Mathematical Modeling of Amyloid Beta Fibril Formation: Equilibria & Stability

Abstract

Protein misfolding and concomitant aggregation towards amyloid formation is the underlying biochemical commonality among a wide range of human pathologies. Amyloid formation involves the conversion of proteins from their native monomeric states (intrinsically disordered or globular) to well-organized, fibrillar aggregates in a nucleation-dependent manner. Understanding the mechanism of aggregation is important not only to gain better insight into amyloid pathology but also to simulate and predict molecular pathways. One of the main impediments in doing so is the highly stochastic nature of interactions that complicates the development of meaningful insights. In this study, we have utilized a well-characterized intermediate along the amyloid-β peptide aggregation called ‘protofibrils' as a model system to investigate the molecular pathways by which they form fibrils using stability and perturbation analysis. Investigation of protofibril aggregation limits both the number of species to be modeled (monomers, and protofibrils), as well as the reactions to two (elongation by monomer addition, and protofibril-protofibril lateral association). Our new model is a reduced order four species model grounded in mass action kinetics. Our prior study required 3200 reactions, which makes determining the reaction parameters prohibitively difficult. using this model, along with a linear perturbation argument, we rigorously determine stable ranges of rate constants for the reactions and ensure they are physically meaningful. This was done by finding the ranges in which the perturbations vanish in a five-parameter sweep, which includes the monomer and protofibril equilibrium concentrations and three of the rate constants. These results are presented and discussed.