  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.
