Stamatakis Michail, Mantzaris Nikos V
Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA.
Chaos. 2007 Sep;17(3):033123. doi: 10.1063/1.2767409.
Astrocytes, a special type of glial cells, were considered to have just a supporting role in information processing in the brain. However, several recent studies have shown that they can be chemically stimulated by various neurotransmitters, such as ATP, and can generate Ca2+ and ATP waves, which can propagate over many cell lengths before being blocked. Although pathological conditions, such as spreading depression and epilepsy, have been linked to abnormal wave propagation in astrocytic cellular networks, a quantitative understanding of the underlying characteristics is still lacking. Astrocytic cellular networks are inhomogeneous, in the sense that the domain they occupy contains passive regions or gaps, which are unable to support wave propagation. Thus, this work focuses on understanding the complex interplay between single-cell signal transduction, domain inhomogeneity, and the characteristics of wave propagation and blocking in astrocytic cellular networks. The single-cell signal transduction model that was employed accounts for ATP-mediated IP3 production, the subsequent Ca2+ release from the ER, and ATP release into the extracellular space. The model is excitable and thus an infinite range of wave propagation is observed if the domain of propagation is homogeneous. This is not always the case for inhomogeneous domains. To model wave propagation in inhomogeneous astrocytic networks, a reaction-diffusion framework was developed and one-gap as well as multiple-gap cases were simulated using an efficient finite-element algorithm. The minimum gap length that blocks the wave was computed as a function of excitability levels and geometric characteristics of the inhomogeneous network, such as the length of the active regions (cells). Complex transient patterns, such as wave reflection, wave trapping, and generation of echo waves, were also predicted by the model, and their relationship to the geometric characteristics of the network was evaluated. Therefore, the proposed model can help in the formulation of testable hypotheses to explain the observed abnormal wave propagation in pathological situations.
星形胶质细胞是一种特殊类型的神经胶质细胞，曾被认为在大脑信息处理过程中仅起支持作用。然而，最近的几项研究表明，它们可被多种神经递质（如ATP）进行化学刺激，并能产生Ca2+和ATP波，这些波在被阻断之前可在多个细胞长度上传播。尽管诸如扩散性抑制和癫痫等病理状况已与星形胶质细胞网络中的异常波传播相关联，但对其潜在特征仍缺乏定量认识。星形胶质细胞网络是不均匀的，因为它们所占据的区域包含无法支持波传播的无源区域或间隙。因此，这项工作着重于理解单细胞信号转导、区域不均匀性以及星形胶质细胞网络中波传播和阻断特征之间的复杂相互作用。所采用的单细胞信号转导模型考虑了ATP介导的IP3生成、随后内质网释放Ca2+以及ATP释放到细胞外空间的过程。该模型具有兴奋性，因此如果传播区域是均匀的，就会观察到无限范围的波传播。但对于不均匀区域情况并非总是如此。为了模拟不均匀星形胶质细胞网络中的波传播，开发了一个反应扩散框架，并使用高效有限元算法对单间隙和多间隙情况进行了模拟。计算出阻断波的最小间隙长度是不均匀网络兴奋性水平和几何特征（如有活性区域（细胞）的长度）的函数。该模型还预测了复杂的瞬态模式，如波反射、波捕获和回波生成，并评估了它们与网络几何特征的关系。因此，所提出的模型有助于形成可检验的假设，以解释在病理情况下观察到的异常波传播现象。
