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.