Breakage of amyloid fibrils. (*A*) A proposed mechanism of amyloid fibril formation involves nucleation (row 1), elongation (row 2), dissociation (row 3), and breakage (row 4). The breakage rate constant was determined from seeded growth experiments. (*B*) For each of 10 independent seeded growth experiments with different initial monomer concentration, the average length as a function of time was monitored by dynamic light scattering (*Inset*). (*C*) The values of *L*_{0} and (*dL/dt*)|_{t=0} were calculated. A linear least-squares fit (red line, slope = 3.6 × 10^{5} M^{−1}·s^{−1}, intercept = −0.54 s^{−1}) was performed on the data. With an average initial length *L*_{0} = 1,361 nm, equivalent to 11,340 monomers, the values of the slope and intercept imply an elongation rate constant of 1.8 ± 0.2 × 10^{5} M^{−1}·s^{−1} and breakage rate constant of 1.7 ± 1.3 × 10^{−8} s^{−1}. Preformed, sonicated insulin fibrils (50 nM) in a solution of insulin (1 μM) were heated at 60°C, and the average length of two-filament insulin fibrils as a function of time was measured with the AFM (points). The differential equations for the nucleated growth model with breakage were solved numerically (shaded region) with the initial conditions of the experiment and the elongation rate constant was determined. The breakage rate constant was varied between the upper and lower bound of that determined. The dashed curve shows the numerical solution to the differential equations in the absence of breakage.

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