1. Modelling Structure and Function in Complex Networks
Andrea Rocco
6th Bioinformatics Day on “Bioinformatics and Network Biology”
October 6th 2005, Oxford Centre for Gene Function

2. Yeast protein interaction network
Outline
Structural Analysis
Global and local properties
Modelling Structure
The degree distribution
What about Dynamics?
Examples and perspectives
Yeast protein interaction network
[Jeong et al., Nature (2001)]

3. Statistical properties: the degree distribution
= Probability that a vertex at random has degree k (In- and Out-)
 Degree distribution (In- and Out-)
[Erdős and Rényi (1959, 1960)]
[Barabási et al., Nature Reviews (2005)]

4. An example: The yeast transcriptional regulatory network
[Guelzim et al., Nature genetics (2002)]
Exp
Power Law

5. Local structural properties
Motifs
Overrepresented subgraphs when compared to a randomized version of the same network. [Milo et al., Science (2002)]
Modules
Ambiguous definition
Topological clustering + functional data (e.g. gene expression levels)
[Babu et al., Current Opinion in Structural Biology (2004)]

6. Modelling Structure: The degree distribution
Growth
At every time step, add a new vertex and connect it to another vertex already present in the network
Preferential Attachment
Assume that the probability that the new vertex is connected to a node is proportional to the degree of that node
[Albert and Barabási, Rev. Mod. Phys. (2002)]
Model:
Solution:

7. What about modelling dynamics?
Epigenetic Modelling
Response of cell/organism to environmental perturbations (plasticity)
Evolutionary Modelling
Construction of network-based phylogenies [ Gail Preston Talk]
Modelling “small” networks
Specific reaction dynamics – Requires knowledge of kinetic parameters
Modelling collective properties
“Dense” networks – Spatiotemporal pattern formation