Pattern formation by lateral inhibition with feedback: A mathematical model of Delta-Notch intercellular signalling
Pattern formation by lateral inhibition with feedback: A mathematical model of Delta-Notch intercellular signalling
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DOI：
10.1006/jtbi.1996.0233
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发表时间：
1996-12-21
影响因子：
2
通讯作者：
Lewis, JH
中科院分区：
文献类型：
--
作者：
Collier, JR;Monk, NAM;Lewis, JH
在许多发育中的组织中，相邻细胞的特征有所不同，从而在不同的分化状态下形成细粒度的细胞模式。有人提出，这种模式可以通过横向抑制产生，横向抑制是一种细胞与细胞之间的相互作用，通过这种相互作用，采取特定命运的细胞会抑制其直接邻居做同样的事情。果蝇、蠕虫和脊椎动物的侧向抑制已有充分记录。在所有这些生物体中，跨膜蛋白Notch和Delta（或其同源物）已被确定为相互作用的介体——Notch作为受体，Delta作为其在邻近细胞上的配体。然而，尚不清楚侧抑制的 Delta-Notch 机制到底在什么条件下可以产生观察到的模式类型，或者该机制是否能够自行产生此类模式。在这里，我们构建并分析了这种接触介导的侧向抑制的简单而通用的数学模型。根据实验数据，该模型假设接受抑制（即激活 Notch）会降低传递抑制（即产生活性 Delta）的能力。这会产生一个反馈回路，可以放大相邻单元之间的差异。我们通过分析和数值模拟研究了该模型的模式形成潜力和时间行为。只要反馈足够强，不均匀性就会自我放大并发展，无需任何其他机制。对于各种初始条件和边界条件，该模型生成类似于在生命系统中观察到的细粒度模式。 (C) 学术出版社有限公司
In many developing tissues, adjacent cells diverge in character so as to create a fine-grained pattern of cells in contrasting states of differentiation. It has been proposed that such patterns can be generated through lateral inhibition-a type of cell-cell interaction whereby a cell that adopts a particular fate inhibits its immediate neighbours from doing likewise. Lateral inhibition is well documented in flies, worms and vertebrates. In all of these organisms, the transmembrane proteins Notch and Delta (or their homologues) have been identified as mediators of the interaction-Notch as receptor, Delta as its ligand on adjacent cells. However, it is not clear under precisely what conditions the Delta-Notch mechanism of lateral inhibition can generate the observed types of pattern, or indeed whether this mechanism is capable of generating such patterns by itself. Here we construct and analyse a simple and general mathematical model of such contact-mediated lateral inhibition. In accordance with experimental data, the model postulates that receipt of inhibition (i.e. activation of Notch) diminishes the ability to deliver inhibition (i.e. to produce active Delta). This gives rise to a feedback loop that can amplify differences between adjacent cells. We investigate the pattern-forming potential and temporal behaviour of this model both analytically and through numerical simulation. Inhomogeneities are self-amplifying and develop without need of any other machinery, provided the feedback is sufficiently strong. For a wide range of initial and boundary conditions, the model generates fine-grained patterns similar to those observed in living systems. (C) Academic Press Limited