Simple Model of the Effect of Solution Conditions on the Nucleation of Amyloid Fibrils

It is well known that peptide and protein fibrillation is strongly affected by the solution conditions, but a fundamental understanding of how amyloid fibril nucleation depends on solution pH, salt concentration, and solvent is absent. Here, we use expressions from Debye-Hückel theory to describe the interactions between charged amino acids in combination with our recently developed nonstandard nucleation theory to predict the concentration dependence of the fibril nucleation rate under different solvent conditions. The general rule that emerges from these considerations is that changes in solution pH, salt concentration, and solvent that increase the bonding energy between the fibril building blocks decrease the fibril solubility and promote fibril nucleation, in line with experimental observations. The simple analytical relations among the nucleation rate, fibril solubility, and binding energies provide a tool to controlling and understanding amyloid fibril formation by changing the solution conditions.