Functional cartography of complex metabolic networks

High-throughput techniques are leading to an explosive growth in the size of biological databases and creating the opportunity to revolutionize our understanding of life and disease. Interpretation of these data remains, however, a major scientific challenge. Here, we propose a methodology that enables us to extract and display information contained in complex networks. Specifically, we demonstrate that one can (i) find functional modules in complex networks, and (ii) classify nodes into universal roles according to their pattern of intra- and inter-module connections. The method thus yields a ``cartographic representation'' of complex networks. Metabolic networks are among the most challenging biological networks and, arguably, the ones with more potential for immediate applicability. We use our method to analyze the metabolic networks of twelve organisms from three different super-kingdoms. We find that, typically, 80% of the nodes are only connected to other nodes within their respective modules, and that nodes with different roles are affected by different evolutionary constraints and pressures. Remarkably, we find that low-degree metabolites that connect different modules are more conserved than hubs whose links are mostly within a single module.Comment: 17 pages, 4 figures. Go to http://amaral.northwestern.edu for the PDF file of the reprin

Size reduction of complex networks preserving modularity

The ubiquity of modular structure in real-world complex networks is being the focus of attention in many trials to understand the interplay between network topology and functionality. The best approaches to the identification of modular structure are based on the optimization of a quality function known as modularity. However this optimization is a hard task provided that the computational complexity of the problem is in the NP-hard class. Here we propose an exact method for reducing the size of weighted (directed and undirected) complex networks while maintaining invariant its modularity. This size reduction allows the heuristic algorithms that optimize modularity for a better exploration of the modularity landscape. We compare the modularity obtained in several real complex-networks by using the Extremal Optimization algorithm, before and after the size reduction, showing the improvement obtained. We speculate that the proposed analytical size reduction could be extended to an exact coarse graining of the network in the scope of real-space renormalization.Comment: 14 pages, 2 figure

Efficiency and response of conilon coffee genotypes to nitrogen supply

The objective of the study was to differentiate genotypes with higher efficiency and responsiveness to nitrogen supply, to understand how the nitrogen supply can impact the dry matter allocation and the accumulation of this nutrient in the different plant compartments of genotypes of conilon coffee, cultivated under contrasting conditions of nitrogen availability in the soil. The plants were cultivated during 150 days in pots containing 10 kg of soil, in greenhouse. The experiment was set up in a 13×2 factorial scheme, following a completely randomized design (CRD) with three replications. The factors were: 13 genotypes and two levels of nitrogen fertilization (0 and 100% of the N recommended level). The N supply increased between 70 and 210% of the total dry matter and between 360 and 680% of the concentration of N content in leaves of the genotypes of conilon coffee. It was possible to observe that the expression of the genotypes was modulated by the availability of N in the soil, since they presented different behaviors in the studied environments (with 0 or 100% of N supply in the soil). The genotypes CV-03, CV-07 and CV-08 were classified as non-efficient and non-responsive, while the genotypes CV- 01, CV-04 and CV-09 of conilon coffee were classified as efficient and responsive.Keywords: Alpha parameter, Coffea canephora (Pierre ex A. Froehner), mineral nutritio

Hierarchical Organization in Complex Networks

Many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. We show that these two features are the consequence of a hierarchical organization, implying that small groups of nodes organize in a hierarchical manner into increasingly large groups, while maintaining a scale-free topology. In hierarchical networks the degree of clustering characterizing the different groups follows a strict scaling law, which can be used to identify the presence of a hierarchical organization in real networks. We find that several real networks, such as the World Wide Web, actor network, the Internet at the domain level and the semantic web obey this scaling law, indicating that hierarchy is a fundamental characteristic of many complex systems

Subgraphs in random networks

Understanding the subgraph distribution in random networks is important for modelling complex systems. In classic Erdos networks, which exhibit a Poissonian degree distribution, the number of appearances of a subgraph G with n nodes and g edges scales with network size as \mean{G} ~ N^{n-g}. However, many natural networks have a non-Poissonian degree distribution. Here we present approximate equations for the average number of subgraphs in an ensemble of random sparse directed networks, characterized by an arbitrary degree sequence. We find new scaling rules for the commonly occurring case of directed scale-free networks, in which the outgoing degree distribution scales as P(k) ~ k^{-\gamma}. Considering the power exponent of the degree distribution, \gamma, as a control parameter, we show that random networks exhibit transitions between three regimes. In each regime the subgraph number of appearances follows a different scaling law, \mean{G} ~ N^{\alpha}, where \alpha=n-g+s-1 for \gamma<2, \alpha=n-g+s+1-\gamma for 2<\gamma<\gamma_c, and \alpha=n-g for \gamma>\gamma_c, s is the maximal outdegree in the subgraph, and \gamma_c=s+1. We find that certain subgraphs appear much more frequently than in Erdos networks. These results are in very good agreement with numerical simulations. This has implications for detecting network motifs, subgraphs that occur in natural networks significantly more than in their randomized counterparts.Comment: 8 pages, 5 figure

The Deleterious Effects of Shiga Toxin Type 2 Are Neutralized In Vitro by FabF8:Stx2 Recombinant Monoclonal Antibody

Hemolytic Uremic Syndrome (HUS) associated with Shiga-toxigenic Escherichia coli (STEC) infections is the principal cause of acute renal injury in pediatric age groups. Shiga toxin type 2 (Stx2) has in vitro cytotoxic effects on kidney cells, including human glomerular endothelial (HGEC) and Vero cells. Neither a licensed vaccine nor effective therapy for HUS is available for humans. Recombinant antibodies against Stx2, produced in bacteria, appeared as the utmost tool to prevent HUS. Therefore, in this work, a recombinant FabF8:Stx2 was selected from a human Fab antibody library by phage display, characterized, and analyzed for its ability to neutralize the Stx activity from different STEC-Stx2 and Stx1/Stx2 producing strains in a gold standard Vero cell assay, and the Stx2 cytotoxic effects on primary cultures of HGEC. This recombinant Fab showed a dissociation constant of 13.8 nM and a half maximum effective concentration (EC50 ) of 160 ng/mL to Stx2. Additionally, FabF8:Stx2 neutralized, in different percentages, the cytotoxic effects of Stx2 and Stx1/2 from different STEC strains on Vero cells. Moreover, it significantly prevented the deleterious effects of Stx2 in a dose-dependent manner (up to 83%) in HGEC and protected this cell up to 90% from apoptosis and necrosis. Therefore, this novel and simple anti-Stx2 biomolecule will allow further investigation as a new therapeutic option that could improve STEC and HUS patient outcomes.Fil: Luz, Daniela. Governo do Estado de Sao Paulo. Secretaria da Saude. Instituto Butantan; BrasilFil: Gomez, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; ArgentinaFil: Ferreira, Raissa L.. Governo do Estado de Sao Paulo. Secretaria da Saude. Instituto Butantan; BrasilFil: Melo, Bruna S.. Governo do Estado de Sao Paulo. Secretaria da Saude. Instituto Butantan; BrasilFil: Guth, Beatriz E. C.. Universidade de Sao Paulo; BrasilFil: Quintilio, Wagner. Governo do Estado de Sao Paulo. Secretaria da Saude. Instituto Butantan; BrasilFil: Moro, Ana Maria. Governo do Estado de Sao Paulo. Secretaria da Saude. Instituto Butantan; BrasilFil: Presta, Agostina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; ArgentinaFil: Sacerdoti, Flavia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; ArgentinaFil: Ibarra, Cristina Adriana. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; ArgentinaFil: Chen, Gang. University of Toronto; CanadáFil: Sidhu, Sachdev S.. University of Toronto; CanadáFil: Amaral, María Marta. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; ArgentinaFil: Fontes Piazza, Roxane María. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; Argentin

Finding and evaluating community structure in networks

We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.Comment: 16 pages, 13 figure

Network 'small-world-ness': a quantitative method for determining canonical network equivalence

Background: Many technological, biological, social, and information networks fall into the broad class of 'small-world' networks: they have tightly interconnected clusters of nodes, and a shortest mean path length that is similar to a matched random graph (same number of nodes and edges). This semi-quantitative definition leads to a categorical distinction ('small/not-small') rather than a quantitative, continuous grading of networks, and can lead to uncertainty about a network's small-world status. Moreover, systems described by small-world networks are often studied using an equivalent canonical network model-the Watts-Strogatz (WS) model. However, the process of establishing an equivalent WS model is imprecise and there is a pressing need to discover ways in which this equivalence may be quantified. Methodology/Principal Findings: We defined a precise measure of 'small-world-ness' S based on the trade off between high local clustering and short path length. A network is now deemed a 'small-world' if S. 1-an assertion which may be tested statistically. We then examined the behavior of S on a large data-set of real-world systems. We found that all these systems were linked by a linear relationship between their S values and the network size n. Moreover, we show a method for assigning a unique Watts-Strogatz (WS) model to any real-world network, and show analytically that the WS models associated with our sample of networks also show linearity between S and n. Linearity between S and n is not, however, inevitable, and neither is S maximal for an arbitrary network of given size. Linearity may, however, be explained by a common limiting growth process. Conclusions/Significance: We have shown how the notion of a small-world network may be quantified. Several key properties of the metric are described and the use of WS canonical models is placed on a more secure footing

Lethality and centrality in protein networks

In this paper we present the first mathematical analysis of the protein interaction network found in the yeast, S. cerevisiae. We show that, (a) the identified protein network display a characteristic scale-free topology that demonstrate striking similarity to the inherent organization of metabolic networks in particular, and to that of robust and error-tolerant networks in general. (b) the likelihood that deletion of an individual gene product will prove lethal for the yeast cell clearly correlates with the number of interactions the protein has, meaning that highly-connected proteins are more likely to prove essential than proteins with low number of links to other proteins. These results suggest that a scale-free architecture is a generic property of cellular networks attributable to universal self-organizing principles of robust and error-tolerant networks and that will likely to represent a generic topology for protein-protein interactions.Comment: See also http:/www.nd.edu/~networks and http:/www.nd.edu/~networks/cel

Conservation of geosites as a tool to protect geoheritage: the inventory of Ceará Central Domain, Borborema Province - NE/Brazil

The Ceará Central Domain, in the northern Borborema Province/NE Brazil, encompasses important geological records (geosites) which allow understanding a relevant period of the Earth’s evolution, mainly associated to Neoproterozoic Brazilian/Pan-African Cycle and West Gondwana amalgamation, besides Neoarchean to Ordovician records. The presented geoheritage inventory aims to characterise the geosites with scienti c relevance of Ceará Central Domain. By applying a method for large areas, the nal selection resulted in eight geological frameworks represented by 52 geosites documented in a single database. This is the rst step for a geoconservation strategy based on systematic inventories, statutory protection, geoethical behaviour and awareness about scienti c, educational and/or cultural relevance of geosites.We specially thank all experts that helped us with this inventory: Afonso Almeida, Carlos E.G. de Araújo, César Veríssimo, Christiano Magini, Clóvis Vaz Parente, Felipe G. Costa, Irani C. Mattos, Neivaldo de Castro, Otaciel de Melo, Sebástian G. Chiozza, Ticiano Santos and Stefano Zincone. We are also thankful to Kátia Mansur, Ricardo Fraga Pereira and anonymous reviewers for their valuable contributions. PM is grateful to Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for PhD mobility scholarship PDSE Program/Process n 88881.132168/2016-01info:eu-repo/semantics/publishedVersio