Design principle of biological networks—network motif

Definition of motifs Motifs are those subgraphs that occur significantly more often in the real network than in randomized networks.

Network motifs Original network Random version of original network

Criteria for network motif

Motifs in genetic network of yeast

Motifs in genetic network of E. coli

Enumeration methods to identify motifs Generating an ensemble of random networks Counting subgraphs in real network and random network

Subgraph concentration

Random sampling of n node subgraphs Pick a random edge from the network and expand the subgraph iteratively by picking random neighboring edges until the subgraph reaches n nodes.

Sampling algorithm

P: probability of sampling a specific subgraph Define a score S i for each subgraph of type i, and set to S i zero initially. S i = S i +1/P until S T samplings are finished. Assume L types of subgraphs were sampled.

Compare between sampling and enumeration

Runtime complexity analysis

Conservation of network motif constituents Homo SapiensMus musculus Drosophila melanogaster C. elegans Arabidopsis thaliana Saccharomyces cerevisiae Four nodes motif Orthologs

Inparanoid: Eukaryotic Ortholog Groups

Evolution conservation of motif

Network motif software

Homework Download the mfinder motif detection software from Uri Alon’s web page, Read the manual and make yourself being familiar with this software. Use this software to find the motifs for the E. coli gene regulatory network. The interaction file can be downloaded from Uri Alon’s homepage.

References Uri Alon, An Introduction to Systems Biology: Design Principles of Biological Circuits