biological networks and their evolution -...

RNA dynamics and Biomolecular Systems Lab, CNRS−UMR168

Hervé ISAMBERT

Institut Curie, Paris, France

Biological Networks and their Evolution

2nd IMSc Complex Systems School, The Institute of Mathematical Sciences, Jan 14 & 15, 2010

I. Introduction: from Genomes to Networks

III. Properties of Biological Networks

II. Different Types of Biological Networks

IV.Network Evolution: from Genes to Organisms

V. Models of Biological Network Evolution


Hervé ISAMBERT, Institut Curie, Paris

... except in the light of evolution""Nothing in biology makes sense...

but is it for FUNCTIONAL reason ??

or is it because they CANNOT be randomby CONSTRUCTION ??

Then what sense does it make to compare them to randomized graphs ??

Very Preliminary Conclusion

Theodosius Dobzhansky (1973)

Biological Networks are NOT Random Graphs !

Mechanisms of Genome Evolution

Long suspected... recently proved!

shuffling of protein domains

Implies important genetic modifications!!

Mechanisms of Genome Evolution

shuffling of protein domains

Kellis et al. 2004Whole Genome Duplication in Yeast Genome

bird

s 1

0,00

0

rept

iles

8,0

00di

nosa

urs

dino

saur

s,

m

amm

als

5,5

00

−20−30

arch

eaba

cter

ia>

10,0

00,0

00 ?

?

x 2x 2

bony fish 24,000tetrapods 28,000

othe

rs (

prot

ists

) 3

0,00

0

plan

ts

330

,000

S. cerev.K. lactis

flowering275,000

eukaryotes

Paramecium

x 2

x 2

A. thalianaP. trichocarpa

x 2

x 2

Carp

X. laevis

x 2

vertebrates 52,000

amph

ibia

6,

000

B. napus

x 2

othe

r 5

5,00

0

x 2TetraodonX. tropicalis

x 2

x 2

−150

−250

−300

−350

viru

ses−1,000

MYA

−450

−500

LampreyLanceletBdelloid T. barreraeH. sapiensNadisBulinus M.incognita

∗< −3,500 ??

chordates

x 2

fung

i 1

00,0

00

sea

urch

in,

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6,0

00

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ges

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aloc

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ates

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ers,

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bs,

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cts,

800

,000

x 2ro

tifer

a >

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atod

a >

25,0

00

x 2x 2

mol

lusc

a 5

0,00

0

bilateria

animals 1,200,000

Whole Genome Duplications in Evolution

−Population bottleneck−Speciation eventsWhole Genome Duplications promote:

x 2x 2

1+1+1

Evolution by Duplication Divergence

1 10

1e-06

1e-04

0.01

1Node degree

Nod

e d

egre

e d

istr

ibut

ion

Number of shared partners

Nod

e p

air

dis

trib

utio

n w

ith s

hare

d p

artn

ers

WGD dupli > 20 x random pairs

WGD dupli > 1,000 x random pairs

k=1k=10

Proba to share k+ partners :

WGD duplirandom

random pairs

degree distributions

WGD dupli pairs

Evidence of Genome Duplication on PPI network

500 duplicates from WGD : 250 with both duplicates in available PPI network

Yeast 6000 genes : 4000 in PPI network

PPI network

1 10

1e-06

1e-04

0.01

1Node degree

Nod

e d

egre

e d

istr

ibut

ion


Nod

e p

air

dis

trib

utio

n w

ith s

hare

d p

artn

ers



k=1k=10


WGD duplirandom

random pairs


WGD dupli pairs




PPI network

NetworkDuplicationunder WGD

1 10

1e-06

1e-04

0.01

1Node degree

Nod

e d

egre

e d

istr

ibut

ion


Nod

e p

air

dis

trib

utio

n w

ith s

hare

d p

artn

ers



k=1k=10


WGD duplirandom

random pairs


WGD dupli pairs



PPI network


Divergence

1 10

1e-06

1e-04

0.01

1Node degree

Nod

e d

egre

e d

istr

ibut

ion


Nod

e p

air

dis

trib

utio

n w

ith s

hare

d p

artn

ers



k=1k=10


WGD duplirandom

random pairs


WGD dupli pairs



PPI network


"Rewiring" ??

1 10

1e-06

1e-04

0.01

1Node degree

Nod

e d

egre

e d

istr

ibut

ion


Nod

e p

air

dis

trib

utio

n w

ith s

hare

d p

artn

ers



k=1k=10


WGD duplirandom

random pairs


WGD dupli pairs



PPI network


Shared Partners

Hervé Isambert, UMR168, Institut Curie, Section de Recherche, Paris

Transcription Networks:

PNAS, 104, 5516−5520 (2007)

Marco Cosentino Lagomarsino

Mol BioSyst, 5, 170−179 (2009)

BMC Syst Biol 1:49 (2007)

Kirill Evlampiev

PNAS, 105, 9863−9868 (2008)

Prot−Prot Interaction Networks:

Human Frontier, Ministere de la Recherche, ANR

Institut Curie, CNRS, Fondation PG de Gennes(from tolweb site)

Tree of Life

Richard Stein

Signaling Networks:

Evolution and Topology of Large Biological Networks

Biol Direct, 4, 28 (2009)

time−lineargrowth

Evolution of PPI Networks

growthexponentialEvlampiev, Isambert BMC Syst. Bio. (2007)

Evlampiev, Isambert PNAS USA (2008)

single

Symmetric divergence

new

dupli

Duplication

Partial Genome

interaction

proteins

n=1

General Duplication−Divergence Model of PPI Network Evolution

4’

41 3

2

2’1−q q

1 2 3 4

Genome

P−P Interaction Network

x (1+q)

GDD Model of PPI Network Evolution

K. Evlampiev1

3

2’ 2

4’4

1

4

2

3


γon

γsn

soγ

γss

γ

γoo

nn

n=1

Duplication

Partial Genome

new

oldsingle

interaction

proteins

Asymmetric divergence

1 2 3 4

K. Evlampiev

Genome


4’

41 3

2

2’1−q q

x (1+q)

GDD Model of PPI Network Evolution

1

4’4

3

2’ 21

4

2

3

Deletion

of Links

δ=1−γ

γon

γsn

soγ

γss

γ

γoo

nn

IterationDuplication

Partial Genome

new

oldsingle

interaction

proteins



1 2 3 4

Genome


4’

41 3

2

2’1−q q

x (1+q)

1

4’4

3

2’ 21

4

2

3

Overview of the Evolutionary Regimes


with respect to p(k)

Deletion

of Links

δ=1−γ

γon

γsn

soγ

γss

γ

γoo

nn


Partial Genome

new

oldsingle

interaction

proteins



1 2 3 4

Genome


4’

41 3

2

2’1−q q

x (1+q)

1

4’4

3

2’ 21

4

2

3

M’ >1 Scale−freeM’ <1 Exponential

3Network Topology Index iΓ

i=s,o,nM’= max( ) > M

Γik

iio

γin

γΓio

ns

kq

i

1−q

i=s,o,n

= (1−q) + q( + )isγNode Degree Growth Rate

Γ >1 Growing NetworkΓ <1 Vanishing NetworksΓ nΓoΓΓ = (1−q) + q + q Network Link Growth Rate

<1 Nonconserved NetworkM>1 Conserved NetworkM

sΓ

Deletion

of Links

δ=1−γ

γon

γsn

soγ

γss

γ

γoo

nn


Partial Genome

new

oldsingle

interaction

proteins


1

2

= (1−q) + q M oΓ < ΓProtein Conservation Index


1 2 3 4

Genome


4’

41 3

2

2’1−q q

x (1+q)

1

4’4

3

2’ 21

4

2

3

ΓM < 1 < Γ1 < M <

10

11

1

Expanding PPI Networks

Non−Conserved Networks Conserved Networks M

Γ

Γ

1

n oo

s

s

s

o

o

o

oo

s

o

s

o

o

s s

n

Network Conservation (M) and Expansion ( )Γ

2

0

1

3

4

5

6

7

8

9

duplication

Vanishing

M < < 1

ΓM < 1 < Γ1 < M <

10

11

1



Γ

Γ

1

n o

s

s

s

o

o

o

oo

s


2

0

1

3

4

5

6

7

8

9

duplication

Vanishing

M < < 1

ΓM < 1 < Γ1 < M <

10

11

1



Γ

Γ

1


2

0

1

3

4

5

6

7

8

9

duplication

Vanishing

M < < 1




Γik

iio

γin

γΓio

ns

kq

i

1−q

i=s,o,n




sΓ

Deletion

of Links

δ=1−γ

γon

γsn

soγ

γss

γ

γoo

nn


Partial Genome

new

oldsingle

interaction

proteins


1

2



1 2 3 4

Genome


4’

41 3

2

2’1−q q

x (1+q)

1

4’4

3

2’ 21

4

2

3




Γik

iio

γin

γΓio

ns

kq

i

1−q

i=s,o,n




sΓ

(M’ > M > 1)necessaryConserved Networks are also Scale−free

Deletion

of Links

δ=1−γ

γon

γsn

soγ

γss

γ

γoo

nn


Partial Genome

new

oldsingle

interaction

proteins


1

2



1 2 3 4

Genome


4’

41 3

2

2’1−q q

x (1+q)

1

4’4

3

2’ 21

4

2

3

γss

soγ

γsn

γoo γ

on

γnn

of Linkswith proba

Deletion

1−γ1−µ

proteins

k k+1

Duplication−Divergence Models Including Self−links

interaction

µnµ

s

µon

µo

Iteration

Duplication

Partial Genome

Self−links leads to time−linear (not exponential) connectivity expansionk k Γ

Self−links do not affect evolutionary regimes butare essential contributors to certain network motifs

x (1+q)

1 2’ 21 2

3 3

4

4’

41

Conservation of Network Motifs

This is in broad agreement with empirical observations !

Eventually: structural orthology functional orthology

M1

γγ

γ

γγ

γ

γγγ 23

Motif conservation index

s/o

s/o

s/o

Network Motifs are NOT Conserved underWhile Proteins are typically Conserved (if M>1)

Long−term Duplication−Divergence Evolution

RalGDS RGL3

GAP

RalGPS1RalGPS2

GAP GAP

GAP GAP82%

60%

H. sapiens

RalBP1 Exocyst

x 2

RGL1

GAP GAP

RGL2RGL4

x 2

D. melanogaster

CG5522

?

28%

GAP

GAP

RalBP1 Exocyst

RGL

D. mel H. sap

x 2

D. rer

x 2x 2

Whole Genome Duplications

RalGDS

RGL1

RGL3

RASGRF1RASGRF2

KSR1

KSR2

ERAS

RIT2

RIT1

STK38

RasGRP3

RalB

RalA

RalGPS1

RGL4

RalGPS2

RalBP1Raf1

BRAF

ARAF

NRAS

HRAS

MRAS

RRAS

RGL2

KRASRRAS2

STK38L RasGRP1

RasGRP2

RasGRP4MAP4K1

MAP4K2

Ras−Ralpathways

RASRAS RAS

RalA RalB

RAS RAS

RalGEF

RAS

RAL

Ral Effectuor

RAS

Ral

Kirill Evlampiev

<N >/<N >=(n)(n+1) ∆(n)

h( )=α∆ = +q Γ(1−q) +q Γα α α

Γs o n

Asymptotic "Characteristic Equation"Network Node Growth Rate

<1{α}0<

αh( )

p ~ 1/k α+1k

Γ

Γ

i

i

h( )=α +q Γ(1−q) +q Γα α α

Γs o n

α∗ >1

<1{α}0<

Asymptotic Topology of PPI Networks

α10

h(1)

Dense

h(1)

Exponential Degree Distribution

h(0)

α∗ >1

Scale−free Degree Distribution

M’=max( ) > 1

kp ~ exp(− k)M’=max( ) < 1 µ

Convex Characteristic Function

<N >/<N >=(n)(n+1) ∆(n)

h( )=α∆ = +q Γ(1−q) +q Γα α α

Γs o n

Asymptotic "Characteristic Equation"Network Node Growth Rate

<1{α}0<

αh( )

p ~ 1/k α+1k

Γ

Γ

i

i

h( )=α +q Γ(1−q) +q Γα α α

Γs o n

α∗ >1

<1{α}0<

oΓiΓ (n)

Conserved Networks are also Scale−freenecessary (M’ > M > 1)

GDD Model + Fluctuations = max( )Πn=1

R R

sΓΠ (n)(n)

n=1

(n)(n)> [(1−q ) + q ] =M’ M

Scale−free

Exponential

[

Asymptotic Topology of PPI Networks

α10

h(1)

Dense

h(1)

Exponential Degree Distribution

h(0)

α∗ >1

Scale−free Degree Distribution

M’=max( ) > 1

kp ~ exp(− k)M’=max( ) < 1 µ

Convex Characteristic Function

= max( )iΓi=s,o,n

M’Asymptotic Network TopologyM’ >1M’ <1

3

]

0.01 0.1 10

0.4

0.8

1.2

0.01 0.1 10

0.4

0.8

1.2

0.01 0.1 10

0.4

0.8

1.2

L/<L> or N/<N> L/<L> or N/<N> L/<L> or N/<N>

20% Growth Rate 50% Growth Rate ~80% Growth Rate

Linear regime N ~ L NL regime N < L

Distribution of Network Sizes

Genome and PPI Network Evolutionunder Protein Domain Shuffling

Domain−Domain Interaction Network

Direct interaction bwn protein domains

Multidomain proteins (random shuffling)

domain1

domain2

Redefining PPI Networks as Domain Interaction Networks

XOR

XOR

protein1=domain1





protein2=

domain2A + domain2B


XOR

XOR

protein1=domain1



Indirect interaction within complexes



Adding some "combinatorial logic" through multidomain proteins


protein2=

AND

domain2A + domain2BXOR

XOR

1 10 1001e-6

1e-4

0.01

1

kp

kk 2 k

.g

kp

(+/− 2σ)WGD Model

(+/− 2σ)

Yeast direct int. data

Yeast direct int. dataWGD Model

γon

γoo=0.1 ( =1 γ

nn )=0γ

on

Node Degree

Protein direct connectivity

Average Connectivityof Neighbours k.g

kDistribution

λ =1.5 prot. bind. domains per protein

Comparison with Yeast Direct Interaction Data

Topology of direct interaction network

A two−parameter Whole Genome Duplication Model

with Random Protein Domain Shuffling λ

1 10 1001e-6

1e-4

0.01

1

kp

kk 2 k

.g

kp


(+/− 2σ)



γon

γoo=0.1 ( =1 γ

nn )=0γ

on

Γ = Γ + Γ = 1 + 2 = 20%γono n

PPI Network growth rate

Seasquirt−Human (2WGD): 25%

Seasquirt−Fugu (3WGD): 11%

Node Degree


Average Connectivityof Neighbours k.g

kDistribution



Topology of direct interaction network

A two−parameter Whole Genome Duplication Model

with Random Protein Domain Shuffling λ

1 10 1001e-6

1e-4

0.01

1

1 10 1001e-6

1e-4

0.01

1

kp

kk 2 k

.g

kp

kk 2 k

.g

kp


(+/− 2σ)




γon

γoo=0.1 ( =1 γ

nn )=0γ

onwith Random Protein Domain Shuffling λA two−parameter Whole Genome Duplication Model

Topology of direct interaction network Topology of direct & indirect interaction network

Comparison with Yeast Direct + Indirect Interaction Data

Node Degree


Average Connectivityof Neighbours

Direct & indirect "matrix" connectivity

k.gk

Distribution


Yeast dir. & indir. int. data

Yeast dir. & indir. int. data


1 10 1001e-6

1e-4

0.01

1

1 10 1001e-3

0.01

0.1

1

1 10 1001e-3

0.01

0.1

1

kp

γnn

k.gk

Node Degree Distribution Average Connectivity of Neighbours

Fit of Yeast Data with a one−parameter WGD Model γ(onγ

oo=1 )=0=0.26

kp


kk 2 k

.g


(+/− 2σ)

phys. interaction dataYeast two−hybrid and

WGD Model


Yeast two−hybrid and

WGD Model (+/− 2σ)

phys. interaction data

1

2

3

4

cspA

gyrA hns

caiF flhDC

fliAZY

nhaA osmC rcsAB stpA

flgAMN

flgBCDEFGHIJK flhBAE fliEfliLMNOPQR flgMN fliC fliDST motABcheAW tarTapcheRBYZ

Evolution and Topology of Transcription Networks

E.coli shallow Transcription Network

No large scale feedbacks

but 60% autoregulators (AR)

Transcription Factor Families

Babu et al., NAR 2006

Babu et al., NAR 2006

TF Family Expansion by Duplication

crp fnrC

G

AT

C

G

A

T

G

CTAG

C

AT

C

GATCGATC

AGT

C

T

AG

G

CAT

G

CATC

GATG

C

A

T

C

G

T

A

G

C

TAG

C

AT

G

ATC

G

T

CATGCAC

G

TA

C

G

A

T

GC

AT

-1 -0.5 0 0.5 1specificity

0

0.5

1

1.5

2

2.5

3

3.5

norm

aliz

ed h

its

autoregulatory sites

CRP

-1 -0.5 0 0.5 1specificity

0

1

2

3

4

norm

aliz

ed h

its

autoregulatory sites

FNR

CGTAC

GTA

CGAT

C

GAT

C

AGT

CAGT

AC

GT

C

TAGGCTAC

G

A

T

C

T

A

T

C

T

G

A

A

C

G

AT

AGCT

GTAC

GTCAG

TAC

GCTAG

CAT

GCAT

crp / fnr example

elimination of crosstalks

AR duplication

Evolutionary decoupling of duplicated ARs?

Regulatoryconflict !

Duplication / Divergence Asymmetry

Cosentino−Lagomarsino, Jona, Bassetti & Isambert,PNAS, 104, 5516 (2007) arxiv.org/abs/q.bio/0701035

Hierarchy and Feedback in the Evolutionof Bacterial Transcription Networks

Iteration

γon

γsn

soγ

γss

ioγ

inγΓi is

γ= (1−q) + q( + )q andΓik

i

Duplication

Partial Genome

new

oldsingle

interaction

proteins


γ

γoo

nn

Inhomogeneous Models of Duplication−Divergence Evolution

While the general "multicolor" inhomogeneous model cannot be solved exactly,

o

ns

kq

i

1−q

i=s,o,n

(n) (n) (n) (n) (n)

one can use a posteriori choices of evolutionary parameters’ values

Deletion

of Links

δ=1−γ

The approach becomes exact for two−color bipartite networks or oriented networks

This approach can model for instance the adaptative expansion of gene families

to mimick positive / negative selection of combinatorial features of networks (approximation)

1 2 3 4

Genome


4’

41 3

2

2’1−q q

x (1+q)

1

4

2

3

1

4’4

3

2’ 2

Bacteria versus Eukaryote Transcriptional Hierarchy

Cosentino−Lagomarsino et al. PNAS 2007 Sellerio et al., submitted 2008

S. cerevisiae has long transcriptional cascades

while bacteria have short ones

S. cerevisiaeEscherichia coli Bacillus subtilis

> 50% of TF ~ 10% of TF

Long

est S

hort

est P

aths






Long

est S

hort

est P

aths






Adaptative Selection ? Random drift ?

Long

est S

hort

est P

aths

OR non−adaptative constraints on bacterial genomes ?? Isambert & Stein, Biol Direct (2009)





Adaptative Selection ? Random drift ?

PopulationDynamics

N.s > 1 N.s << 1N population size

Long

est S

hort

est P

aths

Transcription / translation coupling versus mRNA export out of the nucleus

Apparent genome size constraint ?

Alternatively... Specific Evolutionary Constraints of Bacteria?

but gene conservation required "mutualized" gene pool + gene transfers

Encephalitozoon intestinalis

Selaginella moellendorffii

(M. hapla)

nematode H. sapiensC. elegans D. melanogaster

ANIMALS(Pratylenchus coffeae)

Trichoplax adhaerens

P. aethiopicus,lungfish

tick, argasid

carnivorous plant

G. margaretae

A. thaliana

PLANTS F. assyriaca,lily

rice, O. sativa T. aestivumwheat,

S. castanea(P. carinii)

A. gossypii S. cerevisae

FUNGI

P. ubique E. coli

FREE−LIVINGPROKARYOTES

10 10 10 101010 1010 10

(N. equitans) ARCHAEA

(G. theta)

T. thermophila

PROTISTS

G. polyedra

S. cellulosum(C. ruddii)

green algae

I. hospitalis

M. acetivorans

8 9 10 11 1210 2

(HIV)(HDV)

43 6 75

10 100 1,0001 ~10,000

10

approx. number of genes~20,000 ~30,000

Genome size (bp)

(mamavirus)

(phage T4)

Genome Size Restriction

of Free−living Prokaryotes

FREE−LIVING EUKARYOTESOBLIGATE PARASITES and SYMBIONTS

O. tauri P. tetraurelia A. dubia

EUBACTERIA

VIROIDS VIRUSES


Bacterial genome structure : Apparent genome size constraint ?



Encephalitozoon intestinalis

Selaginella moellendorffii

(M. hapla)

nematode H. sapiensC. elegans D. melanogaster

ANIMALS(Pratylenchus coffeae)

Trichoplax adhaerens

P. aethiopicus,lungfish

tick, argasid

carnivorous plant

G. margaretae

A. thaliana

PLANTS F. assyriaca,lily

rice, O. sativa T. aestivumwheat,

S. castanea(P. carinii)

A. gossypii S. cerevisae

FUNGI

P. ubique E. coli

FREE−LIVINGPROKARYOTES

10 10 10 101010 1010 10

(N. equitans) ARCHAEA

(G. theta)

T. thermophila

PROTISTS

G. polyedra

S. cellulosum(C. ruddii)

green algae

I. hospitalis

M. acetivorans

8 9 10 11 1210 2

(HIV)(HDV)

43 6 75

10 100 1,0001 ~10,000

10

approx. number of genes~20,000 ~30,000

Genome size (bp)

(mamavirus)

(phage T4)

Genome Size Restriction

of Free−living Prokaryotes

FREE−LIVING EUKARYOTESOBLIGATE PARASITES and SYMBIONTS

O. tauri P. tetraurelia A. dubia

EUBACTERIA

VIROIDS VIRUSES


Gene duplications + genome size constraint gene turnover


Bacterial genome structure : Apparent genome size constraint ?


RNA Dynamics and Biomolecular Systems Lab

5’ 3’

A

GCAGG

AGGACG

A

A

G

CAUCCUCCUACG

AAGGUAGGGGGAUGG

AAA

AC C

GUCC

CCCUGC

C

A

AG

C

AGGAGGA

CG

AAGCA

UCCUCCU

ACGA

AGGUAGGGGGAUGG

AAA

A

CCGUCCCCCUGCC

A

5’ 3’

cis / transcontrol

Duplicationof genes

Deletionof Links

Iteration

4

2 1

4’4

3

2’ 21

3

100 nm

II. Evolution of Biological NetworksModeling biological networks under duplication−divergence evolution

Self−assembly of ncRNARNA switches and networks

I. RNA Regulatory and Physical Networks

$$. Human Frontier, ANR, Ministère de la Recherche, Institut Curie, CNRS, Fondation PG de Gennes

Institut Curie, CNRS, Paris

biological networks and their evolution -...

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