Methods
Diameters of β-barrels comprising these models were calculated from the number of strands (N) and sheer number (S) (related to strand tilt) of the barrels (see Murzin et al .40 for early theory and Hayward and Milner-White41 for an extension and modification of this theory to radially symmetric β-barrels and β-helices). The latter analysis does not include the P2 2-fold perpendicular symmetry present in our models. These structures have axes of 2-fold symmetry perpendicular to the radial axis of symmetry and intersecting it at the assembly’s center of mass. This feature constrains symmetric models with concentric β-barrels because all barrels must have the same axes of symmetry. The gap distance between the walls of the adjacent barrels were constrained to be between 0.6 and 1.2 nm42, depending primarily on the side chain sizes. We favor models in which interacting pleats of adjacent β-barrels fit between each other in a manner that reduces clashes among side chains, and in which all pleats that intersect the axes of 2-fold symmetry have the same inward or outward orientation in all concentric β-barrels. We call this type of interaction “Intermeshing Pleats42.” We selected models that maximize hydrogen bonds, salt bridges, interactions among aromatic side chains, burial and tight packing of hydrophobic side chains that are highly conserved among Aβ homologs, and aqueous solvent exposure of hydrophilic side chains, especially for positions that are hypervariable among homologs. Residues with polar side chains and/or that have a high propensity for turn or coil secondary structure35 and that contain proline in some homologs were favored for connecting loops. The final constraints were experimental: the sizes, shapes, molecular weights, and secondary structures of assemblies as determined by EM images of annular protofibrils and other studies, and distance constraints based on NMR studies of tetramers, octamers, and 32mers.
Photoshop43 was used to analyze APF images. Isolated beaded APFs (Fig. 1a) were copied and grouped according to the number and size of beads. Radial image averaging was applied to relatively symmetric bAPFs in which all beads had the same approximate size. The radially averaged images of the same size and shape were superimposed and averaged to obtain the final image. A similar process was used to analyze sAPFs but with the additional constraint of placing the sAPFs into three categories: those with white centers and periodic dots on the perimeters (WCsAPF), those with dark centers and periodic dots (DCsAPF), and those with super smooth outer rings without periodic dots and dark centers (SsAPF). The first two categories of images were then averaged radially with the symmetry based primarily on their diameters and the number and spacing of the perimeter dots. Averaged images that were similar in size and characteristics were then aligned to obtain images averaged over multiple sAPFs (Fig. 1e). When the symmetry was ambiguous numerous symmetries were tried. If a specific symmetry and diameter resembled those obtained from less ambiguous sAPFs the image was included in the multiple sAPF averaging process; otherwise, it was discarded.
Atomic-scale structures were generated with an in-house program and illustrated using the Chimera program44,45.
Sequences of 2500 Aβ homologs were collected and aligned using the Blast program46.