A Network Thermodynamic Analysis of Amyloid Aggregation Along Competing Pathways

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Mathematics and Natural Sciences


© 2020 Self-assembly of proteins towards amyloid aggregates is a significant event in many neurodegenerative diseases. Aggregates of low-molecular weight called oligomers are largely the primary toxic agents in many of these maladies. Therefore, there is an increasing interest in understanding their formation and behavior. In this paper, we build on our previously established theoretical investigations on the interactions between Aβ and lipids (L) that induces off-pathway aggregates under the control of L concentrations. Here, our previously developed competing game theoretic framework between the on- and off-pathway dynamics has been expanded to understand the underlying network topological structures in the reaction kinetics of amyloid formation. The mass-action based dynamical systems are solved to identify dominant pathways in the system with fixed initial conditions, and variations in the occurrence of these dominant pathways are identified as a function of various seeding conditions. The mechanistic approach is supported by thermodynamic free energy computations which helps identify stable reactions. The resulting analysis provides possible intervention strategies that can draw the dynamics away from the off-pathways and potential toxic intermediates. We also draw upon the classic literature on network thermodynamics to suggest new approaches to better understand such complex systems.

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Applied Mathematics and Computation