An approach to evaluate the topological significance of motifs and other patterns in regulatory networks.

BACKGROUND: The identification of network motifs as statistically over-represented topological patterns has become one of the most promising topics in the analysis of complex networks. The main focus is commonly made on how they operate by means of their internal organization. Yet, their contribution to a network's global architecture is poorly understood. However, this requires switching from the abstract view of a topological pattern to the level of its instances. Here, we show how a recently proposed metric, the pairwise disconnectivity index, can be adapted to survey if and which kind of topological patterns and their instances are most important for sustaining the connectivity within a network. RESULTS: The pairwise disconnectivity index of a pattern instance quantifies the dependency of the pairwise connections between vertices in a network on the presence of this pattern instance. Thereby, it particularly considers how the coherence between the unique constituents of a pattern instance relates to the rest of a network. We have applied the method exemplarily to the analysis of 3-vertex topological pattern instances in the transcription networks of a bacteria (E. coli), a unicellular eukaryote (S. cerevisiae) and higher eukaryotes (human, mouse, rat). We found that in these networks only very few pattern instances break lots of the pairwise connections between vertices upon the removal of an instance. Among them network motifs do not prevail. Rather, those patterns that are shared by the three networks exhibit a conspicuously enhanced pairwise disconnectivity index. Additionally, these are often located in close vicinity to each other or are even overlapping, since only a small number of genes are repeatedly present in most of them. Moreover, evidence has gathered that the importance of these pattern instances is due to synergistic rather than merely additive effects between their constituents. CONCLUSION: A new method has been proposed that enables to evaluate the topological significance of various connected patterns in a regulatory network. Applying this method onto transcriptional networks of three largely distinct organisms we could prove that it is highly suitable to identify most important pattern instances, but that neither motifs nor any pattern in general appear to play a particularly important role per se. From the results obtained so far, we conclude that the pairwise disconnectivity index will most likely prove useful as well in identifying other (higher-order) pattern instances in transcriptional and other networks.

The pairwise disconnectivity index as a new metric for the topological analysis of regulatory networks.

BACKGROUND: 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. RESULTS: 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. CONCLUSION: 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.

EndoNet: an information resource about regulatory networks of cell-to-cell communication.

EndoNet is an information resource about intercellular regulatory communication. It provides information about hormones, hormone receptors, the sources (i.e. cells, tissues and organs) where the hormones are synthesized and secreted, and where the respective receptors are expressed. The database focuses on the regulatory relations between them. An elementary communication is displayed as a causal link from a cell that secretes a particular hormone to those cells which express the corresponding hormone receptor and respond to the hormone. Whenever expression, synthesis and/or secretion of another hormone are part of this response, it renders the corresponding cell an internal node of the resulting network. This intercellular communication network coordinates the function of different organs. Therefore, the database covers the hierarchy of cellular organization of tissues and organs as it has been modeled in the Cytomer ontology, which has now been directly embedded into EndoNet. The user can query the database; the results can be used to visualize the intercellular information flow. A newly implemented hormone classification enables to browse the database and may be used as alternative entry point. EndoNet is accessible at: http://endonet.bioinf.med.uni-goettingen.de/.