Pair Distance Distribution Function Research Articles

Coordinate-based simulation of pair distance distribution functions for small and large molecular assemblies: implementation and applications

X-ray scattering has become a major tool in the structural characterization of nanoscale materials. Thanks to the widely available experimental and computational atomic models, coordinate-based X-ray scattering simulation has played a crucial role in data interpretation in the past two decades. However, simulation of real-space pair distance distribution functions (PDDFs) from small- and wide-angle X-ray scattering, SAXS/WAXS, has been relatively less exploited. This study presents a comparison of PDDF simulation methods, which are applied to molecular structures that range in size from β-cyclodextrin [1 kDa molecular weight (MW), 66 non-hydrogen atoms] to the satellite tobacco mosaic virus capsid (1.1 MDa MW, 81 960 non-hydrogen atoms). The results demonstrate the power of interpretation of experimental SAXS/WAXS from the real-space view, particularly by providing a more intuitive method for understanding of partial structure contributions. Furthermore, the computational efficiency of PDDF simulation algorithms makes them attractive as approaches for the analysis of large nanoscale materials and biological assemblies. The simulation methods demonstrated in this article have been implemented in stand-alone software, SolX 3.0, which is available to download from https://12idb.xray.aps.anl.gov/solx.html.

Structure-Elasticity Relationships in Hybrid-Carrageenan Hydrogels Studied by Image Dynamic Light Scattering, Ultra-Small-Angle Light Scattering and Dynamic Rheometry.

Hybrid-carrageenan hydrogels are characterized using novel techniques based on high-resolution speckle imaging, namely image dynamic light scattering (IDLS) and ultra-small-angle light scattering (USALS). These techniques, used to probe the microscopic structure of the system in sol-gel phase separation and at different concentrations in the gel phase, give access to a better understanding of the network's topology on the basis of fractals in the dense phase. Observations of the architecture and the spatial and the size distributions of gel phase and fractal dimension were performed by USALS. The pair-distance distribution function, P(r), extracted from USALS patterns, is a new methodology of calculus for determining the network's internal size with precision. All structural features are systematically compared with a linear and non-linear rheological characterization of the gels and structure-elasticity relationships are identified in the framework of fractal colloid gels in the diffusion limit.

Evaporation-induced self-assembly of Janus pyramid molecules from fractal network to core-shell nanoclusters evidenced by small-angle X-ray scattering

Self-assembly of nanoclusters (NCs) is an effective synthetic method for preparing functionalized nanomaterials. However, the assembly process and mechanisms in solutions still remain ambiguous owing to the limited strategies to monitor intermediate assembled states. Herein, the self-assembly process of amphiphilic molecule 4POSS-DL-POM (consisting of four polyhedral oligomeric silsesquioxanes, a dendritic linker, and one polyoxometalate) by evaporation of acetone in a mixed acetone/n-decane solution is monitored by time-resolved synchrotron small-angle X-ray scattering (SAXS). Scattering data assessments, including Kratky analysis, pair distance distribution function, and model fitting, track the self-assembly process of 4POSS-DL-POM from a fractal network to compact NCs, then to core–shell NCs, and finally to superlattice structure. The calculated average aggregation number of a core–shell NC is 11 according to the parameters obtained from core-shell model fitting, in agreement with electron microscopy. The fundamental understanding of the self-assembly dynamics from heterocluster into NCs provides principles to control building block shape and guide target aggregation, which can further promote the design and construction of highly ordered cluster-assembled functional nanomaterials.

Pd8 Cluster: Too Small to Melt? A BOMD Study.

The question of whether a solid-liquid phase transition occurs in small clusters poses a fundamental challenge. In this study, we attempt to elucidate this phenomenon through a thorough examination of the thermal behavior and structural stability of Pd8 clusters employing ab initio simulations. Initially, a systematic global search is carried out to identify the various isomers of the Pd8 cluster. This is accomplished by employing an ab initio basin-hopping algorithm and using the PBE/SDD scheme integrated in the Gaussian code. The resulting isomers are further refined through reoptimization using the deMon2k package. To ensure the structural firmness of the lowest-energy isomer, we calculated normal modes. The structural stability as a function of temperature is analyzed through the Born-Oppenheimer molecular dynamics (BOMD) approach. Multiple BOMD trajectories at distinct simulated temperatures are examined with data clustering analysis to determine cluster isomers. This analysis establishes a connection between the potential energy landscape and the simulated temperature. To address the question of cluster melting, canonical parallel-tempering BOMD runs are performed and analyzed with the multiple-histogram method. A broad maximum in the heat capacity curve indicates a melting transition between 500 and 600 K. To further examine this transition, the mean-squared displacement and the pair-distance distribution function are calculated. The results of these calculations confirm the existence of a solid-liquid phase transition, as indicated by the heat capacity curve.

Size-refocusing fitting of small-angle X-ray scattering from polydisperse nanoparticles for shape determination

Small-angle X-ray scattering (SAXS) which records reciprocal-space signals with characteristic Bessel-type oscillations is a powerful technique for studying nanoparticles. However, the size polydispersity (or size distribution) of nanoparticles in an ensemble sample smears the oscillational peaks and valleys in the SAXS profile, making it difficult to extract accurate real-space information (e.g. three-dimensional geometry) on the nanoparticles. In this work, a method capable of eliminating the size-distribution-induced smearing effect from SAXS profiles by taking the known size-distribution function into consideration has been developed. The method employs a penalized iterative regression to fit the pair distance distribution function (PDDF) derived from a SAXS profile, recovering the representative PDDF of the nanoparticles. The method has been evaluated with a series of nanoparticle systems of various shapes and size distributions, showing their PDDF profiles to have high fidelity to the reference ideal PDDF profiles. Inverse Fourier transformation of the recovered PDDF profiles gives SAXS profiles presenting the characteristic Bessel-type oscillations, enabling reconstruction of the representative three-dimensional geometry of the nanoparticles. This method will help in the use of SAXS to image synthesized colloidal nanoparticles where size polydispersity is inevitable.

Synthesis and characterization of pH-triggered doxorubicin-conjugated polydopamine-coated cobalt ferrite nanoparticles for in-vitro/in-vivo studies in liver cancer therapy

Polydopamine-coated cobalt ferrite nanoparticles (PDA-coated CF-NPs) were synthesized and characterized for their potential in drug delivery evaluation. Small-angle X-ray scattering (SAXS) showed post-coating spherical shape of magnetic PDA NPs. The scattering intensity at zero angle (I(0)) of PDA-coated CF (0.01) had higher scattering intensity than CF-NPs (0.49 × 10-3). PDA increased the flexibility degree of unfolding on Kratky plot shifting from 1.05 to 1.87 at same qRg values. The pair-distance distribution function (P(r)) of PDA-coated CF-NPs indicated a more homogeneous and compact scattering structure. GNOM indicated larger size for CF, while PDA-coated CF (a narrower and taller peak) displayed a more compact and uniform scattering profile. PDA reduced crystallinity size to 2.51 nm with amorphous peaks at 38.12°, 44.28°, and 64.43° degree and infrared spectrum confirmed PDA incorporation onto CF-NPs. PDA-coated CF had 1.5-fold larger pore size and enhanced surface area. CF and PDA-coated CF exhibited “S” shape behavior in Langevin function without hysteresis. The kinetic models suggested Fickian diffusion and sustainable release for the erosion-dominated release of the PDA-coated CF. In vitro, doxorubicin (DOX)-carried PDA-coated CF (D-P@CF) showed low toxicity to HepG2 cells; in vivo, liver tumor inhibition indicated medication delivery potential for cancer treatment.

Structural characterization of transcription-coupled repair protein UVSSA and its interaction with TFIIH protein

UV-stimulated scaffold protein A (UVSSA) is a key protein in the Transcription-Coupled Nucleotide Excision Repair (TC-NER) pathway. UVSSA, an intrinsically disordered protein, interacts with multiple members of the pathway, tethering them into the complex. Several studies have reported that UVSSA recruits Transcription Factor IIH (TFIIH) via direct interaction, following which CSB is degraded and the lesion recognition TC-NER complex dissociates from the damage site to facilitate the DNA repair. Structural insights into these events remain largely unknown. Herein, we have investigated the interaction of human UVSSA with the Pleckstrin-Homology-domain of p62 subunit of TFIIH (p62-PHD) using biophysical techniques. We observed that UVSSA forms a stable complex with the p62-PHD in vitro. Small-angle scattering measurements using X-rays and neutrons revealed a significant change in pair-distance distribution function for UVSSA662/p62-PHD complex compared to UVSSA alone. Additionally, a significant decrease was observed in the radius of gyration of the complex. Our findings suggest that TFIIH binding to UVSSA causes significant conformational changes in UVSSA. We hypothesize that these conformational changes play an important role in the dissociation of the lesion recognition TC-NER complex.

Resolving domain positions of cellobiose dehydrogenase by small angle X-ray scattering.

The interdomain electron transfer (IET) between the catalytic flavodehydrogenase domain and the electron-transferring cytochrome domain of cellobiose dehydrogenase (CDH) plays an essential role in biocatalysis, biosensors and biofuel cells, as well as in its natural function as an auxiliary enzyme of lytic polysaccharide monooxygenase. We investigated the mobility of the cytochrome and dehydrogenase domains of CDH, which is hypothesised to limit IET in solution by small angle X-ray scattering (SAXS). CDH from Myriococcum thermophilum (syn. Crassicarpon hotsonii, syn. Thermothelomyces myriococcoides) was probed by SAXS to study the CDH mobility at different pH and in the presence of divalent cations. By comparison of the experimental SAXS data, using pair-distance distribution functions and Kratky plots, we show an increase in CDH mobility at higher pH, indicating alterations of domain mobility. To further visualise CDH movement in solution, we performed SAXS-based multistate modelling. Glycan structures present on CDH partially masked the resulting SAXS shapes, we diminished these effects by deglycosylation and studied the effect of glycoforms by modelling. The modelling shows that with increasing pH, the cytochrome domain adopts a more flexible state with significant separation from the dehydrogenase domain. On the contrary, the presence of calcium ions decreases the mobility of the cytochrome domain. Experimental SAXS data, multistate modelling and previously reported kinetic data show how pH and divalent ions impact the closed state necessary for the IET governed by the movement of the CDH cytochrome domain.

Fractal features of pH-sensitive bimodal mesoporous silica-supported bipyridine-proline organocatalysts with core-shell structure and their application in asymmetric aldol reaction

Using poly(acrylic acid) (abbreviated as PAA) as a shell, bimodal mesoporous silicas (abbreviated as BMMs) as a core, and bipyridine-proline (abbreviated as Z) as an active species, a facile approach for preparation of the P-Z@BMMs nanocomposites with core–shell structure was proposed, which was used as a suitable pH-sensitive catalyst for asymmetric aldol reaction between p-nitrobenzaldehyde and cyclohexanone. Their microstructural features and physicochemical properties were extensively characterized by various methods, such as powder X-ray diffraction patterns, N2 adsorption–desorption isotherms, the scanning (and transmission) electron microscopy images, the dynamic light scattering measurements, the thermogravimetric analysis, the elemental analysis, and the Fourier transform infrared spectroscopy spectra. Particularly, their fractal evolution, the pair distance distribution function, and the Porod plots were demonstrated via the small-angle X-ray scattering patterns. The results elucidated that the PAA was successfully incorporated onto the external amino-modified surfaces of the mesoporous BMMs, and the particles having PAA grafted thereon had a pH-responsive shell in thickness of around 0.97 nm for controlled release of Z species by adjusting pH value of the reaction medium. Besides, the synthesized P-Z@BMMs presented the satisfactory catalytic yields (around 80%) in comparison with the homo- and heterogeneous catalytic system using Z or Z@BMMs as the catalysts.

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.

Micromagnetic simulation of neutron scattering from spherical nanoparticles: Effect of pore-type defects

We employ micromagnetic simulations to model the effect of pore-type microstructural defects on the magnetic small-angle neutron scattering cross section and the related pair-distance distribution function of spherical magnetic nanoparticles. Our expression for the magnetic energy takes into account the isotropic exchange interaction, the magnetocrystalline anisotropy, the dipolar interaction, and an externally applied magnetic field. The signatures of the defects and the role of the dipolar energy are highlighted and the effect of a particle-size distribution is studied. The results serve as a guideline to the experimentalist.

Objective Criteria for Estimation of Initial Parameters for the Modeling of Micelle and Liposome Structures from Small-Angle X-ray Scattering Data

The structures of hydrophobic membrane proteins are studied using matrices, which serve as models of cell membranes and are formed by the appropriate amphiphilic molecules, e.g., by surfactant or lipid molecules. To study the structure of a protein incorporated into an artificial membrane, first of all it is necessary to determine the structure of the membrane. The ELLLIP and ELLMIC algorithms were previously developed to address this issue by small-angle X-ray scattering. These algorithms allow the construction of models of ellipsoidal vesicles based on the atomic structure of a lipid or surfactant monomer. However, the results of modeling depend, to a large extent, on the subjective assessment of the initial values of the structural parameters of the matrices and may be wrong due to the ambiguity in the solution of such problems. Here, we present an independent approach to the determination of the initial sizes of model membranes for their subsequent structural modeling, which is based on the analysis of the pair-distance distribution functions derived directly from the small-angle X-ray scattering curve.

Magnetic neutron scattering from spherical nanoparticles with Néel surface anisotropy: atomistic simulations.

A dilute ensemble of randomly oriented non-interacting spherical nanomagnets is considered, and its magnetization structure and ensuing neutron scattering response are investigated by numerically solving the Landau-Lifshitz equation. Taking into account the isotropic exchange interaction, an external magnetic field, a uniaxial magnetic anisotropy for the particle core, and in particular the Néel surface anisotropy, the magnetic small-angle neutron scattering cross section and pair-distance distribution function are calculated from the obtained equilibrium spin structures. The numerical results are compared with the well known analytical expressions for uniformly magnetized particles and provide guidance to the experimentalist. In addition, the effect of a particle-size distribution function is modelled.

Medical contrast agents as promising tools for biomacromolecular SAXS experiments.

Small-angle X-ray scattering (SAXS) has become an indispensable tool in structural biology, complementing atomic-resolution techniques. It is sensitive to the electron-density difference between solubilized biomacromolecules and the buffer, and provides information on molecular masses, particle dimensions and interactions, low-resolution conformations and pair distance-distribution functions. When SAXS data are recorded at multiple contrasts, i.e. at different solvent electron densities, it is possible to probe, in addition to their overall shape, the internal electron-density profile of biomacromolecular assemblies. Unfortunately, contrast-variation SAXS has been limited by the range of solvent electron densities attainable using conventional co-solutes (for example sugars, glycerol and salt) and by the fact that some biological systems are destabilized in their presence. Here, SAXS contrast data from an oligomeric protein and a protein-RNA complex are presented in the presence of iohexol and Gd-HPDO3A, two electron-rich molecules that are used in biomedical imaging and that belong to the families of iodinated and lanthanide-based complexes, respectively. Moderate concentrations of both molecules allowed solvent electron densities matching those of proteins to be attained. While iohexol yielded higher solvent electron densities (per mole), it interacted specifically with the oligomeric protein and precipitated the protein-RNA complex. Gd-HPDO3A, while less efficient (per mole), did not disrupt the structural integrity of either system, and atomic models could be compared with the SAXS data. Due to their elevated solubility and electron density, their chemical inertness, as well as the possibility of altering their physico-chemical properties, lanthanide-based complexes represent a class of molecules with promising potential for contrast-variation SAXS experiments on diverse biomacromolecular systems.

Evaluation of properties and structural transitions of Poly (2-acrylamido-2-methyl-1-propanesulfonic acid-co-acrylonitrile) / β-Galactosidase complex coacervates: effects of pH and aging

The coacervates of the Poly (2-acrylamido-2-methyl-1-propanesulfonic acid-co-acrylonitrile) / β-Galactosidase complex are characterized using several techniques (Turbidimetry, dynamic and static light scattering (DLS / SLS), optical microscopy, image dynamic light scattering (IDLS), and ultra-small angles light scattering (USALS)). Turbidity and SLS were used to accurately determine the critical pHs of complex formation (pHc, pHϕ1, pHopt, and pHϕ2), DLS was used to probe the microscopic structure of coacervate droplets rich in proteins and polyelectrolytes in liquid-liquid phase separation, and IDLS and USALS have been introduced to better understand, during aging, the topology of the network formed of materials based on fractals in the dense phase. Observations of the architecture, the spatial inhomogeneity, and the size distributions of liquid complex coacervate droplets and fractal solid precipitates, were performed by optical microscopy. The pair-distance distribution function, P(r), presented in this review, is a new methodology of calculus for determining with precision the radius of gyration Rg of droplets coacervates. These techniques show that aging improves the stability of swollen condensates, the growth of the coacervate droplets is due to the attractive electrostatic interactions within the complex and does not undergo Ostwald ripening, except for the case of pHopt and having fractal dimensions Df generated by diffusion-limited cluster aggregation (DLCA).

Dimerization-dependent membrane tethering by Atg23 is essential for yeast autophagy.

SUMMARYEukaryotes maintain cellular health through the engulfment and subsequent degradation of intracellular cargo using macroautophagy. The function of Atg23, despite being critical to the efficiency of this process, is unclear due to a lack of biochemical investigations and an absence of any structural information. In this study, we use a combination of in vitro and in vivo methods to show that Atg23 exists primarily as a homodimer, a conformation facilitated by a putative amphipathic helix. We utilize small-angle X-ray scattering to monitor the overall shape of Atg23, revealing that it contains an extended rod-like structure spanning approximately 320 Å. We also demonstrate that Atg23 interacts with membranes directly, primarily through electrostatic interactions, and that these interactions lead to vesicle tethering. Finally, mutation of the hydrophobic face of the putative amphipathic helix completely precludes dimer formation, leading to severely impaired subcellular localization, vesicle tethering, Atg9 binding, and autophagic efficiency.

Synergistic Role of Model‐Independent and Model‐Dependent Approaches for Determining Size and Shape of Au Nanostructures Using SAXS

AbstractThe main objective of this study is to showcase the use of synergistic utilization of model‐independent and model‐dependent approaches for analyzing small angle X‐ray scattering (SAXS) data to determine the shape and size of different nanostructures viz. spherical, nanorod, and core‐shell. Herein, different gold nanostructures viz. spherical, nanorod, and core‐shell are synthesized and analyzed using SAXS. First, the SAXS data are analyzed using Guinier law, PDDF (pair–distance distribution function) plots, double logarithmic plots, and electron density curves to get primary information about the size and shape of nanostructures. This information is utilized for choosing an appropriate model and initial input parameters for fitting the SAXS data. The observations obtained from SAXS studies are compared with transmission electron microscopy and UV–vis spectroscopy. It is believed that this study will help in understanding the analysis of SAXS data using a systematic and synergistic approach of utilizing the two methods. It is believed that the study will further add to the understanding of the technique as an alternative approach for transmission electron microscopy.

Fractal Features of the Catalytic Performances of Bimodal Mesoporous Silica‐Supported Organocatalysts Derived from Bipyridine‐Proline for Asymmetric Aldol Reaction

AbstractThe three bipyridine‐proline chiral ligands (Z) with different structural units as highly active species were successfully introduced on Zn‐modified bimodal mesoporous silicas (BMMs). The representative heterogeneous catalysts (ZZnBMMs‐n) containing different molar ratios of Z/Zn (5, 20, 50, 100, 200%) were prepared, and their catalytic performances were evaluated in the asymmetric aldol reactions between p‐nitrobenzaldehyde and cyclohexanone, showing the satisfactory activities (yields) and good stereoselectivity (dr and ee). Meanwhile, their microstructural features and physicochemical properties were characterized by various methods. Particularly, the fractal evolution, the pair distance distribution function, and the Porod plots of the ZZnBMMs catalysts were demonstrated by SAXS analysis. The results revealed that the interfacial layer thickness and their mass fractal (Dm) value gradually increased with the enhanced molar ratios of Z/Zn, along with the decrease of pore size and densification of volume, suggesting the successful Z‐grafting into the mesoporous channels of Zn‐modified matrixes. The essential relationships between the fractal features and their catalytic performance (yield, dr and ee) were explored, showing the larger the Dm values, the better catalytic performance. Besides, the uniform distributions of Zn and S elements in ZZnBMMs catalysts and the formation of enamine‐imine intermediates during the asymmetric aldol reactions were confirmed.

Small-Angle Scattering from Fractional Brownian Surfaces

Recent developments in nanotechnology have allowed the fabrication of a new generation of advanced materials with various fractal-like geometries. Fractional Brownian surfaces (fBs) are often used as models to simulate and characterize these complex geometries, such as the surface of particles in dilute particulate systems (e.g., colloids) or the interfaces in non-particulate two-phase systems (e.g., semicrystalline polymers with crystalline and amorphous phases). However, for such systems, a realistic simulation involves parameters averaged over a macroscopic volume. Here, a method based on small-angle scattering technique is proposed to extract the main structural parameters of surfaces/interfaces from experimental data. It involves the analysis of scattering intensities and the corresponding pair distance distribution functions. This allows the extraction of information with respect to the overall size, fractal dimension, Hurst and spectral exponents. The method is applied to several classes of fBs, and it is shown that the obtained numerical values of the structural parameters are in very good agreement with theoretical ones.

The synthesis and nanostructure investigation of noble metal-based nanocomposite materials

The presented work follows the theme of applied chemistry toward nanomaterials and multiphase functional systems of practical importance. Structural studies of nanocomposite materials are important due to the correlation between physicochemical/structural properties and their application potential. In this work, we report the fabrication and structural characterization of nanocomposite materials constituting noble metal (plasmonic) nanoparticles (AgNP and AuNP) dispersed on selected types of nanostructured solid hosts (nonporous silica, microporous activated carbon, chitosan biopolymer, and ordered mesoporous silica). The ability to maintain a dispersed state of colloidal precursors throughout their deposition on solid hosts was assessed. The influence of the carrier role in the formation and stabilization of nanometallic phases was evaluated taking into account the physicochemical and textural properties of the support surfaces. The size and shape of nanoobjects, clustering effects, interfacial properties, and stability of the immobilized nanophase were implemented by analyzing relevant parameters of SAXS analysis. The dimensional characteristic of the scatterers was evaluated by volume-weighted particle size distribution Dv(R). The detailed overall shape and maximal particle dimension were described by the analysis of pair distance distribution functions (PDDFs). The radius of gyration (Rg) from PDDF and Guinier approximation was calculated for illustrating the dimension of scattered heterogeneities in the investigated solids. The asymptotic behavior of a scattering curve and Porod theory were applied for determining the diffusion and quality of the interfacial surfaces. The size and morphology of nanoparticles in colloidal precursor solutions have been defined as spherical and bimodal in size (~ 6 nm and 20 nm). It was observed that the spherical shape and dispersed state of nanoparticles were achieved for all systems after deposition. However, the morphology of their final form was conditioned by the solid matrices. The particle properties from SAXS were correlated with properties determined by TEM and low-temperature nitrogen sorption analysis. Obtained results suggest good compatibility and correctness of SAXS data reading of nanocomposite systems and can be successfully applied for quick, nondestructive, and effective evaluation of structural properties of complex systems.Graphical abstract