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.

A new algorithm for the reconstruction of protein molecular envelopes from X-ray solution scattering data

At sufficiently low resolution, the scattering density within the volume occupied by a well folded protein molecule appears relatively flat. By enforcing this condition, three-dimensional protein molecular envelopes may be reconstructed using information obtained from X-ray solution scattering profiles. A practical approach for solving the low-resolution structures of protein molecules from solution scattering data involves modelling the protein shape using a set of volume-filling points (`beads') and transforming the scattering data to a more convenient target, the pair distance distribution function, P(r). Using algorithms described here, the beads interact via a modified Lennard–Jones potential and their positions are adjusted and confined until they fit the expected protein volume and agreement with P(r) is obtained. This methodology allows the protein volume to be modelled by an arbitrary, user-defined number of beads, enabling the rapid reconstruction of protein structures of widely varying sizes. Tests carried out with a variety of synthetic and experimental data sets show that this approach gives efficient and reliable determinations of protein molecular envelopes.

Reduction of small-angle scattering profiles to finite sets of structural invariants

This paper shows how small-angle scattering (SAS) curves can be decomposed in a simple sum using a set of invariant parameters calledKnwhich are related to the shape of the object of study. TheseKn, together with a radiusR, give a complete theoretical description of the SAS curve. Adding an overall constant, these parameters are easily fitted against experimental data giving a concise comprehensive description of the data. The pair distance distribution function is also entirely described by this invariant set and theDmaxparameter can be measured. In addition to the understanding they bring, these invariants can be used to reliably estimate structural moments beyond the radius of gyration, thereby rigorously expanding the actual set of model-free quantities one can extract from experimental SAS data, and possibly paving the way to designing new shape reconstruction strategies.

Indirect Fourier transform in the context of statistical inference

Inferring structural information from the intensity of a small-angle scattering (SAS) experiment is an ill-posed inverse problem. Thus, the determination of a solution is in general non-trivial. In this work, the indirect Fourier transform (IFT), which determines the pair distance distribution function from the intensity and hence yields structural information, is discussed within two different statistical inference approaches, namely a frequentist one and a Bayesian one, in order to determine a solution objectively From the frequentist approach the cross-validation method is obtained as a good practical objective function for selecting an IFT solution. Moreover, modern machine learning methods are employed to suppress oscillatory behaviour of the solution, hence extracting only meaningful features of the solution. By comparing the results yielded by the different methods presented here, the reliability of the outcome can be improved and thus the approach should enable more reliable information to be deduced from SAS experiments.

Small-Angle X-Ray Scattering Studies of ADAMTS13 Demonstrate a Conformational Response to Substrate Binding in Solution

Abstract 1191 The metalloprotease ADAMTS13 inhibits the growth of platelet thrombi by cleaving the Tyr1605-Met1606 peptide bond in the A2 domain of von Willerbrand factor (VWF). Previous studies have shown that when subjected to tensile stress in solution, bound to platelets, or on endothelial cell surfaces, VWF changes conformation and interacts with multiple exosites on ADAMTS13 through a combination of structural features. These close contacts enhance the highly specific interaction between ADAMTS13 and VWF in vivo. Like VWF, ADAMTS13 is a large multidomain protein that could be regulated by large-scale conformational changes induced by substrate binding. Here we report the use of small-angle X-ray scattering (SAXS) to study the structure of ADAMTS13 and its interactions with VWF peptides in solution. ADAMTS13 truncated after the spacer domain, consisting of metalloprotease (M), disintegrin-like (D), thrombospondin type 1 (TSP1, T), Cys-rich (C) and spacer (S) domains (MDTCS), was produced in either T-Rex 293 cells (MDTCS-t) or HEK293S GNTI cells (MDTCS-g). GNTI cells do not have N-acetylglucosaminyltransferase I activity and expressed proteins lack complex N-glycans. In addition, a variant with the mutation E225Q in the M domain was produced in T-Rex 293 cells (MqDTCS-t). Construct MqDTCS-t lacks enzymatic activity but binds normally to VWF. Two VWF peptides were prepared: cVWF63 is a C-terminal A2 domain cleavage product consisting of VWF residues Met1606-Arg1668, and VWF71 consists of VWF residues Gln1599-Arg1668 with an additional Gly at the N-terminus. SAXS data were collected at the SIBYLS beamline (Lawrence Berkeley National Laboratory) for MDTCS variants without and with bound cVWF63 or VWF71. The quality of the SAXS data was evaluated by comparison to an atomic model of ADAMTS13. The M domain was modeled on ADAMTS4, DTCS domains were from the corresponding crystal structure (PDB: 3ghm). The addition of N-glycans to the atomic structure with GLYPROT improved the agreement with experimental scattering profiles determined with CRYSOL, achieving excellent values of X (Chi) < 2.0 (Table 1). Low resolution ab initio solution structures for MDTCS-g were generated from scattering profiles using DAMMIN, averaged (n = 15) using DAMAVER and superimposed on the atomic structure of MDTCS, which also demonstrated excellent agreement (Figure 1. M at top, S at bottom. Views differ by 90° rotation). Pair distance distribution functions were obtained from scattering profiles using DATGNOM. As shown in Figure 2 for MDTCS-g and MqDTCS-t, the entire pair distance distribution shifts upon binding of cVWF63 with a decrease in the maximum particle dimension (Dmax) from 143 angstroms to 132 angstroms, and 148 angstroms to 141 angstroms, respectively, indicating that bound product constrains the conformation of the enzyme. Binding of VWF71 to MqDTCS-t gave similar results.Figure 1.Ab initio model of MDTCS-g.Figure 1. Ab initio model of MDTCS-g.Figure 2.Pair distance distribution function of MDTCS with or without cVWF63.Figure 2. Pair distance distribution function of MDTCS with or without cVWF63. These results show that SAXS clearly distinguishes the structure of ADAMTS13 with or without bound product or substrate analog. ADAMTS13 domains distal to the spacer domain also contribute to VWF binding, and stepwise addition of these TSP-1 and CUB domains to MDTCS will allow the visualization of conformational changes induced by interaction with larger substrate analogs, and construction of a model for a physiologically relevant enzyme-substrate complex. Disclosures: No relevant conflicts of interest to declare.

Scattering functions of Platonic solids

The single-particle small-angle scattering properties of five Platonic solids, including the tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron, are systematically investigated. For each given geometry, the Debye spatial autocorrelation function, pair distance distribution function and intraparticle structure factor (form factor) are calculated and compared with the corresponding scattering function of a spherical reference system. From the theoretical models, the empirical relationship between the dodecahedral and icosahedral structural characteristics and those of the equivalent spheres is found. Moreover, the single-particle scattering properties of icosahedral and spherical shells with identical volume are investigated, and the prospect of using different data analysis approaches to explore their structural differences is presented and discussed.

Irena: tool suite for modeling and analysis of small-angle scattering

Irena, a tool suite for analysis of both X-ray and neutron small-angle scattering (SAS) data within the commercialIgor Proapplication, brings together a comprehensive suite of tools useful for investigations in materials science, physics, chemistry, polymer science and other fields. In addition to Guinier and Porod fits, the suite combines a variety of advanced SAS data evaluation tools for the modeling of size distribution in the dilute limit using maximum entropy and other methods, dilute limit small-angle scattering from multiple non-interacting populations of scatterers, the pair-distance distribution function, a unified fit, the Debye–Bueche model, the reflectivity (X-ray and neutron) using Parratt's formalism, and small-angle diffraction. There are also a number of support tools, such as a data import/export tool supporting a broad sampling of common data formats, a data modification tool, a presentation-quality graphics tool optimized for small-angle scattering data, and a neutron and X-ray scattering contrast calculator. These tools are brought together into one suite with consistent interfaces and functionality. The suite allows robust automated note recording and saving of parameters during export.