System-Biophysik Überblick Life‘s Complexity Pyramid (Oltvai-Barabasi, Science 10/25/02) System Functional Modules Building Blocks Components Zum Begriff „Bio-System“ Input Output Eigenschaften * Komponenten (Spezien) * Netzwerkartige Verknüpfungen (kinetische Raten) * Substrukturen (Knoten,Module, Motive) * Funktionelle Input => Output Relation Ziel * Erforschung der „Bauprinzipen“ (reverse engineering) Vorsicht : Bauprinzip nicht „rational“ sondern Ergebnis eines Evolutionprozesses * Erstellung quantitativer Modelle zur Beschreibung des Systems Large Metabolic Networks: the „usual“ view Network Measures Network Measures Network Measures Network Measures Network Types Random Scale-Free Hierarchical Network Types Random Scale-Free Hierarchical Network Types Random Scale-Free Hierarchical Metabolic networks at different levels of description Metabolic networks: Rather Hierarchical than Scale-free g=2.2 Jeong et al Nature Oct 00 g=2.2 Scale-free complex networks Highly clustered „small worlds“ Nature June 4, 1998 Aug 1999 http://smallworld.sociology.columbia.edu 19 degrees of separation: “The WWW is very big but not very wide” 3 l15=2 [1,2,5] 6 1 l17=4 [1,3,4,6,7] 4 5 2 7 … < l > = ?? Finite size scaling: create a network with N nodes with Pin(k) and Pout(k) < l > = 0.35 + 2.06 log(N) 19 degrees of separation R. Albert et al Nature (99) nd.edu <l> based on 800 million webpages [S. Lawrence et al Nature (99)] IBM A. Broder et al WWW9 (00) Nature July 27, 2000 Yeast protein interaction network Topological robustness 10% proteins with k<5 are lethal BUT 60% proteins with k>15 are lethal red = lethal, green = non-lethal orange = slow growth yellow = unknown Construction of Scale-free networks These scale-free networks do not arise by chance alone. Erdős and Renyi (1960) studied a model of growth for graphs in which, at each step, two nodes are chosen uniformly at random and a link is inserted between them. The properties of these random graphs are not consistent with the properties observed in scale-free networks, and therefore a model for this growth process is needed. The scale-free properties of the Web have been studied, and its distribution of links is very close to a power law, because there are a few Web sites with huge numbers of links, which benefit from a good placement in search engines and an established presence on the Web. Those sites are the ones that attract more of the new links. This has been called the winners take all phenomenon. The mostly widely accepted generative model is Barabasi and Albert's (1999) rich get richer generative model in which each new Web page creates links to existent Web pages with a probability distribution which is not uniform, but proportional to the current in-degree of Web pages. This model was originally discovered by Derek de Solla Price in 1965 under the term cumulative advantage, but did not reach popularity until Barabasi rediscovered the results under its current name. According to this process, a page with many in-links will attract more in-links than a regular page. This generates a power-law but the resulting graph differs from the actual Web graph in other properties such as the presence of small tightly connected communities. More general models and networks characteristics have been proposed and studied (for a review see the book by Dorogovtsev and Mendes). A different generative model is the copy model studied by Kumar et al. (2000), in which new nodes choose an existent node at random and copy a fraction of the links of the existent node. This also generates a power law. However, if we look at communities of interests in a specific topic, discarding the major hubs of the Web, the distribution of links is no longer a power law but resembles more a normal distribution, as observed by Pennock et al. (2002) in the communities of the home pages of universities, public companies, newspapers and scientists. Based on these observations, the authors propose a generative model that mixes preferential attachment with a baseline probability of gaining a link. en.wikipedia.org The origin of the scale-free topology and hubs in biological networks Evolutionary origin of scale-free networks The origin of the scale-free topology and hubs in biological networks Evolutionary origin of scale-free networks Beyond Networktopology Flux-Balance-Analysis dS Nv dt http://www.genome.jp/ligand/ Zusammenfassung Biologische Netzwerke Netzwerke haben eine hierachische Struktur - Komponenten, Blöcke, funktionelle Module, System Universelle Eigenschaften komplexer Netzwerke * „small world property“ (kurze Verbindungswege) * skaleninvarianz (Verteilung der „connectivity“) * Starke Tendenz zu Clustern Große Zahl und inhomogene Komponenten Experimenteller Input durch: * Hochdurchsatztechniken / Datenbanken * Systematische Literaturanalyse (data-mining)