Stability analysis of the ODE model representation of Amyloidogenic processing in Alzheimer's disease in the presence of SORLA
Date of Publication
Master of Science in Mathematics
College of Science
Mathematics and Statistics Department
Leonor Aquino Ruivivar
Defense Panel Member
Jose Tristan Reyes
Derick Erl Sumalapao
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.
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Alcantara, J. (2015). Stability analysis of the ODE model representation of Amyloidogenic processing in Alzheimer's disease in the presence of SORLA. Retrieved from https://animorepository.dlsu.edu.ph/etd_masteral/4814