Bifurcation and chaotic behaviour of a coupled acetylcholinesterase/choline acetyltransferase diffusion-reaction enzymes system

Abstract A novel model is developed for the investigation of the dynamic and static characteristics of the cholinergic neurocycle. In its simplest form it involves a two-enzymes/two-compartments diffusion–reaction system. The bifurcation, instability and chaotic behaviour of this system are investigated with special emphasis on the neural transmission in human brain. Complex dynamic bifurcations, hysteresis, multiplicity, period doubling and period halving, as well as period adding and period subtracting dominate the dynamics of the system. The behaviour of the system using the acetylcholinestrase enzyme activity as the bifurcation parameter is strongly dominated by hysteresis and multiplicity phenomena, in which the neurotransmitter concentration in the postsynaptic cell changes dramatically for different parameter values. A detailed analysis of this behaviour may give an explanation for the phenomenology associated to Alzheimer disease. This type of work may help to stimulate new research directions on cholinergic brain diseases, such as Alzheimer and Parkinson.