Results

Imaging and classification of amyloid fibril segments
Images of β2m amyloid fibrils formed at pH 2.5, acquired by negative staining and cryo-EM, are shown in Fig. 1a. The images revealed long, twisted fibrils with a diameter of around 20 nm and a characteristic pattern of cross-over repeats. As found previously for other amyloid fibrils,18,32 β2m fibrils display a marked heterogeneity in repeat length (120–185 nm). To sort the fibrils into more uniform structural classes, each cross-over repeat unit was treated as a single particle.33–35 This approach revealed two main fibril morphologies, termed here as types A and B. Type A fibrils have polarity, as shown by the arrowhead features in the class average view in Fig. 1b, whereas type B fibrils are bipolar (Fig. 1c). Notably, hints of a globular subunit repeat can be seen in the class averages (Fig. 1b and c), which were determined by reference-free alignment and classification, with no repeat information imposed. This subunit repeat is clearly seen in raw negative stain images, whose power spectra show strong layer lines at spacings in the range of 5.2–6.5 nm, consistent with a subunit repeat of this size (Fig. 1d and e). A small population of fibrils with half the thickness of the type A and type B fibrils (10 nm) was also observed, termed type C (Fig. 2a). This finding, together with the observation that the thicker fibrils were occasionally split into two (data not shown), suggests that the fibrils are assembled from independent halves. Fibrils assembled at pH 7 showed morphologies similar to those generated at low pH, but were associated into bundles, precluding their further structural analysis (Supplementary Fig. 1).

Three-dimensional reconstructions of amyloid fibrils
The intriguing substructure revealed by the images prompted us to undertake a 3D analysis of the fibril architecture. Of particular interest was the appearance of a subunit repeat, reminiscent of an earlier negative stain EM analysis of prion protein fibrils.36 However, this feature contrasts with current models for amyloid based on fibre diffraction, electron paramagnetic resonance, solid-state NMR, 3D crystals of small peptides, and cryo-EM images of fibrils formed from Aβ and other peptides.6,14,37,38 Using estimates of the long-range helical repeat and the subunit repeat determined from the images, 3D maps were calculated from the class average views. Reprojections of the maps compare well with the corresponding input class averages, showing the consistency of the maps with the input data (Fig. 1b and c). From a data set of 2000 repeats, 17 classes of the A-type structures and 14 classes of the B-type were selected, each with clear structural features, yielding a total of 31 individual 3D fibril maps (Fig. 2d and e). Side views, cross-over repeats, and resolution figures are tabulated for a selection of maps in Fig. 3. The resolution was estimated by comparing pairs of similar maps, using the 0.5 Fourier shell correlation criterion (Supplementary Fig. 2). Despite their structural variations, fibrils in the different classes have similar cross sections and bi-lobed globular repeats along the axial columns of density. The twist variation is most pronounced for the A-type classes where, for 85% of the data, the cross-over repeat distance fell into the range 128–152 nm (Fig. 2b and c). Outliers had cross-over repeats up to 185 nm, but their numbers were insufficient for classification and 3D reconstruction. For the B-type classes, the repeat is more constrained at 122–135 nm. A representative 3D map of each type is shown in more detail in Fig. 4, for which the resolutions are estimated as 29 Å (A-type) and 25 Å (B-type). The maps reveal a remarkably elaborate structure composed of two crescent-shaped units. A-type and B-type half-fibrils show a clear structural similarity when overlaid (Fig. 4e), consistent with the notion that the crescent-shaped half-fibrils are independent structural elements that can join back to back in either a parallel fashion (A-type; Fig. 4a and c) or an anti-parallel fashion (B-type; Fig. 4b and d). Each crescent contains three globular regions of density (about 3 nm × 4 nm in cross section), which represent constituent protofilaments (Fig. 4c and d). Most striking, however, is the complexity of the fibril architecture, with different interfaces between protofilaments both within and between the crescents. As shown in Fig. 2d and e, the A-type and B-type reconstructions also revealed considerable flexibility between the protofilaments and between the two crescents, adding to the heterogeneity of the samples obtained.

STEM mass measurements
To study the molecular packing of β2m into this homopolymer, STEM was used to determine mass per unit length (MPL) along the fibrils. The results revealed a major component at 53 ± 3 kDa/nm, as well as fibrils with half the width and a component at 27 ± 3 kDa/nm (Fig. 5). The former is consistent with the A-type and B-type fibrils, while the latter presumably represents the C-type fibrils. The component at 62 ± 3 kDa/nm may correspond to more tightly twisted fibrils, and minor components at higher mass may correspond to different fibril morphologies. The mass measurements of the major component indicate that there are 24 β2m monomers (monomer mass, 11.8 kDa) in each 5.25-nm repeat of the whole B-type fibril, or four monomers in each repeat of each protofilament. The alternating wide and narrow interfaces between density features along the protofilaments (Fig. 4a and b) suggest that the bi-lobed density corresponds to a head-to-head arrangement of each assembly unit. This tetrameric unit has 2-fold symmetry rather than 4-fold symmetry, so that the building block of the protofilament comprises four β2m molecules in a dimer-of-dimers arrangement.
The hierarchical fibril structure is explained schematically in Fig. 6. Three bi-lobed density units assemble into an extended crescent shape. Pairs of these crescent-shaped elements join back to back to form one layer of the fibril structure. Many copies of this assembly stack to form the slowly twisting helical fibril, in which columns of the globular building blocks constitute the six protofilaments of the fibril. In contrast to the generally accepted notion of a continuous cross-β core in amyloid fibrils,4,6 the globular substructure of these protofilaments gives them the appearance of a string of bi-lobed beads. The polarity of the half-fibrils arises from asymmetric connections between the protofilaments in the crescents.