Stability Analysis of 4-Species A Beta Aggregation Model: A Novel Approach to Obtaining Physically Meaningful Rate Constants

Document Type

Article

Publication Date

11-1-2013

Department

Chemistry and Biochemistry

School

Mathematics and Natural Sciences

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 stochastic nature of interactions that impedes thorough experimental characterization and the development of meaningful insights. In this study, we have utilized a well-known intermediate state along the amyloid-β peptide aggregation pathway called protofibrils as a model system to investigate the molecular mechanisms by which they form fibrils using stability and perturbation analysis. Investigation of protofibril aggregation mechanism 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 accomplished by finding the ranges in which the perturbations die-out in a five-parameter sweep, which includes the monomer and protofibril equilibrium concentrations and three of the rate constants. The results presented are a proof-of-concept method in determining meaningful rate constants that can be used as a bonafide way for determining accurate rate constants for other models involving complex biological reactions such as amyloid aggregation.

Publication Title

Applied Mathematics and Computation

Volume

224

First Page

205

Last Page

215

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