Fig. 2.

Integrated rate laws for protein aggregation in the presence of inhibitors. Characteristic kinetic profiles for free species (A), bound species (B), and fibril mass concentration (C) in the presence of an inhibitor that binds free monomers (left column), fibrils ends (middle column), or fibril surfaces (right column). Dashed lines are the analytical integrated rate laws (see SI Appendix, section S2 for explicit expressions), which are in excellent agreement with numerical simulations of Eq. 3 (solid lines). The curves were generated using typical rate parameters for amyloid-forming systems; here, the parameters correspond to experimentally measured rates for in vitro aggregation of the A$\beta$42 peptide of Alzheimer’s disease (43): $m_{\mathrm{t}\mathrm{o}\mathrm{t}}=3\mu$M, $k_{+}=3\times 10^6{\mathrm{M}}^{-1}{\mathrm{s}}^{-1}$, $k_1=10^{-4}{\mathrm{M}}^{-1}{\mathrm{s}}^{-1}$, $k_2=8\times 10^3{\mathrm{M}}^{-2}{\mathrm{s}}^{-1}$, $n_1=n_2=2$, $K_{\times }=0.3\mu {\mathrm{M}}^{-1}$, $k_{\times }^{\mathrm{on}}=1.3\times 10^{-2}{\mathrm{M}}^{-1}{\mathrm{s}}^{-1}$; and $C_i=0.06,0.2,0.4\mu$M (A); $C_i=0.2,0.6,1.3\mu$M (B); and $C_i=0.2,0.8,3\mu$M (C). Dark grey curves are without inhibitor.