Nerve cells like neurons and astrocytes in central nervous system (CNS) take part in the signaling process which means the transformation of the information from one cell to another via signals. The signaling process is affected by various external parameters like buffers calcium-binding proteins, voltage-gated calcium channel. In the present paper, the role of buffers in the cytoplasmic calcium concentration distribution is shown. The elicitation in calcium concentration is due to the presence of lower amount calcium-binding proteins which can be shown graphically. The mathematical model is designed by keeping in mind the physiological condition taking place in CNS of mammalian brain. The thing to be noted here is that the more elicitation in the calcium concentration distribution results in the cell death which finally give neurodegenerative disease to the mammalian brain. The present paper gives a glimpse of Parkinson's diseases in particular. Computational results are performed in Wolfram Mathematica 9.0 and simulated on core(TM) i5-3210M CPU @ 2.50 GHz processing speed and 4 GB memory. It is found that the different types of buffer like ethylene glycol-bis([Formula: see text]-aminoethyl ether)-N,N,N',N'-tetraacetic acid, 1,2-bis(o-aminophenoxy)ethane-N,N,N',N'-tetraacetic acid and calmodulin have noteworthy effect at different fractions of time.

The present paper focuses on the solution of the three-dimensional calcium advection-diffusion equation in the presence of calcium-binding buffers. As buffers play an important role in maintaining cytosolic calcium concentration level, decrease in buffers leads to increase in cytoplasmic calcium which may further lead to toxicity of Alzheimer's disease. The governing three-dimensional differential equation has been further converted into one-dimensional equation using similarity transforms. The solution is obtained analytically using Laplace transforms and suitable boundary conditions. The obtained solution is simulated in MATLAB. The graphs clearly show the impact of buffers on calcium concentration level for normal and Alzheimeric cells.

No abstract

Under the widespread umbrella of dementia, Alzheimer’s disease is the most common form of dementia. Most of the aged people are suffering from Alzheimer’s disease around the world. The reasons for the same are not known in detail and thus various experimental and computational attempts need to be carried out. Calcium, being a second messenger has an immense role in transformation of information. This transformation takes place in the form of signaling in which several parameters play an active role. In present work, an attempt has been made to describe the effect of calcium signaling in nerve cells for Alzheimer’s disease. Here, parameters like advection diffusion and buffering are taken into consideration to visualize the effects of the same on cytosolic calcium concentration. This physiological process is modeled two dimensionally and solved analytically. Laplace and similarity transforms are employed to obtain the desired results. The results are simulated and graphically plotted using MATLAB. The known fact that the higher concentration of calcium has adverse effects on the cell which may result into progression of AD is considered as a lantern in enlightening the physiology of Alzheimer’s disease.

No abstract