嵌套分析深度与网络稳定性
Nested canalyzing depth and network stability
摘要：
我们引入了一个函数的嵌套canalyzing深度，它测量了它保留嵌套canalyzing结构的程度。我们描述了具有给定深度的函数的结构，并计算了变量的预期活动和灵敏度。这个分析量化了canalysis如何导致布尔网络的更高稳定性。它推广了嵌套canalyzing函数（NCF）的概念，这些函数正是具有最大深度的函数。NCF已被提出作为基因调控网络模型，但它们的结构往往过于限制，而且它们非常稀疏。我们发现，功能变得越来越敏感的输入扰动canalyzing深度的增加，但表现出迅速递减的稳定性回报。此外，我们表明，随着深度的增加，使用这些功能的网络的动态迅速接近临界状态，这表明，真正的网络表现出一定程度的canalysing深度，和NCF是没有显着优于功能的许多应用程序的建模和逆向工程的生物网络足够的深度。
英文摘要：
We introduce the nested canalyzing depth of a function, which measures the extent to which it retains a nested canalyzing structure. We characterize the structure of functions with a given depth and compute the expected activities and sensitivities of the variables. This analysis quantifies how canalyzation leads to higher stability in Boolean networks. It generalizes the notion of nested canalyzing functions (NCFs), which are precisely the functions with maximum depth. NCFs have been proposed as gene regulatory network models, but their structure is frequently too restrictive and they are extremely sparse. We find that functions become decreasingly sensitive to input perturbations as the canalyzing depth increases, but exhibit rapidly diminishing returns in stability. Additionally, we show that as depth increases, the dynamics of networks using these functions quickly approach the critical regime, suggesting that real networks exhibit some degree of canalyzing depth, and that NCFs are not significantly better than functions of sufficient depth for many applications of the modeling and reverse engineering of biological networks.
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