System-Biophysik Überblick Components Building Blocks Functional Modules System Lifes Complexity Pyramid (Oltvai-Barabasi, Science 10/25/02)

System-Biophysik Überblick

Components

BuildingBlocks

FunctionalModules

System

Life‘s Complexity Pyramid (Oltvai-Barabasi, Science 10/25/02)

Zum Begriff „Bio-System“

InputOut-put

* Komponenten (Spezien)* Netzwerkartige Verknüpfungen (kinetische Raten)* Substrukturen (Knoten,Module, Motive)* Funktionelle Input => Output Relation

* Erforschung der „Bauprinzipen“ (reverse engineering)Vorsicht : Bauprinzip nicht „rational“ sondern Ergebnis eines Evolutionprozesses

* Erstellung quantitativer Modelle zur Beschreibung des Systems

Eigenschaften

Ziel

Large Metabolic Networks: the „usual“ view

Network Measures

Network Measures

Network Measures

Network Measures

Network TypesRandom Scale-Free Hierarchical

Network TypesRandom Scale-Free Hierarchical

Network TypesRandom Scale-Free Hierarchical

Metabolic networksat different levels of description

Metabolic networks:Rather Hierarchical than Scale-free

Jeon

g et al N

ature O

ct 00

=2.2 =2.2

Scale-free complex networks

Highly clustered „small worlds“

Nature June 4, 1998 Aug 1999

http://smallworld.sociology.columbia.edu

< 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: “The WWW is very big but not very wide”

l15=2 [1,2,5]

l17=4 [1,3,4,6,7]

… < l > = ??

1

2

3

4

5

6

7

nd.edu

19 degrees of separation R. Albert et al Nature (99)

based on 800 million webpages [S. Lawrence et al Nature (99)]

A. Broder et al WWW9 (00)IBM

Nature July 27, 2000

Yeast protein interaction network

red = lethal, green = non-lethalorange = slow growth yellow = unknown

Topological robustness

10% proteins with k<5 are lethal BUT60% proteinswith k>15 arelethal

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 hubsin biological networks

Evolutionary origin of scale-free networks

The origin of the scale-free topology and hubsin biological networks

Evolutionary origin of scale-free networks

http://www.genome.jp/kegg/pathway.html#cellular -> MCP, CheY

ZusammenfassungBiologische 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 KomponentenExperimenteller Input durch: * Hochdurchsatztechniken / Datenbanken * Systematische Literaturanalyse (data-mining)