A statistical-mechanical theory of fibril formation in dilute protein solutions.

We outline a theoretical treatment that describes fibril formation in dilute protein solutions. For this, we combine a theory describing self-assembly and conformational transition with a description of the lateral association of linear chains. Our statistical-mechanical model is able to predict the mean degree of polymerization and the length of the fibrils and their precursors, as well as the weight fractions of the different aggregated species in solution. We find that there appear to exist two regimes as a function of concentration, and as a function of the free energies of protein association: one in which low-molecular weight compounds dominate and one in which the fibrils do. The transition between these regimes can be quite sharp, and becomes sharper as more filaments are allowed to associate into a single fibril. The fraction of fibrils consisting of less than the maximum allowed number of filaments turns out to be negligible, in agreement with experimental studies, where the fibril thickness is found to be practically monodisperse. In addition, we find that the description of the fibril ends has a large effect on the predicted fibril length.