Redes de Regulación GénicaIldefonso Casesicases@cnio.es

1

Regulación de la Transcripción

• Resultado de la interacción entre proteínas y DNA.

• El conjunto de proteínas que se unan a su región promotora (directa o indirectamente) va a determinar la expresión de un gen:

! En que tejidos

! En que momento del desarrollo

! Bajo que condiciones ambientales

! etc.

2

3

4

RNA polimerasa II Eukariota

5

6

Redes de Regulación

7

Redes de Regulación

8

9

Otras fuentes de Regulación

•! Elongación

•! Estabilidad del mRNA

•! Micro-RNAs

•! etc.

10

Datos

• Chip-on-Chip• STAGE/SABE• DNA-arrays• Literatura• Predicción

11

Chip-On-Chip

12

Chip-On-Chip II

• PCR Arrays• baja resolución

• Oligo Array• muy caros

• Ambos cubren solo regiones pre-establecidas y cercanas al gen

13

STAGE/SABE

BlastBLAT

SSAHA

Caro, requiere mucha secuenciación para encontrar todos los sitios.

14

Problemas

• Solo encontramos los sitios que están unidos en las condiciones del experimento

• positivo: contexto• negativo: no podemos cubrir todas las

condiciones

• Sabemos que los TF se unen, pero no si estan activos, ni como actúan sobre el gen: ¿reprimiendo o activando?

15

DNA arrays

• Relaciones entre la expresión de TF y otros genes:

• redes bayesianas

• Imposible aplicar a grandes set de genes, solo sub-sistemas

• ambiguos: dan muchas soluciones

• Mejoran con información adicional: Chip-on-Chip

16

Predicción

• “pattern matching”,“pattern discovery”, “phylogenetic footprint”

• Ruidosos, muchos falsos positivos• Problemas comunes:

• sabemos donde se unen los TF, pero no cuando, ni que hacen

• Pueden usarse para filtrar resultados de métodos experimentales

17

•Conocidos “Pattern Matching”

• si sabemos la secuencia que reconoce un factor de transcripción, ¿Podemos encontrar donde se une en un genoma? (“qué genes regula”)

•Desconocidos “Pattern Discovery”

• ¿podemos encontrar sitios en el DNA responsables de su regulación?

Sitios de Unión en el DNA

18

•Describir un sitio de unión:

• Secuencias consenso

• patrones

•matrices (PSSM)

Conocidos: “Pattern Matching”

19

Secuencias consenso

ATCGTGCTATAGGTAAGT

ATCGTGGTATACGTAAGT

ATCGTGCTTTAGGTAAGA

ATCCTGCTATTGCTAAGT

ATCGTGCTATAGGTAAGT

20

Secuencias consenso

ACGTA

CGACGTAGATGACCTACGGATGCACGAACG

CGACGTAGATGACCTACGGATGCACGAACG

CGACGTAGATGACCTACGGATGCACGAACG

CGACGTAGATGACCTACGGATGCACGAACG

21

Patrones

ATCGTGCTATAGGTAAGT

ATCGAGGTATAGGTAAGT

ATGGGGCTACAGGTAAGA

ATGGCGCTATTGGTAAGT

AT[CG][ACGT]G[CG]TA[CT][AT]GGTAAG[AT]

ATSGNGSTAYWGGTAAGW

W= A or T

R= A or G

K= G or T

S= C or G

Y= C or T

M= A or C

22

Matrices

A T C G T G C T A T A G G T A A G T

A T C G T G G T A T A C G T A A G T

A T C G T G C T T T A G G T A A G A

A T C C T G C T A T T G C T A A G T

A 4 0 0 0 0 0 0 0 3 0 3 0 0 0 4 4 0 1

C 0 0 4 1 0 0 3 0 0 0 0 1 1 0 0 0 0 0

G 0 0 0 3 0 4 1 0 0 0 0 3 3 0 0 0 4 0

T 0 4 0 0 4 0 0 4 1 4 1 0 0 4 0 0 0 3

A T G G C T C G A T T G G T A T G T

4+4+0+3+0+4+3+0+3+4+1+3+3+4+4+0+4+3=47

T A G C C A G T T T A T T A G C G T

0+0+0+1+0+0+3+4+1+4+3+0+0+0+0+0+4+3=23

23

A 3 0 0 0 0 0 0 0

C 0 0 4 1 0 0 3 0

G 0 0 0 3 4 0 1 0

T 1 4 0 0 0 4 0 4

A .25 1

C .25 .25

G .75 1 .75

T .75 1 1 1

LLR=log(fi!/f0!); f0a=f0t=0.4;f0c=f0g=0.6

A log(0.25/0.4)

C log(0/0.6)

Logos

• Representación gráfica de un alineamiento

• La altura de cada base es proporcional a su frecuencia

• La altura total de cada posición es proporcional a su conservación (medido en bits de información)

http://www.lecb.ncifcrf.gov/~toms/sequencelogo.htmlhttp://weblogo.berkeley.edu/logo.cgi

25

hasta ahora...

•Se necesita un alineamiento

•No se consideran inserciones o deleciones

•No se consideran correlaciones internas entre posiciones

HMM y Redes Neuronales

26

Sitios especiales

• Promotores• http://www.fruitfly.org/seq_tools/promoter.html

• http://www.softberry.com/berry.phtml?topic=bprom&group=programs&subgroup=gfindb

• http://www.cbs.dtu.dk/services/Promoter/

• Terminadores• http://www.softberry.com/berry.phtml?topic=findterm&group=programs&subgroup=gfindb

• http://cbcb.umd.edu/software/transterm/

27

Bases de Datos de motivos

28

•Factores de transcripción, sitios de unión y sus matrices en eukariotas

•bases de datos y programas relacionados:

• PathoDB: a database on pathologically relevant mutated forms of transcription factors and transcription factor binding sites

• S/Mart:collects information about scaffold/matrix attached regions and the nuclear matrix proteins

• Transcompel: is a database on composite regulatory elements affecting gene transcription in eukaryotes

• Más...

http://www.gene-regulation.com/

29

RegulonDB

•Factores de transcripción, sus sitios de unión y operones en E. coli

•herramientas de visualización y análisis

• Integrado en Ecocyc (www.ecocyc.org)

http://www.cifn.unam.mx/Computational_Genomics/regulondb/

30

Computational Biology and Bioinformatics-CSHL

• TRED: Humanos y ratón• CEPDB: C. elegans• SCPD: Levaduras

• Promotores, sitios de unión, matrices, etc.

http://rulai.cshl.edu/software/index1.htm

31

Encontrando sitios nuevos: “Pattern Discovery”

• Se necesita un conjunto de genes que se sabe/cree co-regulado

• Se toman las regiones promotoras

•Bacterias: 50-300 pb regiones intergenicas

•Eukariotas: 1000 pb

• Se buscan posibles regiones reguladoras

32

Genes Co-regulados

• Perfiles transcripcionales (microarrays)

• Genes ortólogos (footprints filogenéticos)

• Otro tipo de asociaciones:

• Rutas metabólicas

• Misma clasificación funcional

• nombres similares

33

1. Cada experimento compara 2 condiciones

2. Se necesitan varios experimentos

3. Para cada gen se obtiene un perfil

4. Los perfiles se comparan

5. Los genes se agrupan en función de sus perfiles

Microarrays

34

1. Se obtienen grupos de genes ortológos

2. Se asume que la regulación está conservada, al igual que los sitios de unión

• Organismos distantes: no conservación

• Organismos muy cercanos: secuencias no funcionales no han divergido aún

footprints filogenéticos

35

Métodos

• Motivos sobre-representados

• computacionalmente caro

• Exhaustivo

• ruidoso

• Metodos basados en Matrices

• Gibbs Sampling

• rápido

• no exhaustivo: pueden obtenerse resultados distintos cada

• http://bayesweb.wadsworth.org/gibbs/gibbs.html

• Motivos con simetrías

• repeticiones invertidas/directas

36

1. Calcular la frecuencia de cada palabra de longitud n-bases en nuestras secuencias

2. Determinar aquellas que son significativamente más abundantes en nuestro grupo en en otros grupos

Secuencia Esperado Observado

AAAAA 2 3

AAAAC 3 2

AAAAG 5 3

...

ATGCA 13 17

ATGCC 15 143

ATGCG 17 14

...

TTTTG 5 3

TTTTT 2 0

Motivos Sobre-representados

44=256, pero...

412=16.777.216

37

Gibbs Sampling

ACGTAGGTTC

ACGTAGCAGT

ACGGATGCGA

ACGTAGCGTA

2. Eliminar la peor del

alineamiento ACGTAGGTTC

ACGTAGCAGT

ACGGATGCGA

ACGTAGCGTA

ACGTAGGATC

ACGTAGCAGT

ACGGATGCGA

ACGTAGCGTA

3. Sustituir por la mejor en la

misma secuencia

ACGTAGGATC

ACGTAGCAGT

ACGGATGCGA

ACGTAGCGTA

Repetir hasta que se estabiliza la calidad del alineamiento

1. Selecciona al azar

38

• Motivos que solapan

• Motivos que se parecen

AAGTCGGC

AGTCGGCT

GTCGGCTT

------------

AAGTCGGCTT

AGTCGGCA

AGTCGGCT

TGTCGGCT

------------

AGTCGGCT

• Distancia

• euclidea

• correlación de Pearson

• Agrupamiento

• k-means

• agrupamiento jerárquico

Agrupando sitios

39

Programas• Consensus Package

• Consensus: Pattern discovery (fixed length)

• WConsensus: Pattern discovery (unknown length)

• Patser: Pattern Matching

• http://ural.wustl.edu/software.html

• MEME/MAST

• MEME: Patter Discovery

• MAST: Patter Matching

• http://meme.sdsc.edu/meme/intro.html

• Gibbs Samplers:

• AlignACE: http://atlas.med.harvard.edu/

• MotifSampler: http://homes.esat.kuleuven.be/~thijs/Work/MotifSampler.html

40

Patter discovery

Patter Matching Motive Clustering

Work flow

41

Propiedades de las redes de Regulación

42

Propiedades Generales

Genes Regulados

0,01

0,1

1

1 10 100 1000

0,001

0,01

0,1

1

0 5 10

Freq

Reguladores

Freq

Guelzim et al. 2002 Nature Genet. 31:60-63

• Distribución exponencial

• Distribución “Ley de Potencias”

• “libre de escala”

• robustez

• caminos cortos(integracion de señal)

E. coli S. cerevisiae

43

Evolución de Redes1

2

3

©!!""#!Nature Publishing Group!

!

NATURE REVIEWS | MICROBIOLOGY VOLUME 3 | FEBRUARY 2005 | 113

R E V I EW S

can function as repressors or activators depending onwhether they are placed in the C- or N-terminus of theresulting protein81. Finally, modifications at the targetDNA sites that are bound by regulators can also modifytheir activity. Activators generally attach to DNAupstream of the transcription start site, while repressorsbind over or downstream of it79,80, and consequently,insertions and deletions in the promoter region canincline the activity of transcription factors towards beingactivators or repressors. Taken together, all these possibil-ities endow regulatory networks with an extraordinarydegree of plasticity and adaptability.

The building blocks of regulationThere are two aspects to the evolutionary challenge ofexpressing metabolic capabilities at the right timeand in the right place. First, metabolic enzymes mustbe specific for their cognate substrates. The key–lockspecificity of an enzyme for its substrate is bound tooccur only following a long period of affinity andspecificity maturation. One possible hypothesis is thatbroad-substrate-range enzymes preceded those that are

indicative of positive selection. Theoretical andexperimental studies show that FFLs or auto-regulationof transcription factors can be advantageous in someconditions, as they have a faster response to signals thannon-regulated promoters78. FFLs can also filter out shortpulses of signal67,68, possibly by delaying the response ofthe targeted genes70. It therefore seems that differencesin the dynamic properties of network arrangements arethe substrate of natural selection and the origins of theprevalence of some network motifs.

Another factor that can contribute to the evolutionof transcription networks is the modular nature of reg-ulatory proteins. Most bacterial transcription factors(~90% in E. coli) are multi-domain proteins. However,the actual number of different domains for DNA bindingand signal reception–response functions is comparativelysmall — although they are combined in many differentways79,80. Shuffling of input and output domains allowsnew associations between environmental signals andregulated functions. Moreover, the same shufflingprocess can also affect the regulatory activity of any giventranscription factor, as similar DNA-binding domains

Box 3 | The ‘Matthew principle’ of the evolution of transcription networks

Highly connected nodes in a regulatory network tend to acquire still more connections, while those with few connectionsremain poorly connected. This is because the random duplication of genes that inherit their regulatory interactionsproduces large regulons (left) and they keep the power-law distribution of connectivity of transcription networks (right).

In the figure, at stage 1, two transcription factors (orange and green ovals) regulate a set of genes (that is, a regulon)by means of their binding sites (coloured boxes) within the upstream regions of given genes (arrows). The moreconnected orange regulon has a higher probability that one of its members becomes randomly duplicated. In stage 2,when the dark-blue gene of the larger regulon is duplicated it inherits the regulation (orange box) and thereforeincreases the difference in the number of members of the two initial regulons. Finally, after several duplications (stage 3— represented as genes of different shades of pink and blue — the difference keeps on increasing. In the networkrepresentations to the right, this leads to the presence of one highly connected node (orange) and a few poorlyconnected ones (green, not all depicted on the left).

The ‘Matthew principle’:Matthew 13:12,“…for whosoever hath, to him shall be given, and he shall have more abundance:but whosoever hath not, from him shall be taken away even that he hath…”

1

2

3

Cases & de Lorenzo 2005 Nature Rev Microb 3:105-118

44

Duplicación y Evolución

Tecihmann & Babu, 2004 Nature Genetics 36(5):492-6

Regulator

Family 1Family 2

Family 3

van Noort et al., 2004 EMBO Rep 5(3):280-4

Existing network-evolution models cannot account for thecombination of the architecture of the coexpression network and

the correlation between coexpression and sequence similarity inparalogues. The network model of Barabasi & Albert (1999), basedon the concept of preferential attachment (Simon & Bonini, 1958),produces scale-free networks, but not small-world networks(cEcrandom; in a small-world network cbcrandom), even whenintroducing constraints to the number of connections per nodeor to the ageing of nodes (Amaral et al, 2000). The algorithm ofRavasz et al (2002) to realize a small-world, scale-free networkinvolves hierarchical duplication of complete modules andattachment to the central node of the existing module. This modeldoes not lead to a high likelihood of attachment betweenduplicated nodes, and is therefore not explanatory for theevolution of our network. Moreover, in contrast to the predictionsof this model, the explicit testing of the age of genes (see Methods)and the number of their connections did not reveal any positivecorrelation (Pearson correlation¼"0.04, P-value that there is nopositive correlation¼ 0.98). The duplication model of Bhan et al(2002) assumes duplication of genes with partial conservation ofconnections. When seeding this model with a scale-free network,most of the structure persists for a few iterations; however,simulating this model for a higher number of iterations results inan exponential degree distribution of N versus k (Pastor-Satorraset al, 2003). In this model, there is no relation between the timingof a duplication event and the likelihood of attachment of theresulting paralogues. This is because the connections are fixedonce established, as in all previous models. This is not anevolutionarily sound assumption, given the observation thatconnectivity between paralogues is dependent on the timing ofthe duplication event and that coexpression is only partlyconserved between species (Teichmann & Babu, 2002; van Noortet al, 2003).

A’A

1 Gene duplication

A

A

4

A

TFBS deletion

A A

TFBS duplication3

B B

A

2 Gene deletion

Genome evolutionGenome initiation

2

25

1

3...

100 x

.

.

.

.... . .

. ..

...

.

.

.

etc.

A B CNetwork determination

Fig 3 | Evolutionary model of transcription regulation. The evolutionary model consists of a few simple mechanisms. (A) A genome is initiated with 25 genes

with random TFBSs, represented by the small coloured shapes. (B) Possible events are as follows: (1) Gene A is duplicated, gene A0 has the same TFBS as its

duplicate gene A; the duplicates are coexpressed. (2) Gene deletion. (3) Gene A acquires a new TFBS from gene B. The probability of obtaining a specific

TFBS is proportional to its frequency in the genome. The probability of a novel TFBS is (150 " total number of different TFBSs present)/(150þ totalnumber of TFBSs). (4) One of the TFBSs of gene A is deleted. (C) A network is constructed by connecting genes that share TFBSs.

0 20 40 60 80 100Percentage protein identity

0.0

0.2

0.4

0.6

0.8

Frac

tion

coex

pres

sed

A

0 20 40 60 80 100Percentage protein identity

0

1

2

3

Avg

. sha

red

bind

ing

site

s

B

Fig 2 | Coexpression between paralogues in experiments. (A) Fractions of

coexpressed paralogues calculated by correlation in coexpression in the

data set of Hughes et al (2000). (B) Average number of shared regulatory

elements between paralogues in the data set of Lee et al (2002).

Yeast coexpression network

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Duplicación de TFBS

Papp et al,2003. Trends Genet 19:417

46

Red de Co-regulación

to get from one node to any other node) is almost as low as that forrandom networks (Watts & Strogatz, 1998). The scale-free, small-world architecture appears typical for intracellular networks inwhich the nodes are connected when they are involved in thesame biological process. In contrast, another type of network, thegene regulatory network of Saccharomyces cerevisiae, in whichthe connections are between transcription factors and the genesthey regulate, does not have a scale-free but rather an exponentialdistribution of the number of connections per node (Guelzim et al,2002; Lee et al, 2002).

Because of the importance of molecular networks for thefunctioning of the cell, there is a great deal of interest in theevolution and origin of these networks. Yet it remains an openquestion whether the scale-free, small-world architecture is adirect product of selection and thus functionally meaningful,merely a by-product of the requirements of function and ofselection at other levels, or even a natural consequence ofmechanisms such as gene duplication. The evolution of scale-freenetworks has been explained in terms of selection on globalproperties such as robustness (Jeong et al, 2000; Guelzim et al,2002) and the fast spread of perturbations (Fell & Wagner, 2000).It has also been addressed in phenomenological models (Bhanet al, 2002; Ravasz et al, 2002) that do not require selection butthat are not supported by independent data. Here we analyse thenetwork architecture of a general indicator of protein involvementin the same biological process: gene coexpression in S. cerevisiae(Hughes et al, 2000). We show that the gene coexpressionnetwork in S. cerevisiae is a scale-free, small-world network. Byexploiting homology relations between the genes in the coex-pression network, we formulate a neutralist model in which thescale-free, small-world architecture is a natural consequence ofthe mechanisms behind gene regulation evolution. This calls intoquestion global selection mechanisms for the architecture ofintracellular networks.

RESULTSAlthough gene coexpression is a continuous observable, theunderlying principle is discrete: the sharing of regulatoryelements. We therefore translate gene coexpression into a discretenetwork. In the network, the genes are the nodes, which areconnected to each other when coexpressed. Such a networkrepresentation allows a comparison of the global organization ofgene expression with other facets of the intracellular network.Furthermore, relative to protein interaction networks or metabolicnetworks, coexpression covers a more inclusive array of func-tional relations between gene products. As a threshold to establisha link in the network between two genes, we chose a coexpressioncorrelation of 0.6 in a large-scale expression data set (Hughes et al,2000), as higher thresholds do not give higher reliabilities offunctional interaction between the encoded proteins (van Noortet al, 2003). The coexpression network has 4,077 nodes (genes)that are linked by a total of 65,430 connections, the averagenumber of connections per node (k) thus being 32 (eachconnection links two nodes). The distribution of number of linksper node is scale free with degree exponent gE1 (Fig 1). Note thatalthough the average number of connections is 32, most genes areconnected to only one other gene, as reflected by the scale-freedistribution (Fig 1). The clustering coefficient of the network (c, thefraction of cases where if a node has a connection to two other

nodes, these two also have a direct connection to each other) is0.6. Not all nodes are connected in one cluster; the largest clustercontains 3,945 nodes, with an average shortest path length (L) of4. In a random network with the same number of nodes (N) andconnections (k), c¼ 0.008 (k/N) (Barabasi & Albert, 1999) andLE2.8 (from simulations; see Methods). Thus, the yeast coexpres-sion network has all the properties of a small-world (LELrandom,cb crandom), scale-free (N(k)Bk"g) network that is typical forintracellular networks in which the nodes are connected whenthey are involved in the same process. Using thresholds forcoexpression higher than a correlation coefficient of 0.6 gavesimilar results, that is, a scale-free degree distribution and small-world organization (Fig 1). Using lower thresholds leads to theinclusion of ‘random’ connections (van Noort et al, 2003) and anexponential degree distribution with a smaller c (Fig 1). At thethreshold of 0.6, the network statistics are similar to previouslystudied biological networks (Fell & Wagner, 2000; Jeong et al,2000, 2001; Wagner, 2001; Snel et al, 2002), and thus we use thisnetwork for further study.

The coexpression data have another interesting property: acorrelation between the fraction of coexpressed paralogues andtheir sequence similarity (Fig 2A). An independent data set thatalso contains this pattern is the large-scale, experimentaldetermination of transcription factor binding sites (TFBSs) (Leeet al, 2002), in which the number of shared regulatory elementsbetween paralogues increases with protein identity (Fig 2B). Acorrelation between divergence in sequence and in coexpressionis expected if both diverge at constant, clock-like rates (Wagner,2000), and indicates neutral evolution of these two traits. Itappears that in the case of gene duplication, the regulatoryelements tend to be coduplicated with the genes and mutatedafterwards.

1 100 1,000Number of connections (K )

1

10

100

1,000

Num

ber o

f nod

es (N

)

r > 0.4, c = 0.50r > 0.6, c = 0.60r > 0.8, c = 0.57

10

Fig 1 | Distribution of connections per node in the coexpression network.

Nodes are genes and connections are defined by coexpression of two genes,

resulting in a network. The number of nodes (N) with a certain number of

connections (k) in the coexpression network is shown, where coexpression

is defined by a correlation in expression pattern higher than 0.4 (right-

pointing arrows), 0.6 (circles) or 0.8 (left-pointing arrows). The

distributions at thresholds 0.6 and 0.8 are scale free with an exponent gE1.

Yeast coexpression network

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• gamma"-1• c=0.6• libre de escala• “mundo

pequeño”

van Noort et al., 2004 EMBO Rep 5(3):280-4

47

Simulando la evolución

Existing network-evolution models cannot account for thecombination of the architecture of the coexpression network and

the correlation between coexpression and sequence similarity inparalogues. The network model of Barabasi & Albert (1999), basedon the concept of preferential attachment (Simon & Bonini, 1958),produces scale-free networks, but not small-world networks(cEcrandom; in a small-world network cbcrandom), even whenintroducing constraints to the number of connections per node orto the ageing of nodes (Amaral et al, 2000). The algorithm ofRavasz et al (2002) to realize a small-world, scale-free networkinvolves hierarchical duplication of complete modules andattachment to the central node of the existing module. This modeldoes not lead to a high likelihood of attachment betweenduplicated nodes, and is therefore not explanatory for theevolution of our network. Moreover, in contrast to the predictionsof this model, the explicit testing of the age of genes (see Methods)and the number of their connections did not reveal any positivecorrelation (Pearson correlation¼"0.04, P-value that there is nopositive correlation¼ 0.98). The duplication model of Bhan et al(2002) assumes duplication of genes with partial conservation ofconnections. When seeding this model with a scale-free network,most of the structure persists for a few iterations; however,simulating this model for a higher number of iterations results inan exponential degree distribution of N versus k (Pastor-Satorraset al, 2003). In this model, there is no relation between the timingof a duplication event and the likelihood of attachment of theresulting paralogues. This is because the connections are fixedonce established, as in all previous models. This is not anevolutionarily sound assumption, given the observation thatconnectivity between paralogues is dependent on the timing ofthe duplication event and that coexpression is only partlyconserved between species (Teichmann & Babu, 2002; van Noortet al, 2003).

A’A

1 Gene duplication

A

A

4

A

TFBS deletion

A A

TFBS duplication3

B B

A

2 Gene deletion

Genome evolutionGenome initiation

2

25

1

3...

100 x

.

.

.

.... . .

. ..

...

.

.

.

etc.

A B CNetwork determination

Fig 3 | Evolutionary model of transcription regulation. The evolutionary model consists of a few simple mechanisms. (A) A genome is initiated with 25 genes

with random TFBSs, represented by the small coloured shapes. (B) Possible events are as follows: (1) Gene A is duplicated, gene A0 has the same TFBS as its

duplicate gene A; the duplicates are coexpressed. (2) Gene deletion. (3) Gene A acquires a new TFBS from gene B. The probability of obtaining a specific

TFBS is proportional to its frequency in the genome. The probability of a novel TFBS is (150 " total number of different TFBSs present)/(150þ totalnumber of TFBSs). (4) One of the TFBSs of gene A is deleted. (C) A network is constructed by connecting genes that share TFBSs.

0 20 40 60 80 100Percentage protein identity

0.0

0.2

0.4

0.6

0.8

Frac

tion

coex

pres

sed

A

0 20 40 60 80 100Percentage protein identity

0

1

2

3

Avg

. sha

red

bind

ing

site

s

B

Fig 2 | Coexpression between paralogues in experiments. (A) Fractions of

coexpressed paralogues calculated by correlation in coexpression in the

data set of Hughes et al (2000). (B) Average number of shared regulatory

elements between paralogues in the data set of Lee et al (2002).

Yeast coexpression network

V. van Noort et al.

&2004 EUROPEAN MOLECULAR BIOLOGY ORGANIZATION EMBO reports VOL 5 | NO 3 | 2004

scientificreport

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van Noort et al., 2004 EMBO Rep 5(3):280-4

48

We introduce a new, simple model to explain the emergenceof scale-free networks with a high clustering coefficient that isbased on the observation of a positive correlation between theprobability of a connection between two paralogues and theirsequence similarity. In this model, the entities are genes that havea number of TFBSs. Connections between genes are establishedwhen they share a minimum number of TFBSs. At every time step,each gene has a probability of being duplicated, resulting in a newgene (step 1, Fig 3). In the case of duplication, the TFBSs arepassed on to the duplicate gene, corresponding to a highlikelihood of coexpression between recently duplicated paralo-gues in the experimental data. A gene may be deleted (step 2,Fig 3). A TFBS can be acquired from the pool of TFBSs of all genes,where the probability of obtaining a specific TFBS is proportionalto its frequency in the genome (step 3, Fig 3), introducingconnections between nonparalogous genes. New TFBSs areintroduced at a low frequency. All TFBSs have a probability ofbeing deleted (step 4, Fig 3), giving rise to a decrease inconnectivity between duplicates over time and balancing thenumber of TFBSs per gene. We simulated this model by seeding itwith 25 genes with randomly assigned TFBSs and evolving thesefor 100 evolutionary steps, observing three parameter regimes. Inthe first regime (left-pointing arrows, Fig 4), the TFBS duplicationand deletion rates are much higher than the gene rates. Thiseffectively decouples the TFBS from the genes and gives rise to avery loosely connected network (a steep slope), albeit with apower-law distribution of the number of connections per nodeand a high c (c¼ 0.3 in this specific case). In the second regime(circles, Fig 4), the TFBS duplication and deletion rates are in thesame order of magnitude as those for the genes. Here, we observea scale-free degree distribution with a slope similar to the one

observed in the experimental data and a high c. In the third regime(right-pointing arrows, Fig 4), the rates for TFBS duplication anddeletion rates are much lower than those for genes. This couplesthe TFBS to the genes such that almost every pair of paralogues isconnected, resulting in a very tightly connected network, with anexponentially declining degree distribution and a very high c(close to 1).

In a natural situation, we do not expect the evolutionaryparameters to be in the third regime, as pieces of DNA areduplicated by the same mechanisms, be it coding or noncodingDNA. Also, TFBSs are much smaller than genes and are thusexpected rather to have duplication and deletion rates that are atleast as high as those for individual genes. A simulated network inthe intermediary regime exists of, for example, 4,273 nodesconnected by 56,953 connections. The network displays small-world behaviour, indicated by a high clustering coefficient(c¼ 0.2) relative to random networks (crandom¼ 0.003) and inthe largest cluster of 4,070 nodes an average shortest path length(LE3) that is similar to the shortest path length in a randomnetwork (LrandomE3.5). The overall behaviour of this network isvery similar to the coexpression network. This indicates that ascale-free, small-world organization as such can be the result ofneutral evolution. Still, the levels of cliquishness and the slope ofthe scale-free distribution may be the result of natural selection.

DISCUSSIONThe functional relevance of the typical scale-free, small-worldorganization that we observe in intracellular networks is open todebate. In the absence of an experimental system with which totest the functional relevance of the network architecture, we haveto resort to theoretical experiments. These basically answer thefollowing question: what are the minimal conditions under whicha specific network architecture can evolve? To answer thesequestions, we have studied the coexpression network inS. cerevisiae that we show to have a small-world, scale-freearchitecture. Furthermore, the network contains a positivecorrelation between the probability of coexpression of twoparalogues and their sequence similarity. We introduce a networkmodel that reproduces the architecture as well as the homologyrelations in the coexpression network. Its key components are thatgenes are coduplicated with their TFBSs and that multiple sharedTFBSs are required for coexpression. Our observation of a positivecorrelation between sequence similarity and the level of coex-pression contrasts with the results of Wagner (2000), who onlyobserved a very weak correlation. The difference is probablyexplained by the much larger coexpression data (Hughes et al,2000) and the additional data set of TFBSs (Lee et al, 2002)combined with homology relations. This analysis of more datathus offers support for a neutralist’s explanation of the genecoexpression network architecture.

In contrast, not only the scale-free, small-world architecture ofintracellular networks but also one of the network statistics, thediameter, have been argued to be the result of biological selection.It should be noted that with respect to the diameter, the directionof this argument has been rather arbitrary: both the relatively smalldiameter of metabolic networks (Jeong et al, 2000) and therelatively large diameter of protein interaction networks (Maslov &Sneppen, 2002) have been argued to be the result of selection.Subsequent analyses have however shown that in both cases the

101 100 1,000Number of connections (K)

1

10

100

1,000

Num

ber o

f nod

es (N

)

Gene duplication > TFBS duplicationGene duplication =~TFBS duplication

Fig 4 | Distribution of connections per node in the simulated network. The

number of nodes (N) with a certain number of connections (k) in the

simulated network is shown. The minimum number of shared TFBSs for a

connection in the network is three. Gene duplication and deletion are in the

same order of magnitude as TFBS duplication and deletion (circles), gene

duplication and deletion are much smaller than TFBS duplication and

deletion (left-pointing arrows), and gene duplication and deletion are much

larger than TFBS duplication and deletion (right-pointing arrows).

Yeast coexpression network

V. van Noort et al.

EMBO reports VOL 5 | NO 3 | 2004 &2004 EUROPEAN MOLECULAR BIOLOGY ORGANIZATION

scientificreport

4

En ausencia de selección pueden aparecer redes de propiedades similares a las reales

Simulando la Evolución II

van Noort et al., 2004 EMBO Rep 5(3):280-4

49

Motivos

motifs in networks representing a broad rangeof natural phenomena.

We started with networks where the inter-actions between nodes are represented by di-rected edges (Fig. 1A). Each network wasscanned for all possible n-node subgraphs (inthe present study, n ! 3 and 4), and the numberof occurrences of each subgraph was recorded.Each network contains numerous types of n-node subgraphs (Fig. 1B). To focus on thosethat are likely to be important, we compared thereal network to suitably randomized networks(12–16) and only selected patterns appearing inthe real network at numbers significantly higherthan those in the randomized networks (Fig. 2).For a stringent comparison, we used random-ized networks that have the same single-nodecharacteristics as does the real network: Eachnode in the randomized networks has the same

number of incoming and outgoing edges as thecorresponding node has in the real network.The comparison to this randomized ensembleaccounts for patterns that appear only becauseof the single-node characteristics of the network(e.g., the presence of nodes with a large numberof edges). Furthermore, the randomized net-works used to calculate the significance of n-node subgraphs were generated to preserve thesame number of appearances of all (n – 1)-nodesubgraphs as in the real network (17, 18). Thisensures that a high significance was not as-signed to a pattern only because it has a highlysignificant subpattern. The “network motifs”are those patterns for which the probability P ofappearing in a randomized network an equal orgreater number of times than in the real networkis lower than a cutoff value (here P ! 0.01).Patterns that are functionally important but not

statistically significant could exist, whichwould be missed by our approach.

We applied the algorithm to several net-works from biochemistry (transcriptional generegulation), ecology (food webs), neurobiology(neuron connectivity), and engineering (elec-tronic circuits, World Wide Web). The networkmotifs found are shown in Table 1. Transcrip-tion networks are biochemical networks re-sponsible for regulating the expression of genesin cells (11, 19). These are directed graphs, inwhich the nodes represent genes (Fig. 1A).Edges are directed from a gene that encodes fora transcription factor protein to a gene transcrip-tionally regulated by that transcription factor.We analyzed the two best characterized tran-scriptional regulation networks, correspondingto organisms from different kingdoms: a eu-karyote (the yeast Saccharomyces cerevisiae)(20) and a bacterium (Escherichia coli) (11,19). The two transcription networks show thesame motifs: a three-node motif termed “feed-forward loop” (11) and a four-node motiftermed “bi-fan.” These motifs appear numeroustimes in each network (Table 1), in nonhomolo-gous gene systems that perform diverse biolog-ical functions. The number of times they appearis more than 10 standard deviations greater thantheir mean number of appearances in random-ized networks. Only these subgraphs, of the 13possible different three-node subgraphs (Fig.1B) and 199 different four-node subgraphs, aresignificant and are therefore considered net-work motifs. Many other three- and four-nodesubgraphs recur throughout the networks, but atnumbers that are less than the mean plus 2standard deviations of their appearance in ran-domized networks.

We next applied the algorithm to ecosystemfood webs (21, 22), in which nodes representgroups of species. Edges are directed from anode representing a predator to the node repre-senting its prey. We analyzed data collected bydifferent groups at seven distinct ecosystems(22), including both aquatic and terrestrial hab-itats. Each of the food webs displayed one ortwo three-node network motifs and one to fivefour-node network motifs. One can define the“consensus motifs” as the motifs shared bynetworks of a given type. Five of the seven foodwebs shared one three-node motif, and all sevenshared one four-node motif (Table 1). In con-trast to the three-node motif (termed “threechain”), the three-node feedforward loop wasunderrepresented in the food webs. This sug-gests that direct interactions between species ata separation of two layers [as in the case ofomnivores (23)] are selected against. The bi-parallel motif indicates that two species that areprey of the same predator both tend to share thesame prey. Both network motifs may thus rep-resent general tendencies of food webs (21, 22).

We next studied the neuronal connectivitynetwork of the nematode Caenorhabditis ele-gans (24). Nodes represent neurons (or neuron

Fig. 2. Schematic view of network motif detection. Network motifs are patterns that recur muchmore frequently (A) in the real network than (B) in an ensemble of randomized networks. Eachnode in the randomized networks has the same number of incoming and outgoing edges as doesthe corresponding node in the real network. Red dashed lines indicate edges that participate in thefeedforward loop motif, which occurs five times in the real network.

150 200 250 300 350 4000

0.005

0.01

0.015

Subnetwork size

Co

nce

ntr

atio

n o

f F

ee

dfo

rwa

rd lo

op

Real

Random

Fig. 3. Concentration C ofthe feedforward loop motifin real and randomizedsubnetworks of the E. colitranscription network (11).C is the number of appear-ances of the motif dividedby the total number of ap-pearances of all connectedthree-node subgraphs (Fig.1B). Subnetworks of size Swere generated by choos-ing a node at random andadding to it nodes con-nected by an incoming oroutgoing edge, until Snodes were obtained, andthen including all of theedges between these Snodes present in the fullnetwork. Each of the sub-networks was randomized(17, 18) (shown are mean and SD of 400 subnetworks of each size).

R E P O R T S

www.sciencemag.org SCIENCE VOL 298 25 OCTOBER 2002 825

Milo et al,2002. Science 298:824

50

Motivos Solapantes

Pajek

A

(1)

(2)

Pajek

B

Pajek

C

(1)

(2)

Pajek

D

1 10k

0.01

0.1

1

Cu

mu

lati

ve

of

P(k

)

Original network

FF motifsBF motifsFF and BF motif superstructure

Giant component

E

1 10 100k

0.01

0.1

1

C(k

)

1 10 100

0.01

0.1

1 Original networkFF motifsFF and BF motif superstructure

Giant component

F

Figure 2

Dobrin et al,2004. BMC Bioiformatics 5:10

51

Milo et al,2002. Science 298:824

Motivos en Redes de Regulación

52

classes), and edges represent synaptic connec-tions between the neurons. We found the feed-forward loop motif in agreement with anatomi-cal observations of triangular connectivity struc-tures (24). The four-node motifs include thebi-fan and the bi-parallel (Table 1). Two ofthese motifs (feedforward loop and bi-fan) were

also found in the transcriptional gene regulationnetworks. This similarity in motifs may point toa fundamental similarity in the design con-straints of the two types of networks. Both net-works function to carry information from sen-sory components (sensory neurons/transcriptionfactors regulated by biochemical signals) to ef-

fectors (motor neurons/structural genes). Thefeedforward loop motif common to both typesof networks may play a functional role in infor-mation processing. One possible function of thiscircuit is to activate output only if the inputsignal is persistent and to allow a rapid deacti-vation when the input goes off (11). Indeed,many of the input nodes in the neural feedfor-ward loops are sensory neurons, which mayrequire this type of information processingto reject transient input fluctuations that areinherent in a variable or noisy environment.

We also studied several technological net-works. We analyzed the ISCAS89 benchmarkset of sequential logic electronic circuits (7, 25).The nodes in these circuits represent logic gatesand flip-flops. These nodes are linked by direct-ed edges. We found that the motifs separate thecircuits into classes that correspond to the cir-cuit’s functional description. In Table 1, wepresent two classes, consisting of five forward-logic chips and three digital fractional multipli-ers. The digital fractional multipliers share threemotifs, including three- and four-node feedbackloops. The forward logic chips share the feed-forward loop, bi-fan, and bi-parallel motifs,which are similar to the motifs found in thegenetic and neuronal information-processingnetworks. We found a different set of motifs ina network of directed hyperlinks betweenWorld Wide Web pages within a single domain(4). The World Wide Web motifs may reflect adesign aimed at short paths between relatedpages. Application of our approach to nondi-rected networks shows distinct sets of motifs innetworks of protein interactions and Internetrouter connections (18).

None of the network motifs shared by thefood webs matched the motifs found in the generegulation networks or the World Wide Web.Only one of the food web consensus motifs alsoappeared in the neuronal network. Differentmotif sets were found in electronic circuits withdifferent functions. This suggests that motifscan define broad classes of networks, each withspecific types of elementary structures. Themotifs reflect the underlying processes that gen-erated each type of network; for example, foodwebs evolve to allow a flow of energy from thebottom to the top of food chains, whereas generegulation and neuron networks evolve to pro-cess information. Information processing seemsto give rise to significantly different structuresthan does energy flow.

We further characterized the statistical sig-nificance of the motifs as a function of networksize, by considering pieces of various sizes(subnetworks) of the full network. The concen-tration of motifs in the subnetworks is about thesame as that in the full network (Fig. 3). Incontrast, the concentration of the correspondingsubgraphs in the randomized versions of thesubnetworks decreases sharply with size. Inanalogy with statistical physics, the number ofappearances of each motif in the real networks

Table 1. Network motifs found in biological and technological networks. The numbers of nodes and edgesfor each network are shown. For each motif, the numbers of appearances in the real network (Nreal) andin the randomized networks (Nrand! SD, all values rounded) (17, 18) are shown. The P value of all motifsis P " 0.01, as determined by comparison to 1000 randomized networks (100 in the case of the WorldWide Web). As a qualitative measure of statistical significance, the Z score # (Nreal – Nrand)/SD is shown.NS, not significant. Shown are motifs that occur at least U # 4 times with completely different sets ofnodes. The networks are as follows (18): transcription interactions between regulatory proteins and genesin the bacterium E. coli (11) and the yeast S. cerevisiae (20); synaptic connections between neurons inC. elegans, including neurons connected by at least five synapses (24); trophic interactions in ecologicalfood webs (22), representing pelagic and benthic species (Little Rock Lake), birds, fishes, invertebrates(Ythan Estuary), primarily larger fishes (Chesapeake Bay), lizards (St. Martin Island), primarily inverte-brates (Skipwith Pond), pelagic lake species (Bridge Brook Lake), and diverse desert taxa (CoachellaValley); electronic sequential logic circuits parsed from the ISCAS89 benchmark set (7, 25), where nodesrepresent logic gates and flip-flops (presented are all five partial scans of forward-logic chips and threedigital fractional multipliers in the benchmark set); and World Wide Web hyperlinks between Web pagesin a single domain (4) (only three-node motifs are shown). e, multiplied by the power of 10 (e.g., 1.46e6# 1.46$ 106).

*Has additional four-node motif: (X3Z, W; Y3Z, W; Z3W), Nreal# 150, Nrand# 85! 15, Z# 4. †Has additionalfour-node motif: (X3Y, Z; Y3Z; Z3W), Nreal# 204, Nrand# 80! 20, Z# 6. The three-node pattern (X3Y, Z; Y3Z;Z3Y) also occurs significantly more than at random. It is not a motif by the present definition because it does notappear with completely distinct sets of nodes more than U # 4 times. ‡Has additional four-node motif: (X3Y;Y3Z, W; Z3X; W3X), Nreal # 914, Nrand # 500 ! 70, Z # 6. §Has two additional three-node motifs: (X3Y, Z;Y3Z; Z3Y), Nreal # 3e5, Nrand # 1.4e3 ! 6e1, Z # 6000, and (X3Y, Z; Y3Z), Nreal # 5e5, Nrand # 9e4 ! 1.5e3,Z # 250.

Network Nodes Edges Nreal Nrand ± SD Z score Nreal Nrand ± SD Z score Nreal Nrand ± SD Z score

Gene regulation

(transcription)

X

Y

Z

Feed-

forward

loop

X Y

Z W

Bi-fan

E. coli 424 519 40 7 ± 3 10 203 47 ± 12 13

S. cerevisiae* 685 1,052 70 11 ± 4 14 1812 300 ± 40 41

Neurons X

Y

Z

Feed-

forward

loop

X Y

Z W

Bi-fan X

Y Z

W

Bi-

parallel

C. elegans† 252 509 125 90 ± 10 3.7 127 55 ± 13 5.3 227 35 ± 10 20Food webs X

Y

Z

Three

chain

X

Y Z

W

Bi-

parallel

Little Rock 92 984 3219 3120 ± 50 2.1 7295 2220 ± 210 25

Ythan 83 391 1182 1020 ± 20 7.2 1357 230 ± 50 23

St. Martin 42 205 469 450 ± 10 NS 382 130 ± 20 12

Chesapeake 31 67 80 82 ± 4 NS 26 5 ± 2 8

Coachella 29 243 279 235 ± 12 3.6 181 80 ± 20 5

Skipwith 25 189 184 150 ± 7 5.5 397 80 ± 25 13

B. Brook 25 104 181 130 ± 7 7.4 267 30 ± 7 32

Electronic circuits

(forward logic chips)

X

Y

Z

Feed-

forward

loop

Bi-fan X

Y Z

W

Bi-

parallel

s15850 10,383 14,240 424 2 ± 2 285 1040 1 ± 1 1200 480 2 ± 1 335

s38584 20,717 34,204 413 10 ± 3 120 1739 6 ± 2 800 711 9 ± 2 320

s38417 23,843 33,661 612 3 ± 2 400 2404 1 ± 1 2550 531 2 ± 2 340

s9234 5,844 8,197 211 2 ± 1 140 754 1 ± 1 1050 209 1 ± 1 200

s13207 8,651 11,831 403 2 ± 1 225 4445 1 ± 1 4950 264 2 ± 1 200

Electronic circuits

(digital fractional multipliers)

X

Y Z

Three-

node

feedback

loop

Bi-fan X Y

Z W

Four-

node

feedback

loop

s208 122 189 10 1 ± 1 9 4 1 ± 1 3.8 5 1 ± 1 5

s420 252 399 20 1 ± 1 18 10 1 ± 1 10 11 1 ± 1 11

s838‡ 512 819 40 1 ± 1 38 22 1 ± 1 20 23 1 ± 1 25World Wide Web X

Y

Z

Feedback

with two

mutual

dyads

X

Y Z

Fully

connected

triad

X

Y Z

Uplinked

mutual

dyad

nd.edu§ 325,729 1.46e6 1.1e5 2e3 ± 1e2 800 6.8e6 5e4±4e2 15,000 1.2e6 1e4 ± 2e2 5000

X Y

Z W

X Y

Z W

R E P O R T S

25 OCTOBER 2002 VOL 298 SCIENCE www.sciencemag.org826

classes), and edges represent synaptic connec-tions between the neurons. We found the feed-forward loop motif in agreement with anatomi-cal observations of triangular connectivity struc-tures (24). The four-node motifs include thebi-fan and the bi-parallel (Table 1). Two ofthese motifs (feedforward loop and bi-fan) were

also found in the transcriptional gene regulationnetworks. This similarity in motifs may point toa fundamental similarity in the design con-straints of the two types of networks. Both net-works function to carry information from sen-sory components (sensory neurons/transcriptionfactors regulated by biochemical signals) to ef-

fectors (motor neurons/structural genes). Thefeedforward loop motif common to both typesof networks may play a functional role in infor-mation processing. One possible function of thiscircuit is to activate output only if the inputsignal is persistent and to allow a rapid deacti-vation when the input goes off (11). Indeed,many of the input nodes in the neural feedfor-ward loops are sensory neurons, which mayrequire this type of information processingto reject transient input fluctuations that areinherent in a variable or noisy environment.

We also studied several technological net-works. We analyzed the ISCAS89 benchmarkset of sequential logic electronic circuits (7, 25).The nodes in these circuits represent logic gatesand flip-flops. These nodes are linked by direct-ed edges. We found that the motifs separate thecircuits into classes that correspond to the cir-cuit’s functional description. In Table 1, wepresent two classes, consisting of five forward-logic chips and three digital fractional multipli-ers. The digital fractional multipliers share threemotifs, including three- and four-node feedbackloops. The forward logic chips share the feed-forward loop, bi-fan, and bi-parallel motifs,which are similar to the motifs found in thegenetic and neuronal information-processingnetworks. We found a different set of motifs ina network of directed hyperlinks betweenWorld Wide Web pages within a single domain(4). The World Wide Web motifs may reflect adesign aimed at short paths between relatedpages. Application of our approach to nondi-rected networks shows distinct sets of motifs innetworks of protein interactions and Internetrouter connections (18).

None of the network motifs shared by thefood webs matched the motifs found in the generegulation networks or the World Wide Web.Only one of the food web consensus motifs alsoappeared in the neuronal network. Differentmotif sets were found in electronic circuits withdifferent functions. This suggests that motifscan define broad classes of networks, each withspecific types of elementary structures. Themotifs reflect the underlying processes that gen-erated each type of network; for example, foodwebs evolve to allow a flow of energy from thebottom to the top of food chains, whereas generegulation and neuron networks evolve to pro-cess information. Information processing seemsto give rise to significantly different structuresthan does energy flow.

We further characterized the statistical sig-nificance of the motifs as a function of networksize, by considering pieces of various sizes(subnetworks) of the full network. The concen-tration of motifs in the subnetworks is about thesame as that in the full network (Fig. 3). Incontrast, the concentration of the correspondingsubgraphs in the randomized versions of thesubnetworks decreases sharply with size. Inanalogy with statistical physics, the number ofappearances of each motif in the real networks

Table 1. Network motifs found in biological and technological networks. The numbers of nodes and edgesfor each network are shown. For each motif, the numbers of appearances in the real network (Nreal) andin the randomized networks (Nrand! SD, all values rounded) (17, 18) are shown. The P value of all motifsis P " 0.01, as determined by comparison to 1000 randomized networks (100 in the case of the WorldWide Web). As a qualitative measure of statistical significance, the Z score # (Nreal – Nrand)/SD is shown.NS, not significant. Shown are motifs that occur at least U # 4 times with completely different sets ofnodes. The networks are as follows (18): transcription interactions between regulatory proteins and genesin the bacterium E. coli (11) and the yeast S. cerevisiae (20); synaptic connections between neurons inC. elegans, including neurons connected by at least five synapses (24); trophic interactions in ecologicalfood webs (22), representing pelagic and benthic species (Little Rock Lake), birds, fishes, invertebrates(Ythan Estuary), primarily larger fishes (Chesapeake Bay), lizards (St. Martin Island), primarily inverte-brates (Skipwith Pond), pelagic lake species (Bridge Brook Lake), and diverse desert taxa (CoachellaValley); electronic sequential logic circuits parsed from the ISCAS89 benchmark set (7, 25), where nodesrepresent logic gates and flip-flops (presented are all five partial scans of forward-logic chips and threedigital fractional multipliers in the benchmark set); and World Wide Web hyperlinks between Web pagesin a single domain (4) (only three-node motifs are shown). e, multiplied by the power of 10 (e.g., 1.46e6# 1.46$ 106).

*Has additional four-node motif: (X3Z, W; Y3Z, W; Z3W), Nreal# 150, Nrand# 85! 15, Z# 4. †Has additionalfour-node motif: (X3Y, Z; Y3Z; Z3W), Nreal# 204, Nrand# 80! 20, Z# 6. The three-node pattern (X3Y, Z; Y3Z;Z3Y) also occurs significantly more than at random. It is not a motif by the present definition because it does notappear with completely distinct sets of nodes more than U # 4 times. ‡Has additional four-node motif: (X3Y;Y3Z, W; Z3X; W3X), Nreal # 914, Nrand # 500 ! 70, Z # 6. §Has two additional three-node motifs: (X3Y, Z;Y3Z; Z3Y), Nreal # 3e5, Nrand # 1.4e3 ! 6e1, Z # 6000, and (X3Y, Z; Y3Z), Nreal # 5e5, Nrand # 9e4 ! 1.5e3,Z # 250.

Network Nodes Edges Nreal Nrand ± SD Z score Nreal Nrand ± SD Z score Nreal Nrand ± SD Z score

Gene regulation

(transcription)

X

Y

Z

Feed-

forward

loop

X Y

Z W

Bi-fan

E. coli 424 519 40 7 ± 3 10 203 47 ± 12 13

S. cerevisiae* 685 1,052 70 11 ± 4 14 1812 300 ± 40 41

Neurons X

Y

Z

Feed-

forward

loop

X Y

Z W

Bi-fan X

Y Z

W

Bi-

parallel

C. elegans† 252 509 125 90 ± 10 3.7 127 55 ± 13 5.3 227 35 ± 10 20Food webs X

Y

Z

Three

chain

X

Y Z

W

Bi-

parallel

Little Rock 92 984 3219 3120 ± 50 2.1 7295 2220 ± 210 25

Ythan 83 391 1182 1020 ± 20 7.2 1357 230 ± 50 23

St. Martin 42 205 469 450 ± 10 NS 382 130 ± 20 12

Chesapeake 31 67 80 82 ± 4 NS 26 5 ± 2 8

Coachella 29 243 279 235 ± 12 3.6 181 80 ± 20 5

Skipwith 25 189 184 150 ± 7 5.5 397 80 ± 25 13

B. Brook 25 104 181 130 ± 7 7.4 267 30 ± 7 32

Electronic circuits

(forward logic chips)

X

Y

Z

Feed-

forward

loop

Bi-fan X

Y Z

W

Bi-

parallel

s15850 10,383 14,240 424 2 ± 2 285 1040 1 ± 1 1200 480 2 ± 1 335

s38584 20,717 34,204 413 10 ± 3 120 1739 6 ± 2 800 711 9 ± 2 320

s38417 23,843 33,661 612 3 ± 2 400 2404 1 ± 1 2550 531 2 ± 2 340

s9234 5,844 8,197 211 2 ± 1 140 754 1 ± 1 1050 209 1 ± 1 200

s13207 8,651 11,831 403 2 ± 1 225 4445 1 ± 1 4950 264 2 ± 1 200

Electronic circuits

(digital fractional multipliers)

X

Y Z

Three-

node

feedback

loop

Bi-fan X Y

Z W

Four-

node

feedback

loop

s208 122 189 10 1 ± 1 9 4 1 ± 1 3.8 5 1 ± 1 5

s420 252 399 20 1 ± 1 18 10 1 ± 1 10 11 1 ± 1 11

s838‡ 512 819 40 1 ± 1 38 22 1 ± 1 20 23 1 ± 1 25World Wide Web X

Y

Z

Feedback

with two

mutual

dyads

X

Y Z

Fully

connected

triad

X

Y Z

Uplinked

mutual

dyad

nd.edu§ 325,729 1.46e6 1.1e5 2e3 ± 1e2 800 6.8e6 5e4±4e2 15,000 1.2e6 1e4 ± 2e2 5000

X Y

Z W

X Y

Z W

R E P O R T S

25 OCTOBER 2002 VOL 298 SCIENCE www.sciencemag.org826

Milo et al,2002. Science 298:824

Motivos en Redes de Regulación II

53

Perfiles

To understand the design principles of com-plex networks, it is important to compare the localstructure of networks from different fields. Themain difficulty is that these networks can be ofvastly different sizes [for example, World WideWeb (WWW) hyperlink networks with millionsof nodes and social networks with tens of nodes]and degree sequences. Here, we present an ap-proach for comparing network local structure,based on the significance profile (SP). To calcu-late the SP of a network, the network is comparedto an ensemble of randomized networks with thesame degree sequence. The comparison to ran-domized networks compensates for effects due tonetwork size and degree sequence. For each sub-graph i, the statistical significance is described bythe Z score (11):

Zi ! !Nreali " )/std(Nrandi)

where Nreali is the number of times the sub-

graph appears in the network, and "Nrandi#and std(Nrandi) are the mean and standarddeviation of its appearances in the random-ized network ensemble. The SP is the vectorof Z scores normalized to length 1:

SPi$Zi/(%Zi2)1/2

The normalization emphasizes the relativesignificance of subgraphs, rather than the ab-solute significance. This is important forcomparison of networks of different sizes,because motifs (subgraphs that occur muchmore often than expected at random) in largenetworks tend to display higher Z scores thanmotifs in small networks (7).

We present in Fig. 1 the SP of the 13possible directed connected triads (triad sig-nificance profile, TSP) for networks fromdifferent fields (12). The TSP of these net-works is almost always insensitive to removal

of 30% of the edges or to addition of 50%new edges at random, demonstrating that it isrobust to missing data or random data errors(SOM Text). Several superfamilies of net-works with similar TSPs emerge from thisanalysis. One superfamily includes sensorytranscription networks that control gene ex-pression in bacteria and yeast in response toexternal stimuli. In these transcription net-works, the nodes represent genes or operonsand the edges represent direct transcriptionalregulation (6, 13–15). Networks from threemicroorganisms, the bacteria Escherichiacoli (6) and Bacillus subtilis (14) and theyeast Saccharomyces cerevisiae (7, 15), wereanalyzed. The networks have very similarTSPs (correlation coefficient c # 0.99). Theyshow one strong motif, triad 7, termed “feed-forward loop.” The feedforward loop hasbeen theoretically and experimentally shown

Fig. 1. The triad significance profile (TSP) of networks from variousdisciplines. The TSP shows the normalized significance level (Z score) foreach of the 13 triads. Networks with similar characteristic profiles aregrouped into superfamilies. The lines connecting the significance valuesserve as guides to the eye. The networks are as follows (where N and Eare the number of nodes and edges, respectively) (12): (i) Direct tran-scription interactions in the bacteria E. coli (6) (TRANSC-E.COLI N$ 424,E$ 519) and B. subtilis (14) (TRANSC-B.SUBTILIS N$ 516, E$ 577) andin the yeast S. cerevisiae [TRANC-YEAST N $ 685, E $ 1052 (7) andTRANSC-YEAST-2 N $ 2341, E$3969 (15)]. (ii) Signal-transductioninteractions in mammalian cells based on the signal transduction knowl-edge environment (STKE, http://stke.sciencemag.org/) (SIGNAL-TRANS-DUCTION N $ 491, E $ 989), transcription networks that guide devel-opment in fruit fly (from the GeNet literature database, www.csa.ru/Inst/gorb_dep/inbios/genet/genet.htm) (TRANSC-DROSOPHILA N$ 110, E$307), endomesoderm development in sea urchin (20) (TRANSC-SEA-

URCHIN N $ 45, E $ 83), and synaptic connections between neurons inC. elegans (NEURONS N $ 280, E $ 2170). (iii) WWW hyperlinksbetween Web pages in the www.nd.edu site (3) (WWW-1 N $ 325729,E $ 1469678), pages related to literary studies of Shakespeare (21)(WWW-2 N $ 277114, E $ 927400), and pages related to tango,specifically the music of Piazzolla (21) (WWW-3 N $ 47870, E $235441); and social networks, including inmates in prison (SOCIAL-1 N$67, E $ 182), sociology freshmen (22) (SOCIAL-2 N $ 28, E $ 110), andcollege students in a course about leadership (SOCIAL-3 N$ 32, E$ 96).(iv) Word-adjacency networks of a text in English (ENGLISH N $ 7724,E $ 46281), French (FRENCH N $ 9424, E $ 24295), Spanish (SPANISHN $ 12642, E $ 45129), and Japanese (JAPANESE N $ 3177, E $ 8300)and a bipartite model with two groups of nodes of sizes N1 $ 1000 andN2 $ 10 with probability of a directed or mutual edge between nodes ofdifferent groups being p $ 0.06 and q $ 0.003, respectively, and no edgesbetween nodes within the same group (BIPARTITE N $ 1010, E $ 1261).

R E P O R T S

www.sciencemag.org SCIENCE VOL 303 5 MARCH 2004 1539

Milo et al. 2004 Science 303:1538-1542

54

Evolución de Motivos

FFL

Bi-fans

NO: En E. coli no hay reguladores homologos en el mismo motivo

Tecihmann & Babu, 2004 Nature Genetics 36(5):492-6

55

Conant & Wagner,2003. Nat Genet. 34:264

Evolución de Motivos II

56

Shen-Orr et al.,2002. Nat Genet. 31:64

Propiedades de los motivos

57

Figure 1

R

S

0 0.5 1

1

3

2

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0.5

S

ATP ADP

H2OP

i

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te (

dR

/dt)

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te (

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t)R

ate

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RP/d

t)R

ate

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R/d

t)R

ate

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R/d

t)R

ate

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R/d

t)R

ate

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R/d

t)

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sp

on

se

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)R

esp

on

se

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)R

esp

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se

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)R

esp

on

se

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)

RP

RP

Re

sp

on

se

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P)

Re

sp

on

se

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P)

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Hyperbolic

R

S

RP

ATP ADP

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SX

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Mutual inhibition

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Current Opinion in Cell Biology

222 Cell regulation

Current Opinion in Cell Biology 2003, 15:221–231 www.current-opinion.com

Figure 1

R

S

0 0.5 1

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3

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0

0.5

S

ATP ADP

H2OP

i

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Ra

te (

dR

/dt)

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te (

dR

P/d

t)R

ate

(d

RP/d

t)R

ate

(d

R/d

t)R

ate

(d

R/d

t)R

ate

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R/d

t)R

ate

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R/d

t)

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sp

on

se

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)R

esp

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)R

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)R

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)R

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P)

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Hyperbolic

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RP

ATP ADP

R

SX

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X

R

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Current Opinion in Cell Biology

222 Cell regulation

Current Opinion in Cell Biology 2003, 15:221–231 www.current-opinion.com

Figure 1

R

S

0 0.5 1

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3

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0

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S

ATP ADP

H2OP

i

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te (

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/dt)

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te (

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t)R

ate

(dR

P/d

t)R

ate

(dR

/dt)

Rate

(dR

/dt)

Rate

(dR

/dt)

Rate

(dR

/dt)

Response (

R)

Response (

R)

Response (

R)

Response (

R)

RP

RP

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spo

nse (

RP)

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onse (

RP)

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Current Opinion in Cell Biology

222 Cell regulation

Current Opinion in Cell Biology 2003, 15:221–231 www.current-opinion.com

Toggle switches have also been realized in artificialgenetic networks based on mutual inhibition [41] ormutual activation [42!]. These networks were designedand built in explicit reliance on theoretical ideas of thekind we have described.

Negative feedback: homeostasis andoscillationsIn negative feedback, the response counteracts the effectof the stimulus. In Figure 1g, the response element, R,inhibits the enzyme catalysing its synthesis; hence, therate of production of R is a sigmoidal decreasing functionof R. The signal in this case is the demand for R— that is,the rate of consumption of R is given by k2SR. The steadystate concentration of R is confined to a narrow windowfor a broad range of signal strengths, because the supply ofR adjusts to its demand. This type of regulation, com-monly employed in biosynthetic pathways, is calledhomeostasis. It is a kind of imperfect adaptation, but it

is not a sniffer because stepwise increases in S do notgenerate transient changes in R.

Negative feedback can also create an oscillatory response.A two-component, negative feedback loop, X!R—|X,can exhibit damped oscillations to a stable steady statebut not sustained oscillations [43]. Sustained oscillationsrequire at least three components: X!Y!R––|X. Thethird component (Y) introduces a time delay in the feed-back loop, causing the control system repeatedly to over-shoot and undershoot its steady state.

In Figure 2a (column 1), we present a wiring diagram for anegative-feedback control loop. For intermediate signalstrengths, the system executes sustained oscillations(column 2) in the variables X(t), YP(t) and RP(t). In thesignal-response curve (column 3), we plot RP;ss as afunction of S, noting that the steady-state response isunstable for Scrit1 < S < Scrit2. Within this range, RP(t)

Figure 2

(a)

(b)

(c)

0 25 500

0.5

1

0 2 4 6

S

X

Y YP

R RP

(2)

(1)

Time

XYP

RP Response (

RP)

Signal (S)

Scrit2

Scrit1

Scrit2Scrit1

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1

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2

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X

R

R

S

EP E

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X

R

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R)

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R

S

EP E

X

0

5

0.0

0.1

0.2

0.3

0.4

0.5

Scrit2Scrit1

Response (

R)

Signal (S)

Oscillatory networks. In this tableau, the rows correspond to (a) negative feedback, (b) activator-inhibitor and (c) substrate-depletion oscillators. Theleft column presents wiring diagrams and the right column signal-response curves. The centre column presents time courses (a) or phase planes (b,c).The kinetic equations corresponding to each wiring diagram are displayed in Box 1, along with the parameter values for which the other two columnsare drawn. S, signal; R, response; E, X and Y, other components of the signaling network; EP, phosphorylated form of E; etc. (a) There are two ways toclose the negative feedback loop: first, RP inhibits the synthesis of X; or second, RP activates the degradation of X. We choose case 2. Centrecolumn: oscillations of X (black, left ordinate), YP (red, right ordinate) and RP (blue, right ordinate) for S ¼ 2. Right column: the straight line is thesteady-state response (RP;ss) as a function of S; solid line indicates stable steady states, dashed line indicates unstable steady states. For a fixedvalue of S between Scrit1 and Scrit2, the unstable steady state is surrounded by a stable periodic solution. For example, the solution in the centrecolumn oscillates between RPmax ¼ 0:28 and RPmin ¼ 0:01. These two numbers are plotted as filled circles (at S ¼ 2) in the signal-response curve tothe right. Scrit1 and Scrit2 are so-called points of Hopf bifurcation, where small-amplitude periodic solutions are born as a steady state loses stability.Centre column, (b,c): phase plane portraits for S ¼ 0:2; red curve, (X,R) pairs that satisfy dR=dt ¼ 0; blue curve, (X,R) pairs that satisfy dX=dt ¼ 0;open circle, unstable steady state. Right column, (b,c): solid line, stable steady states; dashed line, unstable steady states; closed/open circles,maximum and minimum values of R during a stable/unstable oscillation. Scrit1 and Scrit2 are called subcritical Hopf bifurcation points.

Sniffers, buzzers, toggles and blinkers Tyson, Chen and Novak 225

www.current-opinion.com Current Opinion in Cell Biology 2003, 15:221–231

Tyler et al. 2003 Current Opinion in Cell Biology 15:221–231

Circuitos

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Dinámica de Redes de Regulación

Luscombe et al., 2004 Nature 431:308

59

Luscombe et al., 2004 Nature 431:308

Dinámica de Redes de Regulación

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Luscombe et al., 2004 Nature 431:308

Endogenous Exogenous

Dinámica de Redes de Regulación

61

Gracias!Preguntas?

62

Practicas:

• http://rsat.scmbb.ulb.ac.be/rsat/• Misc>Tutorials

• 1. Sequence retrieval

• 3. Pattern Matching

• 2 patser

• 4. Patten Discovery

• 1.1 oligo-analysis

• 2.1 Gibbs Motif Sampler

• 3.1 Microarrays

63