Date of Award

1-2018

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Ashwin Vaidya

Committee Member

David Trubatch

Committee Member

Arup Mukherjee

Subject(s)

Amyloid beta-protein--Mathematical models, Aggregation (Chemistry)

Abstract

The primary purpose of this paper is to investigate the mechanics of Aβ protein aggregation within the brain through mathematical modeling and simulation. Aggregation of Aβ is the cause of plaques within the brain of Alzheimer’s Disease sufferers. Because the pathways of aggregation from monomer to oligomer to polymer are numerous and complex, we have had to simplify our model to a limited number of species. Of great concern, too, is the process by which Aβ can form as “off-pathway” species, which is when Aβ reacts with fatty acid micelles. It is this species of Aβ, which due to its toxicity to neurons, that is now believed to cause Alzheimer’s Disease. Although the precise mechanism of Aβ aggregation continues to be heavily debated, evidence suggests a rate-limiting mechanism. Thus we will use Mass Action Kinetics to write a system of differential equations for the purpose of simulating aggregation of the Aβ protein in its different forms. We will analyze the stability of the system under different reaction rate regimes, as well as the system’s preferences for particular equilibrium states. Finally, we will examine the thermodynamics of the system.

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