Deciphering two-dimensional calcium fractional diffusion of membrane flux in neuron

Calcium is a decisive messenger for neuronal vivid functions. The calcium intracellular sequestering major unit is the Endoplasmic Reticulum (ER). Brownian motion of calcium could be bound to different buffers like S100B, calmodulin, etc, and different organelles. Plasma membrane channels like volta...

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Bibliographic Details
Published inJournal of applied mathematics & computing Vol. 70; no. 5; pp. 4133 - 4156
Main Authors Vatsal, Vora Hardagna, Jha, Brajesh Kumar, Singh, Tajinder Pal
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2024
Subjects
Computational Mathematics and Numerical Analysis
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Original Research
Theory of Computation
Buffer
Calcium distribution
92C20
Neuron
35R11
35A22
ER fluxes
Laplace transforms
35K57
Fractional derivative
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Summary:Calcium is a decisive messenger for neuronal vivid functions. The calcium intracellular sequestering major unit is the Endoplasmic Reticulum (ER). Brownian motion of calcium could be bound to different buffers like S100B, calmodulin, etc, and different organelles. Plasma membrane channels like voltage-gated calcium channels (VGCC) and Plasma Membrane Calcium ATPase (PMCA), Orai channel could perturb the calcium concentration. To investigate the calcium interplay for intracellular signaling we have developed the two-dimensional time fractional reaction–diffusion equation. To solve this model analytically, we have used the Laplace and Fourier cosine integral transform method. By using Green’s function we obtained the compact solution in closed form with Mainardi’s function and Wright’s function. Uniqueness and existence proved the more fundamental approach to the fractional reaction–diffusion problem. The fractional Caputo approach gives better insight into this real-life problem by its nonlocal nature. Significant effects of different parameters on free calcium ions were obtained and the results are interpreted with normal and Alzheimeric cells. Non-local property and dynamical aspects are graphically presented which might provide insight into the Stromal interaction molecule (STIM) and S100B parameters.
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-024-02115-2