Kinetic theory of fibrillogenesis of amyloid beta-protein

Prior quasielastic light scattering (QLS) studies of fibrillogenesis of synthetic amyloid beta-protein (A beta)-(1-40) at low pH have suggested a kinetic model in which: (i) fibrillogenesis requires a nucleation step; (ii) nuclei are produced bt A beta micelles in addition to seeds initially present; and (iii) fibril elongation occurs by irreversible binding of A beta monomers to the fibril ends, Here we present the full mathematical formulation of this model, We describe the temporal evolution of the concentrations of A beta 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 A beta concentrations both below and above c*, the critical concentration for A beta 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 A beta plaque formation.