Kinetic Theory of Fibrillogenesis of Amyloid β -protein

Prior quasielastic light scattering (QLS) studies of fibrillogenesis of synthetic amyloid β -protein (Aβ )-(1-40) at low pH have suggested a kinetic model in which: (i) fibrillogenesis requires a nucleation step; (ii) nuclei are produced by Aβ micelles in addition to seeds initially present; and (iii) fibril elongation occurs by irreversible binding of Aβ monomers to the fibril ends. Here we present the full mathematical formulation of this model. We describe the temporal evolution of the concentrations of Aβ monomers and micelles as well as the concentration and size distribution of fibrils. This formulation enables deduction of the fundamental parameters of the model--e.g., the nucleation and elongation rate constants k_n and k_e--from the time dependency of the apparent diffusion coefficient measured by QLS. The theory accurately represents the experimental observations for Aβ concentrations both below and above c^*, the critical concentration for Aβ micelle formation. We suggest that the method of QLS in combination with this theory can serve as a powerful tool for understanding the molecular factors that control Aβ plaque formation.