Non-linear feedback modeling and bifurcation of the acetylcholine neurocycle and its relation to Alzheimer's and Parkinson's diseases

Abstract

A novel two-enzyme-two-compartment model is proposed in order to explore the bifurcation, dynamics, and chaotic characteristics of the acetylcholine neurocycle. The model takes into consideration the physiological events of the choline uptake into the presynaptic neuron and choline release in the postsynaptic neuron. The effects of hydrogen ion feed concentrations, acetylcholinesterase (AChE) activity, and acetylcholine (ACh) feed concentrations, as bifurcation parameters, on the system performance are studied. It is found that hydrogen ions play an important role, where they create potential differences through the plasma membranes. The concentrations of ACh, choline and acetate were affected to be affected by the activity of acetylcholinesterase (AChE) through a certain range of their concentrations, where the activity of AChE was inhibited completely after reaching certain values. A detailed bifurcation analysis over a wide range of parameters is carried out in order to uncover some important features of the system, such as hysteresis, multiplicity, Hopf bifurcation, period doubling, chaotic characteristics, and other complex dynamics. These findings are related to the real phenomena occurring in the neurons, like periodic stimulation of neural cells and non-regular functioning of acetylcholine receptors. The results of this model are compared to the results of physiological experiments and other published models. As there is strong evidence that cholinergic brain diseases like Alzheimer's disease and Parkinson's disease are related to the concentration of acetylcholine (ACh), the present findings are useful for uncovering some of the characteristics of these diseases and encouraging more physiological research.