Date of Award

5-2020

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

Mathematics

Thesis Sponsor/Dissertation Chair/Project Chair

Ashwin Vaidya

Committee Member

Bong Jae Chung

Committee Member

Bogdan Nita

Abstract

The formation of large AB fibril plaques in the human brain is considered important to the pathogenesis of Alzheimer's disease (AD), as protein aggregation elsewhere in the body underpins many human ailments. Now however, low-molecular weight intermediate AB oligomers, more than large fibrils, are thought to be a primary precursor in early AD etiology. The main obstacle in the study of AD is the lack of understanding we have pertaining to the evolution of the disease in a living brain. For this reason, a thorough study of AB aggregation begs exploration. Prior conjectures and new experiments emphasize the interaction between AB and environmental catalysts which force aggregation to occur in alternative pathway mechanisms. These Off-pathway aggregates are being singled out as especially related to AD. It is this the goal of this study to better understand the origins of the Off-pathway kinetics and explore ways to control their aggregation. To such ends, we develop a reduced order (six species) chemical network model which captures the essential biophysical traits of the On­ and Off-pathway aggregation processes. We apply a game-theoretic approach to the mass­ action based complex dynamical system which represents the evolutions of healthy and toxic amyloid plaques. Numerical computations of the system help us determine the conditions under which like species in each of the pathways dominate. The pathway domination is aptly represented using a phase diagram. A very useful outcome of this phase analysis is the identification of specific reaction topologies, along which the dominant reactions occur. Of the eight individual network topologies identified, four end up as On-pathway fibrils while the other half end up as Off-pathway fibrils. The question we wish to address is if and how we can seek out interventions which can skew the dominant paths in our system, i.e. can we alter dominant network topologies to terminate in an On-pathway (a pathologically healthy state). This is mathematically performed by means of seeding by appropriate oligomers and fibrils which is seen to significantly change the observed phases. The presentation will provide details of the seeding studies and the favorable interventions. By varying the parameters and studying their interplay we can determine regimes where pathologically preferential paths are dominant. The network's complexity gives rise to intense dependence on parameters and initial conditions. One further focus will be on studying thermodynamic properties of our network. We will examine quantities integral to the underlying chemical networks like free energy. We will also utilize tools of classic network thermodynamics to lend more understanding toward the stability and behavior of our model.

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Available for download on Wednesday, December 09, 2020

Included in

Mathematics Commons

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