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title title. The Architecture of Complexity: From the WWW to network biology. www.nd.edu/~networks. Bio-Map. GENOME. protein-gene interactions. PROTEOME. protein-protein interactions. METABOLISM. Bio-chemical reactions. Citrate Cycle. Connect with probability p. p=1/6 N=10 k ~ 1.5.

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title title
titletitle

The Architecture of Complexity: From the WWW to network biology

www.nd.edu/~networks

bio map
Bio-Map

GENOME

protein-gene interactions

PROTEOME

protein-protein interactions

METABOLISM

Bio-chemical reactions

Citrate Cycle

slide3

Connect with probability p

p=1/6 N=10 k ~ 1.5

Poisson distribution

Erdös-Rényi model(1960)

Pál Erdös(1913-1996)

- Democratic

- Random

slide4
WWW

Expected

P(k) ~ k-

Found

World Wide Web

Nodes: WWW documents Links: URL links

Over 3 billion documents

ROBOT:collects all URL’s found in a document and follows them recursively

R. Albert, H. Jeong, A-L Barabasi, Nature, 401 130 (1999).

airlines

What does it mean?

Airlines

Poisson distribution

Power-law distribution

Random Network

Scale-free Network

internet
Internet

INTERNET BACKBONE

Nodes: computers, routers Links: physical lines

(Faloutsos, Faloutsos and Faloutsos, 1999)

slide8

Swedish sex-web

Nodes: people (Females; Males)

Links: sexual relationships

4781 Swedes; 18-74;

59% response rate.

Liljeros et al. Nature 2001

slide9

Many real world networks have the same architecture:

Scale-free networks

WWW, Internet (routers and domains), electronic circuits, computer software, movie actors, coauthorship networks, sexual web, instant messaging, email web, citations, phone calls, metabolic, protein interaction, protein domains, brain function web, linguistic networks, comic book characters, international trade, bank system, encryption trust net, energy landscapes, earthquakes, astrophysical network…

ba model
BA model

Scale-free model

(1) Networks continuously expand by the addition of new nodes

WWW : addition of new documents

(2) New nodes prefer to link to highly connected nodes.

WWW : linking to well known sites

P(k) ~k-3

GROWTH:

add a new node with m links

PREFERENTIAL ATTACHMENT:the probability that a node connects to a node with k links is proportional to k.

Barabási & Albert, Science286, 509 (1999)

bio map1
Bio-Map

GENOME

protein-gene interactions

PROTEOME

protein-protein interactions

METABOLISM

Bio-chemical reactions

Citrate Cycle

slide12

METABOLISM

Bio-chemical reactions

Citrate Cycle

metab movie
Metab-movie

Nodes: chemicals (substrates)

Links: bio-chemical reactions

Metabolic Network

meta p k
Meta-P(k)

Metabolic network

Archaea

Bacteria

Eukaryotes

Organisms from all three domains of life are scale-free networks!

H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, and A.L. Barabasi, Nature, 407 651 (2000)

bio map2
Bio-Map

GENOME

protein-gene interactions

PROTEOME

protein-protein interactions

METABOLISM

Bio-chemical reactions

Citrate Cycle

slide17

PROTEOME

protein-protein interactions

prot p k
Prot P(k)

Topology of the protein network

Nodes: proteins

Links: physical interactions (binding)

H. Jeong, S.P. Mason, A.-L. Barabasi, Z.N. Oltvai, Nature 411, 41-42 (2001)

slide19

Perfect copy

Mistake: gene duplication

Origin of the scale-free topology: Gene Duplication

Proteins with more interactions are more likely to get a new link:

Π(k)~k

(preferential attachment).

Wagner (2001); Vazquez et al. 2003; Sole et al. 2001; Rzhetsky & Gomez (2001);

Qian et al. (2001); Bhan et al. (2002).

robustness
Robustness

1

node failure

S

fc

0

1

Fraction of removed nodes, f

Robustness

Complex systems maintain their basic functions even under errors and failures (cell  mutations; Internet  router breakdowns)

robust sf
Robust-SF

Robustness of scale-free networks

1

S

0

1

f

Attacks

Failures

  3 : fc=1

(R. Cohen et al PRL, 2000)

fc

Albert, Jeong, Barabasi, Nature 406 378 (2000)

prot robustness
Prot- robustness

Yeast protein network

- lethality and topological position -

Highly connected proteins are more essential (lethal)...

H. Jeong, S.P. Mason, A.-L. Barabasi, Z.N. Oltvai, Nature 411, 41-42 (2001)

slide23

Traditional view of modularity:

Modularity in Cellular Networks

  • Hypothesis:

Biological function are carried by discrete functional modules.

  • Hartwell, L.-H., Hopfield, J. J., Leibler, S., & Murray, A. W. (1999).
  • Question: Is modularity a myth, or a structural property of biological networks?

(are biological networks fundamentally modular?)

slide25

3. Clustering coefficient scales

# links between k neighbors

C(k)=

k(k-1)/2

Hierarchical Networks

scaling of the clustering coefficient c k
Scaling of the clustering coefficient C(k)

The metabolism forms a hierachical network.

Ravasz, Somera, Mongru, Oltvai, A-L. B,Science 297, 1551 (2002).

can we identify the modules
Can we identify the modules?

li,j is 1 if there is a direct link between i and j, 0 otherwise

slide30

System level experimental analysis of essentiality in E. coli

Whole-Genome Essentiality by Transposomics

Aerobic growth:

620 essential

3,126 dispensable

genes

Gerdes et al.

J Bact. 185, 5673-5684 (2003).

slide32

System level analysis of the full E coli metabolism

Essentiality:

Red: highly essential

Green: dispensable

Evolutionary conservation:

Red: highly conserved

Green: non-conserved

(reference: 32 bacteria)

Gerdes et al.

J Bact. 185, 5673-5684 (2003).

slide33

Characterizing the links

Metabolism:

Flux Balance Analysis (Palsson)

Metabolic flux for each reaction

Edwards, J. S. & Palsson, B. O, PNAS97, 5528 (2000).

Edwards, J. S., Ibarra, R. U. & Palsson, B. O. Nat Biotechnol19, 125 (2001).

Ibarra, R. U., Edwards, J. S. & Palsson, B. O. Nature420, 186 (2002).

slide34

SUCC: Succinate uptake

GLU : Glutamate uptake

Central Metabolism,

Emmerling et. al, J Bacteriol184, 152 (2002)

Global flux organization in the E. coli metabolic network

E. Almaas, B. Kovács, T. Vicsek, Z. N. Oltvai, A.-L. B. Nature, 2004.

slide35

~ k -0.27

Mass flows along linear pathways

Mass flows along linear pathways

Succinate rich substrate

Glutamate rich substrate

Inhomogeneity in the local flux distribution

pyramid
Pyramid

Life’s Complexity Pyramid

Z.N. Oltvai and A.-L. B. (2002).

http www nd edu networks
Http://www.nd.edu/~networks

Zoltán N. Oltvai, Northwestern Med. School

Hawoong Jeong, KAIST, Corea

Réka Albert, Penn State

Ginestra Bianconi, Friburg/Trieste

Erzsébet Ravasz, Notre Dame

Stefan Wuchty, Notre Dame

Eivind Almaas, Notre Dame

Baldvin Kovács, Budapest

Tamás Vicsek, Budapest

http://www.nd.edu/~networks

http www nd edu networks1
Http://www.nd.edu/~networks

http://www.nd.edu/~networks

bacon map
Bacon-map

#876

Kevin Bacon

#1

Rod Steiger

Donald Pleasence

#2

#3

Martin Sheen

bacon list
Bacon-list

NO!

876 Kevin Bacon 2.786981 46 1811

Bonus: Why Kevin Bacon?

Measure the average distance between Kevin Bacon and all other actors.

No. of movies : 46 No. of actors : 1811 Average separation: 2.79

Kevin Bacon

Is Kevin Bacon the most connected actor?

summary
SUMMARY

Science collaboration

WWW

Language

Hierarchical Networks

Scale-free

Citation pattern

Cell

Internet

Modular

C(N)=const.

Hierarchical

C(k)~k-β

Scale-free

P(k)~k-γ

slide43

Traditional modeling: Network as a static graph

Given a network with N nodes and L links

Create a graph with statistically identical topology

RESULT: model the static network topology

PROBLEM: Real networks are dynamical systems!

Evolving networks

OBJECTIVE: capture the network dynamics

  • identify the processes that contribute to the network topology
  • develop dynamical models that capture these processes

METHOD :

BONUS: get the topology correctly.

meta all p k
Meta+all P(k)

Whole cellular network

slide45

Protein network

Nodes: proteins Links: physical interaction (binding)

Proteomics : identify and determine the properties of the proteins. (related to structure of proteins)

slide46

Nodes: chemicals (substrates)

Links: chem. reaction

Metabolic Network

achilles heel
Achilles Heel

Achilles’ Heel of complex network

failure

attack

Internet

Protein network

R. Albert, H. Jeong, A.L. Barabasi, Nature 406 378 (2000)

slide49

Taxonomy using networks

A: Archaea

B: Bacteria

E: Eukaryotes

slide50

Watts-Strogatz

Clustering: My friends will know each other with high probability!

Probability to be connected C»p

# of links between 1,2,…n neighbors

C =

n(n-1)/2

N nodes forms a regular lattice. With probability p, each edge is rewired randomly.

(Nature 393, 440 (1998))

19 degrees
19 degrees

 Finite size scaling: create a network with N nodes with Pin(k) and Pout(k)

< l > = 0.35 + 2.06 log(N)

19 degrees of separation R. Albert et al Nature (99)

based on 800 million webpages [S. Lawrence et al Nature (99)]

nd.edu

< l >

IBM

A. Broder et al WWW9 (00)

19 degrees of separation

3

l15=2 [125]

l17=4 [1346  7]

… < l > = ??

6

1

4

7

5

2

citation
Citation

33

3212

SCIENCE CITATION INDEX

Nodes: papers Links: citations

Hopfield J.J.,

PNAS1982

1736 PRL papers (1988)

P(k) ~k-

( = 3)

(S. Redner, 1998)

summary1
SUMMARY

Complexity

Network

Science collaboration

WWW

Food Web

Scale-free network

Citation pattern

Cell

Internet

UNCOVERING ORDER HIDDEN WITHIN COMPLEX SYSTEMS

slide54

Combining Modularity and the Scale-free Property

Deterministic Scale-Free Networks

Barabási, A.-L., Ravasz, E., & Vicsek, T.

(2001) Physica A299, 559.

Dorogovtsev, S. N., Goltsev, A. V., &

Mendes, J. F. F. (2001) cond-mat/0112143.

(DGM)

slide55

C is independent of N

C decreases with N

Problems with the scale-free model

Ci=2ni/ki(ki-1) Watts, Strogatz, 1998

slide56

Internet (router),

Vazquez et al, ‘01

Power Grid

Exceptions:

Geographically Organized Networks:

Common feature:

economic pressures towards shorter links

slide57

Is the hierarchical exponent β universal?

  • For most systems:

Connect a p fraction of nodes to the central module using preferential attachment

slide58

Many highly connected small clusters

combine into

few larger but less connected clusters

combine into

even larger and even less connected clusters

Real Networks Have a Hierarchical Topology

What does it mean?

  • The degree of clustering follows:
slide60

Metabolic networks

Protein networks

Hierarchy in biological systems

slide61
MFT

Mean Field Theory

, with initial condition

γ = 3

A.-L.Barabási, R. Albert and H. Jeong, Physica A 272, 173 (1999)

slide62
P53

Nature 408 307 (2000)

“One way to understand the p53 network is to compare it to the Internet. The cell, like the Internet, appears to be a ‘scale-free network’.”

p53 p k
P53 P(k)

p53 network (mammals)

slide64

Hollywood

Language

Internet (AS)

Vaquez et al,'01

WWW

Eckmann & Moses, ‘02

Real Networks

achilles heel1
Achilles Heel

Achilles’ Heel of complex networks

failure

attack

Internet

R. Albert, H. Jeong, A.L. Barabasi, Nature 406 378 (2000)

cells sf or er
Cells-SF or ER?

Argument 1:

Cellular networks are scale-free!

Reason: They formed one node at a time…

Argument 2:

Cellular networks are exponential!

Reason: They have been streamlined by evolution...

What is the topology of cellular networks?

actors
Actors

ACTOR CONNECTIVITIES

Nodes: actors Links: cast jointly

Days of Thunder (1990) Far and Away (1992) Eyes Wide Shut (1999)

N = 212,250 actors k = 28.78

P(k) ~k-

=2.3

prot interaction map
Prot Interaction map

Yeast protein network

Nodes: proteins

Links: physical interactions (binding)

P. Uetz, et al.Nature403, 623-7 (2000).

http www nd edu networks2
Http://www.nd.edu/~networks

Interplay between network structure and evolution

Removing thecomplexes

S. Wuchty,

Z.N. Oltvai,

A.-L.B., 2003.

slide71

1. Scale-free

2. Clustering coefficient

independent of N

Properties of hierarchical networks

meta diameter
Meta-diameter

Node-node distance in metabolic networks

Scale-free networks:

D~log(N)

Larger organisms are expected

to have a larger diameter!

3

D15=2 [125]

D17=4 [134  67]

… D = ??

6

1

4

7

5

2

slide73

Connect with probability p

p=1/6 N=10 k ~ 1.5

Poisson distribution

Erdös-Rényi model(1960)

Pál Erdös(1913-1996)

- Democratic

- Random

slide74
WWW

Expected

P(k) ~ k-

Found

World Wide Web

Nodes: WWW documents Links: URL links

Over 1 billion documents

ROBOT:collects all URL’s found in a document and follows them recursively

R. Albert, H. Jeong, A-L Barabasi, Nature, 401 130 (1999).

airlines1

What does it mean?

Airlines

Poisson distribution

Power-law distribution

Random Network

Scale-free Network

internet1
Internet

INTERNET BACKBONE

Nodes: computers, routers Links: physical lines

(Faloutsos, Faloutsos and Faloutsos, 1999)

new york times
New York Times

Complex systems

Made of many non-identical elements connected by diverse interactions.

NETWORK

slide79

Random Networks

Connect each pair of nodes with probability p

p=1/6 N=10 k ~ 1.5

Erdös-Rényi, 1960

ba model1
BA model

Scale-free networks

Growth:Networks expand by the addition of new nodes

Preferential attachment:New nodes prefer to link to highly connected nodes

P(k) ~k-3

A.-L.Barabási, R. Albert, Science 286, 509 (1999)

meta diameter1
Meta-diameter

Small World Features: distance in metabolic networks

3

D15=2 [125]

D17=4 [134  67]

… D = ??

6

1

4

7

5

2

Random Networks:

D~log(N)

(small world effect)

Scale-Free Networks:P(k)~k-γ

log N γ>3

D = log log N 2<γ<3

const γ=2

(ultra small world)

Cohen,Havlin, PRL’03

modularity in the metabolism
Modularity in the metabolism

Clustering Coefficient:

# links between k neighbors

C(k)=

k(k-1)/2

Metabolic network

(43 organisms)

 Scale-free model

bacon 1
Bacon 1

Austin Powers: The spy who shagged me

Let’s make it legal

Robert Wagner

Wild Things

What Price Glory

Barry Norton

A Few Good Man

Monsieur Verdoux

slide85

Can Latecomers Make It?Fitness ModelSF model: k(t)~t ½(first mover advantage)Real systems: nodes compete for links -- fitnessFitness Model: fitness (h )k(h,t)~tb(h)whereb(h) =h/CG. Bianconi and A.-L. Barabási, Europhyics Letters.54, 436 (2001).

bose einstein condensation in evolving networks

Network

Bose gas

Fit-gets-rich

Bose-Einstein condensation

Bose-Einstein Condensation in Evolving Networks

G. Bianconi and A.-L. Barabási, Physical Review Letters 2001; cond-mat/0011029