What drives amyloid molecules to assemble into oligomers and fibrils?

We develop a general theory for three states of equilibrium of amyloid peptides: the monomer, oligomer, and fibril. We assume that the oligomeric state is a disordered micelle-like 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 and steric packing, in addition to specific hydrophobic sidechain contacts. The model makes a broad set of predictions, consistent with experiments: (i) Similar to surfactant micellization, amyloid oligomerization should increase with bulk peptide concentration. (ii) The onset of fibrillization limits the concentration of oligomers in the solution. (iii) The average fibril length \emph{vs.} monomer concentration agrees with data on $\alpha$-synuclein, (iv) Full fibril length distributions follow those of $\alpha$-synuclein, (v) Denaturants should `melt out' fibrils, and (vi) Added salt should stabilize fibrils by reducing repulsions between amyloid peptide chains. Interestingly, small changes in solvent conditions can: (a) tip the equilibrium balance between oligomer and fibril, and (b) 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.