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
Z
N real   N rand 
 rand
 2.0
N real : number of subgraph in real network
 N rand : average number of subgraph in random network
 rand : standard deviation of number of subgraph
among random networks
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
Ni
Ci 
 Ni
i
N i : The number of appearance sof subgraphs of type i with n nodes
Ci : Concentrat ion of n node subgraph of type i
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
sampled.
Ci 
Si
L
S
k 1
k
Compare between sampling and enumeration
Runtime complexity analysis
Conservation of network motif constituents
Homo Sapiens
Mus musculus
Drosophila
melanogaster
Orthologs
Four nodes motif
Saccharomyces
cerevisiae
C. elegans
Arabidopsis thaliana
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