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.
展开▼
机译：考虑具有前馈结构的大型布尔网络。给定输入的概率分布，是否可以找到可能很小的输入节点集合来确定网络中其他大多数节点的状态？为了回答这个问题，需要一种在网络中节点的状态上量化输入的确定能力的概念。我们认为，某个节点i的输入> X = {X1，...，Xn}的给定子集与其关联函数fi（> X ）量化这组输入在节点i上的确定能力。我们将一组输入的确定能力与对这些输入的扰动灵敏度进行比较，发现可能令人惊讶的是，对扰动具有较大灵敏度的输入不一定具有较大的确定能力。但是，对于在基因调控网络中发挥重要作用的统一功能，我们发现MI与微扰敏感性之间存在直接关系。作为我们结果的应用，我们分析了大肠杆菌的大规模调节网络。我们确定了最具决定性的节点，并表明其中的一小部分可显着降低网络状态的总体不确定性。此外，发现网络可以容忍其输入的干扰。
展开▼
