Network Clustering
Experimental network mappingGraph theory and terminology
Scale-free architectureIntegrating with gene essentiality
Robustness
Lecturer: Trey Ideker
2
Measurements of molecular interactions
Protein-protein interactions• Yeast-two-hybrid• Kinase-substrate assays• Co-immunoprecipitation w/ mass spec
Protein-DNA interactions• ChIP-on-chip and ChIP-seq
Genetic interactions• Systematic Genetic Analysis
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Yeast two-hybrid method
Fields and Song
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Kinase-target interactions
Mike Snyder and colleagues
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Protein interactions by protein immunoprecipitation followed by mass spectrometry
Gavin / Cellzome
TEV = Tobacco Etch Virus proteolytic site
CBP = Calmodulin binding peptide
Protein A = IgG binding from Staphylococcus
ChIP measurement of protein→DNA interactions
From Figure 1 of Simon et al. Cell 2001
Genetic interactions: synthetic lethals and suppressors
• Genetic Interactions:
• Widespread method used by geneticists to discover pathways in yeast, fly, and worm
• Implications for drug targeting and drug development for human disease
• Thousands are now reported in literature and systematic studies
• As with other types, the number of known genetic interactions is exponentially increasing…
Adapted from Tong et al., Science 2001
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Most recorded genetic interactions are synthetic lethal relationships
Adapted from Hartman, Garvik, and Hartwell, Science 2001
A B A ΔB ΔA B ΔA ΔB
α
ω
A
B
Parallel Effects (Redundant or Additive)
Sequential Effects (Additive)
Single A or B mutations typically abolish their biochemical activities
Single A or B mutations typically reduce their biochemical activities
Interpretation of genetic interactions (Guarente T.I.G. 1990)
α
ω
A B
GOAL: Identify downstream physical
pathways
Yeast protein-protein interaction network
What are its network properties?
Graphs
• Graph G=(V,E) is a set of vertices V and edges E
• A subgraph G’ of G is induced by some V’ V and E’ E
• Graph properties:– Node degree– Directed vs. undirected– Loops– Paths– Cyclic vs. acyclic– Simple vs. multigraph– Complete– Connected– Bipartite
Paths
A path is a sequence {x1, x2,…, xn} such that (x1,x2), (x2,x3), …, (xn-1,xn) are edges of the graph.
A closed path xn=x1 on a graph is called a graph cycle or circuit.
Network measures
• Degree ki
The number of edges involving node i
• Degree distribution P(k)The probability (frequency) of nodes of degree k
• Mean path lengthThe avg. shortest path between all node pairs
• Network Diameter“The longest shortest path”
How do the above definitions differ between undirected and directed networks?
WHAT DOES SCALE FREE
REALLY MEAN, ANYWAY?
P(k) is probability of each degree k
For scale free: P(k) ~ k
What happens for
small vs. large ?
Random vs Preferential Attachment
• Erdos-RenyiStart with N nodes and connect each pair with equal probability p
• Scale-freeAdd nodes incrementally. New nodes connect to each existing node I with probability proportional to its degree:
J
J
I
k
k
Scale-free networks have small avg. path lengths ~ log (log N)– this is called the ‘small world’ effect
Clustering coefficient
12
2
kk
nkn
C III
The combination “k choose 2”
# edges between node I’s neighbors
# of neighbors of I
The density of the network surrounding node I, characterized as the number of triangles through I.Related to network modularity
C(k) = avg. clustering coefficient for nodes of degree k
Directionality and Degree
What is the clustering coefficient of A in either case?
Integrating networks with functional gene information:Gene replacement for yeast & other model species
Using HR-based gene replacement, genes can be replaced with drug resistance cassette, tagged with GFP, epitope tagged, etc.
Systematic phenotyping
yfg1Δ yfg2Δ yfg3Δ
CTAACTC TCGCGCA TCATAATBarcode
(UPTAG):
DeletionStrain:
Growth 6hrsin minimal media
(how many doublings?)
Rich media
…
Harvest and label genomic DNA
Systematic phenotyping with a barcode array
Ron Davis and friends…
• These oligo barcodes are also spotted on a DNA microarray
• Growth time in minimal media:
– Red: 0 hours– Green: 6 hours
The amazing result from that paper
% E
ssen
tial
P(k
)
k k
Robustness
• Complex systems, from the cell to the Internet, can be amazingly resilient to component failure
• Network topology plays an important role in this robustness
• Even if ~80% of nodes fail, the remaining ~20% still maintain network connectivity
• This also leads to attack vulnerability if hubs are selectively targeted
• In yeast, only ~20% of proteins are lethal when deleted, and are 5 times more likely to have degree k>15 than k<5.
Network Motifs (Milo, Alon et al.)
• Motifs are “patterns of interconnections occurring in complex networks.”
• That is, connected subgraphs of a particular isomorphic topology
• The approach queries the network for small motifs (e.g., of < 5 nodes) that occur much more frequently than would be expected in random networks
• Significant motifs have been found in a variety of biological networks and, for instance, correspond to feed-forward and feed-back loops that are well known in circuit design and other engineering fields.
• Pioneered by Uri Alon and colleagues
Motif searches in 3 different contexts
All 3-node directed subgraphs
What is the frequency of each in the network?
Outline of the Approach
• Search network to identify all possible n-node connected subgraphs (here n=3 or 4)
• Get # occurrences of each subgraph type
• The significance for each type is determined using permutation testing, in which the above process is repeated for many randomized networks (preserving node degrees– why?)
• Use random distributions to compute a p-value for each subgraph type. The “network motifs” are subgraphs with p < 0.001
Schematic view of network motif detection
Networks are randomized preserving node degree
Concentration of feedforward motif:
Mean+/-SD of 400 subnetworks
(Num. appearances of motif divided byall 3 node connected subgraphs)
Transcriptional network results
Neural networks
Food webs
World Wide Web
Electronic circuits
Interesting questions
• Which networks have motifs in common?• Which networks have completely distinct motifs versus
the others?• Does this tell us anything about the design constraints
on each network?• E.g., the feedforward loop may function to activate
output only if the input signal is persistent (i.e., reject noisy or transient signals) and to allow rapid deactivation when the input turns off
• E.g., food webs evolve to allow flow of energy from top to bottom (?!**!???), whereas transcriptional networks evolve to process information