Figure 1

Amyloid growth through diffusive sampling of an energy surface $G$. The reaction rate is determined through the flux from the reactants ($A≔F_j+M$) to the product ($B≔F_{j+1}$). An arbitrary path $\gamma$ from $A$ to $B$ in the proximity of the saddle point $‡$ is shown in black. The current at the saddle point is in the $z$ direction as discussed in the text and the plane for the perpendicular degrees of freedom $y_i$ is shown in gray.Reuse & Permissions

Figure 2

(a) Schema illustrating the determination of amyloid growth rates through measurements of the mass increase of a fibril population elongating on a quartz crystal transducer, as described in the text. (b) Elongation rate of insulin fibrils as a function of the concentration of soluble insulin; rates under different conditions [with 100 mM NaCl and 20% ${\mathrm{CH}}_3\mathrm{COOH}$ (squares) and data from 18 without salt (triangles)] can be scaled to collapse on to a master curve. A two-parameter fit to Eq. (7) gives $\tilde{c}=4.5\times {10}^{23}{\mathrm{m}}^{-3}$ (equivalent to $4.3\mathrm{mg}/\mathrm{ml}$ for insulin with molar mass $M_I=5800$ Da), and $v_{\max }=264\mathrm{ng}{\mathrm{cm}}^{-3}{\min }^{-1}$. (c) analogous experiment carried out with bovine $\alpha$ lactalbumin. Here the fit to Eq. (7) yields $\tilde{c}=1.8\times {10}^{22}{\mathrm{m}}^{-3}$ (equivalent to $0.42\mathrm{mg}/\mathrm{ml}$ for $\alpha$ lactalbumin with molar mass $M_I=14200$ Da), and $v_{\max }=16.3\mathrm{ng}{\mathrm{cm}}^{-2}{\min }^{-1}$. The insets in (b) and (c) show AFM micrographs of a sensor surface before growth from which the seed density can be measured.Reuse & Permissions

Figure 3

Measurements of the enthalpic contribution $H^{‡}$ to the activation barrier $G^{‡}=H^{‡}-T{S}^{‡}$ for insulin and $\alpha$ lactalbumin in the linear low concentration regime (solid black line) and saturated high concentration regime (dashed gray line) through the relation $\log (\Phi )=H^{‡}{k}_B^{-1}{T}^{-1}+\mathrm{const}$. Measurements are performed in 20% acetic acid with 100 mM NaCl (insulin) and HCl $p\mathrm{H}=1.2$ with 100 mM NaCl ($\alpha$ lactalbumin).Reuse & Permissions