Structural characterisation of α-synuclein-membrane interactions and the resulting aggregation using small angle scattering

The presence of amyloid fibrils is a hallmark of several neurodegenerative diseases. Some amyloidogenic proteins, such as α-synuclein and amyloid β, interact with lipids, and this interaction can strongly favour the formation of amyloid fibrils. In particular the primary nucleation step, i.e. the de novo formation of amyloid fibrils, has been shown to be accelerated by lipids. However, the exact mechanism of this acceleration is still mostly unclear. Here we use a range of scattering methods, such as dynamic light scattering (DLS) and small angle X-ray and neutron scattering (SAXS and SANS) to obtain structural information on the binding of α-synuclein to model membranes formed from negatively charged lipids and their co-assembly into amyloid fibrils. We find that the model membranes take an active role in the reaction. The binding of α synuclein to the model membranes immediately induces a major structural change in the lipid assembly, which leads to a break-up into small and mostly disc- or rod-like lipid-protein particles. This transition can be reversed by temperature changes or proteolytic protein removal. Incubation of the small lipid-α-synuclein particles for several hours, however, leads to amyloid fibril formation, whereby the lipids are incorporated into the amyloid fibrils.

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.

Modeling of flexible membrane-bound biomolecular complexes for solution small-angle scattering

Recent advances in protein expression protocols, sample handling, and experimental set up of small-angle scattering experiments have allowed users of the technique to structurally investigate biomolecules of growing complexity and structural disorder. Notable examples include intrinsically disordered proteins, multi-domain proteins and membrane proteins in suitable carrier systems. Here, we outline a modeling scheme for calculating the scattering profiles from such complex samples. This kind of modeling is necessary for structural information to be refined from the corresponding data. The scheme bases itself on a hybrid of classical form factor based modeling and the well-known spherical harmonics-based formulation of small-angle scattering amplitudes. Our framework can account for flexible domains alongside other structurally elaborate components of the molecular system in question. We demonstrate the utility of this modeling scheme through a recent example of a structural model of the growth hormone receptor membrane protein in a phospholipid bilayer nanodisc which is refined against experimental SAXS data. Additionally we investigate how the scattering profiles from the complex would appear under different scattering contrasts. For each contrast situation we discuss what structural information is contained and the related consequences for modeling of the data.

Mapping hyperbolic order in curved materials

Nature employs an impressive range of topologically complex ordered nanostructures that occur in various forms in both natural and synthetic materials. A particular class of these exhibits negative curvature and forms periodic saddle-shaped surfaces in three dimensions. Unlike pattern formation on flat or positively curved surfaces like spherical systems, the understanding of patterning on such surfaces is highly complicated due to the structures being intrinsically intertwined in three dimensions. We present a new method for visualisation and analysis of patterns on triply periodic negatively curved surfaces by mapping to two-dimensional hyperbolic space analogous to spherical projections in cartography thus effectively creating a more accessible "hyperbolic map" of the pattern. Specifically, we exemplify the method via the simplest triply periodic minimal surfaces: the Primitive, Diamond, and Gyroid in their universal cover along with decorations from a soft materials, whose structures involve decorations of soft matter on negatively curved surfaces, not necessarily minimal.

Travel light: Essential packing for membrane proteins with an active lifestyle

We review the considerable progress during the recent decade in the endeavours of designing, optimising, and utilising carrier particle systems for structural and functional studies of membrane proteins in near-native environments. New and improved systems are constantly emerging, novel studies push the perceived limits of a given carrier system, and specific carrier systems consolidate and entrench themselves as the system of choice for particular classes of target membrane protein systems. This review covers the most frequently used carrier systems for such studies and emphasises similarities and differences between these systems as well as current trends and future directions for the field. Particular interest is devoted to the biophysical properties and membrane mimicking ability of each system and the manner in which this may impact an embedded membrane protein and an eventual structural or functional study.

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.

Non-ionic detergent assists formation of supercharged nanodiscs and insertion of membrane proteins

Nanodiscs are used to stabilize membrane proteins in a lipid environment and enable investigations of the function and structure of these. Membrane proteins are often only available in small amounts, and thus the stability and ease of use of the nanodiscs are essential. We have recently explored circularizing and supercharging membrane scaffolding proteins (MSPs) for nanodisc formation and found increased temporal stability at elevated temperatures. In the present study, we investigate six different supercharged MSPs and their ability to form nanodiscs: three covalently circularized and the three non-circularized, linear versions. Using standard reconstitution protocols using cholate as the reconstitution detergent, we found that two of the linear constructs formed multiple lipid-protein species, whereas adding n-Dodecyl-B-D-maltoside (DDM) with the cholate in the reconstitution gave rise to single-species nanodisc formation for these MSPs. For all MSPs, the formed nanodiscs were analyzed by small-angle X-ray scattering (SAXS), which showed similar structures for each MSP, respectively, suggesting that the structures of the formed nanodiscs are independent of the initial DDM content, as long as cholate is present. Lastly, we incorporated the membrane protein proteorhodopsin into the supercharged nanodiscs and observed a considerable increase in incorporation yield with the addition of DDM. For the three circularized MSPs, a single major species appeared in the size exclusion chromatography (SEC) chromatogram, suggesting monodisperse nanodiscs with proteorhodopsin incorporated, which is in strong contrast to the samples without DDM showing almost no incorporation and high polydispersity.

Global fitting of multiple data frames from SEC–SAXS to investigate the structure of next-generation nanodiscs

The combination of online size-exclusion chromatography and small-angle X-ray scattering (SEC–SAXS) is rapidly becoming a key technique for structural investigations of elaborate biophysical samples in solution. Here, a novel model-refinement strategy centred around the technique is outlined and its utility is demonstrated by analysing data series from several SEC–SAXS experiments on phospholipid bilayer nanodiscs. Using this method, a single model was globally refined against many frames from the same data series, thereby capturing the frame-to-frame tendencies of the irradiated sample. These are compared with models refined in the traditional manner, in which refinement is based on the average profile of a set of consecutive frames from the same data series without an in-depth comparison of individual frames. This is considered to be an attractive model-refinement scheme as it considerably lowers the total number of parameters refined from the data series, produces tendencies that are automatically consistent between frames, and utilizes a considerably larger portion of the recorded data than is often performed in such experiments. Additionally, a method is outlined for correcting a measured UV absorption signal by accounting for potential peak broadening by the experimental setup.

Mg2+-dependent conformational equilibria in CorA and an integrated view on transport regulation

The CorA family of proteins regulates the homeostasis of divalent metal ions in many bacteria, archaea, and eukaryotic mitochondria, making it an important target in the investigation of the mechanisms of transport and its functional regulation. Although numerous structures of open and closed channels are now available for the CorA family, the mechanism of the transport regulation remains elusive. Here, we investigated the conformational distribution and associated dynamic behaviour of the pentameric Mg²⁺ channel CorA at room temperature using small-angle neutron scattering (SANS) in combination with molecular dynamics (MD) simulations and solid-state nuclear magnetic resonance spectroscopy (NMR). We find that neither the Mg²⁺-bound closed structure nor the Mg²⁺-free open forms are sufficient to explain the average conformation of CorA. Our data support the presence of conformational equilibria between multiple states, and we further find a variation in the behaviour of the backbone dynamics with and without Mg²⁺. We propose that CorA must be in a dynamic equilibrium between different non-conducting states, both symmetric and asymmetric, regardless of bound Mg²⁺ but that conducting states become more populated in Mg²⁺-free conditions. These properties are regulated by backbone dynamics and are key to understanding the functional regulation of CorA.

The intrinsic group-subgroup structures of the Diamond and Gyroid minimal surfaces in their conventional unit cells

The intrinsic, hyperbolic crystallography of the Diamond and Gyroid minimal surfaces in their conventional unit cells is introduced and analysed. Tables are constructed of symmetry subgroups commensurate with the translational symmetries of the surfaces as well as group-subgroup lattice graphs.

Experimental noise in small-angle scattering can be assessed using the Bayesian indirect Fourier transformation

Small-angle X-ray and neutron scattering are widely used to investigate soft matter and biophysical systems. The experimental errors are essential when assessing how well a hypothesized model fits the data. Likewise, they are important when weights are assigned to multiple data sets used to refine the same model. Therefore, it is problematic when experimental errors are over- or underestimated. A method is presented, using Bayesian indirect Fourier transformation for small-angle scattering data, to assess whether or not a given small-angle scattering data set has over- or underestimated experimental errors. The method is effective on both simulated and experimental data, and can be used to assess and rescale the errors accordingly. Even if the estimated experimental errors are appropriate, it is ambiguous whether or not a model fits sufficiently well, as the `true' reduced χ2 of the data is not necessarily unity. This is particularly relevant for approaches where overfitting is an inherent challenge, such as reweighting of a simulated molecular dynamics trajectory against small-angle scattering data or ab initio modelling. Using the outlined method, it is shown that one can determine what reduced χ2 to aim for when fitting a model against small-angle scattering data. The method is easily accessible via the web interface BayesApp.

Structural and Biophysical Properties of Supercharged and Circularized Nanodiscs

Nanodiscs based on membrane scaffold proteins (MSPs) and phospholipids are used as membrane mimics to stabilize membrane proteins in solution for structural and functional studies. Combining small-angle X-ray scattering (SAXS), differential scanning calorimetry (DSC), and time-resolved small-angle neutron scattering (TR-SANS), we characterized the structure and lipid bilayer properties of five different nanodiscs made with dimyristoylphosphatidylcholine and different MSPs varying in size, charge, and circularization. Our SAXS modeling showed that the structural parameters of the embedded lipids are all similar, irrespective of the MSP properties. DSC showed that the lipid packing is not homogeneous in the nanodiscs and that a 20 Å wide boundary layer of lipids with perturbed packing is located close to the MSP, while the packing of central lipids is tighter than in large unilamellar vesicles. Finally, TR-SANS showed that lipid exchange rates in nanodiscs decrease with increasing nanodisc size and are lower for the nanodiscs made with supercharged MSPs compared to conventional nanodiscs. Altogether, the results provide a thorough biophysical understanding of the nanodisc as a model membrane system, which is important in order to carry out and interpret experiments on membrane proteins embedded in such systems.

Order and disorder-An integrative structure of the full-length human growth hormone receptor

Because of its small size (70 kilodalton) and large content of structural disorder (>50%), the human growth hormone receptor (hGHR) falls between the cracks of conventional high-resolution structural biology methods. Here, we study the structure of the full-length hGHR in nanodiscs with small-angle x-ray scattering (SAXS) as the foundation. We develop an approach that combines SAXS, x-ray diffraction, and NMR spectroscopy data obtained on individual domains and integrate these through molecular dynamics simulations to interpret SAXS data on the full-length hGHR in nanodiscs. The hGHR domains reorient freely, resulting in a broad structural ensemble, emphasizing the need to take an ensemble view on signaling of relevance to disease states. The structure provides the first experimental model of any full-length cytokine receptor in a lipid membrane and exemplifies how integrating experimental data from several techniques computationally may access structures of membrane proteins with long, disordered regions, a widespread phenomenon in biology.

Aescin - a natural soap for the formation of lipid nanodiscs with tunable size

The saponin β-aescin from the seed extract of the horse chestnut tree Aesculus hippocastanum has demonstrated a beneficial role in clinical therapy which is in part related to its strong interaction with biological membranes. In this context the present work investigates the self-assembly of nm-sized discoidal lipid nanoparticles composed of β-aescin and the phospholipid 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). The discoidal lipid nanoparticles reassemble from small discs into larger discs, ribbons and finally stacks of sheets upon heating from gel-phase to fluid phase DMPC. The morphological transition of the lipid nano-particles is mainly triggered by the phospholipid phase state change. The final morphology depends on the phospholipid-to-saponin ratio and the actual temperature. The study is conducted by small-angle X-ray scattering (SAXS) and transmission (TEM) and freeze fracture electron microscopy (FFEM) are used to cover larger length scales. Two different models, representing a disc and ribbon-like shape are applied to the SAXS data, evaluating possible geometries and molecular mixing of the nano-particles. The stacked sheets are analysed by the Caillé theory.

Schwarzite nets: a wealth of 3-valent examples sharing similar topologies and symmetries

We enumerate trivalent reticulations of two- and three-periodic hyperbolic surfaces by equal-sided n -gonal faces, ( n , 3), where n  = 7, 8, 9, 10, 12. These are the simplest hyperbolic generalizations of the planar graphene net, (6, 3) and dodecahedrane, (5, 3). The enumeration proceeds by deleting isometries of regular reticulations of two-dimensional hyperbolic space until the ( n , 3) nets can be embedded in euclidean three-space via periodic hyperbolic surfaces. Those nets are then symmetrized in euclidean space retaining their net topology, leading to explicit crystallographic net embeddings whose edges are as equal as possible, affording candidtae patterns for graphitic schwarzites. The resulting schwarzites are the most symmetric examples. More than one hundred topologically distinct nets are described, most of which are novel.

Evolution of local motifs and topological proximity in self-assembled quasi-crystalline phases

Using methods from the field of topological data analysis, we investigate the self-assembly and emergence of three-dimensional quasi-crystalline structures in a single-component colloidal system. Combining molecular dynamics and persistent homology, we analyse the time evolution of persistence diagrams and particular local structural motifs. Our analysis reveals the formation and dissipation of specific particle constellations in these trajectories, and shows that the persistence diagrams are sensitive to nucleation and convergence to a final structure. Identification of local motifs allows quantification of the similarities between the final structures in a topological sense. This analysis reveals a continuous variation with density between crystalline clathrate, quasi-crystalline, and disordered phases quantified by 'topological proximity', a visualization of the Wasserstein distances between persistence diagrams. From a topological perspective, there is a subtle, but direct connection between quasi-crystalline, crystalline and disordered states. Our results demonstrate that topological data analysis provides detailed insights into molecular self-assembly.

Aescin-Induced Conversion of Gel-Phase Lipid Membranes into Bicelle-like Lipid Nanoparticles

Mixtures of the phospholipid 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and the saponin β-aescin spontaneously form monodisperse, bilayered discoidal micelles (also known as "bicelles" or "nanodisks") in aqueous solution. Such bicelles form below the melting temperature of DMPC when the phospholipids are in the rigid L_β' state and are precursors of spontaneously formed vesicles. The aescin concentration must be far above the cmc_aescin (≈0.3-0.4 mM). It was found that the shape and size of the bicelles are tunable by composition. High amounts of aescin decrease the size of the bicelles from diameters of ∼300 Å at 7 mol % to ∼120 Å at 30 mol % β-aescin. The structures are scrutinized by complementary small-angle X-ray and neutron scattering experiments. The scattering curves are subsequently analyzed by a model-independent (indirect Fourier transform analysis) and a model-based approach where bicelles are described as polydisperse bilayer disks encircled by a β-aescin rim. Moreover, the monomodal distribution and low polydispersity of the samples were confirmed by photon correlation spectroscopy. The discoidal structures were visualized by transmission electron microscopy.

PSX, Protein–Solvent Exchange: software for calculation of deuterium-exchange effects in small-angle neutron scattering measurements from protein coordinates

Recent developments in neutron scattering instrumentation and sample handling have enabled studies of more complex biological samples and measurements at shorter exposure times. The experiments are typically conducted in D2O-based buffers to emphasize or diminish scattering from a particular component or to minimize background noise in the experiment. To extract most information from such experiments it is thus desirable to determine accurate estimates of how and when closely bound hydrogen atoms from the biomolecule exchange with the deuterium in the solvent. This article introduces and documents software, PSX, for exploring the effect of hydrogen–deuterium exchange for proteins solubilized in D2O as well as the underlying bioinformatical models. The software aims to be generally applicable for any atomistic structure of a protein and its surrounding environment, and thus captures effects of both heterogenous exchange rates throughout the protein structure and varying the experimental conditions such as pH and temperature. The paper concludes with examples of applications and estimates of the effect in typical scenarios emerging in small-angle neutron scattering on biological macromolecules in solution. The analysis presented here suggests that the common assumption of 90% exchange is in many cases an overestimate with the rapid sample handling systems currently available, which leads to fitting and calibration issues when analysing the data. Source code for the presented software is available from an online repository in which it is published under version 3 of the GNU publishing licence.

Introducing SEC–SANS for studies of complex self-organized biological systems

Small-angle neutron scattering (SANS) is maturing as a method for studying complex biological structures. Owing to the intrinsic ability of the technique to discern between 1H- and 2H-labelled particles, it is especially useful for contrast-variation studies of biological systems containing multiple components. SANS is complementary to small-angle X-ray scattering (SAXS), in which similar contrast variation is not easily performed but in which data with superior counting statistics are more easily obtained. Obtaining small-angle scattering (SAS) data on monodisperse complex biological structures is often challenging owing to sample degradation and/or aggregation. This problem is enhanced in the D2O-based buffers that are typically used in SANS. In SAXS, such problems are solved using an online size-exclusion chromatography (SEC) setup. In the present work, the feasibility of SEC–SANS was investigated using a series of complex and difficult samples of membrane proteins embedded in nanodisc particles that consist of both phospholipid and protein components. It is demonstrated that SEC–SANS provides data of sufficient signal-to-noise ratio for these systems, while at the same time circumventing aggregation. By combining SEC–SANS and SEC–SAXS data, an optimized basis for refining structural models of the investigated structures is obtained.

Surface embeddings of the Klein and the Möbius-Kantor graphs

This paper describes an invariant representation for finite graphs embedded on orientable tori of arbitrary genus, with working examples of embeddings of the Möbius-Kantor graph on the torus, the genus-2 bitorus and the genus-3 tritorus, as well as the two-dimensional, 7-valent Klein graph on the tritorus (and its dual: the 3-valent Klein graph). The genus-2 and -3 embeddings describe quotient graphs of 2- and 3-periodic reticulations of hyperbolic surfaces. This invariant is used to identify infinite nets related to the Möbius-Kantor and 7-valent Klein graphs.

Hyperbolic crystallography of two-periodic surfaces and associated structures

This paper describes the families of the simplest, two-periodic constant mean curvature surfaces, the genus-two HCB and SQL surfaces, and their isometries. All the discrete groups that contain the translations of the genus-two surfaces embedded in Euclidean three-space modulo the translation lattice are derived and enumerated. Using this information, the subgroup lattice graphs are constructed, which contain all of the group-subgroup relations of the aforementioned quotient groups. The resulting groups represent the two-dimensional representations of subperiodic layer groups with square and hexagonal supergroups, allowing exhaustive enumeration of tilings and associated patterns on these surfaces. Two examples are given: a two-periodic [3,7]-tiling with hyperbolic orbifold symbol {\sf {2223}} and a {\sf {22222}} surface decoration.

Small-angle X-ray scattering of the cholesterol incorporation into human ApoA1-POPC discoidal particles

Structural and functional aspects of high-density lipoproteins have been studied for over half a century. Due to the plasticity of this highly complex system, new aspects continue to be discovered. Here, we present a structural study of the human Apolipoprotein A1 (ApoA1) and investigate the role of its N-terminal domain, the so-called globular domain of ApoA1, in discoidal complexes with phospholipids and increasing amounts of cholesterol. Using a combination of solution-based small-angle x-ray scattering (SAXS) and molecular constrained data modeling, we show that the ApoA1-1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)-based particles are disk shaped with an elliptical cross section and composed by a central lipid bilayer surrounded by two stabilizing ApoA1 proteins. This structure is very similar to the particles formed in the so-called nanodisc system, which is based on N-terminal truncated ApoA1 protein. Although it is commonly agreed that the nanodisc is plain disk shaped, several more advanced structures have been proposed for the full-length ApoA1 in combination with POPC and cholesterol. This prompted us to make a detailed comparative study of the ApoA1 and nanodisc systems upon cholesterol uptake. Based on the presented SAXS analysis it is found that the N-terminal domains of ApoA1-POPC-cholesterol particles are not globular but instead an integrated part of the protein belt stabilizing the particles. Upon incorporation of increasing amounts of cholesterol, the presence of the N-terminal domain allows the bilayer thickness to increase while maintaining an overall flat bilayer structure. This is contrasted by the energetically more strained and less favorable lens shape required to fit the SAXS data from the N-terminal truncated nanodisc system upon cholesterol incorporation. This suggests that the N-terminal domain of ApoA1 actively participates in the stabilization of the ApoA1-POPC-cholesterol discoidal particle and allows for a more optimal lipid packing upon cholesterol uptake.

Quantification of the information in small-angle scattering data

Small-angle X-ray and neutron scattering have become increasingly popular owing to improvements in instrumentation and developments in data analysis, sample handling and sample preparation. For some time, it has been suggested that a more systematic approach to the quantification of the information content in small-angle scattering data would allow for a more optimal experiment planning and a more reliable data analysis. In the present article, it is shown how ray-tracing techniques in combination with a statistically rigorous data analysis provide an appropriate platform for such a systematic quantification of the information content in scattering data. As examples of applications, it is shown how the exposure time at different instrumental settings or contrast situations can be optimally prioritized in an experiment. Also, the gain in information by combining small-angle X-ray and neutron scattering is assessed. While solution small-angle scattering data of proteins and protein–lipid complexes are used as examples in the present case study, the approach is generalizable to a wide range of other samples and experimental techniques. The source code for the algorithms and ray-tracing components developed for this study has been made available on-line.

Self-assembling peptides form nanodiscs that stabilize membrane proteins

New methods to handle membrane bound proteins, e.g. G-protein coupled receptors (GPCRs), are highly desirable. Recently, apoliprotein A1 (ApoA1) based lipoprotein particles have emerged as a new platform for studying membrane proteins, and it has been shown that they can self-assemble in combination with phospholipids to form discoidal shaped particles that can stabilize membrane proteins. In the present study, we have investigated an ApoA1 mimetic peptide with respect to its solution structure when in complex with phospholipids. This was achieved using a powerful combination of small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS) supported by coarse-grained molecular dynamics simulations. The detailed structure of the discs was determined in unprecedented detail and it was found that they adopt a discoidal structure very similar to the ApoA1 based nanodiscs. We furthermore show that, like the ApoA1 and derived nanodiscs, these peptide discs can accommodate and stabilize a membrane protein. Finally, we exploit their dynamic properties and show that the 18A discs may be used for transferring membrane proteins and associated phospholipids directly and gently into phospholipid nanodiscs.

Small-angle scattering gives direct structural information about a membrane protein inside a lipid environment

Monomeric bacteriorhodopsin (bR) reconstituted into POPC/POPG-containing nanodiscs was investigated by combined small-angle neutron and X-ray scattering. A novel hybrid approach to small-angle scattering data analysis was developed. In combination, these provided direct structural insight into membrane-protein localization in the nanodisc and into the protein-lipid interactions. It was found that bR is laterally decentred in the plane of the disc and is slightly tilted in the phospholipid bilayer. The thickness of the bilayer is reduced in response to the incorporation of bR. The observed tilt of bR is in good accordance with previously performed theoretical predictions and computer simulations based on the bR crystal structure. The result is a significant and essential step on the way to developing a general small-angle scattering-based method for determining the low-resolution structures of membrane proteins in physiologically relevant environments.

WillItFit: a framework for fitting of constrained models to small-angle scattering data

A software framework for analysis of small-angle scattering data is presented. On the basis of molecular constraints and prior knowledge of the chemical composition of the sample, the software is capable of simultaneously fitting small-angle X-ray and neutron scattering data to analytical or semi-analytical models of biomacromolecules. The software features various fitting routines along with the possibility of incorporating instrumental resolution effects on the fit. Finally, trust region estimation, based on the profile likelihood strategy, is implemented. The algorithms and models are written in C, whereas the user interface is written in Python. Parallelization is implemented using the OpenMP extensions to C. The source code is available for free upon request orviathe associated code repository. The software runs on Linux, Windows and OSX and is available as an open-source initiative published under the General Publishing License.