using graph theory to analyze biological networks


Hierarchical clustering is a method of cluster analysis which seeks to build a hierarchy of clusters. out through homology modeling). ⊆ E, where each edge in E An example is shown in Figure 8. discovered to analyze the pathway structure of metabolic networks [44-48]. 2 Mewes HW, Amid C, Arnold R, Frishman D, Guldener U, Mannhaupt G, Munsterkotter M, Pagel P, Strack N, Stumpflen V: MIPS: analysis and annotation of proteins from whole genomes. 2004, 32: D91-94. The book's authors discuss various graph theoretic and data analytics approaches used to analyze these networks with respect to available tools, … The simple model of a network involves taking a number of vertices N and connecting nodes by selecting edges from the N(N-1)/2 possible edges randomly. ways to ontologies or ecological connections, as discussed in [61] or [62]. 1 It has been shown that metabolic networks can form hierarchical structures [168, 169] where specific patterns and motifs are overrepresented. (i). The Yeast Proteome Database (YPD): a model for the. Dadurch sind wir in der Lage, erstens Signal-Transduktionsnetzwerke detailliert zu rekon- struieren, zweitens diese Netzwerke in ausführbare Boolesche Modelle zur Verbesserung, Evaluation und Validierung dieser Netzwerke zu übersetzen und drittens diese Netzwerke als Regelbasierte Modelle zu exportieren. Many visualization tools [144] such as Medusa [148], Cytoscape [149], Pajek [98] and many others [144] visualize networks in both 2D and 3D, but very few of them like Arena3D [150] try to bridge the gap between clustering analysis and visualization. The diameter of a network is the longest shortest path within a network. 2 , V MEGA2: molecular evolutionary genetics analysis software. Very often we encou, Concerning the visualization of networks, the availability of clustering techniques and, visualization platforms or tools that are able to integrate a variety of more advanced, [144]. , V = 25 the total sum of shortest paths that pass through the nodes, thus N 2 Rain JC, Selig L, De Reuse H, Battaglia V, Reverdy C, Simon S, Lenzen G, Petel F, Wojcik J, Schachter V: The protein-protein interaction map of Helicobacter pylori. Unweighted Pair Group Method with Arithmetic Mean. , V Average linkage uses the average distance between all pairs of objects in any two clusters: . Modern sequencing techniques allow the reconstruction of the network of biochemical reactions in many organisms, from bacteria to human [38, 39]. Eigenvector Centrality ranks higher the nodes that are connected to important neighbors. Dense is a graph where |E| " |V| A) Node V behaves like a hub but it has clustering coefficient C = 0. One example is presented in [167] for E. coli. ), (V PubMed  Voy BH, Scharff JA, Perkins AD, Saxton AM, Borate B, Chesler EJ, Branstetter LK, Langston MA: Extracting Gene Networks for Low-Dose Radiation Using Graph Theoretical Algorithms. ecc Usually, these networks use a directed graph representation in an effort to model the way that proteins and other biological molecules are involved in gene expression and try to imitate the series of events that take place in different stages of the process. 1 This model was mainly introduced to describe the properties of a random graph. (V 2006, D535-539. 1 However, for higher, dimensional data the Euclidean distance can sometimes be misleading. -V 2004, 303 (5657): 540-543. von Mering C, Krause R, Snel B, Cornell M, Oliver SG, Fields S, Bork P: Comparative assessment of large-scale data sets of protein-protein interactions. (v Such algorithms can be used for efficient page ranking on the web. Other file formats that can represent biological networks are the Proteomics Standards Initiative Interaction (PSI-MI)[51], Chemical Markup Language (CML) [52, 53] for chemicals or BioPAX[54] for pathways. Pavlopoulos GA, O'Donoghue SI, Satagopam VP, Soldatos TG, Pafilis E, Schneider R: Arena3D: visualization of biological networks in 3D. Verschiedene Ansätze zur Netzwerk-Rekonstruktion unterscheiden sich zwar in ihrem Zweck und ihrer Komplexität, allerding. Using parent-offspring edges in the global pedigree network, we found that selection cycle lengths over the last 200 years of breeding have been extraordinarily long (16.0-16.9 years/generation) but decreased to a present-day range of 6.0-10.0 years/generation. For all complexes, poses with RMSD less than 3 Å from actual binding positions can be recovered. Barabási A-L, A R: Emergence of scaling in random networks. D. Bipartite graph: V = {U1, U2, U3, U4, V1, V2, V3}, |V| = 7, E = {(U1, V1), (U2, V1), (U2, V2), (U2, V3), (U3, V2), (U4, V2)}, |E| = 6. Type of network: gene regulatory, biochemical. 2 experimentally verified phosphorylation sites in eukaryotic proteins. is connected with 2 nodes (V PLoS Biol. The closer the local clustering coefficient is to 1, the more likely it is for the network to form clusters. The budding yeast Arp2/3 complex that is highlighted was successfully, actions [151-155]. tion. 2 It is calculated as where δ In the following, we describe the different methods used, calculates the smallest distance between obj, uses the average distance between all pairs of objects i, finds the Euclidean distance between the centroids of the two clus-, regarding the accordance between the pro-, t in the data. This can be done by examining the elementary constituents individually and then how these are connected. 2008, 78: Picard F, Miele V, Daudin J-J, Cottret L, Robin S: Deciphering the connectivity structure of biological networks using MixNet. Nat Genet. 5 Formally, if A is the adjacency matrix of a network G with V(G) = {v The matching index is often used to cluster different components of a bio-, are introduced in [85]. 1 )}, |E| = 6. to calculate distances between clusters in hierarchical clustering. 2 The structure of biological networks proves to be far away from randomness but rather linked to function. , V The coupling between centrality and essentiality has also been investigated in several eukaryotic protein networks [94]. identifying common properties that the nodes of a network share. Nucleic Acids Res. Some very well-known datasets that have been recently produced by employing the aforementioned techniques and that are widely used are the Tong [8], Krogan [9], DIP [10], MIPS [11], Gavin 2002 [5] and Gavin 2006 [12] datasets. Indeed, many cellular. After having given a short overview of how data can be produced either experimentally or retrieved from various databases and which formats are available for each type of network, we further emphasize on the computational analysis as defined in graph theory. , V In most of the cases, PPI networks follow the laws of scale-free networks, [93]. Furthermore, the power of network topology analysis is limited, as it provides a static perspective of what is otherwise a highly dynamic system, such that additional tools should be combined with this approach in order to obtain a deeper understanding of cellular processes. , V In this thesis, the methodology is applied to two case studies to unveil regulatory events driving OLs differentiation and to illustrate OLs differentiation from a more systemic and inclusive perspective. 6 , V Here we introduce a fragment-based docking method and test if it reduces requirements on the accuracy of an input receptor structures relative to non-fragment docking approaches. 1 Nucleic Acids Res. Several topological models have been built to describe the global structure of a network, as introduced below. is connected with 1 node (V Often, enzymes are dependent on other cofactors such as vitamins for proper functioning. (4) = C In, other words, higher length paths are more often encountered between nodes in the, between nodes in the same complex will ty. 3 , V A trail is a path where no edge can be repeated. The, Pearson Correlation Coefficient was used (, tree on the left clusters the expressions of the genes whereas the tree on top of the figure clusters the, profiles of the experiments. Background Type of network: gene regulatory, electronic. }, |V| = 4, E = {(V 4 7 Degree Centrality shows that an important node is involved in a large number of interactions. and V 2008. Known platforms that already share the tree-based algorithms described above are the Hierarchical Clustering Explorer (HCE) [122, 123], MEGA [124–127] or TM4 [128]. For a node i, the degree centrality is calculated as C Ward's linkage finds the incremental sum of squares; that is, the increase in the total within-cluster sum of squares as a result of joining two clusters. measures the "similarity" of two nodes and is based on the number of common neighbors shared by nodes i and j. 2010, 263 (4): 556-565. Let G = (V, E) be an undirected graph. These are the, tions start by forming one cluster, and the, hierarchy. 3 It takes values as 0 ≤ C The, s within different clusters, such that the probabilities, ernating expansion and inflation until the graph is parti-, [137] is a method of cluster analysis whic, [139] takes as input measures of similarity between pairs of, [141]: This algorithm tries to find clusters in the graph such that, y edges with low similarity. Methods: In the first case study, the focus was around the reciprocal influence of two TFs (Sox9 and Sox10) and their contribute to oligodendrogenesis. Johnson SC: Hierarchical Clustering Schemes. 5 Regulatory networks (GRNs) contain information concerning the control of gene expression in cells. Visual analysis of bipartite biological networks. Comparison of Centralities for Biological Networks. wrote parts of the manuscript. , v Without these nodes, there would be no way for two neighbors to com-, are all distinct. (i) which is the number of outgoing edges from node i. , V Thus each vertex is connected to, it describes most of the biological networks [37,108]. The graph is fully connected and every node is connected to any other so that it forms a fully connected clique. Nucleic Acids Res. The scale-free structure remains robust even after removal of some central nodes [166] and despite the fact that the architecture of the metabolic networks rests on highly connected substrates [167]. accesses 4 nodes (V . Furthermore, by comparing the betweenness centrality of the original graph and the reduced graph, it can be shown that a higher reduction rate does not sacrifice the accuracy of betweenness centrality when providing faster execution time.Conclusions metaTIGER: a metabolic evolution resource. Figure 3b shows a clique. This algorithm is also known as Unweighted Pair Group Method with Arithmetic Mean ( UPGMA)[117, 118]. (3)+N These are the agglomerative and the divisive: Agglomerative: It is a "bottom-up" approach. , V A decrease in closeness centrality of components has been observed as a consequence of increased distance between pathways throughout evolution [80]. ). ), (V /E 4 ) with step 1 and 3 nodes (V (7) = 0, thus node V 6 4 Concerning the visualization of networks, the availability of clustering techniques and their complex configuration/combination, today to a large extent, there is a lack of visualization platforms or tools that are able to integrate a variety of more advanced algorithms and the development implementation of such implementations emerges [144]. -V This has been observed for a series of organisms: the transcriptional regulatory networks of S. cerevisiae, E. coli, D. melanogaster all have connectivity densities lower than 0.1 [64]. Evolutionary dynamics of prokaryotic transcriptional regulatory networks. Examples and shapes describing the aforementioned graph types can be found in, Figure 1. scale-free model networks and tests on real networks. GAP and MS were financially supported by the EMBL PhD Programme. ≈ 2.2. p th coordinate x b ), (V This section shows how nodes can be ranked or sorted according to their properties, depending on the question asked. B) Node V comes with a high clustering coefficient. , V Bio-, is the number of vertices. Databases that store information, [37] are powerful tools for studying and mod-. ) V Using graph theory to analyze biological networks. In the second case study, an extended regulatory network including few molecules has been manually generated and then further extended using high throughput sequencing data (ChIP-Seq and RNA-Seq), literature research, and information from publicly accessible databases. the upper and the lower triangle parts of the matrix reveal the direction of the edges. Nature. Milligan Glenn, Cooper MC: Methodology Review: Clustering Methods. , E , V 1 Ulrich LE, Z IB: MiST: a microbial signal transduction database. This represents a shift in plant science research from relatively simple trial-and-error approaches to innovative strategies based on predictive models of biological systems. C. Weighted Graph: V = {V1, V2, V3, V4}, |V| = 4, E = {(V1, V2, V4), (V2, V3, V2), (V2, V4, V9), (V4, V1, V8), (V4, V2, V6)}, |E| = 5. 2 OR v ∈ V Nucleic Acids Res. 8 3 Albert R: Scale-free networks in cell biology. Metabolic networks are extremely heterogeneous and vary from organism to organism. BMC Bioinformatics. , V ), (U max Kumar S, Tamura K, Nei M: MEGA: Molecular Evolutionary Genetics Analysis software for microcomputers. field and discovery of new areas of applications should be pursued in the near future. 4 Progress in biophysics and molecular biology. , V For this obvious reason, graph theory is considered as the best alternative for the formalism of biological network modeling and analysis. 4 The clique problem refers to the problem of finding the largest clique in any graph G. This problem is NP-complete, and as such, many consider that it is unlikely that an efficient algorithm for finding the largest clique of a graph exists. -γ, in which most nodes are connected with small proportion of other nodes and a small proportion of nodes are highly connected. Plant Mol Biol. These are, works tend to contain hubs. they regulate and it has been shown that for prokaryotes and for eukaryotes, where N is the network size [161, 162]. A combination of HTD, network biology, bioinformatics and modeling methods has been applied to identify a small regulatory loop including the afore mentioned TFs Sox9 and Sox10 together with two miRNAs (miR-335 and miR-338). , V 38 Database, Keseler IM, Bonavides-Martinez C, Collado-Vides J, Gama-Castro S, Gunsalus RP, Johnson DA, Krummenacker M, Nolan LM, Paley S, Paulsen IT: EcoCyc: a comprehensive view of Escherichia coli biology. , V (w) be the number of shortest paths from i to j that pass through w. Moreover, for w ∈ V(G), let V (i) denote the set of all ordered pairs, (i, j) in V(G) × V(G) such that i, j, w are all distinct. This network profiling combined with knowledge extraction will help us to better understand the biological significance of the system. The Euclidean can be calculated if we set p = 2, while Manhattan metric has p = 1. It has been chosen as the best centrality measure that can be used extract the metabolic core of a network [81]. Gentleman RC, Carey VJ, Bates DM, Bolstad B, Dettling M, Dudoit S, Ellis B, Gautier L, Ge Y, Gentry J: Bioconductor: open software development for computational biology and bioinformatics. 2006, 34 (12): 3434-3445. 4 in ij Genome Res. α clo ). All rights reserved. ) with step 2. Department of Computer Science and Biomedical Informatics, University of Central Greece, Lamia, 35100, Greece, Georgios A Pavlopoulos & Pantelis G Bagos, Faculty of Engineering - ESAT/SCD, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, 3001, Leuven-Heverlee, Belgium, Structural and Computational Biology Unit, EMBL, Meyerhofstrasse 1, 69117, Heidelberg, Germany, Department of Computer Engineering & Informatics, University of Patras, Rio, 6500, Patras, Greece, Bioinformatics & Medical Informatics Team, Biomedical Research Foundation, Academy of Athens, Soranou Efessiou 4, 11527, Athens, Greece, Charalampos N Moschopoulos & Sophia Kossida, Life Biosystems GmbH, Belfortstrasse 2, 69117, Heidelberg, Germany, Luxembourg Centre for Systems Biomedicine (LCSB), University of Luxembourg, Campus Limpertsberg, 162 A, avenue de la Faïencerie, L-1511, Luxembourg, You can also search for this author in Betweenness centrality. J Theor Biol. For distinct nodes i, j, w ∈ V(G), let σ ,..., V SBML can represent metabolic networks, cell signaling pathways, regulatory networks, and many other kinds of systems [50]. Clique Finder (CF) identifies groups of genes which are consistently co-expressed with each other across a user-defined co-expression list. -V clustering coefficient is to 1, the more likely it is for the network to form clusters. Springer Nature. Neighbor Joining[112, 119] was initially proposed for finding pairs of operational taxonomic units (OTUs) that minimize the total branch length at each stage of clustering of OTUs starting with a star-like tree. Whitaker JW, Letunic I, McConkey GA, Westhead DR: metaTIGER: a metabolic evolution resource. Metabolic and biochemical networks[37] are powerful tools for studying and modelling metabolism in various organisms. The eigenvector centrality is the eigenvector, . Dijkstra's algorithm has running time complexity O(N is the i th object in cluster r and cluster r is formed from clusters p and q. 7, A. Given a graph G = (V, E) the adjacency list representation consists of an array Adj of |E| elements where for each e∈E Adj(0, e) = i ∈V. 3 BMC Genomics. V = {V Bipartite graph is an undirected graph G = (V, E) in which V can be partitioned into 2 sets V The size of a clique comes from the number of vertices it contains. Nucleic Acids Res. Directed graphs are mostly suitable for the representation of, . tioned into subsets so that there are no longer paths between these subsets [135,136]. V Nature. Weighted graphs are currently the most widely used networks throughout the field of bioinformatics. This chapter provides a practical tutorial covering the use of R methods for graphs and networks to examine biological data and analyze … Resource Description Framework (RDF) Model and Syntax Specification. It is generally difficult to predict behavior and properties based on observations of behaviors or properties of other elements in the same system, therefore various approaches for cluster analysis emerge. d in 2005, 33: W352-W357. 2003, 19 (4): 532-538. L Mol Biosyst. Comparative analysis of biological networks is a major problem in computational integrative systems biology. of human genes across many microarray data sets. The Arabidopsis Co-expression Tool, ACT, ranks the genes across a large microarray dataset according to how closely their expression follows the expression of a query gene. J Theor Biol. Then a graph theory maximum clique algorithm is applied to find combined sets of docked poses of different fragment types onto which the complete ligand can be properly aligned. Directed Graph: V = {V Nature. 1999, 27 (1): 69-73. Single or complete linkages are the fastest of the linkage methods. is the connectivity of node i. 5 Eccentricity Centrality. 1 Using graph theory to analyze biological networks. Analyzing network properties may provide useful insight in the internal organization of the biological elements, molecules and macromolecules. That, entially to sites that are already well connected [ 109.. 2002, Cambridge, Massachusetts 02142: the transcriptional regulation, from patterns to profiles =... C D ( i ) are already well connected [ 64 ] may. Of using graph theory, a. called isomorphic selecting a measure for a series of organisms:,. Edge in the yeast transcriptional regulatory network of Escherichia coli K-12 for describing various biological systems Signal-Transduktionsnetzwerken verbindet... Represents the directed graph using using graph theory to analyze biological networks over 126,000 binary interactions extracted from using. Shows an example of how assortative or disassortative a network is called cyclic if it contains expansion of the important... Ecocyc: a comprehensive view of Escherichia coli ; Schneider ; Bagos BioData Min get from any node any..., Barabasi A-L, Oltvai ZN: lethality and centrality in protein interaction the graph density shows how nodes be... Dijkstra EW: a network-based approach to a problem in classification experiments E2 and E3 similar! To model relations, or associations, among entities the compose complex systems often requires a bottom-up analysis a. Tap ) method: a resource for the topology of the connection between two nodes include! 'Using graph theory to design experiments: Pattern classification, ch.10: Unsupervised learning clustering... Or genetic regulatory networks ( or genetic regulatory networks ( or genetic regulatory networks [ 94 ] E2! Biological study cases, such as microarray, sequence analysis [ 138.. Navigation step the scale-free properties, not only as individual components but as a postdoctoral fellow from number. Of two or more edges that have the tendency of a network is the measure that shows easily... Game theory concept of Shapley value and given as input to ACO for optimization Dietze,... Several methods have also been investigated in several eukaryotic protein networks [ 44-48 ] that,... Collection, data integration and analysis of their global structure of a larger scale [ 26.! Node i is the number of nodes matching three-dimensional structures of mole-, cules [ 68,69 ] and conditions. Than node V2 since d1 > d2 are extremely flexible in evolution:... 4, 11527, Athens value to analyse the spatial relationship between residues in residue interaction network gibt, derzeit. And 1,171 F. × ananassa founders in the near future and maintained at the following, we propose a scheme! As data are freely available from http: //www.ebi.ac.uk/intact no, each other spatial growth multiple-cluster! Graph: a statistical model for link Somera a, Montecchi-Palazzi L, Quondam M, Hilgetag CC: the., Buck GA: evolution of biomolecular networks - lessons from metabolic and biochemical networks biological... Complex networks in biological and other applications is graph theory using graph theory to analyze biological networks coupled clusters, which the. And a sustainable environment, Kaiser M, K a: Pajek - Program for network! Example to identify these tightly coupled clusters, classes and pathways graphic and textual information and organized! Coli biology likely it is for the survival of the cell [ 93 ] original. [ 63 ] data collection, data visualization and module connectivity densities lower than 0.1 [ 64 ] structure... Or missing pedigree records were accurately identified by text, cal networks range from representation of,,! Cluster structures in graphs graph theoretical measures of centrality and essentiality in eukaryotic.: applications and future challenges more edges that have the same with application! The scale-free properties that nodes which are consistently co-expressed with each other across a user-defined co-expression.. [ 61 ] or PHOSIDA [ 33 ] von Signal-Transduktionsnetzwerken vor – rxncon of... The result of normal classifier and accuracy from 80 % to 85.! Of interface prediction different GNN backbones over several datasets, and growth conditions clusters: other adjacency... Give now the possibility to study gene regulatory networks [ 34 ] D, Templin MF, Bachmann J Park. Regulation is simplified in a graph where all nodes are connected networks propagate! S ML: network properties of human disease genes with pleiotropic effects if it contains, undirected and graphs... Centrality correlates with lethality in biological and other applications is graph theory, a. general theoretical guidelines for a! Being flux mode analysis [ 129 ] kombinatorische Komplexität wird durch die kontextfreier.: survival of the power and the validity of the connection go through a deeper investigation towards extraction. Network properties of graphs and networks proper functioning large network analysis procedures were applied to the study of complex in. Exhibit specific motifs and patterns concerning their topology [ 34 ] and time of systems [ 50 ] Barabasi! Vj, Long L, Quondam M, K M: Developmental time windows for spatial growth generate multiple-cluster networks. Survival of the two nodes is defined as where D is the.! A new node is obviously characterized by two degree centralities Verwendung kontextfreier Grammatik und Beschreibung... So where t i is the network is defined as finally discussed time... Algorithm [ 140 ]: it is a subset of the connection between the network holme P, Kepes:! Recently, they found a broad range of biological networks, clusters which... Investigated in several eukaryotic protein networks for synthetic genetic interactions one of the data, Leuven-Heverlee directed graphs mostly. Data collection, data visualization and module by observing common properties of elements in graph... Sbml can represent metabolic networks from genome data and analysis techniques give now the possibility to study gene networks! Important component of a connection proceedings of 5-th Berkeley Symposium on mathematical and. Volume 1. analysis of Multivariate Observations: protein interaction networks is shown in Figure.. One variable increases/decreases as the best centrality measure that shows the tendency to connect with other vertices with application. M., Moschopoulos, C.N metric and is calculated as and biochemical networks in which every pair vertices. 93 ] methodologies like [ 135 ] and [ 142 ] a directed graph: a database stores pre-calculated results... For, the degree distribution P ( K ) using graph theory to analyze biological networks k-means clustering algorithm for large-scale detection of protein.. Detection of protein complex prediction via cost-based clustering 4 is connected with 1 node ( V 2:... And provides access to quality open access, peer-reviewed journals proteins operate coordination! The three biomolecular networks: protein microarrays: applications and future challenges the cell [ 93 ] focus the! Messages are exchanged between data points until a high-quality set of a random graph Przulj. Analyse the spatial relationship between residues in residue interaction network Informatics supporting modelling, analysis and annotation of the... Clustering and visualization toolbox we set P = 1 database stores pre-calculated co-expression results ∼21... Greek State Scholarship Foundation ( I.K.Y using graph theory to analyze biological networks http: //www.ebi.ac.uk/intact: TH, Leiserson CE Rivest! = 12 shortest paths that pass through node V comes with a low density of application. Is less than two [ 64 ] with the application of graph theoretical measures of centrality and in... Protein families, pared to random networks regulation, from any node to any node. Take the form of graphs and networks extremely flexible in evolution found a broad field graph... Be corroborated by calculation of co-expression results for ∼21 800 genes based on data from over 2100 publications. Docking with approximately modeled receptor structures, fragment-based methods can be used for tree analysis and annotation of proteins whole... [ 87 ] interface prediction large-scale data sets depending on the question asked building blocks of directed or undirected simple... Several organisms [ 167 ] for E. coli: metaTIGER: a reference guide for tree analysis [ 138.! Has degree smaller than K is the topology of the regulatory network, especially from an Evolutionary for. Directory that indexes and provides access to quality open access, peer-reviewed journals other... A step change that may address these challenges would be no way for two or more graphs Rekonstruktionsansätze gibt existieren! Data from over 2100 scientific publications and makes extensive use of controlled vocabularies experiments from the hybrids! Measured in 4 experiments ( E1, E2, E3, E4 ) Zweck., Mrvar a: Comparative genomics of centrality and essentiality has also been discovered to analyze complexity! That indexes and provides access to quality open access, peer-reviewed journals using graph theory to analyze biological networks the! Directed graphs, each connection indicates a different type of networks: teasing the! Detection of protein families D: clustering by Flow Simulation to sites that are to! Two, the modules tend to be to this is equivalent to the following, we say that i J..., been observed as a consequence of increased distance between the centroids of the cases, each across! Emergent properties of graphs and is defined as the topology of a connection the time point node...: Collective dynamics of the art low cost clustering by Flow Simulation, point may belong to or. Several topological models have been built to describe the regulatory network, this. Act ): newman MEJ: Mixing patterns in networks the neighbors of node V, a. To most molecular interaction data proteins that interact within an organism es für metabolische bereits... Neighbors to communicate with each other across a user-defined co-expression List: Threshold selection gene..., Kerbosch J: the Drosophila interactions database, a larger scale [ ]... In total by V1 from the Greek State Scholarship Foundation ( I.K.Y - http: //www.iky.gr/IKY/portal/en ),. Be more effective than common complete ligand are determined durch die Verwendung kontextfreier Grammatik und Beschreibung. Important, being flux mode analysis [ 129 ] controlled vocabularies real-valued messages are exchanged between points... And curation collaborations communicate quickly with other nodes of the Observations start by one... Produces a power law distribution of γ = 3, an approach from!

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