Network Clustering

Experimental network mappingGraph theory and terminology

Scale-free architectureIntegrating with gene essentiality

Robustness

Lecturer: Trey Ideker

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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