Figure 1

(a),(c) Schemas of the two modes of spatial propagation considered here. In (a), aggregates spread primarily through diffusion while they grow through elongation and multiply through a secondary pathway (illustrated as filament fragmentation). In (c), the aggregates instead spread primarily through their growth, as they multiply through a secondary pathway (illustrated as secondary nucleation). The fragmentation and secondary nucleation events are highlighted with stars. (b),(d) Comparison of the corresponding analytical results (solid lines) and the results of Monte Carlo simulations [28] (data points) for the concentration profiles at increasing times. Panel (b) shows the linear number density $\int dy\int dzP$ from (3) for diffusion, and panel (d) shows the radial density $4\pi r^{2}P$ from (7) for radial spreading through growth. The insets show the farthest position where a threshold density, $\theta =5\mu {\mathrm{m}}^{-1}$, is reached in the numerical concentration profiles (data points); the front velocity is given by the slope and compared to the analytical results (solid lines) derived in the text. The parameters are $k_{+}=9\times {10}^4{\mathrm{M}}^{-1}{\mathrm{s}}^{-1}$, $m=5\mathrm{mM}$, $k_{-}=k_2{m}^{n_2}=2\times {10}^{-8}{\mathrm{s}}^{-1}$ in (b) and (d) respectively, giving a ratio $S=2.2$ of the diffusion to growth controlled propagation velocities. The prefactors were $\delta =1\AA$, $\eta =0.5\mathrm{mPa}\mathrm{s}$, $d=8\mathrm{nm}$, $T=330\mathrm{K}$.Reuse & Permissions

Figure 2

Representative images of the progression over time of experiments [28] involving diffusion (a) and growth (c) dominated propagation of insulin aggregation, as described in the text. In both cases, aggregation was monitored by means of the fluorescent probe thioflavin $T$, which has a high affinity for the amyloid scaffold [16]. (a) Single microdroplet and (c) five spherulites. (b),(d) Corresponding measurements of the velocity of the reaction fronts for these systems at two different concentrations of NaCl (black, 0 mM; gray, 10 mM; both in the presence of 50 mM HCl). Note that the velocity in (a) and (b) is much greater than in (c) and (d), consistent with the fact that the propagation in (a) and (b) is controlled by diffusion and not growth. In addition, note that the growth of a dense crystal phase would not result in a volume filling process as observed in (a), since only a small volume fraction, $\sim 3\%$ in our experiments, is protein.Reuse & Permissions