Neuronal calcium signals propagating by simple diffusion and reaction with mobile and stationary buffers are limited to cellular microdomains. The distance intracellular calcium signals can travel may be significantly increased by means of calcium-induced calcium release from internal calcium stores, notably the endoplasmic reticulum. The organelle, which can be thought of as a cell-within-a-cell, is able to sequester large amounts of cytosolic calcium ions via SERCA pumps and selectively release them into the cytosol through ryanodine receptor channels leading to the formation of calcium waves. In this study, we set out to investigate the basic properties of such dendritic calcium waves and how they depend on the three parameters dendrite radius, ER radius and ryanodine receptor density in the endoplasmic membrane. We demonstrate that there are stable and abortive regimes for calcium waves, depending on the above morphological and physiological parameters. In stable regimes, calcium waves can travel across long dendritic distances, similar to electrical action potentials. We further observe that abortive regimes exist, which could be relevant for spike-timing dependent plasticity, as travel distances and wave velocities vary with changing intracellular architecture. For some of these regimes, analytic functions could be derived that fit the simulation data. In parameter spaces, that are non-trivially influenced by the three-dimensional calcium concentration profile, we were not able to derive such a functional description, demonstrating the mathematical requirement to model and simulate biochemical signaling in three-dimensional space.

中文翻译：

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神经元钙波需要什么？数值参数研究。

通过简单的扩散和与移动和固定缓冲液反应传播的神经元钙信号仅限于细胞微区。细胞内钙信号可以传播的距离可以通过钙诱导的钙从内部钙储存库（尤其是内质网）释放而显着增加。该细胞器可以被认为是细胞内的细胞，能够通过 SERCA 泵隔离大量的细胞溶质钙离子，并通过兰尼碱受体通道选择性地将它们释放到细胞质中，从而形成钙波。在这项研究中，我们着手研究这种树突状钙波的基本特性，以及它们如何依赖于三个参数树突半径、ER 半径和内质膜中的兰尼碱受体密度。我们证明了钙波存在稳定和失败的状态，具体取决于上述形态和生理参数。在稳定的状态下，钙波可以穿过很长的树突距离，类似于电动作电位。我们进一步观察到存在流产状态，这可能与尖峰时间相关的可塑性有关，因为行进距离和波速随着细胞内结构的变化而变化。对于其中一些方案，可以导出适合模拟数据的分析函数。在不受三维钙浓度分布影响的参数空间中，我们无法得出这样的功能描述，证明了在三维空间中建模和模拟生化信号的数学要求。