Conformational entropy limits the transition from nucleation to elongation in amyloid aggregation

The formation of β-sheet-rich amyloid fibrils in Alzheimer's disease and other neurodegenerative disorders is limited by a slow nucleation event. To understand the initial formation of β-sheets from disordered peptides, we used all-atom simulations to parameterize a lattice model that treats each amino acid as a binary variable with β- and non-β-sheet states. We show that translational and conformational entropy give the nascent β-sheet an anisotropic surface tension that can be used to describe the nucleus with 2D classical nucleation theory. Since translational entropy depends on concentration, the aspect ratio of the critical β-sheet changes with protein concentration. Our model explains the transition from the nucleation phase to elongation as the point where the β-sheet core becomes large enough to overcome the conformational entropy cost to straighten the terminal molecule. At this point the β-strands in the nucleus spontaneously elongate, which results in a larger binding surface to capture new molecules. These results suggest that nucleation is relatively insensitive to sequence differences in coaggregation experiments because the nucleus only involves a small portion of the peptide.