侧抑制的布尔分析
Boolean analysis of lateral inhibition
摘要：
我们研究布尔网络是高度保守的Delta-Notch系统的简单空间模型。该模型假设每个细胞中的Delta被同一细胞中的Notch抑制，并且在周围细胞中Delta存在的情况下Notch被激活。我们认为完全异步动态无向图表示细胞之间的邻居关系。在这个框架中，可以证明所有吸引子都是系统的不动点，与相邻关系无关，例如通过使用模型的简化版本的已知属性，其中每个细胞仅定义一个物种。固定点对应于所谓的细粒度的“模式”，出现在离散和连续的侧抑制模型。我们研究了不动点的可达性，给出了完整和简化模型的陷阱空间和吸引盆地的特征。此外，我们使用的陷阱空间的特征来研究模式的扰动的鲁棒性。这种定性分析的结果可以补充和指导基于模拟的方法，并作为调查更复杂的机制的基础。
英文摘要：
We study Boolean networks which are simple spatial models of the highly conserved Delta-Notch system. The models assume the inhibition of Delta in each cell by Notch in the same cell, and the activation of Notch in presence of Delta in surrounding cells. We consider fully asynchronous dynamics over undirected graphs representing the neighbour relation between cells. In this framework, one can show that all attractors are fixed points for the system, independently of the neighbour relation, for instance by using known properties of simplified versions of the models, where only one species per cell is defined. The fixed points correspond to the so-called fine-grained "patterns" that emerge in discrete and continuous modelling of lateral inhibition. We study the reachability of fixed points, giving a characterisation of the trap spaces and the basins of attraction for both the full and the simplified models. In addition, we use a characterisation of the trap spaces to investigate the robustness of patterns to perturbations. The results of this qualitative analysis can complement and guide simulation-based approaches, and serve as a basis for the investigation of more complex mechanisms.
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