Les Réseaux Biologiques et leur Evolution

UMR168, Institut Curie, Section RechercheDynamique de l’ARN et Systèmes Biomoléculaires

Hervé ISAMBERT

Les Réseaux Biologiqueset leur Evolution

Dynamique de l’ARN et Systèmes Biomoléculaires

Duplicationof genes

Deletionof Links

Iteration

4

2 1

4’4

3

2’ 21

3

Evolution des réseaux biologiques

5’ 3’

A

GCAGG

AGGACG

A

A

GCAUCCUCCUACG

AAGGUAGGGGGAUGG

AAA

AC C

GUCC

CCCUGC

C

A

AG

C

AGGAGGA

CG

AAGCA

UCCUCCU

ACGA

AGGUAGGGGGAUGG

AAA

ACCGUCCCCCUGCC

A

5’ 3’

cis / transcontrol

Autoassemblage ARNCommutateurs ARN

100 nm

I. Switches et Réseaux ARN

II. Réseaux Biologiques

Hervé ISAMBERT, UMR168, Institut Curie

PPI Networks: Evlampiev & Isambert, BMC Systems Biology 1:49 (2007)

Hervé Isambert CNRS UMR168, Institut CurieRNA dynamics and Biomolecular Systems Lab

Tree of Life(from tolweb site)

Marco Cosentino Lagomarsino

Kirill Evlampiev

Lagomarsino, Jona, Bassetti & Isambert,

Evlampiev & Isambert, arxiv.org/abs/q−bio.MN/0611070

Transcription Networks:

Evolution and Topology of Large Biological Networks

PNAS, 104, 5516−5520 (2007)

I. Intro: Des Génomes aux Réseaux

III. Propriétés des Réseaux Biologiques

II. Différents Types de Réseaux Biologiques

IV.Evolution des Réseaux: des Gènes aux Organismes

V. Modèles d’Evolution des Réseaux

Les Réseaux Biologiques et leur Evolution

Hervé ISAMBERT, Institut Curie








within some species familiesEven multimodal distribution

5 decades (8 including viruses)

Genome size distributionwhat was known before sequencing

Sparrow 1976

Genome Sequencing Statistics

NCBI, 21 Jan 2008

Human 20,000−25,000

Arabidopsis 29,000

Gallus 20,000−23,000

Paramecium 39,000

Wheat 75,000 ?(allohexaploid)

6,000

19,000

13,000

Ten Years of Genome Sequencing:

Tetraodon 22,000

1 cell

100,000 cells

1,000 cells

Evolution through Duplication−Divergence of Genes and Genomes

few genes... same genes...

Biological Networks

protein1 protein2

interaction

Combinatorial Gene Expression

Detailed interaction logic (AND/OR/NOT)

Combinatorics

Network−like schematic representations :

without logic !!








Biological Networks








Topology of Biological Networks

Yeast Protein−Protein Interaction Network



Exponential versus Scale−free Network Topology

Modularity of Protein Interaction Networks

1 10 100

0,001

0,01

0,1

1

pk,in

pk,out

IN and OUT Degree distributions

B Feed Forward Loop

Bi−FanC

A Autoregulatory Loop

��

��

��

��

��

"Over−represented" Motifs

Shen−Orr (2002) andRegulonDB (2005)

Structures of Regulatory Networks

Coherent and Incoherent Feedforward Loops

Speed up genetic response

Mangan et al, JMB 2006

BUT... such motifs are NOT conserved!

Propriétes Dynamiques des Modules de transcription

Low

High

Repressor

Repressor

Low

High

Activator

Activator

Demand Rule in Gene Regulation

Savageau PNAS (1977)

Demand Rule in Gene Regulation

Savageau PNAS (1977)

HighRepressor

ActivatorRepressor Low

Activator

Low

High

Very Preliminary Conclusion

Biological Networks are NOT Random Graphs !

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 ??



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



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


Theodosius Dobzhansky (1973)









The Ribosome

The Ribosome

34 Euk − Arc only Homologous Ribosomal Proteins 33 Euk − Arc − Bac Universal Ribosomal Proteins

The Ribosome

Ribosomal Protein S8 in Archaea and Bacteria

Universal RibosomalProteins bwn Eukaryotes,

Archaea and Bacteria

Remaining HomologousProteins bwn Eukaryotesand Archaea

Homologies between RNA Polymerases

ArchaeaBacteria

Eukaryote (RNAPol I, II & III)

TATA Box Asymmetry and RNAPol II and III Direction

But... TATA Binding Protein (TBP)is essentially symmetric

TBP / BRF (Pol III) EukaryoteTBP / TFIIB (Pol II) Eukaryote

TBP / TFB Archaea

Transcription Direction given by TFIIB (TFB) and BRF

BidirectionalTranscription inGiardia lamblia

Teodorovic et al NAR 2007

BRF but no TFIIB ??

Independent Aquatic Placental Mammals

Hippopotame

Tapir / Rhinoceros

Seals

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

Kellis et al. 2004Whole Genome Duplication in Yeast Genome

−20−30

arch

eaba

cter

ia>1

0,00

0,00

0 ??

∗−2,500 / 4,000 ??

choa

nofla

gella

tes

bird

s 1

0,00

0

rept

iles

8,0

00di

nosa

urs

dino

saur

s,

m

amm

als

5,5

00x 2x 2

jelly

fish,

mol

lusc

a, s

pide

rs,

crab

s,in

sect

s, 9

00,0

00

flow

erin

g27

5,00

0

x 2

x 2

S. cerevisiaeK. lactis

−150

−250

−300

−350

−450

−500

viru

ses

eukaryotes

−1,000

Paramecium

x 2

othe

rs (

prot

ists

) 30

,000

MYA

x 2

x 2

A. thalianaP. trichocarpa

tuni

cate

s 5

00

bony fish 24,000

x 2

Ciona

x 2

Carp

X. laevis

H. sapiens

x 2

vertebrates 52,000

amph

ibia

6,

000

tetrapods 28,000

chordates

x 2

N. viridulusNadis B. napus

x 2

othe

r 5

5,00

0x 2

x 2

plan

ts

330

,000

x 2

animals 1,200,000

TetraodonX. tropicalisT. barreraefu

ngi

100

,000

x 2

Whole Genome Duplications promote:

Whole Genome Duplications in Evolution

−Speciation events−Shuffling of protein domains

−20−30

arch

eaba

cter

ia>1

0,00

0,00

0 ??

∗−2,500 / 4,000 ??

choa

nofla

gella

tes

bird

s 1

0,00

0

rept

iles

8,0

00di

nosa

urs

dino

saur

s,

m

amm

als

5,5

00x 2x 2

jelly

fish,

mol

lusc

a, s

pide

rs,

crab

s,in

sect

s, 9

00,0

00

flow

erin

g27

5,00

0

x 2

x 2

S. cerevisiaeK. lactis

−150

−250

−300

−350

−450

−500

viru

ses

eukaryotes

−1,000

Paramecium

x 2

othe

rs (

prot

ists

) 30

,000

MYA

x 2

x 2

A. thalianaP. trichocarpa

tuni

cate

s 5

00

bony fish 24,000

x 2

Ciona

x 2

Carp

X. laevis

H. sapiens

x 2

vertebrates 52,000

amph

ibia

6,

000

tetrapods 28,000

chordates

x 2

N. viridulusNadis B. napus

x 2

othe

r 5

5,00

0x 2

x 2

plan

ts

330

,000

x 2

animals 1,200,000

TetraodonX. tropicalisT. barreraefu

ngi

100

,000

x 2

Whole Genome Duplications promote:

Whole Genome Duplications in Evolution

−Speciation events−Shuffling of protein domains

Evolution by Duplication Divergence

Evolution by Duplication Divergence

1 10

1e-06

1e-04

0.01

1Node degree

Nod

e d

egre

e d

istri

butio

n

Number of shared partners

Nod

e p

air

dist

ribut

ion

with

sha

red

par

tner

s

WGD dupli > 20 x random pairsWGD 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 networkYeast 6000 genes : 4000 in PPI network

PPI network

1 10

1e-06

1e-04

0.01

1Node degree

Nod

e d

egre

e d

istri

butio

n


Nod

e p

air

dist

ribut

ion

with

sha

red

par

tner

s


k=1k=10


WGD duplirandom

random pairs


WGD dupli pairs


500 duplicates from WGD : 250 with both duplicates in available PPI networkYeast 6000 genes : 4000 in PPI network

PPI network

NetworkDuplicationunder WGD

1 10

1e-06

1e-04

0.01

1Node degree

Nod

e d

egre

e d

istri

butio

n


Nod

e p

air

dist

ribut

ion

with

sha

red

par

tner

s


k=1k=10


WGD duplirandom

random pairs


WGD dupli pairs


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

PPI network

Yeast 6000 genes : 4000 in PPI network

Divergence

1 10

1e-06

1e-04

0.01

1Node degree

Nod

e d

egre

e d

istri

butio

n


Nod

e p

air

dist

ribut

ion

with

sha

red

par

tner

s


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

istri

butio

n


Nod

e p

air

dist

ribut

ion

with

sha

red

par

tner

s


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

istri

butio

n


Nod

e p

air

dist

ribut

ion

with

sha

red

par

tner

s


k=1k=10


WGD duplirandom

random pairs


WGD dupli pairs



PPI network


SharedPartners








time−lineargrowth

Evolution of PPI Networks

Evlampiev, Isambert q−bio.MN/06011070

growthexponentialEvlampiev, Isambert BMC Syst. Bio. (2007)

time−lineargrowth

Evolution of PPI Networks

Evlampiev, Isambert q−bio.MN/06011070

growthexponentialEvlampiev, Isambert BMC Syst. Bio. (2007)

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 4Genome

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)


1

4’4

3

2’ 21

4

2

3

γon

γsn

soγ

γss

γ

γoo

nn


Duplication

Partial Genome

new

oldsingle

interaction

proteins


n=1

1 2 3 4Genome


4’

41 3

2

2’1−q q

x (1+q)


K. Evlampiev

1

4’4

3

2’ 21

4

2

3

Deletion

of Links

δ=1−γ

γon

γsn

soγ

γss

γ

γoo

nn


Duplication

Partial Genome

new

oldsingle

interaction

proteins


n=1

1 2 3 4Genome


4’

41 3

2

2’1−q q

x (1+q)


K. Evlampiev

1

4’4

3

2’ 21

4

2

3

Deletion

of Links

δ=1−γ

γon

γsn

soγ

γss

γ

γoo

nn


Duplication

IterationPartial Genome

new

oldsingle

interaction

proteins


n=1

1 2 3 4Genome


4’

41 3

2

2’1−q q

x (1+q)


K. Evlampiev

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


Duplication


new

oldsingle

interaction

proteins


n=1

1 2 3 4Genome


4’

41 3

2

2’1−q q

x (1+q)


K. Evlampiev

1

4’4

3

2’ 21

4

2

3

Deletion

of Links

δ=1−γ

γon

γsn

soγ

γss

γ

γoo

nn


Γik

iioγ inγΓi

Duplication


new

oldsingle

interaction

proteins


o

ns

kq

i

1−q

i=s,o,n

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

n=1

1 2 3 4Genome


4’

41 3

2

2’1−q q

x (1+q)


K. Evlampiev

Exponential Dynamics of Genome and 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


Γik

i

Growing NetworkVanishing Network

ioγ inγΓi

sΓ nΓoΓ

Duplication


new

oldsingle

interaction

proteins


o

ns

kq

i

1−q

i=s,o,n

Γ <1Γ >1

= (1−q) + q( + )isγ

Γ = (1−q) + q + q1

Node Degree Growth Rate

Network Link Growth Rate

n=1

1 2 3 4Genome


4’

41 3

2

2’1−q q

x (1+q)


K. Evlampiev


1

4’4

3

2’ 21

4

2

3

Deletion

of Links

δ=1−γ

γon

γsn

soγ

γss

γ

γoo

nn


Γik

i


ioγ inγΓi

sΓ nΓoΓ

sΓ oΓ= (1−q) + qMNetwork Conservation Index

Duplication


new

oldsingle

interaction

proteins


o

ns

kq

i

1−q

i=s,o,n

<1>1 Conserved Network

Nonconserved Network

MM

Γ <1Γ >1

= (1−q) + q( + )isγ

Γ = (1−q) + q + q

2

1



n=1

1 2 3 4Genome


4’

41 3

2

2’1−q q

x (1+q)


K. Evlampiev


1

4’4

3

2’ 21

4

2

3

Deletion

of Links

δ=1−γ

γon

γsn

soγ

γss

γ

γoo

nn


Γik

i


ioγ inγΓi

sΓ nΓoΓ

sΓ oΓ= (1−q) + qMNetwork Conservation Index

Duplication


new

oldsingle

interaction

proteins


o

ns

kq

i

1−q

i=s,o,n



MM

Γ <1Γ >1

= (1−q) + q( + )isγ

Γ = (1−q) + q + q

2

1



n=1

1 2 3 4Genome


4’

41 3

2

2’1−q q

x (1+q)


K. Evlampiev


1

4’4

3

2’ 21

4

2

3

Deletion

of Links

δ=1−γ

γon

γsn

soγ

γss

γ

γoo

nn



Network Conservation Index

GDD Model + Fluctuations


Γik

i


ioγ inγΓi

sΓ oΓ= (1−q) + qM

sΓ nΓoΓ

oΓ (n)(n)

Duplication


new

oldsingle

interaction

proteins


o

ns

kq

i

1−q

i=s,o,n



MM

Γ <1Γ >1

= (1−q) + q( + )isγ

Γ = (1−q) + q + q

R

sΓΠ (n)(n)

n=1M = [(1−q ) + q ]

2

1

1 2 3 4Genome


4’

41 3

2

2’1−q q

x (1+q)


K. Evlampiev


[ ]

1

4’4

3

2’ 21

4

2

3

ΓM < 1 < Γ1 < M <

1011

1

Expanding PPI Networks

Non−Conserved Networks Conserved Networks M

Γ

Γ

1

n oo

s

s

s

o

oo

oo

so

so

o

s s

n

Network Conservation (M) and Expansion ( )Γ

2

0

1

3

4

5

67

89

duplication

Vanishing

M < < 1

ΓM < 1 < Γ1 < M <

1011

1



Γ

Γ

1

n oo

s

s

s

o

oo

oo

so

so

o

s s

n


2

0

1

3

4

5

67

89

duplication

Vanishing

M < < 1

ΓM < 1 < Γ1 < M <

1011

1



Γ

Γ

1

n o

s

s

s

o

oo

oo

s


2

0

1

3

4

5

67

89

duplication

Vanishing

M < < 1

ΓM < 1 < Γ1 < M <

1011

1



Γ

Γ

1


2

0

1

3

4

5

67

89

duplication

Vanishing

M < < 1

<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 DistributionM’=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 DistributionM’=max( ) > 1

kp ~ exp(− k)M’=max( ) < 1 µ

Convex Characteristic Function

= max( )iΓi=s,o,n

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

3

]

γ ss

soγ

γsn

γoo γon

γnn

of Linkswith proba

Deletion

1−γ1−µ

proteins

k k+1

Duplication−Divergence Models Including Self−links

interaction

µnµs

µonµo

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

While Proteins are typically ConservedNetwork Motifs are NOT Conserved under

(if M>1)

Duplication−Divergence Evolution

Conservation of Network Motifs

M1

γγ

γ

γγ

γ

γγγ 23

Motif conservation index

s/o

s/o

s/o

This is in broad agreement with empirical observations !

Kirill Evlampiev

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

1 1.5 2 2.5 3-1

-0.5

0

0.5

1

networks

Conservedscale−free

interaction

protein

interactionsproteins

oΓ

oΓPhase Diagram of Asymptotic Networks

networks

networks


exponential Dense networksNon−conserved

Network growth rate

Div

erge

nce

asy

mm

etry

Stationary Non−stationary

proteinIteration

DuplicationGenome

InteractionDeletion

newγ

γold

γcross

Protein Network Evolution under Duplication

+

234

o−

Γ

Divergenceasymmetry

Networkeffective growth

Γn

Γ n

Γn

Asymmetric Divergence of Duplicates is RequiredWhole Genome Duplication Limit (q=1)

PPI Network Evolution in terms of protein domains

x 2x 4

1

4

2

1

3’3

4’4

22’

1 1.5 2 2.5 3-1

-0.5

0

0.5

1

networks


interaction

protein


oΓ


networks

networks



Network growth rate

Div

erge

nce

asy

mm

etry


proteinIteration

DuplicationGenome

InteractionDeletion

newγ

γold

γcross


+

234

o−

ΓOrigin of Divergence Asymmetry ?

"Spontaneous Symmetry Breaking" between duplicated binding sites

Divergenceasymmetry


Γn

Γ n

Γn



New

Old

Protein

x 2x 4

Protein binding partner 1



1

4

2

1

3’3

4’4

22’

1 1.5 2 2.5 3-1

-0.5

0

0.5

1

networks


interaction

protein


oΓ


networks

networks



Network growth rate

Div

erge

nce

asy

mm

etry


proteinIteration

DuplicationGenome

InteractionDeletion

newγ

γold

γcross


+

234

o−



Divergenceasymmetry


Γn

Γ n

Γn



New

Old

Gene Duplicates

x 2x 4




1

4

2

1

3’3

4’4

22’

1 1.5 2 2.5 3-1

-0.5

0

0.5

1

networks


interaction

protein


oΓ


networks

networks



Network growth rate

Div

erge

nce

asy

mm

etry


proteinIteration

DuplicationGenome

InteractionDeletion

newγ

γold

γcross


+

234

o−



Divergenceasymmetry


Γn

Γ n

Γn

Old

New



x 2x 4




1

4

2

1

3’3

4’4

22’

1 1.5 2 2.5 3-1

-0.5

0

0.5

1

networks


interaction

protein


oΓ


networks

networks



Network growth rate

Div

erge

nce

asy

mm

etry


proteinIteration

DuplicationGenome

InteractionDeletion

newγ

γold

γcross


+

234

o−




Divergenceasymmetry


Γn

Γ n

Γn

Old

New


x 2x 4




1

4

2

1

3’3

4’4

22’

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

kpkk 2 k.g

kp

(+/− 2σ)WGD Model

(+/− 2σ)

Yeast direct int. data

Yeast direct int. dataWGD Model

γon γoo=0.1 ( =1 γnn )=0γon

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 Modelwith Random Protein Domain Shuffling λ

1 10 1001e-6

1e-4

0.01

1

kpkk 2 k.g

kp


(+/− 2σ)



γon γoo=0.1 ( =1 γnn )=0γon

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 Modelwith Random Protein Domain Shuffling λ

1 10 1001e-6

1e-4

0.01

1

1 10 1001e-6

1e-4

0.01

1

kpkk 2 k.g

kp

kk 2 k.g

kp


(+/− 2σ)




γon γoo=0.1 ( =1 γnn )=0γonwith Random Protein Domain Shuffling λ

A 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

Hierarchy and Feedback in the Evolution

of Bacterial Transcription Networks

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

Transcription in Bacteria

Regulatory Interactions

?

Operons : 648TFs : 147ARs : 85 (58% TFs)Reg Int : 1170

Operons : 423TFs : 117ARs : 59 (50% TFs)Reg Int : 578

Shen−Orr Dataset (2002)

RegulonDB 5.5 (2006)

0 10 20 30 40 50 6000.010.020.030.040.050.06 Randomized

E.colifnr

arcA thrS_infC_rpmI_rplT_pheMST_ihfA

gadAX

gadW

dusB_fis

hns marRAB

idnDOTR

gntRKU

rob

Hierarchy with Mostly Self−Regulatory Feedback

No Feedback Core

Feedback Core SizesSmall Feedback Core

0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

E. coli

RandomizedE.coli

0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

E. coli

RandomizedE.coli

0 10 20 30 400

0.05

0.1

0.15

0.2RandomizedE.coli

0 5 10 15 20 250

0.05

0.1

0.15

0.2 RandomizedE.coli

RegulonDB 5.5 (2006)

0 10 20 30 400

0.05

0.1

0.15 RandomizedSubtilis

0 10 20 30 400

0.05

0.1

RandomizedSubtilis

Escherichia coliShen Orr et al (2002)

Num

ber

of L

ayer

sou

tsid

e c

ore

Long

est S

horte

st P

aths

Hierarchy with few Transcriptional Layers

Bacillus subtilis

Transcription Factor Families

Babu et al., NAR 2006

Babu et al., NAR 2006

TF Family Expansion by Duplication

A’a’pAap A’ap

Aa’p

Evolutionary Decoupling of Duplicated ARs

AR Duplication

Crosstalks+

Crosstalks+

A’a’pAap A’ap

Aa’p


AR Duplication

Crosstalks+

rpoE_rseABC rpoH

crp cytR dnaA

lysR

lysA

tdcABCDEFG

crp fnr himA tdcAR

rpoE_rseABC (rpsU_dnaG_)rpoD

lexA_dinF

cspA

caiF flhDC fliAZY nhaA osmC rcsAB

stpA

lrp

hns

exuR

exuT uxaCA

uxuABR

uidRABC

A’a’pAap A’ap

Aa’p

A few partial decoupling


AR Duplication

Crosstalks+

crp fnrC

GAT

C

GAT

GCTA

GCAT

CGAT

CGAT

CAGT

CTAG

GCAT

GCAT

CGAT

G

C

AT

C

G

TA

GCTA

GCAT

GATC

GTCA

TGCA

CGTA

CGAT

GCAT

-1 -0.5 0 0.5 1specificity

00.5

11.5

22.5

33.5

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

CGTA

CGTA

CGAT

CGAT

CAGT

CAGT

ACGT

CTAG

GCTA

C

GAT

C

T

A

T

CTGA

A

CGAT

AGCT

GTAC

GTCA

GTAC

GCTA

GCAT

GCAT

rpoE_rseABC rpoH

crp cytR dnaA

lysR

lysA

tdcABCDEFG

crp fnr himA tdcAR

rpoE_rseABC (rpsU_dnaG_)rpoD

lexA_dinF

cspA

caiF flhDC fliAZY nhaA osmC rcsAB

stpA

lrp

hns

exuR

exuT uxaCA

uxuABR

uidRABC

A’a’pAap A’ap

Aa’p

Most fully decoupledA few partial decoupling


crp / fnr example

AR Duplication

Bacteria versus Eukaryote Transcriptional Hierarchy

Cosentino−Lagomarsino, Jona, Bassetti & Isambert, 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

horte

st P

aths






Long

est S

horte

st P

aths






Long

est S

horte

st P

aths






Adaptative Selection ? Random drift ?

Long

est S

horte

st P

aths






Adaptative Selection ? Random drift ?

PopulationDynamics

Long

est S

horte

st P

aths

Documents

Les Réseaux Biologiques et leur Evolution