One Hub-One Process: A Tool Based View on Regulatory Network Topology

The relationship between the regulatory design and the functionality of molecular networks is a key issue in biology. Modules and motifs have been associated to various cellular processes, thereby providing anecdotal evidence for performance based localization on molecular networks. To quantify structure-function relationship we investigate similarities of proteins which are close in the regulatory network of the yeast Saccharomyces Cerevisiae. We find that the topology of the regulatory network show weak remnants of its history of network reorganizations, but strong features of co-regulated proteins associated to similar tasks. This suggests that local topological features of regulatory networks, including broad degree distributions, emerge as an implicit result of matching a number of needed processes to a finite toolbox of proteins.Comment: 18 pages, 3 figures, 5 supplementary figure

Parameters of proteome evolution from histograms of amino-acid sequence identities of paralogous proteins

Background: The evolution of the full repertoire of proteins encoded in a given genome is mostly driven by gene duplications, deletions, and sequence modifications of existing proteins. Indirect information about relative rates and other intrinsic parameters of these three basic processes is contained in the proteome-wide distribution of sequence identities of pairs of paralogous proteins. Results: We introduce a simple mathematical framework based on a stochastic birth-and-death model that allows one to extract some of this information and apply it to the set of all pairs of paralogous proteins in H. pylori, E. coli, S. cerevisiae, C. elegans, D. melanogaster, and H. sapiens. It was found that the histogram of sequence identities p generated by an all-to-all alignment of all protein sequences encoded in a genome is well fitted with a power-law form ∼ p−γ with the value of the exponent γ around 4 for the majority of organisms used in this study. This implies that the intra-protein variability of substitution rates is best described by the Gamma-distribution with the exponent α ≈ 0.33. Different features of the shape of such histograms allow us to quantify the ratio between the genome-wide average deletion/duplication rates and the amino-acid substitution rate. 1 Conclusions: We separately measure the short-term (“raw”) duplication and deletion rates r ∗ dup, r ∗ del whic

Species–area relationships always overestimate extinction rates from habitat loss : comment

Author Posting. © Ecological Society of America, 2013. This article is posted here by permission of Ecological Society of America for personal use, not for redistribution. The definitive version was published in Ecology 94 (2013): 761–763, doi:10.1890/12-0047.1.The species–area relationship summarizes the relationship between the average number of species in a region and its area. This relationship provides a basis for predicting the loss of species associated with loss of habitat (e.g., Pimm and Raven 2000). The approach involves two steps. First, as discussed in more detail below, the species–area relationship is used to predict the number of species that are endemic to the habitat at risk based on its area. Second, these endemic species are assumed to become extinct should this habitat be lost. In a controversial paper, He and Hubbell (2011) argued that the way in which the species–area relationship is used to predict the number of endemic species is incorrect when individual organisms are aggregated in space and argued that this explains a discrepancy between predicted and observed extinction rates associated with habitat loss. The controversy surrounding the paper focused primarily on the second part of their argument (Brooks 2011, Evans et al. 2011, He and Hubbell 2012, Pereira et al. 2012, Thomas and Williamson 2012). Here, we focus on the details underlying the first part.U. Roll is supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities. L. Stone is supported by the Israeli Science Foundation

Degree Landscapes in Scale-Free Networks

We generalize the degree-organizational view of real-world networks with broad degree-distributions in a landscape analogue with mountains (high-degree nodes) and valleys (low-degree nodes). For example, correlated degrees between adjacent nodes corresponds to smooth landscapes (social networks), hierarchical networks to one-mountain landscapes (the Internet), and degree-disassortative networks without hierarchical features to rough landscapes with several mountains. We also generate ridge landscapes to model networks organized under constraints imposed by the space the networks are embedded in, associated to spatial or, in molecular networks, to functional localization. To quantify the topology, we here measure the widths of the mountains and the separation between different mountains.Comment: 4 pages, 5 figure

Cost and Capacity of Signaling in the Escherichia coli Protein Reaction Network

In systems biology new ways are required to analyze the large amount of existing data on regulation of cellular processes. Recent work can be roughly classified into either dynamical models of well-described subsystems, or coarse-grained descriptions of the topology of the molecular networks at the scale of the whole organism. In order to bridge these two disparate approaches one needs to develop simplified descriptions of dynamics and topological measures which address the propagation of signals in molecular networks. Here, we consider the directed network of protein regulation in E. coli, characterizing its modularity in terms of its potential to transmit signals. We demonstrate that the simplest measure based on identifying sub-networks of strong components, within which each node could send a signal to every other node, indeed partitions the network into functional modules. We then suggest measures to quantify the cost and spread associated with sending a signal between any particular pair of proteins. Thereby, we address the signalling specificity within and between modules, and show that in the regulation of E.coli there is a systematic reduction of the cost and spread for signals traveling over more than two intermediate reactions.Comment: 21 pages, 6 figure

Degree landscapes in scale-free networks

We generalize the degree-organizational view of real-world networks with broad degree distributions in a landscape analog with mountains ͑high-degree nodes͒ and valleys ͑low-degree nodes͒. For example, correlated degrees between adjacent nodes correspond to smooth landscapes ͑social networks͒, hierarchical networks to one-mountain landscapes ͑the Internet͒, and degree-disassortative networks without hierarchical features to rough landscapes with several mountains. To quantify the topology, we here measure the widths of the mountains and the separation between different mountains. We also generate ridge landscapes to model networks organized under constraints imposed by the space the networks are embedded in, associated to spatial or in molecular networks to functional localization