a–c, Experimental measurements of the fibril formation at varying initial concentrations of Aβ42 (from Cohen et al.16) (centre column) and the time evolution of the concentration of oligomers recorded starting from 5 μM Aβ42 and best fits (solid lines) to the integrated rate laws that correspond to different mechanistic scenarios for Aβ42 oligomer dynamics (right column) (Supplementary Sections 3–5). a, One-step nucleation that produces elongation-competent oligomers. b, Two-step nucleation via oligomer conversion to growth-competent fibrils. c, Two-step nucleation via conversion of unstable oligomers. Supplementary Section 6 and Supplementary Table 1 give a detailed description of the fitting procedure and a list of fitting parameters. d,e, Experimental measurements of fibril and oligomer kinetics at 5 μM Aβ42 in the absence (d) and presence (e) of 5 μM Brichos chaperone domain from proSP-C to detect the presence of off-pathway oligomers, that is, oligomers that do not appreciably contribute to the reactive flux towards fibrils on the timescale of the experiment. Fibril mass measurements were fitted to the analytical expression for the aggregation time course (Supplementary Equation (25)) to determine how the overall rate constants for primary and secondary nucleation are affected by Brichos (Supplementary Section 6.4). The rate parameters determined in this way were then used to predict successfully the effect of Brichos on the oligomer concentration, without introducing any additional fitting parameters (Supplementary Equation (28)); this shows that suppressing oligomer formation on fibril surfaces affects equally the reactive fluxes towards oligomers and fibrils, which indicates that the majority of oligomers are on-pathway to fibrils.