Potapov Anatolij P, Goemann Björn, Wingender Edgar
Department of Bioinformatics, Medical School, Georg August University of Göttingen, Goldschmidtstrasse 1, D-37077 Göttingen, Germany.
BMC Bioinformatics. 2008 May 2;9:227. doi: 10.1186/1471-2105-9-227.
Currently, there is a gap between purely theoretical studies of the topology of large bioregulatory networks and the practical traditions and interests of experimentalists. While the theoretical approaches emphasize the global characterization of regulatory systems, the practical approaches focus on the role of distinct molecules and genes in regulation. To bridge the gap between these opposite approaches, one needs to combine 'general' with 'particular' properties and translate abstract topological features of large systems into testable functional characteristics of individual components. Here, we propose a new topological parameter--the pairwise disconnectivity index of a network's element - that is capable of such bridging.
The pairwise disconnectivity index quantifies how crucial an individual element is for sustaining the communication ability between connected pairs of vertices in a network that is displayed as a directed graph. Such an element might be a vertex (i.e., molecules, genes), an edge (i.e., reactions, interactions), as well as a group of vertices and/or edges. The index can be viewed as a measure of topological redundancy of regulatory paths which connect different parts of a given network and as a measure of sensitivity (robustness) of this network to the presence (absence) of each individual element. Accordingly, we introduce the notion of a path-degree of a vertex in terms of its corresponding incoming, outgoing and mediated paths, respectively. The pairwise disconnectivity index has been applied to the analysis of several regulatory networks from various organisms. The importance of an individual vertex or edge for the coherence of the network is determined by the particular position of the given element in the whole network.
Our approach enables to evaluate the effect of removing each element (i.e., vertex, edge, or their combinations) from a network. The greatest potential value of this approach is its ability to systematically analyze the role of every element, as well as groups of elements, in a regulatory network.
目前，大型生物调节网络拓扑结构的纯理论研究与实验学家的实践传统和兴趣之间存在差距。虽然理论方法强调调节系统的全局特征，但实践方法侧重于不同分子和基因在调节中的作用。为了弥合这些相反方法之间的差距，需要将“一般”属性与“特殊”属性相结合，并将大型系统的抽象拓扑特征转化为单个组件的可测试功能特征。在此，我们提出一种新的拓扑参数——网络元素的成对不连通性指数，它能够实现这种弥合。
成对不连通性指数量化了单个元素对于维持以有向图表示的网络中连通顶点对之间通信能力的关键程度。这样的元素可以是一个顶点（即分子、基因）、一条边（即反应、相互作用），也可以是一组顶点和/或边。该指数可以被视为连接给定网络不同部分的调节路径的拓扑冗余度量，以及该网络对每个单独元素存在（不存在）的敏感性（稳健性）度量。相应地，我们分别根据顶点的相应入向、出向和介导路径引入了顶点路径度的概念。成对不连通性指数已应用于分析来自各种生物体的几个调节网络。单个顶点或边对网络连贯性的重要性由给定元素在整个网络中的特定位置决定。
我们的方法能够评估从网络中移除每个元素（即顶点、边或它们的组合）的效果。这种方法的最大潜在价值在于其能够系统地分析调节网络中每个元素以及元素组的作用。
