Bhattacharyya Rituparna, Jha Brajesh Kumar
Department of Mathematics, School of Technology, Pandit Deendayal Energy University, Raisan, Gandhinagar, Gujarat, 382426, India.
Cell Biochem Biophys. 2025 Mar;83(1):1071-1086. doi: 10.1007/s12013-024-01541-0. Epub 2024 Oct 7.
Mathematical neuroscience investigates how calcium distribution in nerve cells affects the neurological system. The interaction of numerous systems is necessary for the operation of several cellular processes in neuron cells, such as calcium, buffer, ER etc. The dynamics of interacting parameters give useful information on neural cell function. This work uses a mathematical model to analyze the dynamic interactions of buffer and ER inside neurons, considering their spatial properties. While buffers bind to calcium ions and lower their concentration, the endoplasmic reticulum (ER) serves as a reservoir, holding a significant number of free calcium ions. The uncertainty of initial values of calcium concentration poses challenges for researchers to develop calcium signaling models. In this article, we examined the exact solution and approximate solution of the mathematical model that was analyzed using the fuzzy undetermined coefficient approach. MATLAB is being used to perform the simulation. Endoplasmic reticulum and buffer have been found to have a substantial impact on calcium signaling. Fuzzy differential equation Provides a useful tool for evaluating complicated processes with imprecise values when ordinary differential equations perform not precisely. They allow for the examination of dynamic processes under fuzzy settings, which contributes to advances research.
数学神经科学研究神经细胞中钙的分布如何影响神经系统。神经元细胞中多种细胞过程的运作需要众多系统的相互作用，比如钙、缓冲液、内质网等。相互作用参数的动态变化为神经细胞功能提供了有用信息。这项工作使用一个数学模型来分析神经元内部缓冲液和内质网的动态相互作用，并考虑它们的空间特性。缓冲液与钙离子结合并降低其浓度，而内质网则作为一个储存库，容纳大量游离钙离子。钙浓度初始值的不确定性给研究人员开发钙信号模型带来了挑战。在本文中，我们研究了使用模糊待定系数法分析的数学模型的精确解和近似解。我们正在使用MATLAB进行模拟。已发现内质网和缓冲液对钙信号有重大影响。当常微分方程处理不够精确时，模糊微分方程为评估具有不精确值的复杂过程提供了一个有用工具。它们允许在模糊环境下研究动态过程，这有助于推进研究。
