A Fractional Mathematical Model to Study the Effect of Buffer on Calcium Distribution in Parkinson's Disease

Calcium (Ca2+) is a vital and very important cation for proper functioning of the nerve cells. There is abundant amount of Ca2+ in human nerve cells among them very few amount lies in the cytosol in the form of free Ca2+. These free amounts of Ca2+ react with calbindin-D28k which works as buffer species and significantly lower down the intracellular Ca2+ concentration. Parkinson's disease is a brain disorder of the human nerve cells associated with alteration in Ca2+ signalling process. In present study an attempt has been made by considering fractional advection diffusion equation to study the effect of buffer on Ca2+ diffusion in Parkinsonic nerve cells. An appropriate initial and boundary condition is taken according to the physiology of the problem. Analytical solution is obtained corresponding to time fractional advection diffusion equation and space fractional advection diffusion equation. The obtained results are simulated in MATLAB and interpreted with the Ca2+ distribution in nerve cells.