Heckel Reinhard, Schober Steffen, Bossert Martin
Department of Information Technology and Electrical Engineering, ETH, Zürich, Zürich, Switzerland.
EURASIP J Bioinform Syst Biol. 2013 May 4;2013(1):6. doi: 10.1186/1687-4153-2013-6.
: 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={X1,...,Xn} of some node i and its associated function fi(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.
考虑一个具有前馈结构的大型布尔网络。给定输入上的概率分布，能否找到（可能很小的）输入节点集合，这些集合能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能力。我们认为，某个节点(i)的给定输入子集(X = {X_1, \ldots, X_n})与其关联函数(f_i(X))之间的互信息（MI）量化了这组输入对节点(i)的决定性能力。我们将一组输入的决定性能力与对这些输入扰动的敏感性进行比较，发现也许令人惊讶的是，对扰动具有高敏感性的输入不一定具有高决定性能力。然而，对于在基因调控网络中起重要作用的单态函数，我们发现互信息与对扰动的敏感性之间存在直接关系。作为我们结果的一个应用，我们分析了大肠杆菌的大规模调控网络。我们识别出最具决定性的节点，并表明其中一小部分节点能显著降低网络状态的整体不确定性。此外，发现该网络对其输入的扰动具有耐受性。
