Changes in cellular Ca[Formula: see text] concentration control a variety of physiological activities including hormone and neurotransmitter release, muscular contraction, synaptic plasticity, ionic channel permeability, apoptosis, enzyme activity, gene transcription and reproduction process. Spatial–temporal Ca[Formula: see text] dynamics due to Ca[Formula: see text] release, buffering and re-uptaking plays a central role in studying the Ca[Formula: see text] regulation in T lymphocytes. In most cases, Ca[Formula: see text] has its major signaling function when it is elevated in the cytosolic compartment. In this paper, a two-dimensional mathematical model to study spatiotemporal variations of intracellular Ca[Formula: see text] concentration in T lymphocyte cell is proposed and investigated. The cell is assumed to be a circular shaped geometrical domain for the representation of properties of Ca[Formula: see text] dynamics within the cell including important parameters. Ca[Formula: see text] binding proteins for the dynamics of Ca[Formula: see text] are itself buffer and other physiological parameters located in Ca[Formula: see text] stores. The model incorporates the important biophysical processes like diffusion, reaction, voltage-gated Ca[Formula: see text] channel, leak from endoplasmic reticulum (ER), efflux from cytosol to ER via sarco–ER Ca[Formula: see text] adenosine triphosphate (SERCA) pumps, buffers and Na[Formula: see text] exchanger. The proposed mathematical model is solved using a finite difference method and the finite element method. Appropriate initial and boundary conditions are incorporated in the model based on biophysical conditions of the problem. Computer simulations in MATLAB R2019b are employed to investigate mathematical models of reaction–diffusion equation. The effect of source, buffer, Na[Formula: see text]/Ca[Formula: see text] exchanger, etc. on spatial and temporal patterns of Ca[Formula: see text] in T lymphocyte has been studied with the help of numerical results. From the obtained results, it is observed that, the coordinated combination of the incorporated parameters plays a significant role in Ca[Formula: see text] regulation in T lymphocytes. ER leak and voltage-gated Ca[Formula: see text] channel provides the necessary Ca[Formula: see text] to the cell when required for its proper functioning, while on the other side buffers, SERCA pump and Na[Formula: see text]/Ca[Formula: see text] exchanger makes balance in the Ca[Formula: see text] concentration, so as to prevent the cell from death as higher concentration for longer time is harmful for the cell and can cause cell death.

中文翻译：

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模拟 T 淋巴细胞中钙调节的机制：一种有限元方法

细胞内Ca的变化[公式：见正文]浓度控制多种生理活动，包括激素和神经递质释放、肌肉收缩、突触可塑性、离子通道通透性、细胞凋亡、酶活性、基因转录和繁殖过程。由于 Ca[公式：参见文本] 的释放、缓冲和再摄取导致的时空 Ca[公式：参见文本] 动力学在研究 T 淋巴细胞中的 Ca[公式：参见文本] 调节中起着核心作用。在大多数情况下，Ca[公式：见正文]在细胞溶质隔室中升高时具有其主要的信号传导功能。本文提出并研究了一个二维数学模型来研究T淋巴细胞中细胞内Ca[公式：见正文]浓度的时空变化。假设细胞是一个圆形几何域，用于表示细胞内 Ca[公式：见文本] 动力学的特性，包括重要参数。Ca[公式：见正文] Ca[公式：见正文] 动力学的结合蛋白本身是缓冲液，其他生理参数位于 Ca[公式：见正文] 存储中。该模型包含重要的生物物理过程，如扩散、反应、电压门控 Ca[公式：见正文] 通道、内质网 (ER) 泄漏、通过 sarco-ER Ca[公式：见正文] 三磷酸腺苷从胞质溶胶流出到 ER (SERCA) 泵、缓冲剂和 Na[公式：见正文] 交换器。使用有限差分法和有限元法求解所提出的数学模型。基于问题的生物物理条件，在模型中加入了适当的初始条件和边界条件。MATLAB R2019b 中的计算机模拟用于研究反应扩散方程的数学模型。借助数值方法研究了来源、缓冲液、Na[公式：见正文]/Ca[公式：见正文]交换剂等对T淋巴细胞中Ca[公式：见正文]的时空格局的影响。结果。从获得的结果可以看出，整合参数的协调组合在T淋巴细胞的Ca[公式：见正文]调节中起重要作用。ER 泄漏和电压门控 Ca[公式：见正文] 通道在需要时为细胞提供必要的 Ca[公式：见正文] 以使其正常运行，而在另一侧缓冲 SERCA 泵和 Na [公式：