NONLINEAR SYSTEM DYNAMICS OF CALCIUM AND NITRIC OXIDE DUE TO CELL MEMORY AND SUPERDIFFUSION IN NEURONS

The integer-order interdependent calcium ([Ca2+]) and nitric oxide (NO) systems are unable to shed light on the influences of the superdiffusion and memory in triggering Brownian motion (BM) in neurons. Therefore, a mathematical model is constructed for the fractional-order nonlinear spatiotemporal systems of [Ca2+] and NO incorporating reaction-diffusion equations in neurons. The two-way feedback process between [Ca2+] and NO systems through calcium feedback on NO production and NO feedback on calcium through cyclic guanosine monophosphate (cGMP) with plasmalemmal [Ca2+]-ATPase (PMCA) was incorporated in the model. The Crank-Nicholson scheme (CNS) with Grunwald approximation along spatial derivatives and L1 scheme along temporal derivatives with Gauss-Seidel (GS) iterations were employed. The numerical outcomes were analyzed to get insights into superdiffusion, buffer, and memory exhibiting BM of [Ca2+] and NO systems. The conditions, events and mechanisms leading to dysfunctions in calcium and NO systems and causing different diseases like Parkinson’s were explored in neurons.