Resilience of protein-protein interaction networks as determined by their large-scale topological features

The relationship between the structure and function of biological networks constitutes a fundamental issue in systems biology. Particularly, the structure of protein-protein interaction networks is related to important biological functions. In this work, we investigated how such a resilience is determined by the large scale features of the respective networks. Four species are taken into account, namely yeast Saccharomyces cerevisiae, worm Caenorhabditis elegans, fly Drosophila melanogaster and Homo sapiens. We adopted two entropy-related measurements (degree entropy and dynamic entropy) in order to quantify the overall degree of robustness of these networks. We verified that while they exhibit similar structural variations under random node removal, they differ significantly when subjected to intentional attacks (hub removal). As a matter of fact, more complex species tended to exhibit more robust networks. More specifically, we quantified how six important measurements of the networks topology (namely clustering coefficient, average degree of neighbors, average shortest path length, diameter, assortativity coefficient, and slope of the power law degree distribution) correlated with the two entropy measurements. Our results revealed that the fraction of hubs and the average neighbor degree contribute significantly for the resilience of networks. In addition, the topological analysis of the removed hubs indicated that the presence of alternative paths between the proteins connected to hubs tend to reinforce resilience. The performed analysis helps to understand how resilience is underlain in networks and can be applied to the development of protein network models.

Evolution of a rift basin dominated by subaerial deposits: The Guaritas Rift, Early Cambrian, Southern Brazil

Most existing models for the evolution of rift basins predict the development of deep-water depositional systems during the stage of greatest tectonic subsidence, when accommodation generation potentially outpaces sedimentation. Despite this, some rift basins do not present deep-water systems, instead being dominated by subaerial deposits. This paper focuses on one of these particular rift basins, the Cambrian Guaritas Rift, Southern Brazil, characterized by more than 1500 m of alluvial and aeolian strata deposited in a 50-km-wide basin. The deposits of the Guaritas Rift can be ascribed to four depositional systems: basin-border alluvial fans, bedload-dominated ephemeral rivers, mixed-load ephemeral rivers and aeolian dune fields. These four systems are in part coeval and in part succeed each other, forming three stages of basin evolution: (i) Rift Initiation to Early Rift Climax stage, (ii) Mid to Late Rift Climax stage, and (iii) Early Post-Rift stage. The first stage comprises most of the Guaritas Group and is characterized by homogeneous bed-load-dominated river deposits, which do not clearly record the evolution of subsidence rates. The onset of sedimentation of finer-grained deposits occurred as a consequence of a reactivation event that changed the outline of the basin and the distribution of the nearby highlands. This strongly suggests that the capture of the main river system to another depression decreased the sediment supply to the basin. The study of the Guaritas Rift indicates that rift basins in which the sediment supply exceeds the accommodation generation occur as a consequence of moderate subsidence combined with the capture of a major river system to the basin during the initial stages of basin evolution. In these basins, changes in the average discharge of the river system or tectonic modification of the drainage network may be the major control on the stratigraphic architecture. (c) 2009 Published by Elsevier B.V.

SCALING LIMIT FOR A DRAINAGE NETWORK MODEL

We consider the two-dimensional version of a drainage network model introduced ill Gangopadhyay, Roy and Sarkar (2004), and show that the appropriately rescaled family of its paths converges in distribution to the Brownian web. We do so by verifying the convergence criteria proposed in Fontes, Isopi, Newman and Ravishankar (2002).