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Fractional-order mathematical model for calcium distribution in nerve cells. (English) Zbl 1449.35443

Summary: Calcium (Ca\(^{2+})\) ions are known as a second messenger, involved in a variety of signalling process. It regulates various physiological processes like signal transduction, proliferation, etc. Calbindin-D\(_{28k}\) reacts with free Ca\(^{2+}\) ions and significantly lowers down the cytosolic free calcium concentration ([Ca\(^{2+}])\) in nerve cell. Voltage-gated calcium channel (VGCC) works as an outward source of Ca\(^{2+}\) which initiates and sustains Ca\(^{2+}\) signalling process for the smooth functioning of the cells. An alteration in Ca\(^{2+}\) signalling process leads to the early symptoms of Parkinson’s disease (PD). In this piece of work two major analyses has done. First, we have developed a mathematical model in the form of a fractional reaction-diffusion equation. Second, the obtained results are interpreted with a neuronal disorder, i.e., PD. Hence the physiological role of calbindin-D\(_{28k}\) and VGCC in PD is analyze using mathematical model by incorporating all important parameters like diffusion coefficient, fluxes, etc. Appropriate initial and boundary conditions are used according to the biophysical conditions of the cell.

MSC:

35R11 Fractional partial differential equations
92B05 General biology and biomathematics
97M10 Modeling and interdisciplinarity (aspects of mathematics education)
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