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Calcium signaling in nerve cells is a crucial activity for the human brain to execute a diversity of its functions. An alteration in the signaling process leads to cell death. To date, several attempts registered to study the calcium distribution in nerve cells like neurons, astrocytes, etc. in the form of the integer-order model. In this paper, a fractional-order mathematical model to study the spatiotemporal profile of calcium in nerve cells is assembled and analyzed. The proposed model is solved by the finite element method for space derivative and finite difference method for time derivative. The classical case of the calcium dynamics model is recovered by setting the fractional parameter and that validates the model for classical sense. The numerical computations have systematically presented the impact of a fractional parameter on nerve cells. It is observed that calbindin-D28k provides a significant effect on the spatiotemporal variation of calcium profile due to the amalgamation of the memory of nerve cells. The presence of excess amounts of calbindin-D28k controls the intracellular calcium level and prevents the nerve cell from toxicity. [ABSTRACT FROM AUTHOR]

The maintenance of free calcium in the cytoplasm is requisite for cell integrity and the regime of the multi-cellular process. Overproduction and degradation to manage this cellular entity produce offensive changes in tissue performance and as a result, commence fibrotic diseases. Thus, there is a necessity to know the cellular process for the inclusion and extrusion of free calcium. Here, a mathematical model is framed to investigate the role of buffer and calcium concentration on fibroblast cells. In this context, the Caputo-Fabrizio advection reaction-diffusion model along with apposite biophysical initial and boundary conditions is considered. The analytical solution is obtained and used to analyze the diverse mechanisms of calcium on fibroblast cells. The obtained results reveal that when the fractional order goes to one, the Caputo-Fabrizio fractional derivative provides a concise calcium profile and well-managed cellular entity due to the exponential kernel law. [ABSTRACT FROM AUTHOR]

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 2 8 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 2 8 k . In the present paper, the neuroprotective role of calbindin- D 2 8 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 2 8 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. [ABSTRACT FROM AUTHOR]