ORIGINAL RESEARCH ARTICLE Portraying the Effect of Calcium-Binding Proteins on Cytosolic Calcium Concentration Distribution Fractionally in Nerve Cells Brajesh Kumar Jha 1 • Hardik Joshi 2 • Devanshi D. Dave 1 Received: 22 June 2016 / Revised: 2 October 2016 / Accepted: 8 November 2016 Ó International Association of Scientists in the Interdisciplinary Areas and Springer-Verlag Berlin Heidelberg 2016 Abstract 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 cal- cium-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 dis- tribution results in the cell death which finally give neu- rodegenerative disease to the mammalian brain. The present paper gives a glimpse of Parkinson’s diseases in particular. Computational results are performed in Wol- fram 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(b-aminoethyl ether)-N,N,N 0 ,N 0 -te- traacetic acid, 1,2-bis(o-aminophenoxy)ethane-N,N,N 0 ,N 0 - tetraacetic acid and calmodulin have noteworthy effect at different fractions of time. Keywords Buffers  Nerve cells  Parkinson’s disease (PD)  Fractional approach 1 Introduction Computational neuroscience is an up-and-coming area in the field of mathematical modeling. The models depicting the physiological processes of complexed biology help one and all in knowing the effects, outcomes, drawbacks, etc., of the processes taking place in situ. One of the remarkable processes of neuroscience is the calcium signaling in ner- vous system. Nervous systems can be called as neuron-glial systems. Nerve cells in CNS and peripheral nervous system (PNS) include neurons, astrocytes, fibrocytes, myocytes, oocytes. [1]. The calcium signaling in each one of them has a peculiar effect physiologically. The signaling has a note- worthy effect in presence of internal and external parame- ters like buffer VGCC [2]. In this study, the calcium signaling is studied analytically using fractional approach in presence of excess buffers like EGTA, BAPTA and calmodulin. Calcium signals are often faster in smaller cells and depend highly on type and capacity of calcium-binding proteins. This effect is a function of both Ca 2þ affinity and amount of buffers. It is a class of cytoplasmic Ca 2þ binding proteins affecting both the temporal and spatial aspects of this transient increase in calcium concentration [3]. Astro- cytes are the most ubiquitous type of glial cells present in the nervous system of mammalian brain. They work as the supporting system to the neuronal populations. Astrocytes & Hardik Joshi hardik.joshi8185@gmail.com Brajesh Kumar Jha brajeshjha2881@gmail.com Devanshi D. Dave ddave1822@gmail.com 1 Department of Mathematics and Computer Science, School of Technology, Pandit Deendayal Petroleum University, Gandhinagar, India 2 L.J. Institute of Engineering & Technology, Gujarat Technological University, Ahmedabad, Gujarat 382210, India 123 Interdiscip Sci Comput Life Sci DOI 10.1007/s12539-016-0202-7