Complex bifurcation/chaotic behavior of acetylcholinesterase and cholineacetyltransferase enzymes system

• Published in: Applied mathematical modelling 2006-09, Vol.30 (9), p.824-853
• Main Authors: Garhyan, Parag, Mahecha-Botero, Andrés, Elnashaie, S.S.E.H.
• Format: Article
• Language: English
• Subjects: Acetylcholine; Acetylcholinesterase; Alzheimer’s disease; Bifurcation; Biological and medical sciences; Central nervous system; Chaos; Cholineacetyltransferase; Exact sciences and technology; Fundamental and applied biological sciences. Psychology; Parkinson’s disease; Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Transport processes; Vertebrates: nervous system and sense organs
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2005.06.009

This investigation utilizes available biokinetic information for the formulation of a diffusion-reaction model in order to simulate the in vivo behavior of acetylcholinesterase (AChE) and cholineacetyltransferase (ChAT) coupled enzymes system. A novel two-enzymes/two-compartments model is used to explore the bifurcation and chaotic behavior of this enzyme system simulating the acetylcholine neurocycle in the brain. Detailed bifurcation analysis over a wide range of parameters is carried out in order to uncover some important information about this system. The results of this investigation relate to the phenomena occurring in the physiological experiments, like periodic stimulation of neural cells and non-regular functioning of acetylcholine receptors. These results can be used to direct more systematic research on cholinergic brain diseases like Alzheimer’s and Parkinson’s diseases as there are strong evidences that these brain disorders are related to concentration of acetylcholine (ACh) in the brain.