Diffusion-Reaction Modeling, Nonlinear Dynamics, Feedback, Bifurcation and Chaotic Behavior

The disturbances and abnormalities occurring in the components of the Acetylcholine (ACh) neurocycle are considered one of the main features of cholinergic sicknesses like Parkinson's and Alzheimer's diseases. A fundamental understanding of the ACh neurocycle is therefore very critical in order to design drugs that keep the ACh concentrations in the normal physiological range. In this dissertation, a novel two-enzyme-two-compartment model is proposed in order to explore the bifurcation, dynamics, and chaotic characteristics of the ACh neurocycle. The model takes into consideration the physiological events of the choline uptake into the presynaptic neuron and the ACh release in the postsynaptic neuron. In order to approach more realistic behavior, two complete kinetic mechanisms for enzymatic processes pH-dependent are built: the first mechanism is for the hydrolysis reaction catalyzed by the acetylcholinesterase (AChE) and the other is for the synthesis reaction catalyzed by the cholineacetyltransferase (ChAT).