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.