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 ß, 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

The saponin ß-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 ß-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.

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 ß-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 Lß' state and are precursors of spontaneously formed vesicles. The aescin concentration must be far above the cmcaescin (≈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 % ß-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 ß-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.

Circularized and solubility-enhanced MSPs facilitate simple and high-yield production of stable nanodiscs for studies of membrane proteins in solution.

Recently, an enzymatic reaction was utilized to covalently link the N and C termini of membrane scaffold proteins to produce circularized nanodiscs that were more homogeneous and stable than standard nanodiscs. We continue this development and aim for obtaining high yields of stable and monodisperse nanodiscs for structural studies of membrane proteins by solution small-angle scattering techniques. Based on the template MSP1E3D1, we designed an optimized membrane scaffold protein (His-lsMSP1E3D1) with a sortase recognition motif and high abundance of solubility-enhancing negative charges. With these modifications, we show that high protein expression is maintained and that the circularization reaction is efficient, such that we obtain a high yield of circularized membrane scaffold protein (csMSP1E3D1) and downstream circularized nanodiscs. We characterize the circularized protein and corresponding nanodiscs biophysically by small-angle X-ray scattering, size-exclusion chromatography, circular dichroism spectroscopy, and light scattering and compare to noncircularized samples. First, we show that circularized and noncircularized (lsMSP1E3D1) nanodiscs are structurally similar and have the expected nanodisc structure. Second, we show that lsMSP1E3D1 nanodiscs are more stable compared to the template MSP1E3D1 nanodiscs as an effect of the extra negative charges and that csMSP1E3D1 nanodiscs have further improved stability as an effect of circularization. Finally, we show that a membrane protein can be efficiently incorporated in csMSP1E3D1 nanodiscs. Large-scale production methods for circularized nanodiscs with improved thermal and temporal stability will facilitate better access to the nanodisc technology and enable applications at physiologically relevant temperatures.

Polyhedra and packings from hyperbolic honeycombs.

We derive more than 80 embeddings of 2D hyperbolic honeycombs in Euclidean 3 space, forming 3-periodic infinite polyhedra with cubic symmetry. All embeddings are "minimally frustrated," formed by removing just enough isometries of the (regular, but unphysical) 2D hyperbolic honeycombs [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] to allow embeddings in Euclidean 3 space. Nearly all of these triangulated "simplicial polyhedra" have symmetrically identical vertices, and most are chiral. The most symmetric examples include 10 infinite "deltahedra," with equilateral triangular faces, 6 of which were previously unknown and some of which can be described as packings of Platonic deltahedra. We describe also related cubic crystalline packings of equal hyperbolic discs in 3 space that are frustrated analogues of optimally dense hyperbolic disc packings. The 10-coordinated packings are the least "loosened" Euclidean embeddings, although frustration swells all of the hyperbolic disc packings to give less dense arrays than the flat penny-packing even though their unfrustrated analogues in [Formula: see text] are denser.

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.

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.

Invisible detergents for structure determination of membrane proteins by small-angle neutron scattering.

A novel and generally applicable method for determining structures of membrane proteins in solution via small-angle neutron scattering (SANS) is presented. Common detergents for solubilizing membrane proteins were synthesized in isotope-substituted versions for utilizing the intrinsic neutron scattering length difference between hydrogen and deuterium. Individual hydrogen/deuterium levels of the detergent head and tail groups were achieved such that the formed micelles became effectively invisible in heavy water (D2 O) when investigated by neutrons. This way, only the signal from the membrane protein remained in the SANS data. We demonstrate that the method is not only generally applicable on five very different membrane proteins but also reveals subtle structural details about the sarco/endoplasmatic reticulum Ca2+ ATPase (SERCA). In all, the synthesis of isotope-substituted detergents makes solution structure determination of membrane proteins by SANS and subsequent data analysis available to nonspecialists.

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.