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

0.2

rand

randreal NNZ

networks random among

subgraph ofnumber ofdeviation standard :

network randomin subgraph ofnumber average :

network realin subgraph ofnumber :

rand

rand

real

N

N

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

i typeofsubgraph noden ofion Concentrat :

nodesn with i typeof subgraphs sofappearance ofnumber The :

i

i

ii

ii

C

N

N

NC

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 Si for each subgraph of type i, and set to Si zero initially.

• Si= Si+1/P until ST samplings are finished.• Assume L types of subgraphs were sampl

ed.

L

kk

ii

S

SC

1

Compare between sampling and enumeration

Runtime complexity analysis

Conservation of network motif constituents

Homo Sapiens Mus musculus Drosophila melanogaster

C. elegans Arabidopsis thaliana

Saccharomyces cerevisiae

Four nodes motif

Orthologs

Inparanoid: Eukaryotic Ortholog Groups

Evolution conservation of motif

Evolution conservation of motif

Network motif software

Homework

• Download the mfinder motif detection software from Uri Alon’s web page, http://www.weizmann.ac.il/mcb/UriAlon 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