Stability analysis of the ODE model representation of Amyloidogenic processing in Alzheimer's disease in the presence of SORLA

Date of Publication

2015

Document Type

Master's Thesis

Degree Name

Master of Science in Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Leonor Aquino Ruivivar

Defense Panel Member

Polly Sy
Angelyn Lao
Jose Tristan Reyes
Derick Erl Sumalapao

Abstract/Summary

Central to the pathology of Alzheimer's Disease (AD) is the proteolytic processing of amyloid precursor protein (APP) into amyloid plaques. SORLA (sorting protein-related receptor with A-type repeats) has a major in influence in such process as it alters the form of the substrate APP that is preferred by the enzymes and secretases, therefore inhibiting the amyloidogenic processing. This paper analyzed the temporal behavior of the solutions of the system of 20 ordinary differential equations (ODE) that models the biochemical system describing APP processing under the influence of SORLA, by performing a stability analysis of the ODE model.

The number of equations in the model was reduced to 9 by considering only the coupled equations in the system and by imposing initial conditions on the system. Only one biochemically meaningful equilibrium point was computed. By means of linearization, Hartman-Grobman Theorem, and Routh- Hurwitz Test, it was shown that is a locally asymptotically stable equilibrium point. The region of attraction of was approximated by using the Fluctuation Lemma. Immediate consequence of the stability analysis of the reduced system to the temporal behavior of the solutions of the original system was also obtained.

Abstract Format

html

Language

English

Format

Electronic

Accession Number

CDTG005918

Shelf Location

Archives, The Learning Commons, 12F Henry Sy Sr. Hall

Physical Description

1 disc ; 4 3/4 inches

Keywords

Alzheimer's disease

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