Amyloid fibril proliferation occurs through a two-step nucleation mechanism that involves oligomer formation followed by oligomer conversion into fibrillar structures. The heterogeneous ensemble of oligomers not only includes converting species but also consists mainly of unstable oligomers that can dissociate back to monomers. Oligomers undergo repeated cycles of formation–dissociation before eventually converting into species that are able to grow into new fibrils. The reaction rates are shown here for Aβ42 at a concentration of 5 μM (rate constants are given in Supplementary Section 6.3) and are to be interpreted as averages over the heterogeneous ensemble of oligomers. The geometric mean of the rates of oligomer formation, oligomer conversion and fibril elongation (which constitute the autocatalytic cycle of fibril self-replication (Supplementary Section 5.3)) yields the characteristic rate of amyloid fibril formation (Supplementary Section 6.5 and Supplementary Fig. 17).