Network Motifs
Zach Saul
CS 289
Network Motifs: Simple Building Blocks of Complex Networks
R. Milo et al.
Network Models
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Interactions are represented as directed
nodes (as presented in class)
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Example problems include gene networks,
neural nets, ecological models and
computer networking models
Network Motifs
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Patterns that appear more often in real
networks than in randomly generated
networks
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Many notions of a random network
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Naïve algorithm
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Erdos

Renyi random graphs
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Scale free networks
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Even more specialized?
Random Graphs
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Three node motifs
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Preserve degree for each node
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Four node motifs
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Preserve degree for each node
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Preserve the number of three node motifs
Example Motif
Method
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Using brute force, searched target network for
every possible subgraph, counting results
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Similarly, searched random network
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Motifs are patterns that occur greater or equal
number of times in random networks more than
1% of the time.
Results
Results (cont.)
Gene/Neural Net Analysis
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The nematode neural net and the gene net
both contain similar structures
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Feed forward
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Bi

fan
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Both are information processing networks
with sensory and acting components
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Sensory neurons/transcription factors
regulated by biochemical signals
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Motor neurons/structural genes
Food Web Analysis
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Food Webs do not show feed

forward
motifs
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Suggests that direct interaction between
species at a separation of two layers selected
against (e.g. Omnivores)
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Bi

parallel suggests that prey of same
predator share prey
Electronic Circuit Analysis
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Circuits can be classified by function using
network motifs
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Circuits from benchmark set showed
different motifs for each functional class
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Some info processing circuits show similar
motifs to biological info processing circuits
Web Analysis
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Network of hyperlinks
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Many more bidirectional links
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Motifs indicate a design that allows the
shortest path among sets of related pages
Conclusions
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Technique robust to data errors
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Motifs can indicate common function
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..or could indicate similar evolutionary
constraints
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Scalability to other types of networks
possible
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Scalability to larger subgraphs difficult
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