Research ArticleNo Access

Fractionally delineate the neuroprotective function of calbindin- $D_{28 k}$ $D_{28 k}$ in Parkinson’s disease

http://orcid.org/0000-0003-2014-3765

Department of Mathematics, School of Technology, Pandit Deendayal Petroleum University, Gandhinagar, Gujarat 382007, India

E-mail Address: hardik.joshi8185@gmail.com

Corresponding author.

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Brajesh Kumar Jha

Department of Mathematics, School of Technology, Pandit Deendayal Petroleum University, Gandhinagar, Gujarat 382007, India

E-mail Address: brajeshjha2881@gmail.com

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https://doi.org/10.1142/S1793524518501036Cited by:19 (Source: Crossref)

Abstract

Neuron is a fundamental unit of the brain, which is specialized to transmit information throughout the body through electrical and chemical signals. Calcium ( ${Ca}^{2 +}$ ) ions are known as second messengers which play important roles in the movement of the neurotransmitter. Calbindin- $D_{28 k}$ is a ${Ca}^{2 +}$ binding protein which is involved in regulation of intracellular ${Ca}^{2 +}$ ions and maintains ${Ca}^{2 +}$ homeostasis level, it also alters the cytosolic calcium concentration ([ ${Ca}^{2 +}$ ]) in nerve cells to keep the cell alive. Parkinson’s disease (PD) is a chronic progressive neurodegenerative brain disorder of the nervous system. Several regions of the brain indicate the hallmark of the PD. The symptoms of PD are plainly linked with the degeneration and death of dopamine neurons in the substantia nigra pars compacta located in midbrain which is accompanied by depletion in calbindin- $D_{28 k}$ . In the present paper, the neuroprotective role of calbindin- $D_{28 k}$ in the cytoplasmic [ ${Ca}^{2 +}$ ] distribution is studied. The elicitation in [ ${Ca}^{2 +}$ ] is due to the presence of low amount of calbindin- $D_{28 k}$ which can be portrayed and is a hallmark of PD. A one-dimensional space time fractional reaction diffusion equation is designed by keeping in mind the physiological condition taking place inside Parkinson’s brain. Computational results are performed in MATLAB.

Keywords:

AMSC: 92B05, 26A33, 35R11, 35Q92, 97M10, 62P10

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