Computational model of interacting system dynamics of calcium, IP<sub>3</sub> and <i>β</i>-amyloid in ischemic neuron cells
Anand Pawar, Kamal Raj Pardasani
Abstract
Abstract The study of single independent dynamics of calcium ([Ca 2+ ]), IP 3 , and β -amyloid (A β ) in neurons provide limited information. Some attempts are reported for the dynamics of two interacting systems of [Ca 2+ ] and IP 3 , and calcium and A β , which gave some novel insights about the phenomena. However, the interactions of these three systems have not been analyzed till date in neurons. Therefore, a novel model is constructed to study the interactions of the spatiotemporal systems of [Ca 2+ ], IP 3 , and A β in neurons. A two-way feedback mechanism between [Ca 2+ ] and IP 3 , and [Ca 2+ ] and A β has been incorporated into the model. The model is formulated by coupling three reaction-diffusion equations of [Ca 2+ ], IP 3 and A β , respectively. This coupling automatically takes care of the indirect two-way feedback process between IP 3 and β -amyloid in neuron cells. The finite element method (FEM) with the Crank-Nicolson scheme (CNS) is utilized to study the contribution of various ER-associated processes like RyR, IP 3 R, SERCA pump, buffer approximation, etc on the neuronal interactions of [Ca 2+ ], IP 3 , and β -amyloid during Ischemia. The numerical findings provide novel insights into alterations in ER handling during Ischemia, resulting in disturbances in the neuronal calcium, IP 3 , and A β levels, which may cause the advancement of Alzheimer’s illness and be responsible for neurotoxicity and cell death.