Modeling Periodic and Aperiodic Behavior of Acetylcholine Hydrolysis

A two compartments model with the acetylcholinesterase activity localized in one compartment only has been used to investigate the periodic and aperiodic behavior of acetylcholine hydrolysis process. The investigation based on a well established kinetic scheme and kinetic data. The model has accounts for the effects of hydrogen ions concentrations on the kinetics and its role in creating membrane potential assuming no other charged ions are exist. Both autonomous and non-autonomous cases are investigated considering the two common mechanisms of applying acetylcholine in practical physiological situations (constant and quantal). The investigation uncovered a wealth of static and dynamic bifurcations of the system including multiplicity of steady states, isola, periodic and aperiodic behavior. The periodic and aperiodic behavior characterized by different patterns of spikes. Two spikes per cycle in membrane potential is the dominating pattern all over most of the considered range. Changing the feeding mechanism of acetylcholine from constant steady feeding to constant quantal feeding causes dramatic changes in the dynamic behavior of the system. This is an element of establishing a complete descriptive model for the neurocycle acetylcholinestrase/choline acetyltransferas biosystem