What drives amyloid molecules to assemble into oligomers and fibrils?

Abstract

We develop a theory for three states of equilibrium of amyloid peptides: the monomer, oligomer, and fibril. We assume that the oligomeric state is a disordered micellelike collection of a few peptide chains held together loosely by hydrophobic interactions into a spherical hydrophobic core. We assume that fibrillar amyloid chains are aligned and further stabilized by steric zipper interactions-hydrogen bonding, steric packing, and specific hydrophobic side-chain contacts. The model makes a broad set of predictions that are consistent with experimental results: 1), Similar to surfactant micellization, amyloid oligomerization should increase with peptide concentration in solution. 2), The onset of fibrillization limits the concentration of oligomers in the solution. 3), The extent of Aβ fibrillization increases with peptide concentration. 4), The predicted average fibril length versus monomer concentration agrees with data on α-synuclein. 5), Full fibril length distributions agree with data on α-synuclein. 6), Denaturants should melt out fibrils. And finally, 7), added salt should stabilize fibrils by reducing repulsions between amyloid peptide chains. It is of interest that small changes in solvent conditions can tip the equilibrium balance between oligomer and fibril and cause large changes in rates through effects on the transition-state barrier. This model may provide useful insights into the physical processes underlying amyloid diseases.

Figure 1

(Upper) Model of amyloid aggregation equilibria. Each black line indicates the peptide backbone. Each red line represents one hydrogen bond. (State A) Isolated peptide monomers in solution. (State B) Oligomeric assembly of a few peptide chains. (State C) Nucleus of β-sheet structure. The peptide backbone runs perpendicular to the fiber axis. (State D) Postcritical nucleus structure showing more β-structure. (State E) A protofilament is a single long thread of β-structure consisting of a β-sandwich and two face-to-face β-sheet planes. (State F) The full fibril, a bundle of protofilaments shown here to contain p = 2 protofilament threads. (Lower) Schematic representations of the free-energy (F) landscape at low (left), intermediate (middle), and high (right) peptide concentrations, as described by our model. Labels correspond to the states depicted above. At low concentrations, the monomer state (state A) is the free-energy minimum, whereas at high concentrations, the fibril (State F) is the minimum. At intermediate concentrations, the solution depends sensitively on the relative stabilities of the fibril and oligomer states.

Figure 2

Assembly hierarchy of amyloid fibrils shown in atomistic cartoon representation (left) and schematically, with β-sheets as blocks (right). (a) A single β-sheet comprised of parallel β-strands. (b) A β-sheet observed along the fibrillization axis. (c) Assembled β-sandwich (protofilament) consisting of two β-sheets. Note the steric zipper interactions shown as interdigitating side chains (left) and as a green layer (right). (d) Mature fibril consisting of p = 2 protofilaments.

Figure 3

Schematic representation of the parameter n_s. Here, each peptide chain contributes one (a), two (b), and four (c) β-strands to the fibril. For clarity, adjacent peptide chains are shown in alternating colors.

Figure 4

Phase diagram for peptides with p, n_s = 1, ℓ = 15, N = 10, lng = 0.6, and lnγ = −2 as a function of peptide concentration and lng/χ. Lines depict phase boundaries computed from Eq. S12 (long-dashed), Eq. S8 (short-dashed), and Eq. S4 (solid). Colors (colored figure available online) show the numerical solution of Eq. 7 as follows: green =c₁/c₀ (monomers); blue = c_oligo/c₀ (oligomers); and red =c_fibril/c₀ (fibrils).

Figure 5

Plot of c_fibril as a function of the bulk peptide concentration compared to circular dichroism data of Terzi et al. for Aβ_1–40 (44). L = 26, n_s = 2, p = 2, g = 1.66, and γ = 0.54.

Figure 6

Average length of fibrils versus peptide concentration, and in comparison to experiments on α-synuclein (46). −Llng = −15.5 and −ℓplnγ = 32.3.

Figure 7

Comparison of the computed fibril length distribution as a function of the bulk peptide concentration to the experimental distributions of α-synuclein for peptide concentrations ranging from 20 to 250 μM (46). −Llng = −15.5 and −ℓplnγ = 32.3.

Figure 8

Phase diagram for Aβ as a function of peptide concentration and urea concentration. The colors represent monomers (green), oligomers (blue), and fibrils (red). N = 4 and χNL = 36.4 (19), and all other parameters are identical to those in Fig. 5. This diagram explains a discrepancy between the experiments of Chen and Glabe (19) and Kim et al. (50). The black line indicates the denaturation pathway of Chen and Glabe, who found no intermediate oligomers. For the Kim experiments, denaturation is indicated by the white line and shows an oligomeric state at intermediate urea concentrations.

Figure 9

Predicted solubility of Aβ₄₀ as a function of salt concentration and net peptide charge. Data points at q = 3.9 are from Klement et al. (52) and the point at q = 2.8 is from Terzi et al. (44).