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