A Minimalistic Kinetic Model for Amyloid Self-Assembly

Abstract

Amyloid aggregation is a phenomenon in which proteins/peptides self-assemble into highly ordered structures that are associated with diseases (e.g. Alzheimer's and Parkinson's) as well as several native biological functions. A wide range of proteins/peptides can form these structures while displaying remarkable phenomenological similarities, both structural and kinetic. Thus, there is a need for a unifying framework that would enable a better understanding of the phenomenon of amyloid formation. In the current work, we develop a coarse-grained model for amyloid formation that accounts for experimentally known phenomenon like polymerization, depolymerization (under different polymer-states) and the conformational transition of monomers during aggregation. The model is analytically solvable, and can be simulated for timescales and lengthscales that are biologically relevant. Our mathematical model and kinetic Monte carlo simulations shed light on the vital signatures of amyloid growth, including a plausible explanation for the concentration-independence of fibril growth velocities at large free-monomer concentrations. Interestingly, our simulations also reveal the relationship between the heterogeneity in filament lengths (variances) and the rate of conformational transition. The length fluctuation data suggest that an increased rate of conformational transition not only alters the extent of fluctuation in filament lengths, but also the timescales at which the heterogeneity is maximum. Using our analytical expressions for aggregation and beta-sheet growth velocities, we predict a multi-phasic behavior of proteins/peptides in response to varying kinetic parameters. Our model also captures other interesting aspects of amyloid growth including the potential of growing fibrils to generate mechanical forces and the experimentally observed phenomenon of intermittent nature of filament growth. Overall, the study could significantly augment our fundamental understanding of the complex phenomenon of amyloid aggregation.