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Computational and Mathematical Methods in Medicine
Volume 2015, Article ID 923762, 20 pages
http://dx.doi.org/10.1155/2015/923762
Research Article

Modeling the Interaction between β-Amyloid Aggregates and Choline Acetyltransferase Activity and Its Relation with Cholinergic Dysfunction through Two-Enzyme/Two-Compartment Model

1Department of Mathematics and Statistics, University of Guelph, Guelph, ON, Canada N1G 2W1
2Biomedical Engineering Department, Faculty of Engineering at Helwan, Helwan University, Helwan, Cairo 11792, Egypt
3Chemical Engineering Department, University of Waterloo, Waterloo, ON, Canada N2L 3G1

Received 25 March 2015; Accepted 14 July 2015

Academic Editor: David A. Winkler

Copyright © 2015 Hedia Fgaier et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The effect of β-amyloid aggregates on activity of choline acetyltransferase (ChAT) which is responsible for synthesizing acetylcholine (ACh) in human brain is investigated through the two-enzyme/two-compartment (2E2C) model where the presynaptic neuron is considered as compartment 1 while both the synaptic cleft and the postsynaptic neuron are considered as compartment 2 through suggesting three different kinetic mechanisms for the inhibition effect. It is found that the incorporation of ChAT inhibition by β-amyloid aggregates into the 2E2C model is able to yield dynamic solutions for concentrations of generated β-amyloid, ACh, choline, acetate, and pH in addition to the rates of ACh synthesis and ACh hydrolysis in compartments 1 and 2. It is observed that ChAT activity needs a high concentration of β-amyloid aggregates production rate. It is found that ChAT activity is reduced significantly when neurons are exposed to high levels of β-amyloid aggregates leading to reduction in levels of ACh which is one of the most significant physiological symptoms of AD. Furthermore, the system of ACh neurocycle is dominated by the oscillatory behavior when ChAT enzyme is completely inhibited by β-amyloid. It is observed that the direct inactivation of ChAT by β-amyloid aggregates may be a probable mechanism contributing to the development of AD.