Searching for network modules

When analyzing complex networks a key target is to uncover their modular structure, which means searching for a family of modules, namely node subsets spanning each a subnetwork more densely connected than the average. This work proposes a novel type of objective function for graph clustering, in the form of a multilinear polynomial whose coefficients are determined by network topology. It may be thought of as a potential function, to be maximized, taking its values on fuzzy clusterings or families of fuzzy subsets of nodes over which every node distributes a unit membership. When suitably parametrized, this potential is shown to attain its maximum when every node concentrates its all unit membership on some module. The output thus is a partition, while the original discrete optimization problem is turned into a continuous version allowing to conceive alternative search strategies. The instance of the problem being a pseudo-Boolean function assigning real-valued cluster scores to node subsets, modularity maximization is employed to exemplify a so-called quadratic form, in that the scores of singletons and pairs also fully determine the scores of larger clusters, while the resulting multilinear polynomial potential function has degree 2. After considering further quadratic instances, different from modularity and obtained by interpreting network topology in alternative manners, a greedy local-search strategy for the continuous framework is analytically compared with an existing greedy agglomerative procedure for the discrete case. Overlapping is finally discussed in terms of multiple runs, i.e. several local searches with different initializations.Comment: 10 page

Graph Theory and Networks in Biology

In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of bio-molecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape

Clades of huge phages from across Earth's ecosystems.

Bacteriophages typically have small genomes1 and depend on their bacterial hosts for replication2. Here we sequenced DNA from diverse ecosystems and found hundreds of phage genomes with lengths of more than 200 kilobases (kb), including a genome of 735 kb, which is-to our knowledge-the largest phage genome to be described to date. Thirty-five genomes were manually curated to completion (circular and no gaps). Expanded genetic repertoires include diverse and previously undescribed CRISPR-Cas systems, transfer RNAs (tRNAs), tRNA synthetases, tRNA-modification enzymes, translation-initiation and elongation factors, and ribosomal proteins. The CRISPR-Cas systems of phages have the capacity to silence host transcription factors and translational genes, potentially as part of a larger interaction network that intercepts translation to redirect biosynthesis to phage-encoded functions. In addition, some phages may repurpose bacterial CRISPR-Cas systems to eliminate competing phages. We phylogenetically define the major clades of huge phages from human and other animal microbiomes, as well as from oceans, lakes, sediments, soils and the built environment. We conclude that the large gene inventories of huge phages reflect a conserved biological strategy, and that the phages are distributed across a broad bacterial host range and across Earth's ecosystems