Mathematical Modeling of Calcium Oscillatory Patterns in a Neuron

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ORIGINAL RESEARCH ARTICLE

Mathematical Modeling of Calcium Oscillatory Patterns in a Neuron Devanshi D. Dave1   · Brajesh Kumar Jha1 Received: 15 May 2020 / Revised: 21 October 2020 / Accepted: 24 October 2020 © International Association of Scientists in the Interdisciplinary Areas 2020

Abstract  Calcium oscillations are an imperative mode of signaling phenomenon. These oscillations are due to the active interactions taking place between some of the parameters like voltage gated calcium channels (VGCC), sodium calcium exchanger (NCX), calcium binding buffers, endoplasmic reticulum (ER) and mitochondria. The present paper focuses on the problem of higher level of calcium concentration in neurons which may further result into Alzheimer’s Disease (AD). For this, a three-dimensional mathematical model having a system of differential equations depicting the changes in cytosolic calcium (in presence of buffers, VGCC and NCX), ER calcium and mitochondrial calcium, is formulated. A three-dimensional neuronal structure is targeted as the domain which is further discussed and solved using finite element technique in Comsol Multiphysics 5.4. Apposite boundary conditions matching well with the in-situ conditions are assumed. The obtained results clearly show the significance of the lower amount of the buffer and higher calcium mediated activities of VGCC, NCX, ER and mitochondria on calcium profile. These changes may lead to AD. To transit from AD condition to normal, exogenous buffers are added to check their significance. The results thus show that the replenishment of buffer may balance the amount of cell calcium and hence can affect positively on Alzheimer’s affected cells. Graphic abstract

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Interdisciplinary Sciences: Computational Life Sciences

Keywords  Calcium oscillations · Neurons · Alzheimer’s Disease · 3D Finite element analysis

1 Introduction Being a second messenger, calcium plays diversified roles in numerous signaling pathways, thus regulating many cellular functions, gene expression, synaptogenesis, cell differentiation and several fundamental phenomena underlying learning and memory [20]. The spatiotemporal calcium signals are modified and modulated by more than a few mechanisms like calcium extrusion, calcium buffering and sequestration of calcium via internal cellular compartments. These signals arise and start by a passive entry of calcium through several calcium dependent channels like VGCC [2]. Subsequently, calcium is diffused into the cell cytoplasm where it reacts with the calcium binding buffers present at the cell’s periphery. The free calcium is then sequestered at other cellular entities. These free calcium ions move in an oscillatory pattern and further these oscillations are modified due to the calcium interactions taking place between cytosol and endoplasmic reticulum (ER) [3]. Over and above this, mitochondria also play an active role in sequestering the calcium ions and thus affecting and modu

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