2 nd International Conference on Multidisciplinary Research & Practice Page | 207 Volume III Issue I IJRSI ISSN 2321-2705 Modeling the Effect of VGCC on Cytosolic Calcium Distribution in Nerve Cells Devanshi D. Dave, Brajesh Kumar Jha Department of Mathematics and Computer Science, School of Technology, Pandit Deendayal Petroleum University Raisan, Gandhinagar-382007, Gujarat, India Abstract— Calcium ion, the second messenger, plays pivotal role in many physiological processes like, contraction, signaling, prolification, etc. [2]. Due to calcium ions, nerve cells are able to move from one cytosole to synapse or other cytosole. A mathematical model is developed in the form of advection- diffusion equation to study the effect of different physiological parameters like diffusion coefficient, potential difference, flux at boundary, etc. Laplace transform is employed to find the solution. Graphical results are obtained with the help of MATLAB. In present study it is observed that the effect of advection on cytosolic calcium distribution is significant at high speed flux. VGCC also make the significant effect on cytosolic calcium concentration to increase the concentration. Keywords— Advection diffusion, VGCC, Laplace transforms, Nerve cell, Similarity transform I. INTRODUCTION athematical model plays an important role in understanding various real world problems in science and engineering. In biology, now a days, investigations are made with the help of mathematical models. Neuroscience, one of them, is an emerging area where calcium dynamics are studied through mathematical models. In our nervous system, many kind of nerve cells are found like neuron, astrocytes (glial cells), myocytes, fibrocytes, etc. Neuron and Glial cells are found in central nervous system (CNS) and rests of the cells are found in peripheral nervous system (PNS) [5]. Nerve impulse moves from one cell to another cell and thus information moves from one part to another part of our body. Movement of the neurotransmitter is due to the free calcium ions 2 [ ] Ca  . As calcium ions enter into the nerve cells, due to the high calcium concentration, the nerve impulse (neurotransmitter) moves towards the synapse with the help of protein. The way how the calcium ions enter into cell is different. Calcium ions are diffused into the cell due to concentration difference. It also moves into the cytosole due to potential difference via various ion channels. Four types of 2 Ca  -permeable voltage channels are found. They are P, N, L, and Q-type channels [1]. In present study L-type voltage gated calcium channel is considered. Free calcium ions enter into cytosole through voltage gated cacium channel and work as a second messenger in electrical signaling, which starts various different inter and intracellular events. In neuron, synaptic transmission is started as 2 Ca  ion enters into the cytosole via voltage gated channels [3,4,6]. In many other cells it regulates enzyme activity, gene expression and other bio-chemical processes [7]. Thus voltage gated calcium channel plays an important role in many cellular processes. Calcium ions also enter via diffusion process into the cytosole. Diffusion is the process in which free calcium ions move from one place (post synapse) to another place (cytosole), in straight direction due to concentration difference. In literature, many authors have studied the calcium distribution in the form of diffusion equation in presence of voltage gated channel [11,13,16,22]. Mathematical models are solved using various analytical and numerical techniques [9-18,21]. Very few efforts have been made to study the calcium distribution in the form of advection diffusion. Jha et.al have studied the effect of buffer, VGCC, and advection on cytosolic calcium distribution in astrocytes [13]. Panday and Pardasani have studied the role of advection diffusion in calcium regulation in oocytes [15]. In this paper we have studied the combined effect of VGCC and advection diffusion on cytosolic calcium distribution in nerve cells like neuron, astrocytes, etc. Shuai Z et.al investigated the possible role of VGCC in 2 Ca  oscillations in astrocytes [22]. A. Mathematical Formulation The concentration profile of 2 Ca  is taken into account in the form of advection-diffusion. It is supposed that due to aqueous medium, coupling between various ions and chemical activity, advection-diffusion of 2 Ca  takes place [12]. Figure 1: Mass transfers in domain [12] Advection is the process in which diffusion takes place in the cross flow direction. Smith et.al have shown the nonlinear advection diffusion in presence of rapid buffers in neuron [19]. The theoretical analysis and interpretation of the advection term is based on the conservation law in differential form. [5,22]. M