents of aggregation.

Densification of Two Forms of Nanostructured TATB under Uniaxial Die Pressures: A USAXS-SAXS Study

Sequential ultra-small-angle and small-angle and X-ray scattering (USAXS and SAXS) measurements of hierarchical microstructure of a common energetic material, the high explosive 2,4,6-Triamino-1,3,5-trinitrobenzene (TATB), were performed to follow the microstructure evolution upon applied pressure. The pellets were prepared by two different routes-die pressed from a nanoparticle form and a nano-network form of TATB powder. The derived structural parameters, such as void size, porosity, and the interface area, reflected the response of TATB under compaction. Three populations of voids were observed in the probed q range from 0.007 to 7 nm^-1. The inter-granular voids with size larger than 50 nm were sensitive to low pressures and had a smooth interface with the TATB matrix. The inter-granular voids with size of ~10 nm exhibited a less volume-filling ratio at high pressures (>15 kN) as indicated by a decrease of the volume fractal exponent. The response of these structural parameters to external pressures implied that the main densification mechanisms under die compaction were the flow, fracture, and plastic deformation of the TATB granules. Compared to the nanoparticle TATB, the applied pressure strongly influenced the nano-network TATB due to its more uniform structure. The findings and research methods of this work provide insights into the structural evolution of TATB during densification.

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.

Intensified Nonequilibrium Effect of Polymer Nanocomposites with Decreasing Nanoparticle Size

What are the most important and decisive parameters that determine the structure and the property of polymer nanocomposites (PNCs)? Previous studies answered that controlling the nanoparticle interface is critical, which can be achieved with a choice of a compatible nanoparticle, a proper surface modification, and a change in the polymer chain length. In addition to these parameters, the processing condition of PNCs has recently emerged as an influential parameter for controlling PNC properties, suggesting the existence of the nonequilibrium effect of PNCs. In this regard, we chose the solvent as a main change in the processing condition and investigated the initial solvent-driven nonequilibrium effect of PNCs with varied nanoparticle (NP) sizes. We found that the type of the initial solvent is indeed crucial in determining the ultimate properties of the PNCs, and this becomes more influential as the size of NPs decreases. The decreasing size of NPs causes a conformational change in the adsorbed polymers from tightly packed layers to loosely dangling chains. This results in much greater differences in NP microstructures and rheological properties of PNCs, indicating a stronger nonequilibrium effect with smaller NPs.

Updates in SASfit for fitting analytical expressions and numerical models to small-angle scattering patterns

Small-angle scattering is an increasingly common method for characterizing particle ensembles in a wide variety of sample types and for diverse areas of application. SASfit has been one of the most comprehensive and flexible curve-fitting programs for decades, with many specialized tools for various fields. Here, a selection of enhancements and additions to the SASfit program are presented that may be of great benefit to interested and advanced users alike: (a) further development of the technical basis of the program, such as new numerical algorithms currently in use, a continuous integration practice for automated building and packaging of the software, and upgrades on the plug-in system for easier adoption by third-party developers; (b) a selection of new form factors for anisotropic scattering patterns and updates to existing form factors to account for multiple scattering effects; (c) a new type of a very flexible distribution called metalog [Keelin (2016). Decis. Anal. 13, 243-277], and regularization techniques such as the expectation-maximization method [Dempster et al. (1977). J. R. Stat. Soc. Ser. B (Methodological), 39, 1-22; Richardson (1972) J. Opt. Soc. Am. 62, 55; Lucy (1974). Astron. J. 79, 745; Lucy (1994). Astron. Astrophys. 289, 983-994], which is compared with fits of analytical size distributions via the non-linear least-squares method; and (d) new structure factors, especially for ordered nano- and meso-scaled material systems, as well as the Ornstein-Zernike solver for numerical determination of particle interactions and the resulting structure factor when no analytical solution is available, with the aim of incorporating its effects into the small-angle scattering intensity model used for fitting with SASfit.

Functional amyloid in a lipid-like environment: a merry dance of many steps

Functional amyloid, which unlike its pathological counterpart serves a biological purpose, is produced in a carefully orchestrated sequence of events. In bacteria, the major amyloid component is transported over the periplasm and through the outer membrane to assemble on the bacterial cell surface. During its life time, the amyloid protein may be exposed to both membrane lipids and extracellular surfactant, making it relevant to study its interactions with these components in vitro. Particularly for charged surfactants, the interaction is quite complex and highly dependent on the surfactant:protein molar ratio. Low ratios typically promote aggregation, likely by binding the proteins to micelles and thus increasing the local concentration of proteins, while higher concentrations see an inhibition of the same process as the protein is diluted out and immobilized on individual micelles. This is particularly pronounced for strongly anionic surfactants like SDS; the naturally occurring biosurfactant rhamnolipid interacts more weakly with the protein, which still not only allows aggregation but also leads to less detrimental effects at higher ratios. Similarly, anionic vesicle-forming lipids largely stimulate aggregation likely because of weaker interactions. Anionic lysolipids, thanks to their micelle-forming properties, resemble SDS in their impact on fibrillation. There are also examples of systems where membrane binding sequesters an otherwise amyloidogenic sequence and prevents fibrillation or-quite the opposite- liberates another part of the protein to engage in self-assembly. Thus, membranes and surfactants have very varied roles to play in the biogenesis and function of bacterial amyloid.

Lactoferricins impair the cytosolic membrane of Escherichia coli within a few seconds and accumulate inside the cell

We report the real-time response of Escherichia coli to lactoferricin-derived antimicrobial peptides (AMPs) on length scales bridging microscopic cell sizes to nanoscopic lipid packing using millisecond time-resolved synchrotron small-angle X-ray scattering. Coupling a multiscale scattering data analysis to biophysical assays for peptide partitioning revealed that the AMPs rapidly permeabilize the cytosolic membrane within less than 3 s-much faster than previously considered. Final intracellular AMP concentrations of ∼80-100 mM suggest an efficient obstruction of physiologically important processes as the primary cause of bacterial killing. On the other hand, damage of the cell envelope and leakage occurred also at sublethal peptide concentrations, thus emerging as a collateral effect of AMP activity that does not kill the bacteria. This implies that the impairment of the membrane barrier is a necessary but not sufficient condition for microbial killing by lactoferricins. The most efficient AMP studied exceeds others in both speed of permeabilizing membranes and lowest intracellular peptide concentration needed to inhibit bacterial growth.

Erratum: Growing a thriving international community for small-angle scattering through collaboration. Corrigendum

[This corrects the article DOI: 10.1107/S1600576721007561.].

Small-angle scattering for beginners

A non-technical yet rigorous introduction to small-angle scattering is proposed, through the systematic use of Fresnel–Feynman analysis of interference phenomena.

Many experimental methods are available for the characterization of nanostructures, but most of them are limited by stringent experimental conditions. When it comes to analysing nanostructures in the bulk or in their natural environment – even as ordinary as water at room temperature – small-angle scattering (SAS) of X-rays or neutrons is often the only option. The rapid worldwide development of synchrotron and neutron facilities over recent decades has opened unprecedented possibilities for using SAS in situ and in a time-resolved way. But, in spite of its huge potential in the field of nanomaterials in general, SAS is covered far less than other characterization methods in non-specialized curricula. Presented here is a rigorous discussion of small-angle scattering, at a technical level comparable to the classical undergraduate coverage of X-ray diffraction by crystals and which contains diffraction as a particular case.

Ambiguities in and completeness of SAS data analysis of membrane proteins: the case of the sensory rhodopsin II-transducer complex

Membrane proteins (MPs) play vital roles in the function of cells and are also major drug targets. Structural information on proteins is vital for understanding their mechanism of function and is critical for the development of drugs. However, obtaining high-resolution structures of membrane proteins, in particular, under native conditions is still a great challenge. In such cases, the low-resolution methods small-angle X-ray and neutron scattering (SAXS and SANS) might provide valuable structural information. However, in some cases small-angle scattering (SAS) provides ambiguous ab initio structural information if complementary measurements are not performed and/or a priori information on the protein is not taken into account. Understanding the nature of the limitations may help to overcome these problems. One of the main problems of SAS data analysis of solubilized membrane proteins is the contribution of the detergent belt surrounding the MP. Here, a comprehensive analysis of how the detergent belt contributes to the SAS data of a membrane-protein complex of sensory rhodopsin II with its cognate transducer from Natronomonas pharaonis (NpSRII-NpHtrII) was performed. The influence of the polydispersity of NpSRII-NpHtrII oligomerization is the second problem that is addressed here. It is shown that inhomogeneity in the scattering length density of the detergent belt surrounding a membrane part of the complex and oligomerization polydispersity significantly impacts on SAXS and SANS profiles, and therefore on 3D ab initio structures. It is described how both problems can be taken into account to improve the quality of SAS data treatment. Since SAS data for MPs are usually obtained from solubilized proteins, and their detergent belt and, to a certain extent, oligomerization polydispersity are sufficiently common phenomena, the approaches proposed in this work might be used in SAS studies of different MPs.

Nanocrystalline protein domains via salting-out

Protein salting-out is a well established phenomenon that in many cases leads to amorphous structures and protein gels, which are usually not considered to be useful for protein structure determination. Here, microstructural measurements of several different salted-out protein dense phases are reported, including of lysozyme, ribonuclease A and an IgG1, showing that salted-out protein gels unexpectedly contain highly ordered protein nanostructures that assemble hierarchically to create the gel. The nanocrystalline domains are approximately 10-100 nm in size, are shown to have structures commensurate with those of bulk crystals and grow on time scales in the order of an hour to a day. Beyond revealing the rich, hierarchical nanoscale to mesoscale structure of protein gels, the nanocrystals that these phases contain are candidates for structural biology on next-generation X-ray free-electron lasers, which may enable the study of biological macromolecules that are difficult or impossible to crystallize in bulk.

Direct Structural Evidence for Interfacial Gradients in Asymmetric Polymer Nanocomposite Blends

Understanding the complex structure of polymer blends filled with nanoparticles (NPs) is key to design their macroscopic properties. Here, the spatial distribution of hydrogenated (H) and deuterated (D) polymer chains asymmetric in mass is studied by small-angle neutron scattering. Depending on the chain mass, a qualitatively new large-scale organization of poly(vinyl acetate) chains beyond the random-phase approximation is evidenced in nanocomposites with attractive polymer-silica interactions. The silica is found to systematically induce bulk segregation. Only with long H-chains, a strong scattering signature is observed in the q range of the NP size: it is the sign of interfacial isotopic enrichment, that is, of contrasted polymer shells close to the NP surface. A quantitative model describing both the bulk segregation and the interfacial gradient (over ca. 10-20 nm depending on the NP size) is developed, showing that both are of comparable strength. In all cases, NP surfaces trap the polymer blend in a non-equilibrium state, with preferential adsorption around NPs only if the chain length and isotopic preference toward the surface combine their entropic and enthalpic driving forces. This structural evidence for interfacial polymer gradients will open the road for quantitative understanding of the dynamics of many-chain nanocomposite systems.

Computational Reverse-Engineering Analysis for Scattering Experiments of Assembled Binary Mixture of Nanoparticles

In this paper, we describe a computational method for analyzing results from scattering experiments on dilute solutions of supraparticles, where each supraparticle is created by the assembly of nanoparticle mixtures. Taking scattering intensity profiles and nanoparticle mixture composition and size distributions in each supraparticle as input, this computational approach called computational reverse engineering analysis for scattering experiments (CREASE) uses a genetic algorithm to output information about the structure of the assembled nanoparticles (e.g., real space pair correlation function, extent of nanoparticle mixing/segregation, sizes of domains) within a supraparticle. We validate this method by taking as input in silico scattering intensity profiles from coarse-grained molecular simulations of a binary mixture of nanoparticles, forming a close-packed structure and testing if our computational method can correctly reproduce the nanoparticle structure observed in those simulations. We test the strengths and limitations of our method using a variety of in silico scattering intensity profiles obtained from simulations of a spherical or a cubic supraparticle comprising binary nanoparticle mixtures with varying chemistries, with and without dispersity in sizes, that exhibit well-mixed to strongly segregated structures. The strengths of the presented method include its capability to analyze scattering intensity profiles even when the wavevector q range is limited, to handily provide all of the pairwise radial distribution functions, and to correctly determine the extent of segregation/mixing of the nanoparticles assembled in complex geometries.

Growing a thriving international community for small-angle scattering through collaboration

Small-angle scattering emerged as a tool for studying noncrystalline structures from early observations around 1930 that there was a relationship between the extent of the scattering and the size of the scattering object. André Guinier, a leading figure in the development of the field, noted in his summary findings from the first Conference on Small Angle Scattering in 1958 that the technique would be of value to study 'submicroscopical inhomogeneities' and further provided a means of 'observation [that had] in the past restricted the field of application of the X-ray method.' In 1965 the first of what became a highly successful series of Small-Angle Scattering (SAS) meetings held approximately every three years took place in Syracuse, NY, USA, and many of these ongoing meetings published their proceedings and highlights in the International Union of Crystallography (IUCr) Journal of Applied Crystallography. Since the early 2000s, the relationship between the international SAS community represented at the triennial SAS meetings and the IUCr has been strengthened and deepened through formal cooperation and collaboration in a number of mutually beneficial activities that have supported the growth and health of the field and the IUCr.

Apolipoprotein E Binding Drives Structural and Compositional Rearrangement of mRNA-Containing Lipid Nanoparticles

Emerging therapeutic treatments based on the production of proteins by delivering mRNA have become increasingly important in recent times. While lipid nanoparticles (LNPs) are approved vehicles for small interfering RNA delivery, there are still challenges to use this formulation for mRNA delivery. LNPs are typically a mixture of a cationic lipid, distearoylphosphatidylcholine (DSPC), cholesterol, and a PEG-lipid. The structural characterization of mRNA-containing LNPs (mRNA-LNPs) is crucial for a full understanding of the way in which they function, but this information alone is not enough to predict their fate upon entering the bloodstream. The biodistribution and cellular uptake of LNPs are affected by their surface composition as well as by the extracellular proteins present at the site of LNP administration, e.g., apolipoproteinE (ApoE). ApoE, being responsible for fat transport in the body, plays a key role in the LNP's plasma circulation time. In this work, we use small-angle neutron scattering, together with selective lipid, cholesterol, and solvent deuteration, to elucidate the structure of the LNP and the distribution of the lipid components in the absence and the presence of ApoE. While DSPC and cholesterol are found to be enriched at the surface of the LNPs in buffer, binding of ApoE induces a redistribution of the lipids at the shell and the core, which also impacts the LNP internal structure, causing release of mRNA. The rearrangement of LNP components upon ApoE incubation is discussed in terms of potential relevance to LNP endosomal escape.

Small-Angle X-Ray and Neutron Scattering on Photosynthetic Membranes

Ultrastructural membrane arrangements in living cells and their dynamic remodeling in response to environmental changes remain an area of active research but are also subject to large uncertainty. The use of noninvasive methods such as X-ray and neutron scattering provides an attractive complimentary source of information to direct imaging because in vivo systems can be probed in near-natural conditions. However, without solid underlying structural modeling to properly interpret the indirect information extracted, scattering provides at best qualitative information and at worst direct misinterpretations. Here we review the current state of small-angle scattering applied to photosynthetic membrane systems with particular focus on data interpretation and modeling.

Evolution of the analytical scattering model of live Escherichia coli

A previously reported multi-scale model for (ultra-)small-angle X-ray (USAXS/SAXS) and (very) small-angle neutron scattering (VSANS/SANS) of live Escherichia coli was revised on the basis of compositional/metabolomic and ultrastructural constraints. The cellular body is modeled, as previously described, by an ellipsoid with multiple shells. However, scattering originating from flagella was replaced by a term accounting for the oligosaccharide cores of the lipopolysaccharide leaflet of the outer membrane including its cross-term with the cellular body. This was mainly motivated by (U)SAXS experiments showing indistinguishable scattering for bacteria in the presence and absence of flagella or fimbrae. The revised model succeeded in fitting USAXS/SAXS and differently contrasted VSANS/SANS data of E. coli ATCC 25922 over four orders of magnitude in length scale. Specifically, this approach provides detailed insight into structural features of the cellular envelope, including the distance of the inner and outer membranes, as well as the scattering length densities of all bacterial compartments. The model was also successfully applied to E. coli K12, used for the authors' original modeling, as well as for two other E. coli strains. Significant differences were detected between the different strains in terms of bacterial size, intermembrane distance and its positional fluctuations. These findings corroborate the general applicability of the approach outlined here to quantitatively study the effect of bactericidal compounds on ultrastructural features of Gram-negative bacteria without the need to resort to any invasive staining or labeling agents.

MATSAS: a small-angle scattering computing tool for porous systems

MATSAS analyses X-ray and neutron small-angle scattering data obtained from porous systems. MATSAS delivers a full suite of pore characterizations, including specific surface area, porosity, pore size distribution and fractal dimensions.

MATSAS is a script-based MATLAB program for analysis of X-ray and neutron small-angle scattering (SAS) data obtained from various facilities. The program has primarily been developed for sedimentary rock samples but is equally applicable to other porous media. MATSAS imports raw SAS data from .xls(x) or .csv files, combines small-angle and very small angle scattering data, subtracts the sample background, and displays the processed scattering curves in log–log plots. MATSAS uses the polydisperse spherical (PDSP) model to obtain structural information on the scatterers (scattering objects); for a porous system, the results include specific surface area (SSA), porosity (Φ), and differential and logarithmic differential pore area/volume distributions. In addition, pore and surface fractal dimensions (D_p and D_s, respectively) are obtained from the scattering profiles. The program package allows simultaneous and rapid analysis of a batch of samples, and the results are then exported to .xlsx and .csv files with separate spreadsheets for individual samples. MATSAS is the first SAS program that delivers a full suite of pore characterizations for sedimentary rocks. MATSAS is an open-source package and is freely available at GitHub (https://github.com/matsas-software/MATSAS).

Membrane Protein Structures in Lipid Bilayers; Small-Angle Neutron Scattering With Contrast-Matched Bicontinuous Cubic Phases

This perspective describes advances in determining membrane protein structures in lipid bilayers using small-angle neutron scattering (SANS). Differentially labeled detergents with a homogeneous scattering length density facilitate contrast matching of detergent micelles; this has previously been used successfully to obtain the structures of membrane proteins. However, detergent micelles do not mimic the lipid bilayer environment of the cell membrane in vivo. Deuterated vesicles can be used to obtain the radius of gyration of membrane proteins, but protein-protein interference effects within the vesicles severely limits this method such that the protein structure cannot be modeled. We show herein that different membrane protein conformations can be distinguished within the lipid bilayer of the bicontinuous cubic phase using contrast-matching. Time-resolved studies performed using SANS illustrate the complex phase behavior in lyotropic liquid crystalline systems and emphasize the importance of this development. We believe that studying membrane protein structures and phase behavior in contrast-matched lipid bilayers will advance both biological and pharmaceutical applications of membrane-associated proteins, biosensors and food science.

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.

Simulations of foil-based spin-echo (modulated) small-angle neutron scattering with a sample using McStas

For the further development of spin-echo techniques to label elastic scattering it is necessary to perform simulations of the Larmor precession of neutron spins in a magnetic field. The details of some of these techniques as implemented at the reactor in Delft are simulated. First, the workings of the magnetized foil flipper are simulated. A full virtual spin-echo small-angle neutron scattering instrument is built and tested without and with a realistic scattering sample. It is essential for these simulations to have a simulated sample that also describes the transmitted beam of unscattered neutrons, which usually is not implemented for the simulation of conventional small-angle neutron scattering (SANS) instruments. Finally, the workings of a spin-echo modulated small-angle neutron scattering (SEMSANS) instrument are simulated. The simulations are in good agreement with theory and experiments. This setup can be extended to include realistic magnetic field distributions to fully predict the features of future Larmor labelling elastic-scattering instruments. Configurations can now be simulated for more complicated combinations of SANS with SEMSANS.

Small angle X-ray scattering analysis of ligand-bound forms of tetrameric apolipoprotein-D

Human apolipoprotein-D (apoD) is a glycosylated lipocalin that plays a protective role in Alzheimer's disease due to its antioxidant function. Native apoD from human body fluids forms oligomers, predominantly a stable tetramer. As a lipocalin, apoD binds and transports small hydrophobic molecules such as progesterone, palmitic acid and sphingomyelin. Oligomerisation is a common trait in the lipocalin family and is affected by ligand binding in other lipocalins. The crystal structure of monomeric apoD shows no major changes upon progesterone binding. Here, we used small-angle X-ray scattering (SAXS) to investigate the influence of ligand binding and oxidation on apoD oligomerisation and conformation. As a solution-based technique, SAXS is well suited to detect changes in oligomeric state and conformation in response to ligand binding. Our results show no change in oligomeric state of apoD and no major conformational changes or subunit rearrangements in response to binding of ligands or protein oxidation. This highlights the highly stable structure of the native apoD tetramer under various physiologically relevant experimental conditions.

Algebraic approximations of a polyhedron correlation function stemming from its chord-length distribution

An algebraic approximation, of order K, of a polyhedron correlation function (CF) can be obtained from γ''(r), its chord-length distribution (CLD), considering first, within the subinterval [D_i-1, D_i] of the full range of distances, a polynomial in the two variables (r - D_i-1)^1/2 and (D_i - r)^1/2 such that its expansions around r = D_i-1 and r = D_i simultaneously coincide with the left and right expansions of γ''(r) around D_i-1 and D_i up to the terms O(r - D_i-1)^K/2 and O(D_i - r)^K/2, respectively. Then, for each i, one integrates twice the polynomial and determines the integration constants matching the resulting integrals at the common end-points. The 3D Fourier transform of the resulting algebraic CF approximation correctly reproduces, at large q's, the asymptotic behaviour of the exact form factor up to the term O[q^-(K/2+4)]. For illustration, the procedure is applied to the cube, the tetrahedron and the octahedron.

Molecular Changes in Dengue Envelope Protein Domain III upon Interaction with Glycosaminoglycans

Dengue fever is a rapidly emerging vector-borne viral disease with a growing global burden of approximately 390 million new infections per annum. The Dengue virus (DENV) is a flavivirus spread by female mosquitos of the aedes genus, but the mechanism of viral endocytosis is poorly understood at a molecular level, preventing the development of effective transmission blocking vaccines (TBVs). Recently, glycosaminoglycans (GAGs) have been identified as playing a role during initial viral attachment through interaction with the third domain of the viral envelope protein (EDIII). Here, we report a systematic study investigating the effect of a range of biologically relevant GAGs on the structure and oligomeric state of recombinantly generated EDIII. We provide novel in situ biophysical evidence that heparin and chondroitin sulphate C induce conformational changes in EDIII at the secondary structure level. Furthermore, we report the ability of chondroitin sulphate C to bind EDIII and induce higher-order dynamic molecular changes at the tertiary and quaternary structure levels which are dependent on pH, GAG species, and the GAG sulphation state. Lastly, we conducted ab initio modelling of Small Angle Neutron Scattering (SANS) data to visualise the induced oligomeric state of EDIII caused by interaction with chondroitin sulphate C, which may aid in TBV development.

Assembly of Capsids from Hepatitis B Virus Core Protein Progresses through Highly Populated Intermediates in the Presence and Absence of RNA

The genetic material of viruses is protected by protein shells that are assembled from a large number of subunits in a process that is efficient and robust. Many of the mechanistic details underpinning efficient assembly of virus capsids are still unknown. The assembly mechanism of hepatitis B capsids has been intensively researched using a truncated core protein lacking the C-terminal domain responsible for binding genomic RNA. To resolve the assembly intermediates of hepatitis B virus (HBV), we studied the formation of nucleocapsids and empty capsids from full-length hepatitis B core proteins, using time-resolved small-angle X-ray scattering. We developed a detailed structural model of the HBV capsid assembly process using a combination of analysis with multivariate curve resolution, structural modeling, and Bayesian ensemble inference. The detailed structural analysis supports an assembly pathway that proceeds through the formation of two highly populated intermediates, a trimer of dimers and a partially closed shell consisting of around 40 dimers. These intermediates are on-path, transient and efficiently convert into fully formed capsids. In the presence of an RNA oligo that binds specifically to the C-terminal domain the assembly proceeds via a similar mechanism to that in the absence of nucleic acids. Comparisons between truncated and full-length HBV capsid proteins reveal that the unstructured C-terminal domain has a significant impact on the assembly process and is required to obtain a more complete mechanistic understanding of HBV capsid formation. These results also illustrate how combining scattering information from different time-points during time-resolved experiments can be utilized to derive a structural model of protein self-assembly pathways.

Structure of DNA-PAMAM dendrimer complexes studied using small-angle scattering techniques

Gene therapy is one of the most important developments for modern medicine. As such methods for the compaction and delivery of nucleic acids bearing therapeutic sequences is essential. The quest for non-viral carriers of nucleic acids has produced a number of possible candidates with dendrimer being among the most promising. Their hyper-branched structure and well-defined size together with low cytotoxicity has found success in both ex-vivo and in-vivo studies. The compaction of DNA with dendrimer has produced a rich array of different structures depending on the physiochemical conditions. Mechanisms that drive the compaction have been shown to be a number of physical interactions that reduce the large polymeric entity from 100s of nanometers to some tens of nanometers to fit into the cell nucleus. The mechanisms driving the compaction of DNA will be discussed in detail while the focus will be directed to tuning the structural properties of the complexes and their structural characterization using small-angle scattering techniques.

The chord-length distribution of a polyhedron

The chord-length distribution function [γ''(r)] of any bounded polyhedron has a closed analytic expression which changes in the different subdomains of the r range. In each of these, the γ''(r) expression only involves, as transcendental contributions, inverse trigonometric functions of argument equal to R[r, Δ₁], Δ₁ being the square root of a second-degree r polynomial and R[x, y] a rational function. As r approaches δ, one of the two end points of an r subdomain, the derivative of γ''(r) can only show singularities of the forms |r - δ|^-n and |r - δ|^-m+1/2, with n and m appropriate positive integers. Finally, the explicit analytic expressions of the primitives are also reported.

Small-Angle Scattering and Multifractal Analysis of DNA Sequences

The arrangement of A, C, G and T nucleotides in large DNA sequences of many prokaryotic and eukaryotic cells exhibit long-range correlations with fractal properties. Chaos game representation (CGR) of such DNA sequences, followed by a multifractal analysis, is a useful way to analyze the corresponding scaling properties. This approach provides a powerful visualization method to characterize their spatial inhomogeneity, and allows discrimination between mono- and multifractal distributions. However, in some cases, two different arbitrary point distributions, may generate indistinguishable multifractal spectra. By using a new model based on multiplicative deterministic cascades, here it is shown that small-angle scattering (SAS) formalism can be used to address such issue, and to extract additional structural information. It is shown that the box-counting dimension given by multifractal spectra can be recovered from the scattering exponent of SAS intensity in the fractal region. This approach is illustrated for point distributions of CGR data corresponding to Escherichia coli, Phospholamban and Mouse mitochondrial DNA, and it is shown that for the latter two cases, SAS allows extraction of the fractal iteration number and the scaling factor corresponding to "ACGT" square, or to recover the number of bases. The results are compared with a model based on multiplicative deterministic cascades, and respectively with one which takes into account the existence of forbidden sequences in DNA. This allows a classification of the DNA sequences in terms of random and deterministic fractals structures emerging in CGR.

sasPDF: pair distribution function analysis of nanoparticle assemblies from small-angle scattering data

sasPDF, a method for characterizing the structure of nanoparticle assemblies (NPAs), is presented. The method is an extension of the atomic pair distribution function (PDF) analysis to the small-angle scattering (SAS) regime. The PDFgetS3 software package for computing the PDF from SAS data is also presented. An application of the sasPDF method to characterize structures of representative NPA samples with different levels of structural order is then demonstrated. The sasPDF method quantitatively yields information such as structure, disorder and crystallite sizes of ordered NPA samples. The method was also used to successfully model the data from a disordered NPA sample. The sasPDF method offers the possibility of more quantitative characterizations of NPA structures for a wide class of samples.

Stochastic models of dense or hollow nanoparticles and their scattering properties

A family of stochastic models of disordered particles is proposed, obtained by clipping a Gaussian random field with a function that is space dependent. Depending on the shape of the clipping function, dense or hollow particles can be modelled. General expressions are derived for the form factor of the particles, for their average volume and surface area, and for their density and surface-area distributions against the distance to the particle centre. A general approximation for the form factor is also introduced, based on the density and surface-area distributions, which coincides with the Guinier and Porod expressions in the limits of low and high scattering vector magnitude q. The models are illustrated with the fitting of small-angle X-ray scattering (SAXS) data measured on Pt/Ni hollow nanoparticles. The SAXS analysis and modelling notably capture the collapse of the particles' porosity after being used as oxygen-reduction catalysts.

Structural Properties of Janus Particles with Nano- and Mesoscale Anisotropy

Synthesis of anisotropic Janus particles (AnJPs) is crucial for understanding the fundamental principles behind non-equilibrium self-organization of cells, bacteria, or enzymes, and for the design of novel multicomponent carriers for guided self-assembly, drug delivery or molecular imaging. Their catalytic activity, as well as many other chemical and physical properties are intimately related to the nano- and mesoscale structure. An efficient and fast in situ monitoring of the structural changes involves non-destructive techniques which can probe macroscopic volumes of multicomponent systems, such as small-angle scattering (SAS). However, the interpretation of scattering data is often a difficult task since the existing models deal only with symmetric AnJPs, thus greatly restricting their applicability. Here, a general theoretical framework is developed, which describes scattering from a system containing randomly oriented and placed two-phase AnJPs with arbitrarily tunable geometric and chemical asymmetries embedded in a solution/matrix of different chemical composition. This approach allows an analytic description of the contrast matching point, and it is shown that the interplay between the scattering curves of the two phases gives rise to a rich scaling behavior which allows extracting structural information about each individual phase. To illustrate the above findings, analytic expression for the scattering curves of asymmetric AnJPs are derived, and the results are validated by Monte-Carlo simulations. The broad general features of the scattering curves are explained by using a simple scaling approach which allows gaining more physical insight into the scattering processes as well as for the interpretation of SAS intensity.

Structural Properties of Molecular Sierpiński Triangle Fractals

The structure of fractals at nano and micro scales is decisive for their physical properties. Generally, statistically self-similar (random) fractals occur in natural systems, and exactly self-similar (deterministic) fractals are artificially created. However, the existing fabrication methods of deterministic fractals are seldom defect-free. Here, are investigated the effects of deviations from an ideal deterministic structure, including small random displacements and different shapes and sizes of the basic units composing the fractal, on the structural properties of a common molecular fractal—the Sierpiński triangle (ST). To this aim, analytic expressions of small-angle scattering (SAS) intensities are derived, and it is shown that each type of deviation has its own unique imprint on the scattering curve. This allows the extraction of specific structural parameters, and thus the design and fabrication of artificial structures with pre-defined properties and functions. Moreover, the influence on the SAS intensity of various configurations induced in ST, can readily be extended to other 2D or 3D structures, allowing for exploration of structure-property relationships in various well-defined fractal geometries.

Water as a Good Solvent for Unfolded Proteins: Folding and Collapse are Fundamentally Different

The argument that the hydrophobic effect is the primary effect driving the folding of globular proteins is nearly universally accepted (including by the authors). But does this view also imply that water is a "poor" solvent for the unfolded states of these same proteins? Here we argue that the answer is "no," that is, folding to a well-packed, extensively hydrogen-bonded native structure differs fundamentally from the nonspecific chain collapse that defines a poor solvent. Thus, the observation that a protein folds in water does not necessitate that water is a poor solvent for its unfolded state. Indeed, chain-solvent interactions that are marginally more favorable than nonspecific intrachain interactions are beneficial to protein function because they destabilize deleterious misfolded conformations and inter-chain interactions.

Addressing the challenges of modeling the scattering from bottlebrush polymers in solution

Small-angle scattering measurements of complex macromolecules in solution are used to establish relationships between chemical structure and conformational properties. Interpretation of the scattering data requires an inverse approach where a model is chosen and the simulated scattering intensity from that model is iterated to match the experimental scattering intensity. This raises challenges in the case where the model is an imperfect approximation of the underlying structure, or where there are significant correlations between model parameters. We examine three bottlebrush polymers (consisting of polynorbornene backbone and polystyrene side chains) in a good solvent using a model commonly applied to this class of polymers: the flexible cylinder model. Applying a series of constrained Monte-Carlo Markov Chain analyses demonstrates the severity of the correlations between key parameters and the presence of multiple close minima in the goodness of fit space. We demonstrate that a shape-agnostic model can fit the scattering with significantly reduced parameter correlations and less potential for complex, multimodal parameter spaces. We provide recommendations to improve the analysis of complex macromolecules in solution, highlighting the value of Bayesian methods. This approach provides richer information for understanding parameter sensitivity compared to methods which produce a single, best fit.

Generation of the configurational ensemble of an intrinsically disordered protein from unbiased molecular dynamics simulation

Intrinsically disordered proteins (IDPs) are abundant in eukaryotic proteomes, play a major role in cell signaling, and are associated with human diseases. To understand IDP function it is critical to determine their configurational ensemble, i.e., the collection of 3-dimensional structures they adopt, and this remains an immense challenge in structural biology. Attempts to determine this ensemble computationally have been hitherto hampered by the necessity of reweighting molecular dynamics (MD) results or biasing simulation in order to match ensemble-averaged experimental observables, operations that reduce the precision of the generated model because different structural ensembles may yield the same experimental observable. Here, by employing enhanced sampling MD we reproduce the experimental small-angle neutron and X-ray scattering profiles and the NMR chemical shifts of the disordered N terminal (SH4UD) of c-Src kinase without reweighting or constraining the simulations. The unbiased simulation results reveal a weakly funneled and rugged free energy landscape of SH4UD, which gives rise to a heterogeneous ensemble of structures that cannot be described by simple polymer theory. SH4UD adopts transient helices, which are found away from known phosphorylation sites and could play a key role in the stabilization of structural regions necessary for phosphorylation. Our findings indicate that adequately sampled molecular simulations can be performed to provide accurate physical models of flexible biosystems, thus rationalizing their biological function.

Using the singular value decomposition to extract 2D correlation functions from scattering patterns

The truncated singular value decomposition (TSVD) is applied to extract the underlying 2D correlation functions from small-angle scattering patterns. The approach is tested by transforming the simulated data of ellipsoidal particles and it is shown that also in the case of anisotropic patterns (i.e. aligned ellipsoids) the derived correlation functions correspond to the theoretically predicted profiles. Furthermore, the TSVD is used to analyze the small-angle X-ray scattering patterns of colloidal dispersions of hematite spindles and magnetotactic bacteria in the presence of magnetic fields, to verify that this approach can be applied to extract model-free the scattering profiles of anisotropic scatterers from noisy data.

Hierarchical Morphology of Poly(ether ether ketone) Aerogels

The phase diagram for the thermoreversible gelation of poly(ether ether ketone) (PEEK) in 4-chlorophenol (4CP) was constructed over broad temperature and concentration ranges, revealing that PEEK is capable of dissolving and forming gels in both 4CP and dichloroacetic acid (DCA) up to a concentration of 25 wt %. Highly porous aerogels of PEEK were prepared through simple solvent exchange followed by one of two drying methods of solvent removal from the wet gel: freeze-drying or supercritical CO₂ fluid extraction (SC-drying). The field-emission scanning electron microscopy analysis showed that gelation of PEEK in 4CP, followed by SC-drying, produced aerogels with well-defined lamellar aggregates as compared to less ordered aggregates formed from DCA. Mechanical properties (in compression) were shown to improve with increasing density, resulting in equivalent compressive moduli at comparable density, regardless of the preparation method (gelation solvent selection, concentration variation, or drying method). Nitrogen adsorption-desorption isotherms indicate that PEEK aerogels are comprised of mesopores (2-50 nm diameter pores) formed from stacked crystalline lamella. PEEK aerogels prepared using SC-drying exhibit higher Brunauer-Emmett-Teller surface areas than freeze-dried aerogels of comparable density. The ultra-small-angle X-ray scattering/small-angle X-ray scattering (SAXS)/wide-angle X-ray scattering analysis revealed a hierarchical morphology of the PEEK aerogels with structural features from PEEK crystallites to agglomerates of stacked lamella that spanned a wide range of length scales. SANS contrast-matching confirmed that the morphological origin of the principle scattering feature in PEEK aerogels is stacked crystalline lamella. Nitrogen sorption measurements of porosity and the specific surface area of the PEEK aerogels were correlated with the SAXS analysis to reveal a remarkably high surface area attributed to the platelet-like, lamellar morphology. Contact angle and contact angle hysteresis (CAH) revealed that low-density PEEK aerogels (ρ < 0.15 g/cm³) have water contact angles above the superhydrophobicity cutoff angle (>150°) and a very low CAH near 1°.

Understanding the Static Interfacial Polymer Layer by Exploring the Dispersion States of Nanocomposites

The dynamic and static properties of the interfacial region between polymer and nanoparticles have wide-ranging consequences on performances of nanomaterials. The thickness and density of the static layer are particularly difficult to assess experimentally due to superimposing nanoparticle interactions. Here, we tune the dispersion of silica nanoparticles in nanocomposites by preadsorption of polymer layers in the precursor solutions, and by varying the molecular weight of the matrix chains. Nanocomposite structures ranging from ideal dispersion to repulsive order or various degrees of aggregation are generated and observed by small-angle scattering. Preadsorbed chains are found to promote ideal dispersion, before desorption in the late stages of nanocomposite formation. The microstructure of the interfacial polymer layer is characterized by detailed modeling of X-ray and neutron scattering. Only in ideally well-dispersed systems a static interfacial layer of reduced polymer density over a thickness of ca. 2 nm is evidenced based on the analysis with a form-free density profile optimized using numerical simulations. This interfacial gradient layer is found to be independent of the thickness of the initially adsorbed polymer, but appears to be generated by out-of-equilibrium packing and folding of the preadsorbed layer. The impact of annealing is investigated to study the approach of equilibrium, showing that initially ideally well-dispersed systems adopt a repulsive hard-sphere structure, while the static interfacial layer disappears. This study thus promotes the fundamental understanding of the interplay between effects which are decisive for macroscopic material properties: polymer-mediated interparticle interactions, and particle interfacial effects on the surrounding polymer.