Hierarchical

Organization

of

Modularity

in

Metabolic

Networks

E.

Ravasz

et

al.

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REPORTS

M.

L.

Rosenzweig

Species

Diversity

in

Space

and

Time

-LRB-

Cambridge

Univ.

Press

Cambridge

-RRB-

R.

E.

Ricklefs

D.

Schluter

in

Species

Diversity

in

Ecological

Communities

R.

E.

Ricklefs

D.

Schluter

Eds

-LRB-

Chicago

Univ.

Press

Chicago

-RRB-

pp.

C.

Rahbek

G.

R.

Graves

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

R.

K.

Colwell

D.

C.

Lees

Trends

Ecol

Evol

-LRB-

-RRB-

D.

C.

Lees

C.

Kremen

L.

Andriamampianina

Biol

J.

Linn

Soc

-LRB-

-RRB-

W.

Jetz

C.

Rahbek

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

Materials

and

methods

are

available

as

supporting

material

on

Science

Online

N.

A.

C.

Cressie

Statistics

for

Spatial

Data

-LRB-

Wiley

New

York

-RRB-

J.

J.

Lennon

Ecography

-LRB-

-RRB-

J.

R.

G.

Turner

J.

J.

Lennon

J.

A.

Lawrenson

Nature

-LRB-

-RRB-

J.

J.

Lennon

J.

J.

D.

Greenwood

J.

R.

G.

Turner

J.

Anim

Ecol

-LRB-

-RRB-

R.

K.

Colwell

G.

C.

Hurtt

Am

Nat

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M.

R.

Willig

S.

K.

Lyons

Oikos

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P.

Koleff

K.

J.

Gaston

Ecography

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S.

Anderson

Am

Mus

Novit

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D.

J.

Currie

V.

Paquin

Nature

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A.

Balmford

et

al.

Science

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J.

T.

Kerr

L.

Packer

Nature

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H.

Elenga

et

al.

J.

Biogeogr

-LRB-

-RRB-

G.

R.

Graves

Auk

-LRB-

-RRB-

D.

Pomeroy

Conserv

Biol

-LRB-

-RRB-

T.

M.

Crowe

A.

A.

Crowe

J.

Zool

-LRB-

-RRB-

A.

J.

Stattersfield

D.

R.

Capper

G.

C.

L.

Dutson

Threatened

Birds

of

the

World

-LRB-

BirdLife

International

International

Union

for

Conservation

of

Nature

and

Natural

Resources

Lynx

Edicions

Barcelona

-RRB-

We

thank

D.

Rogers

B.

Bakker

W.

Wint

and

S.

Hay

for

Geographic

Information

Systems

advice

and

discussions

I.

Woodward

for

providing

productivity

data

L.

A.

Hansen

for

assistance

with

access

to

the

African

bird

database

on

behalf

of

the

Zoological

Museum

University

of

Copenhagen

-LRB-

ZMUC

-RRB-

and

E.

Baker

N.

Baker

F.

Dowsett-Lemaire

R.

Dowsett

J.

Fjelds

M.

E.

Gartshore

H.

M.

de

Klerk

M.

Languy

R.

B.

Payn

COC/BirdLife

Cameroon

and

BirdLife

International

for

providing

data

for

the

ZMUC

database

The

manuscript

benefited

tremendously

from

discussions

with

R.

K.

Colwell

and

comments

from

J.

Brown

J.

Fjelds

R.

Freckleton

K.

Gaston

N.

J.

Gotelli

G.

R.

Graves

P.

Harvey

R.

Lande

O.

Lewis

R.

May

I.

Owens

and

D.

Rogers

W.J.

was

supported

by

Natural

Environment

Research

Council

and

German

Scholarship

Foundation

studentships

C.R.

was

supported

by

the

Danish

National

Science

Foundation

-LRB-

grant

J.

nr

-RRB-

Supporting

Online

Material

Materials

and

Methods

Supporting

Text

Tables

to

April

accepted

July

E.

Ravasz

A.

L.

Somera

D.

A.

Mongru

Z.

N.

Oltvai

A.-L

Spatially

or

chemically

isolated

functional

modules

composed

of

several

cellular

components

and

carrying

discrete

functions

are

considered

fundamental

building

blocks

of

cellular

organization

but

their

presence

in

highly

integrated

biochemical

networks

lacks

quantitative

support

Here

we

show

that

the

metabolic

networks

of

distinct

organisms

are

organized

into

many

small

highly

connected

topologic

modules

that

combine

in

a

hierarchical

manner

into

larger

less

cohesive

units

with

their

number

and

degree

of

clustering

following

a

power

law

Within

Escherichia

coli

the

uncovered

hierarchical

modularity

closely

overlaps

with

known

metabolic

functions

The

identified

network

architecture

may

be

generic

to

system-level

cellular

organization

The

identification

and

characterization

of

system-level

features

of

biological

organization

is

a

key

issue

of

postgenomic

biology

-LRB-

-RRB-

The

concept

of

modularity

assumes

that

cellular

functionality

can

be

seamlessly

partitioned

into

a

collection

of

modules

Each

module

is

a

discrete

entity

of

several

elementary

components

and

performs

an

identifiable

task

separable

from

the

functions

of

other

modules

-LRB-

-RRB-

Spatially

and

chemically

isolated

molecular

machines

or

protein

complexes

-LRB-

such

as

ribosomes

and

flagella

-RRB-

are

prominent

examples

of

such

functional

units

but

more

extended

modules

such

as

those

achieving

their

isolation

through

the

initial

binding

of

a

signaling

molecule

-LRB-

-RRB-

are

also

apparent

Simultaneously

it

is

recognized

that

the

Department

of

Physics

University

of

Notre

Dame

Notre

Dame

IN

USA

of

Pathology

Northwestern

University

Chicago

IL

USA

To

whom

correspondence

should

be

addressed

Email

-LRB-

Z.N.O.

-RRB-

and

alb@nd

edu

-LRB-

A.-L.B.

-RRB-

thousands

of

components

of

a

living

cell

are

dynamically

interconnected

so

that

the

cell

's

functional

properties

are

ultimately

encoded

into

a

complex

intracellular

web

of

molecular

interactions

-LRB-

-RRB-

This

is

perhaps

most

evident

with

cellular

metabolism

a

fully

connected

biochemical

network

in

which

hundreds

of

metabolic

substrates

are

densely

integrated

through

biochemical

reactions

Within

this

network

however

modular

organization

-LRB-

i.e.

clear

boundaries

between

subnetworks

-RRB-

is

not

immediately

apparent

Indeed

recent

studies

have

demonstrated

that

the

probability

that

a

substrate

can

react

with

k

other

substrates

-LSB-

the

degree

distribution

P

-LRB-

k

-RRB-

of

a

metabolic

network

-RSB-

decays

as

a

in

all

power

law

P

-LRB-

k

-RRB-

k

with

organisms

-LRB-

-RRB-

suggesting

that

metabolic

networks

have

a

scale-free

topology

-LRB-

-RRB-

A

distinguishing

feature

of

such

scale-free

networks

is

the

existence

of

a

few

highly

connected

nodes

-LRB-

e.g.

pyruvate

or

coenzyme

A

-RRB-

which

participate

in

a

very

large

number

of

metabolic

reactions

With

a

large

number

of

links

these

hubs

integrate

all

substrates

into

a

single

integrated

web

in

SCIENCE

VOL

AUGUST

Downloaded

from

on

May

Hierarchical

Organization

of

Modularity

in

Metabolic

Networks

which

the

existence

of

fully

separated

modules

is

prohibited

by

definition

-LRB-

Fig.

-RRB-

Yet

the

dilemma

of

a

modular

versus

a

highly

integrated

module-free

metabolic

network

organization

remains

A

number

of

approaches

for

analyzing

the

functional

capabilities

of

metabolic

networks

indicate

the

existence

of

separable

functional

elements

-LRB-

-RRB-

Also

from

a

purely

topologic

perspective

the

metabolic

network

of

Escherichia

coli

is

known

to

possess

a

high

clustering

coefficient

-LRB-

-RRB-

a

property

that

is

suggestive

of

a

modular

organization

In

itself

this

implies

that

the

metabolism

of

E.

coli

has

a

modular

topology

potentially

comprising

several

densely

interconnected

functional

modules

of

varying

sizes

that

are

connected

by

few

intermodule

links

-LRB-

Fig.

-RRB-

However

such

clear-cut

modularity

imposes

severe

restrictions

on

the

degree

distribution

implying

that

most

nodes

have

approximately

the

same

number

of

links

which

contrasts

with

the

metabolic

network

's

scale-free

nature

-LRB-

-RRB-

To

determine

whether

such

a

dichotomy

is

indeed

a

generic

property

of

all

metabolic

networks

we

first

calculated

the

average

clustering

coefficient

for

different

organisms

-LRB-

-RRB-

as

a

function

of

the

number

of

distinct

substrates

N

present

in

their

metabolism

The

clustering

coefficient

defined

-LRB-

ki

-RRB-

where

n

denotes

the

as

Ci

number

of

direct

links

connecting

the

ki

nearest

neighbors

of

node

i

-LRB-

-RRB-

is

equal

to

for

a

node

at

the

center

of

a

fully

interlinked

cluster

and

it

is

for

a

metabolite

that

is

part

of

a

loosely

connected

group

-LRB-

Fig.

-RRB-

Therefore

Ci

averaged

over

all

nodes

i

of

a

metabolic

network

is

a

measure

of

the

network

's

potential

modularity

We

found

that

for

all

organisms

the

average

clustering

coefficient

is

about

an

order

of

magnitude

larger

than

that

expected

for

a

scale-free

network

of

similar

size

-LRB-

Fig.

-RRB-

suggesting

that

metabolic

networks

in

all

organisms

are

characterized

by

a

high

intrinsic

potential

modularity

We

also

observed

that

in

contrast

with

REPORTS

the

prediction

of

the

scale-free

model

for

which

the

clustering

coefficient

decreases

as

N

-LRB-

-RRB-

the

clustering

coefficient

of

metabolic

networks

is

independent

of

their

size

-LRB-

Fig.

-RRB-

These

results

demonstrate

a

fundamental

conflict

between

the

predictions

of

the

current

models

of

metabolic

organization

The

high

size-independent

clustering

coefficient

offers

strong

evidence

for

modularity

whereas

the

power

law

degree

distribution

of

all

metabolic

networks

-LRB-

-RRB-

strongly

supports

the

scale-free

model

and

rules

out

a

manifestly

modular

topology

To

resolve

this

apparent

contradiction

we

propose

a

simple

heuristic

model

of

metabolic

organization

which

we

refer

to

as

a

hierarchical

network

-LRB-

Fig.

-RRB-

-LRB-

-RRB-

In

such

a

model

network

our

starting

point

is

a

small

cluster

of

four

densely

linked

nodes

Next

we

generate

three

replicas

of

this

hypothetical

module

and

connect

the

three

external

nodes

of

the

replicated

clusters

to

the

central

node

of

the

old

cluster

obtaining

a

large

module

Subsequently

we

again

generate

three

replicas

of

this

module

and

connect

the

peripheral

nodes

to

the

central

node

of

the

old

module

-LRB-

Fig.

-RRB-

These

replication

and

connection

steps

can

be

repeated

indefinitely

in

each

step

quadrupling

the

number

of

nodes

in

the

system

The

architecture

of

such

a

network

integrates

a

scale-free

topology

with

an

inherent

modular

structure

It

has

a

power

law

degree

distribution

with

degree

exponent

-LRB-

ln

-RRB-

-LRB-

ln

-RRB-

in

agreement

with

observed

in

metabolic

networks

Its

clustering

coefficient

C

is

also

comparable

with

that

observed

for

metabolic

networks

Most

important

the

clustering

coefficient

of

the

model

is

independent

of

the

size

of

the

network

in

agreement

with

the

results

of

Fig.

A

unique

feature

of

the

proposed

network

model

not

shared

by

either

the

scalefree

-LRB-

Fig.

-RRB-

or

modular

-LRB-

Fig.

-RRB-

models

is

its

hierarchical

architecture

This

hierarchy

which

is

evident

from

a

visual

inspection

is

intrinsic

to

the

assembly

by

repeated

quadrupling

of

the

system

The

hierarchy

can

be

characterized

quantitatively

by

using

the

recent

observation

-LRB-

-RRB-

that

in

deterministic

scale-free

networks

the

clustering

coefficient

of

a

node

with

k

links

follows

the

scaling

law

C

-LRB-

k

-RRB-

k

This

scaling

law

quantifies

the

coexistence

of

a

hierarchy

of

nodes

with

different

degrees

of

modularity

as

measured

by

the

clustering

coefficient

and

is

directly

relevant

to

our

model

-LRB-

Fig.

-RRB-

Indeed

the

nodes

at

the

center

of

the

numerous

modules

have

a

clustering

coefficient

C

those

at

the

center

of

a

module

have

k

and

C

and

those

at

the

center

of

the

modules

have

k

and

C

indicating

that

the

higher

a

node

's

connectivity

the

smaller

its

clustering

coefficient

asymptotically

following

the

law

To

investigate

whether

such

hierarchical

organization

is

present

in

cellular

metabolism

we

measured

the

C

-LRB-

k

-RRB-

function

for

the

metabolic

networks

of

all

organisms

As

shown

in

Fig.

C

through

F

for

each

organism

C

-LRB-

k

-RRB-

is

well

approximated

by

C

-LRB-

k

-RRB-

k

in

contrast

to

the

k-independent

C

-LRB-

k

-RRB-

predicted

by

both

the

scale-free

and

modular

networks

This

provides

direct

evidence

for

an

inherently

hierarchical

organization

Such

hierarchical

modularity

reconciles

within

a

single

framework

all

the

observed

properties

of

metabolic

networks

their

scale-free

topology

high

system

size

independent

clustering

coefficient

and

the

power

law

scaling

of

C

-LRB-

k

-RRB-

A

key

issue

from

a

biological

perspective

is

whether

the

identified

hierarchical

architecture

reflects

the

true

functional

organization

of

cellular

metabolism

To

uncover

potential

relations

between

topological

modularity

and

the

functional

classification

of

different

metabolites

we

concentrated

on

the

metabolic

network

of

E.

coli

whose

metabolic

reactions

have

been

exhaustively

studied

both

biochemically

and

genetically

-LRB-

-RRB-

Using

a

previously

established

graph-theoretical

representation

-LRB-

-RRB-

we

first

subjected

E.

coli

's

metabolic

organization

to

a

three-step

reduction

process

replacing

nonbranching

pathways

with

equivalent

links

allowing

us

to

decrease

its

complexity

without

altering

the

network

topology

-LRB-

-RRB-

Next

we

calculated

the

topological

overlap

matrix

OT

-LRB-

i

j

-RRB-

of

the

condensed

metabolic

network

-LRB-

Fig.

-RRB-

A

topological

overlap

of

between

substrates

i

and

j

implies

that

they

are

connected

to

the

same

substrates

whereas

a

value

indicates

that

i

and

j

do

not

share

links

to

common

substrates

among

the

metabolites

they

react

with

The

metabolites

that

are

part

Fig.

Complex

network

A

models

-LRB-

A

-RRB-

A

schematic

illustration

-LRB-

left

-RRB-

of

a

scalefree

network

whose

degree

distribution

follows

a

power

law

In

such

a

network

a

few

highly

connected

nodes

or

hubs

-LRB-

blue

circles

-RRB-

play

an

important

role

in

keeping

the

whole

network

together

A

typical

configuration

-LRB-

right

-RRB-

of

a

scale-free

network

with

nodes

is

also

shown

obtained

using

the

scale-free

model

which

requires

the

B

addition

of

a

new

node

at

each

time

such

that

existing

nodes

with

higher

degrees

of

connectivity

have

a

higher

chance

of

being

linked

to

the

new

nodes

-LRB-

-RRB-

The

nodes

are

arranged

in

space

with

a

standard

clustering

algorithm

-LRB-

-RRB-

to

illustrate

the

absence

of

an

underlying

modularity

-LRB-

B

-RRB-

Schematic

illustration

-LRB-

left

-RRB-

of

a

manifestly

modular

network

made

of

four

highly

interlinked

modules

connected

to

each

other

by

a

few

C

links

This

intuitive

topology

does

not

have

a

scale-free

degree

distribution

as

most

of

its

nodes

have

a

similar

number

of

links

and

hubs

are

absent

A

standard

clustering

algorithm

uncovers

the

network

's

inherent

modularity

-LRB-

right

-RRB-

by

partitioning

a

modular

network

of

N

nodes

into

the

four

isolated

structures

built

into

the

system

-LRB-

C

-RRB-

The

hierarchical

network

-LRB-

left

-RRB-

has

a

scale-free

topology

with

embedded

modularity

The

hierarchical

levels

are

represented

in

increasing

order

from

blue

to

green

to

red

Standard

clustering

algorithms

-LRB-

right

-RRB-

are

less

successful

in

uncovering

the

network

's

underlying

modularity

A

detailed

quantitative

characterization

of

the

three

network

models

is

available

in

-LRB-

-RRB-

AUGUST

VOL

SCIENCE

Downloaded

from

on

May

REPORTS

of

highly

integrated

modules

have

a

high

topological

overlap

with

their

neighbors

and

we

found

that

the

larger

the

overlap

between

two

substrates

within

the

E.

coli

metabolic

network

the

more

likely

it

is

that

they

belong

to

the

same

functional

class

As

the

topological

overlap

matrix

is

expected

to

encode

the

comprehensive

enzyme

catalyzed

functional

relatedness

of

the

substrates

forming

the

metabolic

network

we

investigated

whether

potential

functional

modules

encoded

in

the

network

topology

can

be

uncovered

automatically

Initial

application

of

an

average-linkage

hierarchical

clustering

algorithm

-LRB-

-RRB-

to

the

overlap

matrix

of

the

small

hypothetical

network

shown

in

Fig.

placed

those

nodes

that

have

a

high

topological

overlap

close

to

each

other

-LRB-

Fig.

-RRB-

Also

the

method

identified

the

three

distinct

modules

built

into

the

model

of

Fig.

as

illustrated

by

the

fact

that

the

EFG

and

HIJK

modules

are

closer

to

each

other

in

a

topological

sense

with

the

ABC

module

being

farther

from

both

-LRB-

Fig.

-RRB-

Application

of

the

same

technique

on

the

E.

coli

overlap

matrix

OT

-LRB-

i

j

-RRB-

provides

a

global

topologic

representation

of

E.

coli

metabolism

-LRB-

Fig.

-RRB-

Groups

of

metabolites

forming

tightly

interconnected

clusters

are

visually

apparent

and

on

closer

inspection

the

hierarchy

of

nested

topologic

modules

of

increasing

sizes

and

decreasing

interconnectedness

is

also

evident

To

visualize

the

relation

between

topological

modules

and

the

known

functional

properties

of

the

metabolites

we

color-coded

the

branches

of

the

derived

hierarchical

tree

according

to

the

predominant

biochemical

class

of

the

substrates

it

produces

using

the

classification

of

metabolism

based

on

standard

small

molecule

biochemistry

-LRB-

-RRB-

As

shown

in

Fig.

and

in

the

three-dimensional

representation

in

Fig.

most

substrates

of

a

given

small

molecule

class

are

distributed

on

the

same

branch

of

the

tree

-LRB-

Fig.

-RRB-

and

correspond

to

relatively

well

delimited

regions

of

the

metabolic

network

-LRB-

Fig.

-RRB-

Therefore

there

are

strong

correlations

between

shared

biochemical

classification

of

metabolites

and

the

global

topological

organization

of

E.

coli

metabolism

-LRB-

Fig.

bottom

-RRB-

-LRB-

-RRB-

To

correlate

the

putative

modules

obtained

from

our

graph

theory

based

analysis

to

actual

biochemical

pathways

we

concentrated

on

the

pathways

involving

the

pyrimidine

metabolites

Our

method

divided

these

pathways

into

four

putative

modules

-LRB-

Fig.

-RRB-

which

represent

a

topologically

well-limited

area

of

E.

coli

metabolism

-LRB-

Fig.

blue-shaded

region

-RRB-

As

shown

in

Fig.

all

highly

connected

metabolites

-LRB-

Fig.

red-outlined

boxes

-RRB-

correspond

to

their

respective

biochemical

reactions

within

pyrimidine

metabolism

together

with

those

substrates

that

were

removed

during

the

original

network

reduction

procedure

and

then

added

again

-LRB-

Fig.

green-outlined

boxes

-RRB-

However

it

is

also

apparent

that

putative

module

boundaries

do

not

always

overlap

with

intuitive

biochemistry-based

boundaries

For

instance

the

synthesis

of

uridine

mono

Fig.

Evidence

of

hierarchical

modularity

in

metabolic

networks

-LRB-

A

-RRB-

The

clustering

coefficient

offers

a

measure

of

the

degree

of

interconnectivity

in

the

neighborhood

of

a

node

-LRB-

-RRB-

For

example

a

node

whose

neighbors

are

all

connected

to

each

other

has

C

-LRB-

left

-RRB-

whereas

a

node

with

no

links

between

its

neighbors

has

C

-LRB-

right

-RRB-

-LRB-

B

-RRB-

The

average

clustering

coefficient

C

-LRB-

N

-RRB-

for

organisms

-LRB-

-RRB-

is

shown

as

a

function

of

the

number

of

substrates

N

present

in

each

of

them

Species

belonging

to

archaea

-LRB-

purple

-RRB-

bacteria

-LRB-

green

-RRB-

and

eukaryotes

-LRB-

blue

-RRB-

are

shown

The

dashed

line

indicates

the

dependence

of

the

clustering

coefficient

on

the

network

size

for

a

module-free

scale-free

network

and

the

diamonds

denote

C

for

a

scale-free

network

with

the

same

parameters

-LRB-

N

and

number

of

links

-RRB-

as

observed

in

the

organisms

-LRB-

C

through

E

-RRB-

The

dependence

of

the

clustering

coefficient

on

the

node

's

degree

in

three

organisms

Aquidex

aeolicus

-LRB-

archaea

-RRB-

-LRB-

C

-RRB-

Escherichia

coli

-LRB-

bacterium

-RRB-

-LRB-

D

-RRB-

and

Saccharomyces

cerevisiae

-LRB-

eukaryote

-RRB-

-LRB-

E

-RRB-

-LRB-

F

-RRB-

The

C

-LRB-

k

-RRB-

curves

averaged

over

all

organisms

is

shown

and

the

inset

displays

all

species

together

The

data

points

are

color

coded

as

in

Fig.

In

-LRB-

C

through

F

-RRB-

the

dashed

lines

correspond

to

C

-LRB-

k

-RRB-

k

and

in

-LRB-

C

through

E

-RRB-

the

diamonds

represent

the

C

-LRB-

k

-RRB-

value

expected

for

a

scale-free

network

-LRB-

Fig.

-RRB-

of

similar

size

indicating

the

absence

of

scaling

The

wide

fluctuations

are

due

to

the

small

size

of

the

network

A

A

-LRB-

-RRB-

B

-LRB-

-RRB-

C

-LRB-

-RRB-

B

A

B

C

D

K

J

I

H

E

F

G

F

D

-LRB-

-RRB-

E

I

-LRB-

-RRB-

E

-LRB-

-RRB-

1 1/3

1 2/3

H

I

K

-LRB-

-RRB-

F

-LRB-

-RRB-

G

-LRB-

-RRB-

H

J

K

-LRB-

-RRB-

J

-LRB-

-RRB-

D

Fig.

Uncovering

the

underlying

modularity

of

a

complex

network

C

-LRB-

A

-RRB-

Topological

overlap

illustrated

B

on

a

small

hypothetical

network

For

each

pair

of

nodes

i

and

j

we

define

A

the

topological

overlap

OT

-LRB-

i

j

-RRB-

Jn

-LRB-

i

j

-RRB-

-LSB-

min

-LRB-

ki

kj

-RRB-

-RSB-

where

Jn

-LRB-

i

j

-RRB-

denotes

the

number

of

nodes

to

which

both

i

and

j

are

linked

-LRB-

plus

if

there

is

a

direct

link

between

i

and

j

-RRB-

and

-LSB-

min

-LRB-

ki

kj

-RRB-

-RSB-

is

the

smaller

of

the

ki

and

kj

degrees

On

each

link

we

indicate

the

topological

overlap

for

the

connected

nodes

and

in

parentheses

next

to

each

node

we

indicate

the

node

's

clustering

coefficient

-LRB-

B

-RRB-

The

topological

overlap

matrix

corresponding

to

the

small

network

shown

in

-LRB-

A

-RRB-

The

rows

and

columns

of

the

matrix

were

reordered

by

the

application

of

an

average

linkage

clustering

method

-LRB-

-RRB-

to

its

elements

allowing

us

to

identify

and

place

close

to

each

other

those

nodes

that

have

high

topological

overlap

The

color

code

denotes

the

degree

of

topological

overlap

between

the

nodes

The

associated

tree

reflects

the

three

distinct

modules

built

into

the

model

of

Fig.

as

well

as

the

fact

that

the

EFG

and

HIJK

modules

are

closer

to

each

other

in

the

topological

sense

than

to

the

ABC

module

SCIENCE

VOL

AUGUST

Downloaded

from

on

May

REPORTS

AUGUST

VOL

SCIENCE

Downloaded

from

on

May

REPORTS

Fig.

Identifying

the

topological

modules

in

E.

coli

metabolism

-LRB-

A

-RRB-

The

topologic

overlap

matrix

corresponding

to

E.

coli

metabolism

together

with

the

corresponding

hierarchical

tree

-LRB-

top

-RRB-

that

quantifies

the

relation

between

the

different

modules

The

branches

of

the

tree

are

color

coded

to

reflect

the

predominant

biochemical

classification

of

their

substrates

The

biochemical

classes

that

we

used

to

group

the

metabolites

represent

carbohydrate

metabolism

-LRB-

blue

-RRB-

nucleotide

and

nucleic

acid

metabolism

-LRB-

red

-RRB-

protein

peptide

and

amino

acid

metabolism

-LRB-

green

-RRB-

lipid

metabolism

-LRB-

cyan

-RRB-

aromatic

compound

metabolism

-LRB-

dark

pink

-RRB-

monocarbon

compound

metabolism

-LRB-

yellow

-RRB-

and

coenzyme

metabolism

-LRB-

light

orange

-RRB-

-LRB-

-RRB-

The

color

code

of

the

matrix

denotes

the

degree

of

topological

overlap

shown

in

the

matrix

The

large-scale

functional

map

of

the

metabolism

as

suggested

by

the

hierarchical

tree

is

also

shown

-LRB-

bottom

-RRB-

-LRB-

B

-RRB-

Three-dimensional

representation

of

the

reduced

E.

coli

metabolic

network

Each

node

is

color

coded

by

the

predominant

biochemical

class

to

which

it

belongs

and

is

identical

to

the

color

code

applied

to

the

branches

of

the

tree

shown

in

-LRB-

A

-RRB-

The

different

functional

classes

are

visibly

segregated

into

topologically

distinct

regions

of

metabolism

The

blue-shaded

region

denotes

the

nodes

belonging

to

pyrimidine

metabolism

-LRB-

C

-RRB-

Enlarged

view

of

the

substrate

module

of

pyrimidine

metabolism

The

colored

boxes

denote

the

first

two

levels

of

the

three

levels

of

nested

modularity

suggested

by

the

hierarchical

tree

CDP

cytidine

diphosphate

CMP

cytidine

monophosphate

CTP

cytidine

triphosphate

dCDP

deoxycytidine

diphosphate

dCMP

deoxycytidine

monophosphate

dCTP

deoxycytidine

triphosphate

dUDP

deoxyuridine

diphosphate

dUMP

deoxyuridine

monophosphate

dUTP

deoxyuridine

triphosphate

UTP

uridine

triphosphate

-LRB-

D

-RRB-

A

detailed

diagram

of

the

metabolic

reactions

that

surround

and

incorporate

the

pyrimidine

metabolic

module

Red-outlined

boxes

denote

the

substrates

directly

appearing

in

the

reduced

metabolism

and

the

tree

shown

in

-LRB-

C

-RRB-

Substrates

in

green-outlined

boxes

are

internal

to

pyrimidine

metabolism

but

represent

members

of

nonbranching

pathways

or

end

pathways

branching

from

a

metabolite

with

multiple

connections

-LRB-

-RRB-

Blue

and

black-outlined

boxes

show

the

connections

of

pyrimidine

metabolites

to

other

parts

of

the

metabolic

network

Black-outlined

boxes

denote

core

substrates

belonging

to

other

branches

of

the

metabolic

tree

-LRB-

A

-RRB-

and

blue-outlined

boxes

denote

nonbranching

pathways

-LRB-

if

present

-RRB-

leading

to

those

substrates

With

the

exception

of

carbamoyl

phosphate

and

S-dihydroorotate

all

pyrimidine

metabolites

are

connected

with

a

single

biochemical

reaction

The

shaded

boxes

around

the

reactions

highlight

the

modules

suggested

by

the

hierarchical

tree

The

shaded

blue

boxes

along

the

links

display

the

enzymes

catalyzing

the

corresponding

reactions

and

the

arrows

show

the

direction

of

the

reactions

according

to

theWIT

metabolic

maps

-LRB-

-RRB-

cCMP

cyclic

cytidine

monophosphate

cUMP

cyclic

uridine

monophosphate

dTDP

deoxythymidine

diphosphate

dTMP

deoxythymidine

monophosphate

dT

TP

deoxythymidine

triphosphate

TDP

thymidine

diphosphate

TMP

thymidine

monophosphate

TTP

thymidine

triphosphate

phosphate

-LRB-

UMP

-RRB-

from

L-glutamine

is

expected

to

fall

within

a

single

module

based

on

a

linear

set

of

biochemical

reactions

whereas

the

synthesis

of

uridine

diphosphate

from

UMP

leaps

putative

module

boundaries

Thus

further

experimental

and

theoretical

analyses

will

be

needed

to

understand

the

relation

between

the

decomposition

of

E.

coli

metabolism

offered

by

our

topology-based

approach

and

the

biologically

relevant

subnetworks

The

organization

of

metabolic

networks

is

likely

to

combine

a

capacity

for

rapid

flux

reorganization

with

a

dynamic

integration

with

all

other

cellular

function

-LRB-

-RRB-

Here

we

show

that

the

system-level

structure

of

cellular

metabolism

is

best

approximated

by

a

hierarchical

network

organization

with

seamlessly

embedded

modularity

In

contrast

to

current

intuitive

views

of

modularity

-LRB-

Fig.

-RRB-

which

assume

the

existence

of

a

set

of

modules

with

a

nonuniform

size

potentially

separated

from

other

modules

we

find

that

the

metabolic

network

has

an

inherent

self-similar

property

There

are

many

highly

integrated

small

modules

which

group

into

a

few

larger

modules

which

in

turn

can

be

integrated

into

even

larger

modules

This

is

supported

by

visual

inspection

of

the

derived

hierarchical

tree

-LRB-

Fig.

-RRB-

which

offers

a

natural

breakdown

of

metabolism

into

several

large

modules

which

are

further

partitioned

into

smaller

but

more

integrated

submodules

The

mathematical

framework

proposed

here

to

uncover

the

presence

or

absence

of

such

hierarchical

modularity

and

to

delineate

the

modules

based

on

the

network

topology

could

apply

to

other

cellular

and

complex

networks

as

well

As

scale-free

topology

has

been

found

at

many

different

organizational

levels

ranging

from

genetic

-LRB-

-RRB-

to

protein

interaction

and

protein

domain

-LRB-

-RRB-

networks

it

is

possible

that

biological

networks

are

always

accompanied

by

a

hierarchical

modularity

Some

nonbiological

networks

ranging

from

the

World

Wide

Web

to

the

Internet

often

combine

a

scale-free

topology

with

a

community

structure

-LRB-

i.e.

modularity

-RRB-

-LRB-

-RRB-

therefore

these

networks

are

also

potential

candidates

for

hierarchical

modularity

For

biological

systems

hierarchical

modularity

is

consistent

with

the

notion

that

evolution

may

act

at

many

organizational

levels

simultaneously

The

accumulation

of

many

local

changes

which

affect

the

small

highly

integrated

modules

could

slowly

impact

the

properties

of

the

larger

less

integrated

modules

The

emergence

of

the

hierarchical

topology

through

copying

and

reusing

existing

modules

-LRB-

-RRB-

and

motifs

-LRB-

-RRB-

a

process

reminiscent

of

the

results

of

gene

duplication

-LRB-

-RRB-

offers

a

special

role

to

the

modules

that

appeared

first

in

the

network

Although

the

model

of

Fig.

reproduces

the

large-scale

features

of

the

metabolism

understanding

the

evolutionary

mechanism

that

explains

the

simultaneous

emergence

of

the

observed

hierarchical

and

scale-free

topology

of

the

metabolism

as

well

as

its

generality

to

cellular

organization

is

now

a

prime

challenge

L.

H.

Hartwell

J.

J.

Hopfield

S.

Leibler

A.

W.

Murray

Nature

-LRB-

-RRB-

H.

Kitano

Science

-LRB-

-RRB-

Y.

I.

Wolf

G.

Karev

E.

V.

Koonin

Bioessays

-LRB-

-RRB-

D.

A.

Lauffenburger

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

C.

V.

Rao

A.

P.

Arkin

Annu

Rev.

Biomed

Eng

-LRB-

-RRB-

N.

S.

Holter

A.

Maritan

M.

Cieplak

N.

V.

Fedoroff

J.

R.

Banavar

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

J.

Hasty

D.

McMillen

F.

Isaacs

J.

J.

Collins

Nature

Rev.

Genet

-LRB-

-RRB-

S.

S.

Shen-Orr

R.

Milo

S.

Mangan

U.

Alon

Nature

Genet

-LRB-

-RRB-

U.

Alon

M.

G.

Surette

N.

Barkai

S.

Leibler

Nature

-LRB-

-RRB-

H.

Jeong

B.

Tombor

R.

Albert

Z.

N.

Oltvai

A.-L

Barabasi

Nature

-LRB-

-RRB-

A.

Wagner

D.

A.

Fell

Proc

R.

Soc

London

Ser

B

-LRB-

-RRB-

A.-L

Barabasi

R.

Albert

Science

-LRB-

-RRB-

C.

H.

Schilling

D.

Letscher

B.

O.

Palsson

J.

Theor

Biol

-LRB-

-RRB-

S.

Schuster

D.

A.

Fell

T.

Dandekar

Nature

Biotechnol

-LRB-

-RRB-

R.

Overbeek

et

al.

Nucleic

Acids

Res

-LRB-

-RRB-

Additional

information

is

available

at

D.

J.

Watts

S.

H.

Strogatz

Nature

-LRB-

-RRB-

R.

Albert

A.

L.

Barabasi

Rev.

Mod

Phys

-LRB-

-RRB-

A.-L

Barabasi

E.

Ravasz

T.

Vicsek

Physica

A

-LRB-

-RRB-

S.

N.

Dorogovtsev

A.

V.

Goltsev

J.

F.

F.

Mendes

Phys

Rev.

E

-LRB-

-RRB-

P.

D.

Karp

M.

Riley

S.

M.

Paley

A.

Pellegrini-Toole

M.

Krummenacker

Nucleic

Acids

Res

-LRB-

-RRB-

M.

B.

Eisen

P.

T.

Spellman

P.

O.

Brown

D.

Botstein

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

D.

E.

Featherstone

K.

Broadie

Bioessays

-LRB-

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S.

Wuchty

Mol

Biol

Evol

-LRB-

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G.

W.

Flake

S.

Lawrence

C.

L.

Giles

F.

M.

Coetzee

Computer

-LRB-

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M.

Girvan

M.

E.

J.

Newman

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

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A.

Vazquez

R.

Pastor-Satorras

A.

Vespignani

Phys

Rev.

E

-LRB-

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A.

Vazquez

A.

Flammini

A.

Maritan

A.

Vespignani

in

press

-LRB-

available

at

-RRB-

R.

V.

Sole

R.

Pastor-Satorras

E.

D.

Smith

T.

Kepler

Adv.

Compl

Sys.

-LRB-

-RRB-

The

algorithm

package

is

available

at

fmf.uni-lj

si/pub/networks

pajek

We

thank

T.

Vicsek

and

I.

J.

Farkas

for

discussions

on

the

hierarchical

model

C.

Waltenbaugh

and

J.

W.

Campbell

for

comments

on

the

manuscript

H.

Jeong

for

help

with

analyzing

the

metabolic

databases

and

the

WIT

project

for

making

its

database

available

Research

at

the

University

of

Notre

Dame

and

at

Northwestern

University

was

supported

by

grants

from

the

U.S.

Department

of

Energy

and

NIH

Supporting

Online

Material

Materials

and

Methods

SOM

Text

Figs

to

April

accepted

July

References

and

Notes

SCIENCE

VOL

AUGUST

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from

on

May

O O O B O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O B B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O B O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O O B O O O O O O O O O O B B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O B B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

clustering hierarchy metabolic modularity networks


Vol 438 | 15 December 2005 SPECIAL REPORT Internet encyclopaedias go head to head Jimmy Wales ' Wikipedia comes close to Britannica in terms of the accuracy of its science entries , a Nature investigation finds . ne of the extraordinary stories of the Internet age is that of Wikipedia , a free online encyclopaedia that anyone can edit . This radical and rapidly growing publication , which includes close to 4 million entries , is now a much-used resource . But it is also controversial : if anyone can edit entries , how do users know if Wikipedia is as accurate as established sources such as Encyclopaedia Britannica ? Several recent cases have highlighted the potential problems . One article was revealed as falsely suggesting that a former assistant to US Senator Robert Kennedy may have been involved in his assassination . And podcasting pioneer Adam Curry has been accused of editing the entry on podcasting to remove references to competitors ' work . Curry says he merely thought he was making the entry more accurate . However , an expert-led investigation carried out by Nature -- the first to use peer review to compare Wikipedia and Britannica 's coverage of science -- suggests that such high-profile examples are the exception rather than the rule . The exercise revealed numerous errors in both encyclopaedias , but among 42 entries tested , the difference in accuracy was not O particularly great : the average science entry in Wikipedia contained around four inaccuracies ; Britannica , about three . Considering how Wikipedia articles are written , that result might seem surprising . A solar physicist could , for example , work on the entry on the Sun , but would have the same status as a contributor without an academic background . Disputes about content are usually resolved by discussion among users . But Jimmy Wales , co-founder of Wikipedia and president of the encyclopaedia 's parent organization , the Wikimedia Foundation of St Petersburg , Florida , says the finding shows the potential of Wikipedia . `` I 'm pleased , '' he says . `` Our goal is to get to Britannica quality , or better . '' Wikipedia is growing fast . The encyclopaedia has added 3.7 million articles in 200 languages since it was founded in 2001 . The English version has more than 45,000 registered users , and added about 1,500 new articles every day of October 2005 . Wikipedia has become the 37th most visited website , according to Alexa , a web ranking service . But critics have raised concerns about the 2005 Nature Publishing Group site 's increasing influence , questioning whether multiple , unpaid editors can match paid professionals for accuracy . Writing in the online magazine TCS last year , former Britannica editor Robert McHenry declared one Wikipedia entry -- on US founding father Alexander Hamilton -- as `` what might be expected of a high-school student '' . Opening up the editing process to all , regardless of expertise , means that reliability can never be ensured , he concluded . Yet Nature 's investigation suggests that Britannica 's advantage may not be great , at least when it comes to science entries . In the study , entries were chosen from the websites of Wikipedia and Encyclopaedia Britannica on a broad range of scientific disciplines and sent to a relevant expert for peer review . Each reviewer examined the entry on a single subject from the two encyclopaedias ; they were not told which article came from which encyclopaedia . A total of 42 usable reviews were returned out of 50 sent out , and were then examined by Nature 's news team . Only eight serious errors , such as misinterpretations of important concepts , were 900 AP PHOTO/M . PROBST NATURE | Vol 438 | 15 December 2005 NEWS THE NATURE PODCAST Listen to Wikipedia founder Jimmy Wales talk about our survey and more at www.nature.com/nature/ podcast he was the 13th , to more significant inaccuracies . Wikipedia , for example , incorrectly describes how Mendeleev 's work relates to that of British chemist John Dalton . `` Who wrote this stuff ? '' asked another reviewer . `` Do they bother to check with experts ? '' But to improve Wikipedia , Wales is not so much interested in checking articles with experts as getting them to write the articles in the first place . As well as comparing the two encyclopaedias , Nature surveyed more than 1,000 Nature authors and found that although more than 70 % had heard of Wikipedia and 17 % of those consulted it on a weekly basis , less than 10 % help to update it . The steady trickle of scientists who have contributed to articles describe the experiKurt Jansson -LRB- left -RRB- , president of Wikimedia Deutschland , displays a list of 10,000 Wikipedia authors ; ence as rewarding , if occasionally frustrating Wikipedia 's entry on global warming has been a source of contention for its contributors . -LRB- see ` Challenges of being a Wikipedian ' , below -RRB- . Greater involvement by scientists would lead detected in the pairs of articles reviewed , four Twidale , an information scientist at the from each encyclopaedia . But reviewers also University of Illinois at Urbana-Champaign , to a `` multiplier effect '' , says Wales . Most entries found many factual errors , omissions or mis - says that Wikipedia 's strongest suit is the speed are edited by enthusiasts , and the addition of a leading statements : 162 and 123 in Wikipedia at which it can updated , a factor not consid - researcher can boost article quality hugely . `` Experts can help write specifics in a nuanced ered by Nature 's reviewers . and Britannica , respectively . `` People will find it shocking `` Scientists ' involvement way , '' he says . Editors at Britannica would not discuss Wales also plans to introthe findings , but say their own studies of Wiki - to see how many errors there pedia have uncovered numerous flaws . `` We are in Britannica , '' Twidale would lead to a multiplier duce a ` stable ' version of each entry . Once an article have nothing against Wikipedia , '' says Tom adds . `` Print encyclopaedias are effect . Experts can help reaches a specific quality Panelas , director of corporate communications often set up as the gold stan - write specifics in a threshold it will be tagged as at the company 's headquarters in Chicago . dards of information quality stable . Further edits will be `` But it is not the case that errors creep in on an against which the failings of nuanced way . '' occasional basis or that a couple of articles are faster or cheaper resources can be compared . made to a separate ` live ' version that would poorly written . There are lots of articles in that These findings remind us that we have an replace the stable version when deemed to be a significant improvement . One method for 18-carat standard , not a 24-carat one . '' condition . They need a good editor . '' The most error-strewn article , that on determining that threshold , where users rate Several Nature reviewers agreed with Panelas ' point on readability , commenting that the Dmitry Mendeleev , co-creator of the periodic article quality , will be trialled early next year . Wikipedia article they reviewed was poorly table , illustrates this . Michael Gordin , a sci - Jim Giles structured and confusing . This criticism is ence historian at Princeton University who Additional research by Declan Butler , Jenny Hogan , common among information scientists , wrote a 2004 book on Mendeleev , identified 19 Michael Hopkin , Mark Peplow and Tom Simonite . who also point to other problems with article errors in Wikipedia and 8 in Britannica . These Supplementary information available online at quality , such as undue prominence given to range from minor mistakes , such as describing www.nature.com/news/2005/051212/full/ controversial scientific theories . But Michael Mendeleev as the 14th child in his family when 438900a.html D. I. FRANKE/WIKIMEDIA FDN Challenges of being a Wikipedian Vaughan Bell , a neuropsychologist at the Institute of Psychiatry in London , UK , has reworked Wikipedia 's entry on schizophrenia over the past two years . Around five others regularly contribute to the reworking , most of whom have not revealed whether they have academic backgrounds . Bell says that is not a problem , as disputes are settled through the discussion page linked to the entry , often by citing academic articles . `` It 's about the quality of what you do , not who you are , '' he explains . While admitting it can be difficult settling arguments , Bell says he often learns something by doing so . One user posted a section on schizophrenia and violence that Bell considered little more than a `` rant '' about the need to lock up people with the illness . `` But editing it did stimulate me to look up literature on schizophrenia and violence , '' he says . `` Even people who are a pain in the arse can stimulate new thinking . '' Others , particularly those who contribute to politically sensitive entries , have found the editing process more fraught . William Connolley , a climate researcher at the British Antarctic Survey in Cambridge , has fought for two years with climate-change sceptics over the entry on global warming . When Connolley was insulted by one of the sceptics and the editing became a ` revert war ' -- where editors repeatedly undo each others ' changes -- the matter was referred to the encyclopaedia 's administrators . Two of Connolley 's opponents were banned from editing any climate article for six months , but it was a bumpy process . The Wikipedia editors who oversaw the case took three months to reach a decision . They also punished Connolley for repeatedly changing the sceptics ' edits , placing him on a six-month parole during which he is limited to one revert a day . Users who support Connolley have contested the decision . `` It takes a long time to deal with troublemakers , '' admits Jimmy Wales , the encyclopaedia 's co-founder . `` Connolley has done such amazing work and has had to deal with a fair amount of J.G. nonsense . '' 901 2005 Nature Publishing Group

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