Mathematics PhD Defense - 10/03/25

Abstract:

Alzheimer's disease (AD) is a progressively developing neurological condition leading to cognitive and behavioral decline. The cause of AD is still unknown. Pathologically, hypotheses such as impaired neurotransmission, oxidative stress, metal ions, and amyloid-beta (A$\beta$) aggregation are vital contributors to AD's pathophysiology. Recent research focuses on treatments targeting the brain's A$\beta$ polymer deposits, commonly seen as amyloid plaques. Chapter 1 introduces AD, thesis goals, and its outline. Chapter 2 provides a detailed scientific background on the pathophysiology of AD and key hypotheses from the literature and reviews recent drug treatment research. Chapter 3 aims to develop intuitive mathematical models to elucidate AD treatment with inhibitory drugs. These models clarify the complex kinetics of A$\beta$ formation and drug interactions. We discuss two categories of drugs: first, anti-inflammatory drugs (NSAIDs), which act as monomer inhibitors of A$\beta$ aggregation, and second, drugs that directly interact with A$\beta$ aggregated polymers. We initially analyze each drug independently and then assess their combined effects. Our numerical simulations demonstrate that the first type of drug reduces the equilibrium state value of aggregated filaments, whereas the second model of drug exhibits even greater efficacy in reducing the equilibrium state value of aggregated filaments. Furthermore, we conduct simulations of the simultaneous application of both drugs. The results are compared with the experimental data. Chapter 4 presents a novel and rigorously validated mathematical model to investigate the kinetics of ($A\beta$) aggregation in the presence of biologically relevant metal ions, chelating agents and inhibitor drugs. The model captures the microscopic reaction mechanisms that exist in the dynamics of $A\beta$ and explicitly accounts for the catalytic roles of copper, zinc, and iron ions, key contributors to the formation of neurotoxic plaques in AD. Clearly, our framework integrates dual therapeutic strategies: (i) metal chelation therapy, which binds and neutralizes free metal ions, and (ii) direct inhibition of $A\beta$ aggregation. Simulations in a variety of kinetic regimes reveal how each intervention modulates aggregation pathways, independently or synergistically. These studies focus on developing and analyzing mathematical models that describe the aggregation of $A\beta$ with and without metal ions under different inhibitor drugs and chelation treatment.

PhD Advisor:

Dr. Shantia Yarahmadian