Figure 1: A fragmentation model incorporating a structural transition fits kinetic data for insulin fibril assembly.

(a) Lag time as a function of protein concentration. The experimental data (black squares) are fitted to the function y=Ax^γ with an exponent γ=−0.37±0.02. The simulation data (red circles) have exponent γ=−0.42±0.001, k₊=5 × 10⁴ M⁻¹ s⁻¹ and k_f=3 × 10⁻⁸ s⁻¹. (b) Mean maximal ThT fluorescence as a function of insulin concentration. (c) Growth rate, k_gr, is plotted as a function of insulin concentration. The experimental data (black squares) were obtained from kinetic curves normalized to the fluorescence maxima. The simulation data were obtained from 150 simulations per concentration using a simple fragmentation-dominated model (blue triangles), including suppression of fragmentation once the fibril mass reaches a CFC of 0.4 mg ml⁻¹ (red circles). All data points show mean±s.d. (d) In our model, fibrils grow via two processes: fragmentation, and elongation via monomer addition. These processes are characterized by their respective rates k_f and k₊. Our model predicts distinct fibril length distributions for protein concentrations, c_p greater or less than c_T≈2CFC.