Size Distribution of Amyloid Nanofibrils

We consider the size distribution of amyloid nanofibrils (protofilaments) in nucleating protein solutions when the nucleation process occurs by the mechanism of direct polymerization of beta-strands (extended peptides or protein segments) into beta-sheets. Employing the atomistic nucleation theory, we derive a general expression for the stationary size distribution of amyloid nanofibrils constituted of successively layered beta-sheets. The application of this expression to amyloid beta(1-40) (A beta(40)) fibrils allows us to determine the nanofibril size distribution as a function of the protein concentration and temperature. The distribution is most remarkable with its exhibiting a series of peaks positioned at magic nanofibril sizes (or lengths), which are due to deep local minima in the work for fibril formation. This finding of magic sizes or lengths is consistent with experimental results for the size distribution of aggregates in solutions of A beta(40) proteins. Also, our approach makes it possible to gain insight into the effect of point mutations on the nanofibril size distribution, an effect that may play a role in experimentally observed substantial differences in the fibrillation lag-time of wild-type and point-mutated amyloid-beta proteins.