Theses and Dissertations


Eda Asili

Issuing Body

Mississippi State University


Yarahmadian, Shantia

Committee Member

Wipf, David O.

Committee Member

Oppenheimer, Seth

Committee Member

Miller, T. Len

Committee Member

Miller, Vivien G.

Date of Degree


Document Type

Dissertation - Open Access



Degree Name

Doctor of Philosophy


College of Arts and Sciences


Department of Mathematics and Statistics


The aggregation of amyloid-beta by self-assembly into oligomers or amyloids is a central event in Alzheimer’s disease. In this dissertation, I propose a mathematical model as a set of coupled kinetic equations that governs the self-assembly of amyloid-beta filaments in the presence of transition-metal ions. Metal ions have been hypothesized as an important factor in the pathogenesis of AD. There is a considerable literature supporting the impact of metal ions such as copper (Cu), zinc (Zn) and iron (Fe) in many critical aspects of AD and other neurodegenerative diseases. Our study includes Cu and Zn as main transition-metal ions, where their coordination to amyloid-beta regulates the aggregation process in vivo. Metal ions mostly affect the nucleation phase and change both the structure and the charge of amyloid-beta. Our model describes the general features of the kinetics of fragmenting filamentous structures. The numerical simulations reveal a four timescale dynamics related to three important events, which are the formation of the amyloid-metal, the homogeneous aggregation of the filaments and the non-homogeneous aggregation of the protein-metal. The method of singular perturbation is used to discern between these timescales. These results are studied in the framework of slowast systems. We also compare the metal with the non-metal dynamics and apply optimization theory for realistic values of reaction rates. Simulations shows that in certain cases the presence of metal accelerates the aggregation of filaments in a drastic way.