foundations for network biology: graph theory boolean...
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Network Clustering
Experimental network mapping
Graph theory and terminology
Scale-free architecture
Integrating 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
3
Yeast two-hybrid method
Fields and Song
4
Kinase-target interactions
Mike Snyder and colleagues
5
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
8
Most recorded genetic interactions are
synthetic lethal relationships
Adapted from Hartman, Garvik, and Hartwell, Science 2001
A B A B A B A B
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)
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 length The 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-g
What happens for
small vs. large g?
Random vs Preferential Attachment
• Erdos-Renyi
Start with N nodes and connect each pair with equal
probability p
• Scale-free
Add 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
1
2
2
-
kk
n
k
nC II
I
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
yfg1 yfg2 yfg3
CTAACTC TCGCGCA TCATAAT Barcode
(UPTAG):
Deletion Strain:
Growth 6hrs in 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
ssential
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 by
all 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
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