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

中文翻译：

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神经元中钙振荡模式的数学建模

摘要

钙振荡是信号现象的必要模式。这些振荡是由于一些参数之间发生的积极相互作用，如电压门控钙通道 (VGCC)、钠钙交换器 (NCX)、钙结合缓冲液、内质网 (ER) 和线粒体。本论文重点关注神经元中钙浓度较高的问题，这可能会进一步导致阿尔茨海默病 (AD)。为此，制定了一个三维数学模型，该模型具有描述细胞溶质钙（存在缓冲液、VGCC 和 NCX）、ER 钙和线粒体钙的变化的微分方程系统。以三维神经元结构为目标域，在 Comsol Multiphysics 5.4 中使用有限元技术进一步讨论和求解该域。假设适当的边界条件与原位条件匹配良好。获得的结果清楚地显示了较低量的缓冲液和较高的钙介导的 VGCC、NCX、ER 和线粒体对钙谱的重要性。这些变化可能会导致 AD。为了从 AD 状态过渡到正常状态，添加外源缓冲液以检查其重要性。因此，结果表明缓冲液的补充可以平衡细胞钙的量，因此可以对阿尔茨海默氏症受影响的细胞产生积极影响。为了从 AD 状态过渡到正常状态，添加外源缓冲液以检查其重要性。因此，结果表明缓冲液的补充可以平衡细胞钙的量，因此可以对阿尔茨海默氏症受影响的细胞产生积极影响。为了从 AD 状态过渡到正常状态，添加外源缓冲液以检查其重要性。因此，结果表明缓冲液的补充可以平衡细胞钙的量，因此可以对阿尔茨海默氏症受影响的细胞产生积极影响。

图形摘要