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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

SAXS Assistant: Automated SAXS analysis for structural discovery in biologics and polymeric nanoparticles

Small-angle x-ray scattering (SAXS) is a powerful technique for assessing macromolecular structure. High-throughput SAXS is limited by the time-consuming and, at times, subjective nature of SAXS data interpretation. Here, we present SAXS Assistant, a Python-based script that streamlines SAXS data analysis to extract features for machine learning (ML) and key structural parameters, including the Guinier radius of gyration (R g ), pair distance distribution function (PDDF)-derived R g , maximum particle dimension (D max ), and Kratky plots. The script builds upon BioXTAS RAW and validates reliability via Guinier/PDDF R g agreement, an important indicator of well-measured data sets. For assistance in D max estimation, a multilayer perceptron regressor was trained with 1940 data files from the Small Angle Scattering Biological Data Bank. The model achieved a test set performance R 2 = 0.90 and mean absolute error = 11.7 Å. Training exclusively with experimental data translates analyses from researchers, including experts in the field, to the ML model, which helps assess D max estimations from PDDF. Gaussian mixture model clustering was implemented to classify profiles into structural classes based on entries in the Small Angle Scattering Biological Data Bank. Users may therefore assess the similarity between experimental samples and known biomolecular shapes within the mapped repository entries. This probabilistic clustering aids in quantifying information from Kratky and generating shape-descriptive features. SAXS Assistant accelerates SAXS data analysis through enforced quality control, ML-ready outputs, and flags for low-confidence results. In addition to providing the ability to analyze large data sets at high throughput, this tool is versatile and may serve researchers in both biological and synthetic polymer research fields.

36 MATERIALS SCIENCE↗
DOE OSTI2027

A multi-region approach for the analysis of porous materials and gas-solid reactions using USAXS-SAXS-WAXS: application to CaO carbonation

The reaction rate of gas-solid non-catalytic reactions is typically investigated using reactant conversion data over time and ex-situ measurements of the porous solid reactant textural properties; these data enable the experimental estimation of the initial intrinsic reaction rate, whereas the evolution of the textural properties and the reaction rate over time are evaluated theoretically using reaction models. In this work, a different methodology is presented, based on: a) in-situ time-resolved USAXS-SAXS-WAXS measurements of the solid sample, and b) a multi-region modeling approach; this methodology allows for the estimation of the textural properties and the intrinsic reaction rate at any time during the reaction. Referring to a reaction in which a solid product is obtained from a solid reactant and a gaseous reactant, the porous particle is described as consisting of several distinct regions with different microstructural properties, and both a gas-solid reaction model and a SAXS model are derived and applied to the carbonation of porous CaO. The proposed reaction model highlights the role of the inaccessible reactant and accurately predicts the solid reactant conversion versus time profile. The SAXS model accurately predicts the measured linear trends of the Porod invariant and of the pre-factor of the power law scattering profile versus CaO mass fraction; in the absence of chemical reactions, the proposed equations extend classical SAXS theory to porous materials containing macropores and nonporous solid phases in addition to standard nanoscale inhomogeneous regions.

CO2 solid sorbents↗
DOE OSTI2025

Tutorial: Machine-Learning-Based CREASE-2D Analysis of 2D SAXS Profiles to Characterize Anisotropic Nanostructures in Soft Materials

We present a tutorial to guide users on how to extend the Computational Reverse Engineering Analysis of Scattering Experiments-2D (CREASE-2D) framework to interpret their experimental two-dimensional small-angle scattering (SAS) data from soft materials (e.g., polymers, peptide amphiphiles, biomolecular fibrils). Unlike most traditional SAS analysis approaches, which typically rely on azimuthally averaged onedimensional (1D) profiles, CREASE-2D utilizes the complete 2D scattering profile to reveal information about anisotropy in the structure. In past applications, CREASE has provided insights into complex structural features, including the cross-sectional shapes of assembled nanostructures and dispersity in these features, which are difficult to discern with existing analytical models. While (1D- ) CREASE has been applied to SANS and SAXS data, this tutorial shares the steps for implementing CREASE-2D using an example of a dipeptide solution system, for which we have SAXS data. We present details for these steps involved in using CREASE-2D to interpret SAXS profiles: how to preprocess SAXS data, define relevant structural features, generate three-dimensional real-space structures for specific values of these features, train a machine learning (ML) surrogate model to predict scattering profiles for given structural features, and optimize these features using genetic algorithms (GA). Then, we use these steps to interpret complex 2DSAXS data collected from dipeptide solutions that, in microscopy images, exhibit nanoscale structures that could be elliptical tubes/ flat tapes/cylinders or a combination of these cross sections. Open-source codes, computational hardware, and software requirements, as well as the strengths and limitations of this protocol, are also presented. We expect researchers working with (soft) biomaterials, peptide amphiphiles, amphiphilic polymer solutions, polymer nanocomposites, and blends of particles/polymers will find this CREASE-2D method and this tutorial of use.

CREASE↗
DOE OSTI2025

Ion Clusters in Multicomponent Solutions Determined from X-ray PDF and SAXS Analysis: The NaNO 2 –NaOH–H 2 O System

Here, this study explores ion cluster formation in the NaNO 2 –NaOH–H 2 O system to understand how ion cluster formation is influenced by the composition in multicomponent mixtures. X-ray pair distribution function (PDF) and small-angle X-ray scattering (SAXS) identified complex ion clusters in concentrated NaNO 2 and NaOH solutions as well as their mixtures. PDF analysis showed that the Na–O distance depended primarily on total Na + concentrations rather than anion composition, whereas the nitrite-water oxygen distance stayed the same regardless of concentration or composition. This result indicates that the nitrite ion hydration was relatively independent of composition. SAXS confirms local fluctuations and coherent clusters with notable size differences between NaOH and NaNO 2 solutions. SAXS analysis of mixed solutions shows that their clusters are an average of the individual solutions, indicating mixed clusters.

Reynolds, Jacob G. [Central Plateau Cleanup Compan↗
DOE OSTI2024

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

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

Cell Biology↗
DOE OSTI2025

Integrated structural model of the palladin–actin complex using XL ‐ MS , docking, NMR , and SAXS

Abstract Palladin is an actin‐binding protein that accelerates actin polymerization and is linked to the metastasis of several types of cancer. Previously, three lysine residues in an immunoglobulin‐like domain of palladin have been identified as essential for actin binding. However, it is still unknown where palladin binds to F‐actin. Evidence that palladin binds to the sides of actin filaments to facilitate branching is supported by our previous study showing that palladin was able to compensate for Arp2/3 in the formation of Listeria actin comet tails. Here, we used chemical crosslinking to covalently link palladin and F‐actin residues based on spatial proximity. Samples were then enzymatically digested, separated by liquid chromatography, and analyzed by tandem mass spectrometry. Peptides containing the crosslinks and specific residues involved were then identified for input to the HADDOCK docking server to model the most likely binding conformation. Small‐angle x‐ray scattering was used to provide further insight into palladin flexibility and the binding interface, and NMR spectra identified potential interactions between palladin's Ig domains. Our final structural model of the F‐actin:palladin complex revealed how palladin interacts with and stabilizes F‐actin at the interface between two actin monomers. Three actin residues that were identified in this study also appear commonly in the actin‐binding interface with other proteins such as myotilin, myosin, and tropomodulin. An accurate structural representation of the complex between palladin and actin extends our understanding of palladin's role in promoting cancer metastasis through the regulation of actin dynamics.

Sargent, Rachel [Department of Chemistry and Bioch↗
DOE OSTI2026

Uncertainty-Aware Machine Learning for Small-Angle X-ray Scattering Analysis in Autonomous Experimentation

Small-angle X-ray scattering (SAXS) is a powerful high-throughput characterization tool for probing nanoscale structure in native sample environments, providing real-time morphological information such as nanoparticle size and shape during synthesis. However, automated SAXS data analysis for extracting meaningful structural parameters is non-trivial and remains a bottleneck in closed-loop experimentation towards autonomous materials discovery, which demands fast, reliable, and uncertainty-aware data analysis. Here, we develop a machine-learning approach for automated SAXS analysis tailored to closed-loop nanoparticle synthesis. A Random Forest (RF) regression model is trained on 100,000 synthetic SAXS curves generated from polydisperse spherical nanoparticles with realistic background contributions. Using normalized one-dimensional SAXS intensity profiles as input, the RF model directly predicts nanoparticle radius, size polydispersity, and background parameters, while the ensemble standard deviation across trees provides built-in uncertainty quantification (UQ). On synthetic data, we show that combining fit-quality metrics (R 2 , MAE) with thresholds on prediction uncertainty reliably identifies accurate parameter estimates without access to ground truth. We then apply the trained model to 365 experimental SAXS profiles of citrate-reduced gold nanoparticles synthesized using an automated droplet-flow microreactor with in situ SAXS at a synchrotron beamline, classifying the results into high- and low-confidence subsets based on UQ metrics. Finally, we integrate RF-based SAXS analysis into a simulated closed-loop optimization campaign using Gaussian process Bayesian optimization to minimize nanoparticle polydispersity, benchmarking against conventional automated Levenberg–Marquardt fitting. The RF-guided campaign exhibits substantially faster convergence and lower relative opportunity cost (∼0.07 vs ∼0.3), demonstrating that uncertainty-aware machine-learning SAXS analysis significantly enhances the efficiency and robustness of autonomous nanomaterials synthesis workflows.

Bayesian optimization↗
DOE OSTI2025

Information theory optimization of signals from small-angle scattering measurements

Small-angle X-ray scattering (SAXS) of particles in solution informs on the conformational states and assemblies of biological macromolecules (bioSAXS) outside of cryo- and solid-state conditions. In bioSAXS, the SAXS measurement under dilute conditions is resolution limited, and through an inverse Fourier transform, the measured SAXS intensities directly relate to the physical space occupied by the particles via the P (r)-distribution. Yet, this inverse transform of SAXS data has been historically cast as an ill-posed, ill-conditioned problem requiring an indirect approach. Here, we show that through the applications of matrix and information theories, the inverse transform of SAXS intensity data is a well-conditioned problem. The so-called ill-conditioning of the inverse problem is directly related to the Shannon number. By exploiting the oversampling enabled by modern detectors, a direct inverse Fourier transform of the SAXS data is possible, provided the recovered information does not exceed the Shannon number. The Shannon limit corresponds to the maximum number of significant singular values that can be recovered in a SAXS experiment, suggesting this relationship is a fundamental property of band-limited inverse integral transform problems. This correspondence reduces the complexity of the inverse problem to the Shannon limit and maximum dimension. We propose a hybrid scoring function using an information theory framework that assesses both the quality of the model-data fit as well as the quality of the recovered P (r)-distribution. The hybrid score utilizes the Akaike information criteria and Durbin-Watson statistic that considers parameter-model complexity, i.e., degrees of freedom, and the randomness of the model-data residuals. The described tests and findings extend the boundaries for bioSAXS by completing the information theory formalism initiated by Peter B. Moore to enable a quantitative measure of resolution in SAXS, robustly determine maximum dimension, and more precisely define the best parameter model appropriately representing the observed scattering data.

Rambo, Robert P. [Science and Technology Facilitie↗
DOE OSTI2025

Quantifying dispersity in size and shape of nanoparticles from small-angle scattering data using machine learning based CREASE

Here, we use machine learning (ML) enhanced computational reverse engineering analysis of scattering experiments (CREASE) to interpret small-angle X-ray scattering (SAXS) data obtained from a system of nanoparticles without a priori knowledge of their exact shapes (e.g. spheres or ellipsoids), sizes (0.5–50 nm) and distributions. The SAXS measurements yielded three categories of scattering profiles exhibiting 'strong', 'weak' and 'no' features. Diminishing features (e.g. broadening or disappearing peaks) in scattering profiles have always been attributed to the presence of significant dispersity in the system. Such featureless SAXS data are not suitable for traditional analysis using analytical models. If one were to fit a relevant analytical model (e.g. the lmfit analytical model for polydisperse spheres) to these 'weak' and 'no' SAXS profiles from our nanoparticle systems, one would obtain non-unique interpretations of the data. Relying on electron microscopy to identify the distributions of nanoparticle shapes and sizes is also unfeasible, especially in high-throughput synthesis and characterization loops. In such situations, to identify the distributions of particle sizes and shapes that could be present in the sample, one must rely on methods like ML-CREASE to interpret the data quickly and output all relevant interpretations about the structure present in the system. The ML-CREASE optimization loop takes the experimental scattering profile as input and outputs multiple candidate solutions whose computed scattering profiles match the SAXS profile input. The ML-CREASE method outputs distributions of relevant structural features, such as the volume fraction of the nanoparticles in the system and the mean and standard deviation of the particle size and aspect ratio, assuming a type of distribution (e.g. normal, log-normal) for size and aspect ratio. We find that, for the SAXS profiles analyzed here, accounting for the shape dispersity along with size dispersity of the nanoparticles using ML-CREASE improved the match between the computed scattering profiles and input experimental profiles.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Predicting RNA structure and dynamics with deep learning and solution scattering

Advanced deep learning and statistical methods can predict structural models for RNA molecules. However, RNAs are flexible, and it remains difficult to describe their macromolecular conformations in solutions where varying conditions can induce conformational changes. Small-angle x-ray scattering (SAXS) in solution is an efficient technique to validate structural predictions by comparing the experimental SAXS profile with those calculated from predicted structures. There are two main challenges in comparing SAXS profiles to RNA structures: the absence of cations essential for stability and charge neutralization in predicted structures and the inadequacy of a single structure to represent RNA’s conformational plasticity. We introduce a solution conformation predictor for RNA (SCOPER) to address these challenges. This pipeline integrates kinematics-based conformational sampling with the innovative deep learning model, IonNet, designed for predicting Mg 2+ ion binding sites. Validated through benchmarking against 14 experimental data sets, SCOPER significantly improved the quality of SAXS profile fits by including Mg 2+ ions and sampling of conformational plasticity. We observe that an increased content of monovalent and bivalent ions leads to decreased RNA plasticity. Therefore, carefully adjusting the plasticity and ion density is crucial to avoid overfitting experimental SAXS data. SCOPER is an efficient tool for accurately validating the solution state of RNAs given an initial, sufficiently accurate structure and provides the corrected atomistic model, including ions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Reparameterizing a Lipid Force Field Using Small-Angle X-ray Scattering to Improve Predictions of Multicomponent Membranes under Organic Solvent Stress

Understanding and predicting properties of lipid-bilayer membranes are essential to elucidating organismal physiology and pathophysiology. Therefore, substantial efforts have been undertaken to derive accurate molecular-mechanics force fields (FF) to allow simulation of their properties; however, much of these past efforts focused on tuning force fields to accurately reproduce the properties of model single-component membranes and not multicomponent or stressed membranes. Here, we tuned the CHARMM36 FF for a simple 2-component model of a Gram-positive bacterium. This updated force field is parametrized against a single condensed-phase property, the small-angle X-ray scattering (SAXS) intensities of the 2-component lipid system, using a version of ForceBalance implemented previously (named ForceBalance-SAS) with SAXS and small-angle neutron scattering (SANS) intensities as optimization targets. After tuning, we observe improved agreement with the experimental SAXS of the membrane under 1-butanol and tetrahydrofuran solvent stresses, with a factor of 10.0 and 7.5 reduction, respectively, in χ 2 , the measure of the discrepancy between experimental and computed SAXS intensities. Furthermore, this reparametrized force field yielded improved agreement between experimental and simulated membrane thicknesses for the pure lipid systems. However, we note limitations in transferability and diagnose the source of such limitations, particularly the need for SANS in addition to SAXS.

Demerdash, Omar N. A. [Oak Ridge National Laborato↗
DOE OSTI2025

Depletion of the Protein Hydration Shell with Increasing Temperature Observed by Small-Angle X-ray Scattering and Molecular Simulations

The hydration shell is an integral part of proteins since it plays key roles in conformational transitions, molecular recognition, and enzymatic activity. While the dynamics of the hydration shell have been described by spectroscopic techniques, the structure of the hydration shell remains less understood due to the lack of hydration shell-sensitive structural probes with high spatial resolution. We combined temperature-ramp small-angle X-ray scattering (T-ramp SAXS) from 255 to 335 K with molecular simulations to demonstrate that the hydration shells of the IgG-binding domain of Protein G (GB3) and the villin headpiece are remarkably temperature-sensitive. For proteins in the folded state, T-ramp SAXS data and explicit-solvent SAXS predictions consistently demonstrate decays of protein contrasts and radii of gyration with increasing temperature, which are shown to reflect predominantly temperature-sensitive, depleting hydration shells. The depletion is caused not merely by enhanced disorder within the hydration shells but also by partial displacements of surface-coordinated water molecules. Together, T-ramp SAXS and explicit-solvent SAXS calculations provide a novel structural view of the protein hydration shell, which underlies temperature-dependent processes such as cold denaturation, thermophoresis, or biomolecular phase separation.

electron density↗
DOE OSTI2025

Coupling of Charge Regulation and Geometry in Soft Ionizable Molecular Assemblies

The size, shape, and charge of structures, such as proteins and amphiphile assemblies, respond in an interconnected manner to solution ionic conditions. Here, we analyze assemblies of an amphiphile (C 16 K 2 ), with two ionizable amino acids [lysine (K)] coupled to a 16-carbon alkyl tail, via small-angle X-ray scattering (SAXS), nonlinear Poisson–Boltzmann theory (nl-PB), and hybrid Monte Carlo-molecular dynamics (MC-MD) simulations. SAXS revealed structural transitions from spherical micelles to cylindrical micelles to bilayers with increasing pH. By combining SAXS-determined structural information and nl-PB, we derived the molecular degree of ionization as a function of pH. The back-calculated titration curves matched the experimental data over an extended pH range, without adjustable parameters. Similarly, the SAXS data on the evolution of spherical micelle structure with ionic strength were combined with nl-PB and MC-MD to derive the bare and effective charges. MC-MD, which considered finite ion sizes, showed that bare and effective charges saturate quickly with increasing salt concentration. Furthermore, the calculated effective charges closely matched results from Zeta-potential measurements. The presented approach has advantages over customary methods for charge regulation, such as the Henderson–Hasselbalch (HH) or Hill models, where molecular ionization/deionization in assemblies is described by effective pKs that are distinct from the pK for isolated molecules. However, these models lack a physical explanation for these pK shifts. By contrast, our approach of combining structural details with an electrostatic model and simulations provides a more intuitive understanding of structure-charge coupling and a framework for understanding charge regulation in many synthetic and biological systems.

ionization↗
DOE OSTI2026

Structure of Complex Liquid–Liquid Extraction Organic Phases for Rare Earth Separations

Complex, multicomponent liquids with hierarchical structure and phase transitions are encountered in many natural and industrial processes, including in chemical separations. One notable example is aggregation and organic phase splitting in liquid–liquid extraction (LLE) of metal ions. While these two phenomena that have long been closely associated, a mechanistic link between mesoscale structure and the capacity-limiting organic phase splitting remains elusive due to complexity of these systems. Here, in this study, we combine small-angle X-ray scattering (SAXS), X-ray photon correlation spectroscopy (XPCS), and molecular dynamics simulation to reveal a comprehensive picture of structure at the nano- and mesoscale in these complex solutions. For the representative case of rare earth extraction from an acidic aqueous phase by a malonamide extractant in dodecane, we investigate a wide range of process-relevant extractant and acid concentrations to provide a complete picture of how aggregation depends on composition. We decompose organic phase structure from SAXS into two contributions, which together can capture the scattering at all compositions: composition fluctuations described by the Ornstein–Zernike equation at low wavenumber Q, and nanostructure modeled by a “pre-peak” at intermediate Q. The former contains information about the thermodynamics of demixing, while the latter reflects nanoscopic self-assembly of the extractant and extracted solutes. While fluctuations have typically not been considered in the literature, we find they in fact dominate the total structure for nearly all practical conditions. As only the fluctuations have a strong temperature response, we confirm this attribution with temperature-dependent SAXS measurements, including for extracted europium nitrate complexes. SAXS and XPCS measurements near the critical point find static and dynamic scaling consistent with theory. Overall, this new paradigm for understanding LLE organic phases connects composition, nanoscale, and mesoscale structuring to phase behavior, providing both a comprehensive picture of solution structure and a quantitative link between aggregation and third phase formation.

Peroutka, Allison A. [Argonne National Laboratory ↗
DOE OSTI2026

High-throughput small-angle X-ray scattering reveals effective structure factor transitions linked to high-concentration antibody viscosity

High-concentration monoclonal antibody (mAb) formulations are often constrained by elevated viscosity, largely driven by protein–protein interactions, which complicates manufacturing and limits subcutaneous delivery. Early viscosity risk assessment is essential during discovery, yet traditional measurements require large sample volumes, and lack high-throughput capability. Here, we develop a high-throughput small-angle X-ray scattering (SAXS) protocol to detect mAb self-association at dilute concentrations, enabling early predictive insights into high-concentration viscosity. Synchrotron SAXS measurements were conducted for 21 mAbs formulated in a histidine buffer at pH 6.0. An initial subset of 10 mAbs analyzed across 1–150 mg/mL revealed that effective structure factor transitions in the low-q region, indicative of interparticle interactions, consistently emerged below 25 mg/mL. Subsequently, 11 additional mAbs were analyzed at 1–25 mg/mL using automated liquid handling and flow cells to enable high-throughput screening. High-viscosity mAbs exhibited detectable low-q upturns at concentrations ≤10 mg/mL, whereas low-viscosity mAbs showed downturns. A classification criterion based on effective structure factor transitions accurately classified all high- and low-viscosity mAbs at 150 mg/mL, offering a scalable, sample-efficient alternative to conventional methods. These results extend recent findings on the concentration-dependent sensitivity of SAXS to short-range attractions, demonstrating that they can emerge at lower concentrations than previously reported. This study presents the most comprehensive and diverse SAXS dataset for mAbs reported to date within a single formulation, providing a valuable resource for developing and validating coarse-grained models that can more accurately capture intermolecular interactions governing high-concentration solution behavior, thereby enabling rational antibody engineering and improved developability.

36 MATERIALS SCIENCE↗