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Simulation of nonlinear system dynamics of calcium and dopamine signaling in neurons

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Abstract

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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  1. Department of Mathematics, Bioinformatics, and Computer Applications, Maulana Azad National Institute of Technology, Bhopal, Madhya Pradesh, 462003, India

    Anand Pawar & Kamal Raj Pardasani

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Authors have made equitable contributions to the present work concerning problem design and solution, data correction, literature examination, as well as interpretation of the results. Author (1) created the MATLAB code.

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Correspondence to Anand Pawar.

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Pawar, A., Pardasani, K.R. Simulation of nonlinear system dynamics of calcium and dopamine signaling in neurons. Eur. Phys. J. Plus 139, 390 (2024). https://doi.org/10.1140/epjp/s13360-024-05206-y

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