Title: The Large Scale Structure of Biological Neworks Revisited: Changing Focus in Bow Ties from Nodes to Edges
Authors: M. Ángeles Serrano,
Abstract:Many biological systems can be represented and analyzed as complex networks. This approach is particularly suitable for the study of their large-scale structure, which is intimately related to their functionality and evolution. In particular, global transport processes in flow networks rely on the presence of directed pathways from input to output nodes and edges, which organize in macroscopic connected components. However, the precise relation between such structures and functional or evolutionary aspects remains to be understood. Here, the traditional bow tie structure is reanalyzed in terms of edges to investigate which are the constraints that the global structure of directed networks could impose on transport phenomena. In the percolated phase, nodes in the bow tie mainly organize in three different giant connected components while edges can arrange into five interconnected groups, interfaces bridging the communication of nodes in the strongly connected component and those in the in and out components. Most importantly, the specific conformation of the interfaces could bring new light to the discussion of how a structure is interwoven with functionality in flow networks. We define quantitatively under minimal assumptions the structural efficiency of networks to determine how robust communication between the core and the peripheral components through interface edges could be. We assess that optimal topologies in terms of access to the core should look like hairy balls (after the hairy ball theorem of algebraic topology) so to minimize bottleneck effects and the sensitivity to failures. We focus on two different biological networks: the nervous system of the worm Caenorhabditis elegans, and the metabolism of the bacterium Escherichia coli. In contrast to networks in other realms, these biological networks seem to be close to the optimal layout.
- M. A. Serrano and Paolo De Los Rios, Structural efficiency of percolated landscapes in flow networks, PLoS ONE 3(11): e3654 (2008).
- M. A. Serrano and Paolo De Los Rios, Interfaces and the edge percolation map of random directed networks, Physical Review E 76, 056121 (2007).
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