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
Nv
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)

Evolutionary origin of scale