布尔网络的调和分析：确定幂与扰动
Harmonic Analysis of Boolean Networks: Determinative Power and Perturbations
摘要：
考虑一个具有前馈结构的大型布尔网络。给定输入的概率分布，我们能否找到（可能是很小的）输入节点的集合来决定网络中大多数其他节点的状态？为了回答这个问题，需要一个概念来量化输入对网络中节点状态的决定性影响。我们认为，输入的给定子集X = {X_1，.，X_n}及其相关函数f_i（X）量化了这组输入对节点i的决定性功率。我们比较了一组输入的决定性力量对这些输入的扰动的敏感性，并发现，也许令人惊讶的是，对扰动具有大的敏感性的输入不一定具有大的决定性力量。然而，对于unate功能，这在遗传调控网络中发挥着重要作用，我们发现MI和扰动的敏感性之间有直接的关系。作为我们的研究结果的应用，我们分析了大肠杆菌的大规模调控网络。我们确定了最具决定性的节点，并表明这些节点的一个小子集显着降低了网络状态的整体不确定性。此外，网络被发现是容忍其输入的扰动。
英文摘要：
Consider a large Boolean network with a feed forward structure. Given a probability distribution on the inputs, can one find, possibly small, collections of input nodes that determine the states of most other nodes in the network? To answer this question, a notion that quantifies the determinative power of an input over the states of the nodes in the network is needed. We argue that the mutual information (MI) between a given subset of the inputs X = {X_1, ..., X_n} of some node i and its associated function f_i(X) quantifies the determinative power of this set of inputs over node i. We compare the determinative power of a set of inputs to the sensitivity to perturbations to these inputs, and find that, maybe surprisingly, an input that has large sensitivity to perturbations does not necessarily have large determinative power. However, for unate functions, which play an important role in genetic regulatory networks, we find a direct relation between MI and sensitivity to perturbations. As an application of our results, we analyze the large-scale regulatory network of Escherichia coli. We identify the most determinative nodes and show that a small subset of those reduces the overall uncertainty of the network state significantly. Furthermore, the network is found to be tolerant to perturbations of its inputs.
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