Hierarchy measure for complex networks

Nature, technology and society are full of complexity arising from the intricate web of the interactions among the units of the related systems (e.g., proteins, computers, people). Consequently, one of the most successful recent approaches to capturing the fundamental features of the structure and dynamics of complex systems has been the investigation of the networks associated with the above units (nodes) together with their relations (edges). Most complex systems have an inherently hierarchical organization and, correspondingly, the networks behind them also exhibit hierarchical features. Indeed, several papers have been devoted to describing this essential aspect of networks, however, without resulting in a widely accepted, converging concept concerning the quantitative characterization of the level of their hierarchy. Here we develop an approach and propose a quantity (measure) which is simple enough to be widely applicable, reveals a number of universal features of the organization of real-world networks and, as we demonstrate, is capable of capturing the essential features of the structure and the degree of hierarchy in a complex network. The measure we introduce is based on a generalization of the m-reach centrality, which we first extend to directed/partially directed graphs. Then, we define the global reaching centrality (GRC), which is the difference between the maximum and the average value of the generalized reach centralities over the network. We investigate the behavior of the GRC considering both a synthetic model with an adjustable level of hierarchy and real networks. Results for real networks show that our hierarchy measure is related to the controllability of the given system. We also propose a visualization procedure for large complex networks that can be used to obtain an overall qualitative picture about the nature of their hierarchical structure.Comment: 29 pages, 9 figures, 4 table

Structure of a lectin from Canavalia gladiata seeds: new structural insights for old molecules

<p>Abstract</p> <p>Background</p> <p>Lectins are mainly described as simple carbohydrate-binding proteins. Previous studies have tried to identify other binding sites, which possible recognize plant hormones, secondary metabolites, and isolated amino acid residues. We report the crystal structure of a lectin isolated from <it>Canavalia gladiata </it>seeds (CGL), describing a new binding pocket, which may be related to pathogen resistance activity in ConA-like lectins; a site where a non-protein amino-acid, α-aminobutyric acid (Abu), is bound.</p> <p>Results</p> <p>The overall structure of native CGL and complexed with α-methyl-mannoside and Abu have been refined at 2.3 Å and 2.31 Å resolution, respectively. Analysis of the electron density maps of the CGL structure shows clearly the presence of Abu, which was confirmed by mass spectrometry.</p> <p>Conclusion</p> <p>The presence of Abu in a plant lectin structure strongly indicates the ability of lectins on carrying secondary metabolites. Comparison of the amino acids composing the site with other legume lectins revealed that this site is conserved, providing an evidence of the biological relevance of this site. This new action of lectins strengthens their role in defense mechanisms in plants.</p