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

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)]

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)]

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

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)]

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:

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