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

Abstract

The formation of {beta}-sheet rich amyloid fibrils in Alzheimers disease and other neurodegenerative disorders is limited by a slow nucleation event. To understand the initial formation of {beta}-sheets from disordered peptides, we used all-atom simulations to parameterize a lattice model that treats each amino acid as a binary variable with {beta} and non-{beta} states. We show that translational and conformational entropy give the nascent {beta}-sheet an anisotropic surface tension which can be used to describe the nucleus with two-dimensional Classical Nucleation Theory. Since translational entropy depends on concentration, the aspect ratio of the critical {beta}-sheet changes with protein concentration. Our model explains the transition from the nucleation phase to elongation as the point where the {beta}-sheet core becomes large enough to overcome the conformational entropy cost to straighten the terminal molecule. At this point the {beta}-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 co-aggregation experiments because the nucleus only involves a small portion of the peptide. SIGNIFICANCEThe conversion of soluble proteins to amyloid aggregates is associated with many neurodegenerative diseases. Experiments have shown that this conversion occurs by a slow nucleation step followed by rapid growth. This work identifies the principle contributions to the free energy barrier that separates these two stages. It also shows how factors like protein concentration, sidechain interactions, and interactions with the environment can modify the barrier and affect nucleation times.