A game theoretic approach to deciphering the dynamics of amyloid-β aggregation along competing pathways

Abstract

Aggregation of amyloid {beta} (A{beta}) peptides is a significant event that underpins Alzheimer disease (AD). A{beta} aggregates, especially the low-molecular weight oligomers, are the primary toxic agents in AD pathogenesis. Therefore, there is increasing interest in understanding their formation and behavior. In this paper, we use our previously established investigations on heterotypic interactions between A{beta} and fatty acids (FAs) that adopt off-fibril formation pathway under the control of FA concentrations, to develop a mathematical framework in defining this complex mechanism. We bring forth the use of novel game theoretic framework based on the principles of Nash equilibria to define and simulate the competing on- and off-pathways of A{beta} aggregation. Together with detailed simulations and biophysical experiments, our mathematical models define the dynamics involved in the mechanisms of A{beta} aggregation in the presence of FAs to adopt multiple pathways. Specifically, our game theoretic model indicates that the emergence of off- or on-pathway aggregates are tightly controlled by a narrow set of rate constant parameters, and one could alter such parameters to populate a particular oligomeric species. These models agree with the detailed simulations and experimental data on using FA as a heterotypic partner to modulate temporal parameters. Predicting spatiotemporal landscape along competing pathways for a given heterotypic partner such as biological lipids is a first step towards simulating physiological scenarios in which the generation of specific conformeric strains of A{beta} could be predicted. Such an approach could be profoundly significant in deciphering the biophysics of amyloid aggregation and oligomer generation, which is ubiquitously observed in many neurodegenerative diseases.