https://doi.org/10.1140/epjp/s13360-024-05206-y
Regular Article
Simulation of nonlinear system dynamics of calcium and dopamine signaling in neurons
Department of Mathematics, Bioinformatics, and Computer Applications, Maulana Azad National Institute of Technology, 462003, Bhopal, Madhya Pradesh, India
Received:
27
March
2024
Accepted:
23
April
2024
Published online:
6
May
2024
The study of calcium ([Ca2+]) and dopamine (DA) as independent signaling systems generated limited information on each of these complex adaptive systems. Recently, an integer-order model of these two complex adaptive systems gave better insights into different regulatory mechanisms. However, these integer-order systems cannot generate information regarding the superdiffusion and memory with Brownian motion (BM) mechanisms. Also, the superdiffusion and memory triggering BM of [Ca2+] and dopamine signaling have not been investigated so far in neurons. Here, a fractional-order mathematical framework is proposed to investigate the nonlinear spatiotemporal interactive and adaptive system dynamics of [Ca2+] and dopamine in neurons. The fractional reaction–diffusion equations for [Ca2+] and dopamine with one-way feedback are incorporated in the present framework. The Crank–Nicholson (CN) procedure along with the Grunwald estimation concerning spatial derivatives and the L1 formula concerning temporal derivatives with Gauss–Seidel (GS) iterations have been utilized for numerical simulation. The novel information on the functioning of different mechanisms of [Ca2+] and DA in neurons due to the memory effects causing BM and superdiffusion has been obtained from numerical results. The proposed simulation approach is quite effective in generating the conditions causing the alterations in [Ca2+] and dopamine levels, which may result in neurological illnesses like Parkinson’s disease (PD), etc.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
