MEDUSA: A cloud-based tool for the analysis of X-ray diffuse scattering to obtain the bending modulus from oriented membrane stacks.

An important mechanical property of cells is their membrane bending modulus, κ. Here, we introduce MEDUSA (MEmbrane DiffUse Scattering Analysis), a cloud-based analysis tool to determine the bending modulus, κ, from the analysis of X-ray diffuse scattering. MEDUSA uses GPU (graphics processing unit) accelerated hardware and a parallelized algorithm to run the calculations efficiently in a few seconds. MEDUSA's graphical user interface allows the user to upload 2-dimensional data collected from different sources, perform background subtraction and distortion corrections, select regions of interest, run the fitting procedure and output the fitted parameters, the membranes' bending modulus κ, and compressional modulus B.

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

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

A new UltraScan module for the characterization and quantification of analytical buoyant density equilibrium experiments to determine AAV capsid loading.

A method for characterizing and quantifying peaks formed in an analytical buoyant density equilibrium (ABDE) experiment is presented. An algorithm is derived to calculate the concentration of the density forming gradient material at every point in the cell, provided the rotor speed, temperature, meniscus position, bottom of the cell position, and the loading concentration, molar mass, and partial specific volume of the density gradient-forming material are known. In addition, a new peak fitting algorithm has been developed which allows the user to automatically quantify the peaks formed in terms of density, apparent partial specific volume, and relative abundance. The method is suitable for both ionic and non-ionic density forming materials and can be used with data generated from the UV optical system as well as the AVIV fluorescence optical system. These methods have been programmed in a new UltraScan-III module (us_abde). Examples are shown that demonstrate the application of the new module to adeno-associated viral vector preparations and proteins.

Measuring compressibility in the optima AUC™ analytical ultracentrifuge.

A method is described to accurately measure the compressibility of liquids using an analytical ultracentrifuge. The method makes use of very large pressure gradients, which can be generated in the analytical ultracentrifuge at high speeds to induce a maximum compression signal. Taking advantage of the new Optima AUC, which offers 10 micron radial resolution, a novel calibration centerpiece for measuring rotor stretch, and a speed-ramping procedure, even the weak compressibility of liquids like water, typically considered to be incompressible, could be detected. A model using the standard expression for the secant-average bulk modulus describing the relative compression of a liquid in the analytical ultracentrifuge is derived. The model is a function of the loading volume and the hydrostatic pressure generated in the analytical ultracentrifuge, as well as the secant-average bulk modulus. The compressibility of water and toluene were measured and the linear secant-average bulk modulus and meniscus positions were fitted. In addition to the measurement of the compressibility of liquids, applications for this method include an improved prediction of boundary conditions for multi-speed analytical ultracentrifugation experiments to better describe highly heterogeneous systems with analytical speed-ramping procedures, and the prediction of radius-dependent density variations.

BEES: Bayesian Ensemble Estimation from SAS.

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

High-Resolution Asymmetrical Flow Field-Flow Fractionation Data Evaluation via Richardson-Lucy-Based Fractogram Correction.

Asymmetrical flow field-flow fractionation (AF4) is a chromatographic separation technique that can be used for a broad range of particles or macromolecules. As an orthogonal method to size exclusion chromatography (SEC) with a much broader separation size range (1-800 nm) AF4 is gaining importance. However, the data evaluation capacities are far behind in comparison to other techniques like analytical ultracentrifugation (AUC). A program for evaluation of data from AF4 with a coupled multiangle laser light scattering (MALLS) detector was developed that allows the determination of the distributions of diffusion coefficients ( D), hydrodynamic radii ( Rh), molecular weights ( Mw), and relative concentrations (RC) of the obtained species. In addition, two algorithms to remove broadening effects via deconvolution were implemented and tested for their validity. The first is an extension of the known diffusion broadening correction applying the entire diffusion coefficient distribution instead of a single diffusion coefficient. The second applies the Richardson-Lucy algorithm for the deconvolution of overlapping signals from stars in astronomy. This program allows a reproducible strong enhancement of the fractogram resolution allowing for entire baseline separations of proteins. The comparison of the values for Mw determined by a partial Zimm plot from each data point of the original fractogram and the deconvolved results shows that especially the Richardson-Lucy algorithm maintains a high degree of data robustness.

Recent advances in the UltraScan SOlution MOdeller (US-SOMO) hydrodynamic and small-angle scattering data analysis and simulation suite.

The UltraScan SOlution MOdeller (US-SOMO) is a comprehensive, public domain, open-source suite of computer programs centred on hydrodynamic modelling and small-angle scattering (SAS) data analysis and simulation. We describe here the advances that have been implemented since its last official release (#3087, 2017), which are available from release #3141 for Windows, Linux and Mac operating systems. A major effort has been the transition from the legacy Qt3 cross platform software development and user interface library to the modern Qt5 release. Apart from improved graphical support, this has allowed the direct implementation of the newest, almost two-orders of magnitude faster version of the ZENO hydrodynamic computation algorithm for all operating systems. Coupled with the SoMo-generated bead models with overlaps, ZENO provides the most accurate translational friction computations from atomic-level structures available (Rocco and Byron Eur Biophys J 44:417-431, 2015a), with computational times comparable with or faster than those of other methods. In addition, it has allowed us to introduce the direct representation of each atom in a structure as a (hydrated) bead, opening interesting new modelling possibilities. In the small-angle scattering (SAS) part of the suite, an indirect Fourier transform Bayesian algorithm has been implemented for the computation of the pairwise distance distribution function from SAS data. Finally, the SAS HPLC module, recently upgraded with improved baseline correction and Gaussian decomposition of not baseline-resolved peaks and with advanced statistical evaluation tools (Brookes et al. J Appl Cryst 49:1827-1841, 2016), now allows automatic top-peak frame selection and averaging.

Two-dimensional grid optimization for sedimentation velocity analysis in the analytical ultracentrifuge.

Sedimentation velocity experiments performed in the analytical ultracentrifuge are modeled using finite-element solutions of the Lamm equation. During modeling, three fundamental parameters are optimized: the sedimentation coefficients, the diffusion coefficients, and the partial concentrations of all solutes present in a mixture. A general modeling approach consists of fitting the partial concentrations of solutes defined in a two-dimensional grid of sedimentation and diffusion coefficient combinations that cover the range of possible solutes for a given mixture. An increasing number of grid points increase the resolution of the model produced by the subsequent analysis, with denser grids giving rise to a very large system of equations. Here, we evaluate the efficiency and resolution of several regular grids and show that traditionally defined grids tend to provide inadequate coverage in one region of the grid, while at the same time being computationally wasteful in other sections of the grid. We describe a rapid and systematic approach for generating efficient two-dimensional analysis grids that balance optimal information content and model resolution for a given signal-to-noise ratio with improved calculation efficiency. These findings are general and apply to one- and two-dimensional grids, although they no longer represent regular grids. We provide a recipe for an improved grid-point spacing in both directions which eliminates unnecessary points, while at the same time providing a more uniform resolution that can be scaled based on the stochastic noise in the experimental data.

Simultaneous Identification of Spectral Properties and Sizes of Multiple Particles in Solution with Subnanometer Resolution.

We report an unsurpassed solution characterization technique based on analytical ultracentrifugation, which demonstrates exceptional potential for resolving particle sizes in solution with sub-nm resolution. We achieve this improvement in resolution by simultaneously measuring UV/Vis spectra while hydrodynamically separating individual components in the mixture. By equipping an analytical ultracentrifuge with a novel multi-wavelength detector, we are adding a new spectral discovery dimension to traditional hydrodynamic characterization, and amplify the information obtained by orders of magnitude. We demonstrate the power of this technique by characterizing unpurified CdTe nanoparticle samples, avoiding tedious and often impossible purification and fractionation of nanoparticles into apparently monodisperse fractions. With this approach, we have for the first time identified the pure spectral properties and band-gap positions of discrete species present in the CdTe mixture.

A parametrically constrained optimization method for fitting sedimentation velocity experiments.

A method for fitting sedimentation velocity experiments using whole boundary Lamm equation solutions is presented. The method, termed parametrically constrained spectrum analysis (PCSA), provides an optimized approach for simultaneously modeling heterogeneity in size and anisotropy of macromolecular mixtures. The solutions produced by PCSA are particularly useful for modeling polymerizing systems, where a single-valued relationship exists between the molar mass of the growing polymer chain and its corresponding anisotropy. The PCSA uses functional constraints to identify this relationship, and unlike other multidimensional grid methods, assures that only a single molar mass can be associated with a given anisotropy measurement. A description of the PCSA algorithm is presented, as well as several experimental and simulated examples that illustrate its utility and capabilities. The performance advantages of the PCSA method in comparison to other methods are documented. The method has been added to the UltraScan-III software suite, which is available for free download from http://www.ultrascan.uthscsa.edu.

Characterization of size, anisotropy, and density heterogeneity of nanoparticles by sedimentation velocity.

A critical problem in materials science is the accurate characterization of the size dependent properties of colloidal inorganic nanocrystals. Due to the intrinsic polydispersity present during synthesis, dispersions of such materials exhibit simultaneous heterogeneity in density ρ, molar mass M, and particle diameter d. The density increments ∂ρ/∂d and ∂ρ/∂M of these nanoparticles, if known, can then provide important information about crystal growth and particle size distributions. For most classes of nanocrystals, a mixture of surfactants is added during synthesis to control their shape, size, and optical properties. However, it remains a challenge to accurately determine the amount of passivating ligand bound to the particle surface post synthesis. The presence of the ligand shell hampers an accurate determination of the nanocrystal diameter. Using CdSe and PbS semiconductor nanocrystals, and the ultrastable silver nanoparticle (M4Ag44(p-MBA)30), as model systems, we describe a Custom Grid method implemented in UltraScan-III for the characterization of nanoparticles and macromolecules using sedimentation velocity analytical ultracentrifugation. We show that multiple parametrizations are possible, and that the Custom Grid method can be generalized to provide high resolution composition information for mixtures of solutes that are heterogeneous in two out of three parameters. For such cases, our method can simultaneously resolve arbitrary two-dimensional distributions of hydrodynamic parameters when a third property can be held constant. For example, this method extracts partial specific volume and molar mass from sedimentation velocity data for cases where the anisotropy can be held constant, or provides anisotropy and partial specific volume if the molar mass is known.

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

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

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

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

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.

A database of calculated solution parameters for the AlphaFold predicted protein structures.

Recent spectacular advances by AI programs in 3D structure predictions from protein sequences have revolutionized the field in terms of accuracy and speed. The resulting "folding frenzy" has already produced predicted protein structure databases for the entire human and other organisms' proteomes. However, rapidly ascertaining a predicted structure's reliability based on measured properties in solution should be considered. Shape-sensitive hydrodynamic parameters such as the diffusion and sedimentation coefficients ([Formula: see text], [Formula: see text]) and the intrinsic viscosity ([η]) can provide a rapid assessment of the overall structure likeliness, and SAXS would yield the structure-related pair-wise distance distribution function p(r) vs. r. Using the extensively validated UltraScan SOlution MOdeler (US-SOMO) suite, a database was implemented calculating from AlphaFold structures the corresponding [Formula: see text], [Formula: see text], [η], p(r) vs. r, and other parameters. Circular dichroism spectra were computed using the SESCA program. Some of AlphaFold's drawbacks were mitigated, such as generating whenever possible a protein's mature form. Others, like the AlphaFold direct applicability to single-chain structures only, the absence of prosthetic groups, or flexibility issues, are discussed. Overall, this implementation of the US-SOMO-AF database should already aid in rapidly evaluating the consistency in solution of a relevant portion of AlphaFold predicted protein structures.

A round-robin approach provides a detailed assessment of biomolecular small-angle scattering data reproducibility and yields consensus curves for benchmarking.

Through an expansive international effort that involved data collection on 12 small-angle X-ray scattering (SAXS) and four small-angle neutron scattering (SANS) instruments, 171 SAXS and 76 SANS measurements for five proteins (ribonuclease A, lysozyme, xylanase, urate oxidase and xylose isomerase) were acquired. From these data, the solvent-subtracted protein scattering profiles were shown to be reproducible, with the caveat that an additive constant adjustment was required to account for small errors in solvent subtraction. Further, the major features of the obtained consensus SAXS data over the q measurement range 0-1 Å-1 are consistent with theoretical prediction. The inherently lower statistical precision for SANS limited the reliably measured q-range to <0.5 Å-1, but within the limits of experimental uncertainties the major features of the consensus SANS data were also consistent with prediction for all five proteins measured in H2O and in D2O. Thus, a foundation set of consensus SAS profiles has been obtained for benchmarking scattering-profile prediction from atomic coordinates. Additionally, two sets of SAXS data measured at different facilities to q > 2.2 Å-1 showed good mutual agreement, affirming that this region has interpretable features for structural modelling. SAS measurements with inline size-exclusion chromatography (SEC) proved to be generally superior for eliminating sample heterogeneity, but with unavoidable sample dilution during column elution, while batch SAS data collected at higher concentrations and for longer times provided superior statistical precision. Careful merging of data measured using inline SEC and batch modes, or low- and high-concentration data from batch measurements, was successful in eliminating small amounts of aggregate or interparticle interference from the scattering while providing improved statistical precision overall for the benchmarking data set.

Mechanism of NanR gene repression and allosteric induction of bacterial sialic acid metabolism.

Bacteria respond to environmental changes by inducing transcription of some genes and repressing others. Sialic acids, which coat human cell surfaces, are a nutrient source for pathogenic and commensal bacteria. The Escherichia coli GntR-type transcriptional repressor, NanR, regulates sialic acid metabolism, but the mechanism is unclear. Here, we demonstrate that three NanR dimers bind a (GGTATA)3-repeat operator cooperatively and with high affinity. Single-particle cryo-electron microscopy structures reveal the DNA-binding domain is reorganized to engage DNA, while three dimers assemble in close proximity across the (GGTATA)3-repeat operator. Such an interaction allows cooperative protein-protein interactions between NanR dimers via their N-terminal extensions. The effector, N-acetylneuraminate, binds NanR and attenuates the NanR-DNA interaction. The crystal structure of NanR in complex with N-acetylneuraminate reveals a domain rearrangement upon N-acetylneuraminate binding to lock NanR in a conformation that weakens DNA binding. Our data provide a molecular basis for the regulation of bacterial sialic acid metabolism.

A two-dimensional spectrum analysis for sedimentation velocity experiments of mixtures with heterogeneity in molecular weight and shape.

We report a model-independent analysis approach for fitting sedimentation velocity data which permits simultaneous determination of shape and molecular weight distributions for mono- and polydisperse solutions of macromolecules. Our approach allows for heterogeneity in the frictional domain, providing a more faithful description of the experimental data for cases where frictional ratios are not identical for all components. Because of increased accuracy in the frictional properties of each component, our method also provides more reliable molecular weight distributions in the general case. The method is based on a fine grained two-dimensional grid search over s and f/f (0), where the grid is a linear combination of whole boundary models represented by finite element solutions of the Lamm equation with sedimentation and diffusion parameters corresponding to the grid points. A Monte Carlo approach is used to characterize confidence limits for the determined solutes. Computational algorithms addressing the very large memory needs for a fine grained search are discussed. The method is suitable for globally fitting multi-speed experiments, and constraints based on prior knowledge about the experimental system can be imposed. Time- and radially invariant noise can be eliminated. Serial and parallel implementations of the method are presented. We demonstrate with simulated and experimental data of known composition that our method provides superior accuracy and lower variance fits to experimental data compared to other methods in use today, and show that it can be used to identify modes of aggregation and slow polymerization.

The implementation of SOMO (SOlution MOdeller) in the UltraScan analytical ultracentrifugation data analysis suite: enhanced capabilities allow the reliable hydrodynamic modeling of virtually any kind of biomacromolecule.

The interpretation of solution hydrodynamic data in terms of macromolecular structural parameters is not a straightforward task. Over the years, several approaches have been developed to cope with this problem, the most widely used being bead modeling in various flavors. We report here the implementation of the SOMO (SOlution MOdeller; Rai et al. in Structure 13:723-734, 2005) bead modeling suite within one of the most widely used analytical ultracentrifugation data analysis software packages, UltraScan (Demeler in Modern analytical ultracentrifugation: techniques and methods, Royal Society of Chemistry, UK, 2005). The US-SOMO version is now under complete graphical interface control, and has been freed from several constraints present in the original implementation. In the direct beads-per-atoms method, virtually any kind of residue as defined in the Protein Data Bank (e.g., proteins, nucleic acids, carbohydrates, prosthetic groups, detergents, etc.) can be now represented with beads whose number, size and position are all defined in user-editable tables. For large structures, a cubic grid method based on the original AtoB program (Byron in Biophys J 72:408-415, 1997) can be applied either directly on the atomic structure, or on a previously generated bead model. The hydrodynamic parameters are then computed in the rigid-body approximation. An extensive set of tests was conducted to further validate the method, and the results are presented here. Owing to its accuracy, speed, and versatility, US-SOMO should allow to fully take advantage of the potential of solution hydrodynamics as a complement to higher resolution techniques in biomacromolecular modeling.

The Open AUC Project.

Progress in analytical ultracentrifugation (AUC) has been hindered by obstructions to hardware innovation and by software incompatibility. In this paper, we announce and outline the Open AUC Project. The goals of the Open AUC Project are to stimulate AUC innovation by improving instrumentation, detectors, acquisition and analysis software, and collaborative tools. These improvements are needed for the next generation of AUC-based research. The Open AUC Project combines on-going work from several different groups. A new base instrument is described, one that is designed from the ground up to be an analytical ultracentrifuge. This machine offers an open architecture, hardware standards, and application programming interfaces for detector developers. All software will use the GNU Public License to assure that intellectual property is available in open source format. The Open AUC strategy facilitates collaborations, encourages sharing, and eliminates the chronic impediments that have plagued AUC innovation for the last 20 years. This ultracentrifuge will be equipped with multiple and interchangeable optical tracks so that state-of-the-art electronics and improved detectors will be available for a variety of optical systems. The instrument will be complemented by a new rotor, enhanced data acquisition and analysis software, as well as collaboration software. Described here are the instrument, the modular software components, and a standardized database that will encourage and ease integration of data analysis and interpretation software.