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