Nucleic

Acids

Research

Vol

No.

DOI

RNAsoft

a

suite

of

RNA

secondary

structure

prediction

and

design

software

tools

Mirela

Andronescu

Rosalia

Aguirre-Hernandez

Anne

Condon

and

Holger

H.

Hoos

Department

of

Computer

Science

University

of

British

Columbia

Vancouver

BC

Canada

Received

February

Revised

and

Accepted

April

ABSTRACT

DNA

and

RNA

strands

are

employed

in

novel

ways

in

the

construction

of

nanostructures

as

molecular

tags

in

libraries

of

polymers

and

in

therapeutics

New

software

tools

for

prediction

and

design

of

molecular

structure

will

be

needed

in

these

applications

The

RNAsoft

suite

of

programs

provides

tools

for

predicting

the

secondary

structure

of

a

pair

of

DNA

or

RNA

molecules

testing

that

combinatorial

tag

sets

of

DNA

and

RNA

molecules

have

no

unwanted

secondary

structure

and

designing

RNA

strands

that

fold

to

a

given

input

secondary

structure

The

tools

are

based

on

standard

thermodynamic

models

of

RNA

secondary

structure

formation

RNAsoft

can

be

found

online

at

RNA

Designer

designs

an

RNA

sequence

that

folds

to

a

given

input

secondary

structure

The

tool

is

intended

for

designers

of

RNA

molecules

with

particular

structural

or

functional

properties

The

RNAsoft

web

site

at

provides

online

access

to

all

three

tools

Following

a

brief

overview

of

RNA

secondary

structure

modeling

and

representation

we

describe

the

function

and

output

of

each

of

the

online

services

All

tools

are

based

on

a

standard

free

energy

model

-LRB-

-RRB-

which

provides

a

measure

of

thermodynamic

stability

for

possible

secondary

structures

that

a

molecule

or

molecules

could

form

as

a

function

of

the

base

sequence

and

temperature

in

a

M

NaCl

solution

Here

we

provide

a

brief

overview

of

the

model

If

the

bases

of

a

strand

R

are

indexed

consecutively

starting

from

the

end

then

the

secondary

structure

can

be

represented

as

a

set

of

base

pair

indexes

-LRB-

Fig.

-RRB-

If

there

are

no

base

pairs

-LRB-

i

j

-RRB-

and

-LRB-

-RRB-

with

i

j

then

the

structure

is

pseudoknot

free

The

standard

free

energy

model

pertains

only

to

pseudoknot

free

structures

in

which

the

base

pairs

define

component

loops

and

stacked

pairs

of

the

structure

-LRB-

Fig.

-RRB-

The

free

energy

of

a

structure

is

calculated

as

the

sum

of

the

energies

of

its

component

loops

and

stacked

pairs

which

in

turn

are

calculated

using

experimentally

obtained

thermodynamic

data

-LRB-

-RRB-

-LRB-

Fig.

-RRB-

The

free

energy

model

predicts

that

under

fixed

conditions

such

as

temperature

a

DNA

or

RNA

molecule

will

fold

to

the

structure

that

minimizes

the

free

energy

Throughout

when

we

refer

to

the

minimum

free

energy

structure

for

a

molecule

we

mean

the

minimum

free

energy

pseudoknot

free

structure

for

the

molecule

-LSB-

Methods

for

prediction

of

pseudoknotted

structures

can

be

found

in

the

work

of

Rivas

and

Eddy

-LRB-

-RRB-

and

Gultyaev

et

al.

-LRB-

-RRB-

-RSB-

A

pseudoknot

free

secondary

structure

for

a

molecule

with

n

bases

can

be

uniquely

represented

as

a

sequence

of

length

n

whose

ith

symbol

is

either

if

the

ith

base

is

unpaired

-LRB-

if

the

ith

base

is

paired

with

a

base

of

higher

index

and

-RRB-

if

the

ith

base

is

paired

with

a

base

of

lower

index

-LRB-

Fig.

-RRB-

We

refer

to

this

as

dot-parenthesis

notation

All

three

RNAsoft

tools

use

this

notation

to

represent

DNA

or

RNA

secondary

structures

in

their

input

and

output

Where

possible

output

structures

are

also

provided

in

Connectivity

Table

-LRB-

CT

-RRB-

and

RNAML

formats

An

RNA

sequence

is

represented

as

a

string

over

the

alphabet

-LCB-

A

C

G

U

-RCB-

representing

the

adenine

cytosine

guanine

and

uracil

bases

with

the

end

corresponding

to

the

INTRODUCTION

Software

tools

that

predict

the

secondary

structure

of

a

DNA

or

RNA

strand

from

the

base

sequence

such

as

mfold

-LRB-

-RRB-

and

RNAfold

from

the

Vienna

RNA

Package

-LRB-

-RRB-

are

widely

used

to

shed

insight

on

nucleic

acid

structure

and

function

The

secondary

structure

is

the

set

of

base

pairs

formed

when

the

-LRB-

single

-RRB-

strand

folds

on

itself

with

each

base

occurring

in

at

most

one

pair

Increasingly

RNA

molecules

are

designed

for

new

purposes

as

catalysts

probes

on

arrays

molecular

bar

codes

or

information

storage

media

in

biomolecular

computations

-LRB-

-RRB-

Accordingly

new

variants

of

the

secondary

structure

prediction

and

design

tasks

for

nucleic

acids

arise

RNAsoft

provides

new

tools

for

three

such

tasks

PairFold

predicts

the

minimum

free

energy

secondary

structure

formed

by

two

input

DNA

or

RNA

molecules

PairFold

can

be

used

for

example

to

predict

interactions

between

a

probe

and

target

RNA

molecule

or

between

pairs

of

strands

in

biomolecular

nanostructures

CombFold

predicts

which

strand

out

of

a

combinatorial

set

formed

from

DNA

or

RNA

input

strands

folds

to

a

secondary

structure

with

the

lowest

minimum

free

energy

CombFold

can

for

example

efficiently

test

that

no

strand

in

a

large

tag

library

-LSB-

such

as

the

Brenner

's

library

of

size

-LRB-

-RRB-

-RSB-

forms

unwanted

secondary

structure

To

whom

correspondence

should

be

addressed

Tel

Fax

604 822 5485

Email

condon@cs.ubc.ca

Nucleic

Acids

Research

Vol

No.

Oxford

University

Press

all

rights

reserved

Nucleic

Acids

Research

Vol

No.

Figure

RNA

Secondary

structure

-LRB-

A

-RRB-

Graphical

depiction

of

the

predicted

minimum

free

energy

secondary

structure

S

for

sequence

R

GCCGCACGCGAGACCGCGCACUCCGCGGGAUG

CCCAUAGGAGAAGCGGCAUUACCUGUAGCCAAGCCAGUA

plus

the

list

of

associated

base

pairs

S

is

pseudoknot

free

-LRB-

B

-RRB-

Free

energy

calculation

for

structure

S.

Contributions

of

the

labeled

stems

and

loops

-LRB-

hairpins

bulges

internal

loops

external

loop

and

multiloops

-RRB-

to

the

free

energy

are

summed

to

obtain

the

total

free

energy

which

for

this

strand

is

the

minimum

free

energy

-LRB-

C

-RRB-

Dot-parenthesis

representation

of

secondary

structure

S.

-LRB-

D

-RRB-

Graphical

depiction

of

two

possible

secondary

structures

for

the

pair

of

sequences

-LRB-

-RRB-

-LRB-

GCCGCACGCGAGACCGCGCA

CGCGGUCUCGCGUGCUUGGC

-RRB-

The

structure

on

the

left

is

obtained

by

pairing

bases

in

matching

positions

of

the

two

strands

and

has

free

energy

kcal/mol

as

predicted

by

HYTHERTM

but

this

is

not

the

minimum

free

energy

structure

The

structure

on

the

right

is

predicted

by

PairFold

to

be

the

minimum

free

energy

structure

having

free

energy

kcal/mol

left

end

of

the

sequence

A

DNA

sequence

is

represented

in

the

same

way

except

that

T

for

thymine

replaces

U.

PAIRFOLD

The

PairFold

program

predicts

the

secondary

structure

of

a

pair

of

RNA

or

a

pair

of

DNA

molecules

Extending

the

notion

of

secondary

structure

for

a

single

molecule

a

secondary

structure

for

a

pair

of

molecules

-LRB-

-RRB-

is

a

set

of

base

pairs

with

each

base

of

and

occurring

in

at

most

one

pair

The

model

for

measuring

the

minimum

free

energy

of

a

secondary

structure

for

two

RNA

molecules

at

a

given

temperature

is

very

similar

to

that

for

a

single

molecule

except

that

an

intermolecular

initiation

penalty

is

added

-LRB-

Fig.

-RRB-

The

secondary

structure

can

be

represented

as

a

pair

of

sequences

-LRB-

-RRB-

in

dot-parenthesis

notation

We

define

the

structure

-LRB-

-RRB-

for

the

pair

of

molecules

-LRB-

-RRB-

to

be

pseudoknot

free

if

and

only

if

the

structure

for

the

single

molecule

-LRB-

the

concatenation

of

the

sequences

and

-RRB-

is

pseudoknot

free

PairFold

takes

two

RNA

or

two

DNA

sequences

and

plus

a

temperature

value

in

the

range

C

It

calculates

and

outputs

the

minimum

free

energy

-LRB-

pseudoknot

free

-RRB-

secondary

structure

of

the

pairs

-LRB-

-RRB-

-LRB-

-RRB-

and

-LRB-

-RRB-

at

the

input

temperature

along

with

their

minimum

free

energy

values

Predictions

of

the

enthalpy

entropy

and

melting

temperature

of

minimum

free

energy

structure

are

also

provided

Figure

shows

the

user

interface

for

PairFold

illustrating

its

use

in

predicting

the

secondary

structure

of

a

hairpin

ribozyme

-LRB-

-RRB-

As

with

all

three

online

services

the

user

can

choose

whether

to

view

the

output

on

a

dynamically

generated

web

page

or

to

receive

the

output

via

email

or

both

If

a

computation

takes

more

than

min

the

web

interface

notifies

the

user

that

the

result

will

be

sent

out

via

email

PairFold

differs

from

mfold

and

RNAfold

in

that

it

takes

as

input

two

sequences

rather

than

one

sequence

The

HYTHERTM

software

tool

-LRB-

available

at

-RRB-

does

take

two

sequences

as

input

but

is

more

limited

than

PairFold

because

it

calculates

the

free

energy

of

the

single

secondary

structure

obtained

by

pairing

those

thermodynamically

favorable

base

pairs

at

the

corresponding

positions

in

the

two

input

sequences

as

in

the

first

secondary

structure

of

Figure

rather

than

finding

the

minimum

over

the

class

of

all

pseudoknot

free

structures

Moreover

PairFold

can

accept

sequences

of

different

lengths

whereas

the

sequences

input

to

HYTHERTM

must

have

the

same

length

Other

related

programs

include

OligoWalk

of

Mathews

et

al.

-LRB-

-RRB-

and

ProbeSelect

of

Li

and

Stormo

-LRB-

-RRB-

which

design

probe

oligos

for

RNA

targets

or

genes

respectively

An

algorithm

that

is

essentially

the

same

as

PairFold

is

incorporated

into

OligoWalk

but

is

not

available

on

the

web

PairFold

uses

a

dynamic

programming

algorithm

that

is

a

straightforward

variant

of

the

Zuker

Stiegler

algorithm

for

single

molecules

-LRB-

-RRB-

If

the

lengths

of

the

sequences

and

are

and

respectively

then

the

running

time

of

PairFold

is

O

-LRB-

-LRB-

-RRB-

-RRB-

meaning

that

the

number

of

computer

operations

needed

on

input

is

bounded

by

a

constant

time

-LRB-

-RRB-

In

practice

the

computation

for

sequences

of

bases

each

takes

less

than

CPU

seconds

on

our

Nucleic

Acids

Research

Vol

No.

Figure

PairFold

user

interface

-LRB-

A

-RRB-

The

sequences

GGCCACCUGACAGUCCUCUCC

and

GGAGAGAGAAGUCAACCAGAGAAACACACCAACCCAUUGCACUCCGGGUUGGUGGUAUAUUACCUGGUACGGGGGAAACUUCGUGGUGGCCG

are

entered

in

simple

text

boxes

In

this

example

the

sequences

form

a

hairpin

ribozyme

-LRB-

-RRB-

-LRB-

B

-RRB-

The

dot-parenthesis

representation

of

the

minimum

free

energy

secondary

structure

as

predicted

by

PairFold

-LRB-

C

-RRB-

The

dot-parenthesis

representation

of

the

secondary

structure

found

in

the

crystallization

construct

as

reported

by

Rupert

and

Ferre-D'Amare

-LRB-

-RRB-

The

structure

reported

by

PairFold

for

the

pair

-LRB-

-RRB-

contains

the

four

stems

found

in

the

crystallization

construct

The

difference

in

the

secondary

structure

for

-LRB-

-RRB-

of

-LRB-

B

-RRB-

and

the

secondary

structure

of

-LRB-

C

-RRB-

-LRB-

highlighted

in

orange

in

B

-RRB-

can

be

attributed

to

the

fact

that

the

non-standard

base

pairings

A-A

G-A

and

C-A

found

in

the

true

structure

are

not

accounted

for

in

the

Turner

thermodynamic

parameters

and

thus

can

not

be

predicted

by

software

based

on

these

parameters

current

server

-LRB-

for

information

on

our

server

see

section

on

Implementation

-RRB-

When

allowing

a

maximum

of

CPU

hour

PairFold

can

handle

sequences

of

length

up

to

To

keep

the

load

on

our

server

manageable

and

response

times

of

the

online

services

reasonably

low

we

limit

the

length

of

the

input

sequences

for

the

online

version

of

PairFold

to

bases

and

the

maximal

processing

time

to

h

of

wall-clock

time

-LRB-

using

wall-clock

time

in

this

context

means

that

the

maximal

CPU

time

available

for

processing

the

given

input

may

be

reduced

when

the

server

load

is

high

-RRB-

Applications

of

PairFold

include

predicting

the

stability

of

a

duplex

formed

by

a

probe

oligo

and

target

molecule

predicting

how

a

ribozyme

binds

with

its

RNA

target

-LRB-

-RRB-

or

verifying

that

no

unwanted

secondary

structure

forms

between

two

words

-LRB-

short

single

strands

-RRB-

in

an

RNA

computation

-LRB-

-RRB-

or

between

two

molecular

tags

in

a

polymer

library

-LRB-

-RRB-

In

the

future

PairFold

will

be

incorporated

into

a

tool

for

the

design

of

short

DNA

or

RNA

strands

for

use

in

biomolecular

computations

or

DNA

nanotechnology

and

will

also

be

extended

to

take

more

than

two

sequences

as

input

COMBFOLD

CombFold

predicts

which

strand

from

a

combinatorial

set

of

strands

has

the

lowest

minimum

free

energy

secondary

structure

Combinatorial

sets

of

DNA

strands

are

used

as

molecular

bar

codes

in

applications

such

as

massively

parallel

signature

sequencing

-LRB-

-RRB-

as

well

as

for

information

storage

in

DNA

computations

-LRB-

-RRB-

For

example

Brenner

et

al.

-LRB-

-RRB-

use

DNA

tags

each

of

length

-LRB-

Fig.

-RRB-

In

these

applications

it

is

important

that

of

the

tags

or

strands

fold

on

themselves

in

the

temperature

range

at

which

they

are

used

CombFold

provides

an

efficient

way

to

test

whether

this

is

indeed

the

case

avoiding

the

need

to

run

a

program

like

mfold

on

each

tag

individually

CombFold

takes

as

input

a

description

of

a

combinatorial

set

of

DNA

or

RNA

strands

We

define

a

combinatorial

set

of

strands

as

follows

Let

Sk

be

sets

of

strands

for

some

k

-LRB-

see

Fig.

for

examples

-RRB-

Within

each

Si

all

strands

should

have

the

same

length

We

denote

the

length

of

the

strands

in

set

Si

by

ni

and

the

number

of

strands

in

Si

by

Ni

Then

the

combinatorial

Nucleic

Acids

Research

Vol

No.

Figure

Combinatorial

sets

of

strands

-LRB-

A

-RRB-

The

DNA

tag

set

of

Brenner

et

al.

-LRB-

-RRB-

Each

tag

is

obtained

by

concatenating

eight

one

chosen

from

each

of

the

eight

columns

Thus

each

tag

has

length

and

there

are

16 777 216

tags

in

total

One

such

tag

is

AATCTTACCAAAACATACATTCTACTTTAATC

Column

i

lists

the

strands

in

the

set

Si

for

i

between

and

Also

in

this

example

ni

and

Ni

for

each

i.

-LRB-

B

-RRB-

A

simple

combinatorial

set

used

in

the

screen

shots

of

Figure

This

set

can

also

be

represented

using

IUPAC

code

as

set

formed

from

Sk

is

the

set

of

all

strands

of

the

form

Sk

where

Si

is

a

strand

in

Si

for

each

i

between

and

k.

Note

that

the

length

of

a

strand

in

the

combinatorial

set

is

n

nk

and

the

number

of

strands

in

the

combinatorial

set

is

Nk

A

combinatorial

set

may

be

specified

in

one

of

two

ways

in

the

CombFold

user

interface

The

first

way

is

to

use

IUPAC

code

For

example

represents

the

combinatorial

set

of

in

which

the

first

and

last

bases

are

A

and

G

respectively

the

second

is

a

purine

-LRB-

A

or

G

-RRB-

and

the

third

may

be

any

one

of

A

C

G

U

or

T

In

the

second

way

to

specify

a

combinatorial

set

-LRB-

Fig.

-RRB-

the

strands

in

set

are

entered

one

per

line

in

a

simple

text

area

followed

by

a

line

containing

a

then

the

strands

in

are

entered

one

per

line

followed

by

a

line

containing

a

and

so

on

until

the

strands

in

Sk

are

entered

The

set

of

strands

can

easily

be

pasted

into

the

box

from

a

file

on

the

user

's

computer

The

folding

temperature

may

be

specified

by

the

user

In

addition

the

user

may

specify

the

desired

number

N

of

output

sequences

CombFold

will

return

the

N

strands

with

the

lowest

minimum

free

energy

secondary

structures

at

the

given

temperature

along

with

the

corresponding

structures

and

free

energy

values

CombFold

uses

a

dynamic

programming

algorithm

to

identify

its

output

thereby

avoiding

the

need

to

calculate

the

free

energy

of

each

individual

strand

in

the

combinatorial

set

-LRB-

-RRB-

The

running

time

of

CombFold

is

O

-LRB-

-RRB-

where

N

is

the

maximum

of

the

Ni

and

n

is

the

length

of

the

strands

in

the

combinatorial

set

In

contrast

an

algorithm

that

folds

each

possible

strand

in

the

combinatorial

set

requires

time

proportional

to

Nk

In

applications

of

CombFold

N

is

often

small

compared

to

k

for

example

in

the

combinatorial

set

of

Braich

et

al.

-LRB-

-RRB-

all

of

the

Ni

-LRB-

and

thus

N

-RRB-

and

k

in

which

case

CombFold

is

significantly

faster

than

the

naive

approach

Still

in

practice

the

running

time

of

CombFold

increases

quickly

with

N

k

and

n.

On

an

input

with

sets

two

strands

per

set

and

all

strands

having

length

the

computation

time

is

CPU

seconds

On

an

input

with

eight

sets

eight

strands

in

each

set

and

all

strands

having

length

-LSB-

as

in

Brenner

's

combinatorial

set

-LRB-

-RRB-

-RSB-

the

computation

time

is

CPU

seconds

To

keep

the

load

on

our

server

manageable

and

response

times

reasonably

low

we

limit

the

size

of

CombFold

's

inputs

to

sets

four

strands

per

set

and

strand

length

CombFold

can

be

used

to

test

whether

all

strands

in

a

combinatorial

set

for

use

in

a

DNA

or

RNA

computation

-LRB-

-RRB-

or

as

molecular

tags

-LRB-

-RRB-

have

no

unwanted

secondary

structure

CombFold

can

also

be

useful

to

gain

insight

on

the

range

of

secondary

structures

that

can

be

formed

from

a

consensus

RNA

sequence

or

in

identification

of

good

starting

points

for

mutagenesis

or

SELEX

experiments

Another

application

is

to

determine

which

of

the

many

RNA

strands

that

code

for

a

particular

protein

has

the

most

stable

secondary

structure

-LRB-

-RRB-

In

the

future

CombFold

and

an

extended

version

of

PairFold

will

be

combined

to

determine

the

minimum

free

energy

structure

that

can

be

formed

from

multiple

strands

taken

over

all

of

the

possible

orderings

of

the

individual

strands

RNA

DESIGNER

RNA

Designer

takes

as

input

a

secondary

structure

description

and

outputs

an

RNA

strand

that

is

predicted

to

fold

to

that

secondary

structure

RNA

Designer

can

be

used

to

design

RNA

molecules

with

certain

structural

properties

as

part

of

the

development

of

molecules

with

novel

functional

properties

or

more

fundamentally

in

order

to

understand

which

secondary

structure

elements

are

critical

to

specific

functions

of

cellular

RNAs

RNA

Designer

uses

a

stochastic

local

search

algorithm

which

decomposes

the

input

structure

in

a

hierarchical

fashion

finds

strands

that

fold

to

the

resulting

substructures

and

then

attempts

to

combine

the

strands

for

substructures

into

a

strand

for

the

overall

structure

A

pseudo-random

number

generator

is

used

to

implement

the

stochastic

steps

of

the

algorithm

and

by

fixing

the

seed

for

this

generator

the

behavior

of

RNA

Designer

becomes

completely

deterministic

If

desired

any

run

of

the

algorithm

may

be

reproduced

by

running

the

algorithm

again

with

the

respective

seed

value

RNA

Designer

uses

the

fold

routine

from

the

Vienna

RNA

Package

as

part

of

its

implementation

-LRB-

-RRB-

Due

to

the

stochastic

nature

of

the

algorithm

RNA

Designer

can

be

used

to

probabilistically

sample

the

solution

space

by

performing

multiple

runs

of

the

algorithm

-LRB-

with

different

seed

values

-RRB-

This

allows

the

user

to

easily

obtain

sets

of

sequences

that

all

fold

to

the

desired

structure

from

which

further

selections

according

to

specific

criteria

can

be

made

manually

As

shown

in

Figure

the

input

secondary

structure

is

specified

using

dot-parenthesis

representation

and

is

entered

in

a

simple

text

box

The

temperature

number

of

output

strands

and

optionally

a

seed

for

the

pseudo-random

number

generator

may

all

be

specified

Furthermore

the

user

may

additionally

impose

primary

sequence

constraints

by

providing

a

sequence

specification

using

a

subset

of

IUPAC

code

Two

additional

parameters

can

be

used

to

control

the

target

GC

content

of

Nucleic

Acids

Research

Vol

No.

Figure

CombFold

user

interface

-LRB-

A

-RRB-

Web

interface

for

CombFold

input

The

input

is

the

combinatorial

set

of

Figure

specified

using

IUPAC

code

-LRB-

B

-RRB-

Partial

view

of

web

interface

for

CombFold

output

reporting

that

for

the

given

input

the

sequence

AUGCAAUGCGCAUGCAC

has

the

minimum

free

energy

structure

namely

-LRB-

-LRB-

-LRB-

-LRB-

-RRB-

-RRB-

-RRB-

-RRB-

with

free

energy

kcal/mol

paired

and

unpaired

bases

in

the

given

structure

In

our

current

implementation

these

parameters

allow

the

user

to

specify

a

probabilistic

bias

towards

the

desired

GC

content

in

the

search

process

In

cases

where

many

sequences

exist

for

a

given

structure

-LRB-

or

substructure

-RRB-

RNA

Designer

can

be

expected

to

produce

results

that

closely

match

the

target

GC

content

However

in

cases

where

finding

a

correctly

folding

sequence

with

the

target

GC

content

is

hard

or

impossible

the

search

is

allowed

to

drift

from

the

GC

target

RNA

Designer

outputs

the

specified

number

of

RNA

strands

and

for

each

the

structure

to

which

the

strand

is

predicted

to

fold

at

the

user

specified

temperature

its

free

energy

and

the

random

seed

used

to

produce

the

strand

If

the

user

does

not

provide

a

random

seed

a

seed

is

chosen

based

on

the

time

at

which

the

program

starts

to

run

In

most

cases

the

output

strands

fold

to

the

input

structure

However

if

the

program

fails

to

find

a

strand

which

folds

to

the

input

structure

-LRB-

e.g.

because

no

strand

exists

that

would

fold

into

the

given

structure

-RRB-

it

outputs

the

strand

found

whose

MFE

structure

is

of

minimum

distance

from

the

input

structure

where

the

distance

is

the

number

of

bases

in

the

output

strand

that

are

not

paired

-LRB-

or

unpaired

-RRB-

in

the

output

secondary

structure

as

specified

in

the

input

secondary

structure

The

Vienna

Package

also

contains

a

tool

for

design

of

RNA

strands

that

fold

to

a

given

input

secondary

structure

However

RNA

Designer

is

consistently

able

to

solve

structures

for

which

the

Vienna

Package

program

RNAinverse

is

unable

to

find

solutions

and

its

running

time

is

significantly

lower

than

RNAinverse

Furthermore

RNAinverse

does

not

support

primary

sequence

constraints

We

empirically

evaluated

RNA

Designer

on

computationally

predicted

structures

of

biological

sequences

from

the

Ribosomal

Database

Project

RNA

Designer

found

solutions

to

all

instances

-LRB-

length

bases

-RRB-

while

RNAinverse

solved

only

seven

of

the

instances

Examples

of

sequences

whose

predicted

structures

were

not

solved

by

RNAinverse

include

Bradyrhizobium

sp.

str

Spirochaeta

sp.

and

Methanocaldococcus

fervens

str

DSM

-LRB-

T

-RRB-

RNA

Designer

also

performed

better

than

the

RNAinverse

on

artificially

generated

structures

Further

details

can

be

found

in

a

report

that

is

linked

from

the

RNA

Designer

website

RNA

Designer

when

running

on

our

current

server

typically

finds

RNA

sequences

of

length

bases

for

biologically

plausible

secondary

structures

in

CPU

seconds

When

allowing

a

maximum

runtime

of

CPU

hour

RNA

Designer

can

handle

structures

with

up

to

bases

To

keep

the

load

on

our

server

manageable

and

to

ensure

reasonably

low

response

times

we

limit

the

length

of

the

input

sequences

for

the

online

version

of

RNA

Designer

to

and

the

maximal

processing

time

to

h

of

wall-clock

time

Nucleic

Acids

Research

Vol

No.

Figure

RNA

Designer

user

interface

-LRB-

A

-RRB-

Web

interface

for

RNA

Designer

input

with

input

structure

as

in

Figure

-LRB-

B

-RRB-

Partial

view

of

web

interface

for

RNA

Designer

output

Possible

applications

for

RNA

Designer

include

the

design

of

RNAs

with

specific

secondary

structures

which

may

be

used

in

the

study

and

characterization

of

biological

RNAs

and

their

function

as

well

as

in

building

artificial

RNA

structures

that

can

be

used

for

modulation

of

cellular

RNA

functions

nanostructure

design

or

biomolecular

computations

Future

plans

for

RNA

Designer

include

-LRB-

i

-RRB-

to

support

better

energy

models

of

RNA

structure

-LRB-

in

particular

models

including

pseudoknots

which

provide

the

basis

for

the

algorithmic

design

of

strands

with

pseudoknotted

secondary

structures

-RRB-

-LRB-

ii

-RRB-

to

support

the

design

of

RNAs

with

bi

or

multistable

secondary

structures

and

-LRB-

iii

-RRB-

to

support

the

design

of

complexes

consisting

of

two

or

more

RNA

strands

IMPLEMENTATION

At

the

basis

of

the

RNAsoft

web

services

are

the

three

standalone

programs

PairFold

CombFold

and

RNA

Designer

These

have

been

developed

and

implemented

in

C

under

RedHat

Linux

version

SMP

RNA

Designer

uses

routines

from

the

Vienna

RNA

Package

-LRB-

see

univie.ac.at

-RRB-

These

programs

are

accessed

from

the

RNAsoft

web

site

via

HTML

pages

and

CGI

scripts

implemented

in

Perl

Our

current

server

machine

is

a

PC

with

two

Intel

Xeon

GHz

CPUs

with

KB

CPU

cache

each

and

Gb

of

RAM

running

Redhat

Linux

version

SMP

this

machine

runs

an

Apache

web

server

Thermodynamic

parameters

for

RNA

were

provided

by

Doug

Turner

-LRB-

-RRB-

and

Michael

Zuker

-LRB-

edu

-RRB-

and

parameters

for

DNA

were

provided

by

John

SantaLucia

Jr

-LRB-

-RRB-

-LRB-

chem.wayne.edu

-RRB-

ACKNOWLEDGEMENTS

We

gratefully

acknowledge

the

permission

of

John

SantaLucia

Jr

Doug

Turner

and

Michael

Zuker

for

use

of

their

DNA

and

RNA

thermodynamic

parameters

and

Ivo

Hofacker

et

al.

-LRB-

-RRB-

for

making

the

Vienna

RNA

Package

publically

available

parts

of

which

are

used

in

RNA

Designer

In

addition

we

thank

our

colleagues

Barry

Cohen

Danielle

Dees

Anthony

Fejes

Firas

Hamze

Frank

Hutter

Steven

Skiena

Laura

Slaybaugh

and

Shelly

Zhao

who

collaborated

with

us

on

development

of

algorithms

and

on

earlier

versions

of

this

software

We

thank

our

collaborators

Dan

Tulpan

Rob

Corn

and

Lloyd

Smith

for

their

support

in

the

development

of

PairFold

and

Dave

Brent

for

his

technical

assistance

We

thank

the

anonymous

reviewers

for

their

valuable

suggestions

for

improving

the

functionality

of

the

tools

and

for

pointing

out

additional

useful

applications

This

work

was

funded

by

the

Natural

Sciences

and

Engineering

Research

Council

-LRB-

NSERC

-RRB-

of

Canada

the

US

National

Science

Foundation

under

grant

number

the

Defense

Advanced

Research

Projects

Agency

-LRB-

DARPA

-RRB-

and

Air

Force

Research

Laboratory

Air

Force

Materiel

Command

USAF

under

agreement

number

Nucleic

Acids

Research

Vol

No.

The

US

Government

is

authorized

to

reproduce

and

distribute

reprints

for

Governmental

purposes

notwithstanding

any

copyright

annotation

thereon

The

views

and

conclusions

contained

herein

are

those

of

the

authors

and

should

not

be

interpreted

as

necessarily

representing

the

official

policies

or

endorsements

either

expressed

or

implied

of

the

Defense

Advanced

Research

Projects

Agency

-LRB-

DARPA

-RRB-

the

Air

Force

Research

Laboratory

or

the

US

Government

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R.J.

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Sci

USA

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 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 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 B O O O O O O O O O O B O O O O B O O O B O O O O O O O B O O O O O O O O O O O B B O O O O O O O O O O O B O O O B 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B 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 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 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B O O O O O O O O O O O O O O B 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 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 B O B O O O O O B O O O O O B O O O O O O O O B 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 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 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 B 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 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 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 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 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 B 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 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 O O O O O B 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 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 B 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 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 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 B 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 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 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 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 B 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 O O O O O O O O O O O O O O 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 B 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B 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 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 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 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 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 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letters to nature heterozygosity and fitness through extra-pair matings . Nature 425 , 714 717 -LRB- 2003 -RRB- . 26 . Rico , C. , Kuhnlein , U. & Fitzgerald , G. J. Male reproductive tactics in the threespine stickleback - an evaluation by DNA fingerprinting . Mol . Ecol . 1 , 79 87 -LRB- 1992 -RRB- . 27 . Jones , A. G. , Ostlund-Nilsson , S. & Avise , J. C . A microsatellite assessment of sneaked fertilizations and egg thievery in the fifteenspine stickleback . Evolution 52 , 848 858 -LRB- 1998 -RRB- . 28 . Vos , C. C. , De Jong , A. G. , Goedhart , P. W. & Smulders , M. J. M. Genetic similarity as a measure for connectivity between fragmented populations of the moor frog -LRB- Rana arvalis -RRB- . Heredity 86 , 598 608 -LRB- 2001 -RRB- . 29 . Marshall , T. C. , Slate , J. , Kruuk , L. & Pemberton , J. M. Statistical confidence for likelihood-based paternity inference in natural populations . Mol . Ecol . 7 , 639 655 -LRB- 1998 -RRB- . 30 . Neff , B. D. & Pitcher , T. E. Assessing the statistical power of genetic analyses to detect multiple mating in fishes . J. Fish Biol . 61 , 739 750 -LRB- 2002 -RRB- . Supplementary Information accompanies the paper on www.nature.com/nature . Acknowledgements We thank T. J. C. Beebee , E. Hespeler and M. Fuerst for help with microsatellite techniques . The team of the Respomuso Refuge -LRB- Ursi , Dolores , David , Juani and Javier Abajo -RRB- , X. Gonzalez , J. Palanca and N. Palanca provided help and facilities . The Direccion General del Medio Natural de la Diputacion General de Aragon issued research permits for the Circo de Piedrafita area . D.R.V. was supported by grants of the University of Vigo , Xunta de Galicia and Deutscher Akademischer Austauschdienst . Grants of the Deutsche Forschungsgemeinschaft to M.V. and A.M. and of the Instituto de Estudios Altoaragoneses to M.V. supported the laboratory work . Competing interests statement The authors declare that they have no competing financial interests . Correspondence and requests for materials should be addressed to D.R.V. -LRB- vieites@berkeley.edu -RRB- . ... . Genomic analysis of regulatory network dynamics reveals large topological changes Nicholas M. Luscombe1 * , M. Madan Babu4 * , Haiyuan Yu1 , Michael Snyder2 , Sarah A. Teichmann4 & Mark Gerstein1 ,3 1 Department of Molecular Biophysics and Biochemistry , 2Department of Molecular , Cellular and Developmental Biology , 3Department of Computer Science , Yale University , PO Box 208114 , New Haven , Connecticut 06520-8114 , USA 4 Division of Structural Studies , MRC Laboratory of Molecular Biology , Hills Road , Cambridge CB2 2QH , UK * These authors contributed equally to this work ... . Network analysis has been applied widely , providing a unifying language to describe disparate systems ranging from social interactions to power grids . It has recently been used in molecular biology , but so far the resulting networks have only been analysed statically1 8 . Here we present the dynamics of a biological network on a genomic scale , by integrating transcriptional regulatory information9 11 and gene-expression data12 16 for multiple conditions in Saccharomyces cerevisiae . We develop an approach for the statistical analysis of network dynamics , called SANDY , combining well-known global topological measures , local motifs and newly derived statistics . We uncover large changes in underlying network architecture that are unexpected given current viewpoints and random simulations . In response to diverse stimuli , transcription factors alter their interactions to varying degrees , thereby rewiring the network . A few transcription factors serve as permanent hubs , but most act transiently only during certain conditions . By studying sub-network structures , we show that environmental responses facilitate fast signal propagation -LRB- for example , with short regulatory cascades -RRB- , whereas the cell cycle and sporulation direct temporal progression through multiple stages -LRB- for example , with highly inter-connected transcription factors -RRB- . Indeed , to drive the latter 308 processes forward , phase-specific transcription factors interregulate serially , and ubiquitously active transcription factors layer above them in a two-tiered hierarchy . We anticipate that many of the concepts presented here -- particularly the large-scale topological changes and hub transience -- will apply to other biological networks , including complex sub-systems in higher eukaryotes . We began by assembling a static representation of known regulatory interactions from the results of genetic , biochemical and ChIP -LRB- chromatin immunoprecipitation -RRB- chip experiments . Figure 1 illustrates the complexity of the resultant network , which contains 7,074 regulatory interactions between 142 transcription factors and 3,420 target genes -LRB- interactions can be between transcription factors and non-transcription factor targets , or two transcription factors -RRB- . To get a dynamic perspective , we integrated gene-expression data for the following five conditions : cell cycle13 , sporulation14 , diauxic shift12 , DNA damage16 and stress response15 . From these data , we traced paths in the regulatory network that are active in each condition using a trace-back algorithm -LRB- see Methods -RRB- . Figure 1b presents the sub-networks active under different cellular conditions , and gross changes are apparent in the distinct sections of the network that are highlighted . Recent functional genomics studies have analysed the dynamics of a few transcription factors17 ,18 ; however , Fig. 1 represents the first dynamic view of a genome-scale network . Half of the targets are uniquely expressed in only one condition ; in contrast , most transcription factors are used across multiple processes . The active sub-networks maintain or rewire regulatory interactions , and over half of the active interactions -LRB- 1,476 of 2,476 total -RRB- are completely supplanted by new ones between conditions . Only 66 interactions are retained across four or more conditions ; these comprise ` hot links ' 6 that are always on -LRB- compared with the rest of the network -RRB- and mostly regulate house-keeping functions . The large number of changing interactions makes rigorous comparison of active sub-networks impossible visually . Consequently , we introduce SANDY , an approach that combines : standard measures of network connectivity -LRB- involving global topological statistics6 and local network motifs4 -RRB- , newly derived follow-on statistics , and comparisons against simulated controls to assess the significance of each observation . Overall , our calculations divide the five condition-specific subnetworks into two categories : endogenous and exogenous -LRB- Fig. 1 -RRB- . This allows us to rationalize the different sub-network structures in terms of the biological requirements of each condition . Endogenous processes -LRB- cell cycle and sporulation -RRB- are multi-stage and operate with an internal transcriptional programme , whereas exogenous states -LRB- diauxic shift , DNA damage and stress response -RRB- constitute binary events that react to external stimuli with a rapid turnover of expressed genes . We begin SANDY by examining global topological measures that quantify network architecture -LRB- Fig. 1c -RRB- 6 . The view from recent studies is that these statistics are remarkably constant across many biological networks -LRB- including regulatory systems -RRB- 1,5,6,19,20 . Moreover , most of them remain invariant between randomly simulated sub-graphs of different sizes -LRB- Methods -RRB- . In fact , we show that topological measures change considerably between the endogenous and exogenous sub-networks . -LRB- The probability , P , that their topological measures originate from the same population is ,1024 ; Supplementary Information . -RRB- Furthermore , most of the observed measurements differ significantly from random expectation and are insensitive to addition of noise in the underlying network -LRB- Methods -RRB- . The ` in-degree ' -LRB- k in -RRB- is the number of incoming edges per node -LRB- that is , the number of transcription factors regulating a target -RRB- . Its average across each sub-network decreases by 20 % from endogenous to exogenous conditions -LRB- P , 5 1023 -RRB- . The ` out-degree ' -LRB- k out -RRB- represents the number of NATURE | VOL 431 | 16 SEPTEMBER 2004 | www.nature.com/nature 2004 Nature Publishing Group letters to nature outgoing edges per node -LRB- that is , the number of target genes for each transcription factor -RRB- . Average values double from endogenous to exogenous conditions -LRB- P , 0.338 ; Supplementary Information -RRB- . The ` path length ' -LRB- l -RRB- is the shortest distance between two nodes -LRB- here , it is the number of intermediate regulators between a transcription factor and a terminating target gene -RRB- . Its average halves from endogenous to exogenous conditions -LRB- P , 1023 -RRB- . Finally , the ` clustering coefficient ' -LRB- c -RRB- gauges the level of interconnectivity around a node -LRB- that is , the level of transcription factor inter-regulation -RRB- . Values range from 0 for totally dispersed nodes to 1 for fully connected ones . Average coefficients nearly halve from endogenous to exogenous conditions -LRB- P , 1023 -RRB- . In biological terms , the small in-degrees for target genes in exogenous conditions indicate that transcription factors are regulating in simpler combinations , and the large out-degrees signify that each transcription factor has greater regulatory influence by targeting more genes simultaneously . The short paths imply faster propagation of the regulatory signal . Conversely , long paths in the multi-stage , endogenous conditions suggest slower action arising from the formation of regulatory chains to control intermediate phases . Finally , high clustering coefficients in endogenous conditions signify greater inter-regulation between transcription factors . In summary , sub-networks have evolved to produce rapid , large-scale responses in exogenous states , and carefully coordinated processes in endogenous conditions -LRB- Fig. 1a -RRB- . SANDYalso examines the sub-networks locally by calculating the occurrence of network motifs4 , which are compact , specific patterns of inter-connection between transcription factors and targets . We show the occurrence of the most common motifs in Fig. 1c : singleinput , multiple-input , and feed-forward-loop motifs -LRB- SIMs , MIMs , and FFLs -RRB- . In SIMs a single transcription factor targets many genes ; in MIMs multiple transcription factors co-regulate sets of genes ; and in FFLs a primary transcription factor regulates a secondary one , and both target a final gene . Motifs appear at similar relative frequencies across regulatory networks of diverse organisms -LRB- although individual motifs are not conserved -RRB- 7 , and this is also true for the randomly simulated sub-graphs . Therefore , constancy in motif usage is expected across conditions . However , Fig. 1c shows that the relative occurrence of motifs varies considerably between endogenous and exogenous conditions -LRB- P , 1023 -RRB- . SIMs are favoured in exogenous sub-networks where they comprise .55 % of regulatory interactions in motifs . But the frequency drops to ,35 % in endogenous processes . Instead , these states favour FFLs -LRB- ,44 % -RRB- . MIMs do not significantly change in their frequency . Previous studies defined precise regulatory properties and information processing tasks for motifs4 . SIMs and MIMs are implicated in conferring similar regulation over groups of genes , so they are ideal for directing the large-scale gene activation found in exogenous conditions . FFLs are buffers that respond only to persistent input signals . They are suited for endogenous conditions , as cells can not initiate a new stage until the previous one has stabilized . Though used sparingly in exogenous processes they may be important in filtering spurious external stimuli . Having quantified global and local changes with standard topological measures , we then moved to the follow-on statistics in SANDY -LRB- Fig. 2 -RRB- . Like many large-scale networks , the regulatory system displays scale-free characteristics -LRB- the probability P k that a transcription factor targets k genes is proportional to k 2g for constant g -RRB- . This behaviour -LRB- maintained across all active subnetworks -RRB- signifies the presence of regulatory hubs targeting disproportionately large numbers of genes . Hubs are of general interest Figure 1 Dynamic representation of the transcriptional regulatory network and standard statistics . a , Schematics and summary of properties for the endogenous and exogenous sub-networks . b , Graphs of the static and condition-specific networks . Transcription factors and target genes are shown as nodes in the upper and lower sections of each graph respectively , and regulatory interactions are drawn as edges ; they are coloured by the number of conditions in which they are active . Different conditions use distinct NATURE | VOL 431 | 16 SEPTEMBER 2004 | www.nature.com/nature sections of the network . c , Standard statistics -LRB- global topological measures and local network motifs -RRB- describing network structures . These vary between endogenous and exogenous conditions ; those that are high compared with other conditions are shaded . -LRB- Note , the graph for the static state displays only sections that are active in at least one condition , but the table provides statistics for the entire network including inactive regions . -RRB- 309 2004 Nature Publishing Group letters to nature as they represent the most influential components of a network6 and , accordingly , tend to be essential21 . They are thought to target a broad spectrum of gene functions4 ,11,22 and are commonly located upstream in the network2 to expand their influence via secondary transcription factors23 . These observations suggest that hubs would be invariant features of the network across conditions , and this expectation is supported by the random simulations that converge on similar sets of transcription factor hubs . Figure 2a shows the observed regulatory hubs in each of the five conditions -LRB- Methods -RRB- . They divide into two groups . The smaller one represents permanent hubs , which , in line with expectation , are important regardless of cellular state . They mainly comprise multifunctional transcription factors -LRB- such as Abf1 -RRB- and house-keeping regulators -LRB- such as Mig1/2 -RRB- , and are responsible for maintaining the hot links . However , contrary to expectation , most hubs -LRB- 78 % -RRB- are transient ; that is , they are influential in one condition , but less so in others . Exogenous conditions have fewer transient hubs , suggesting a more centralized command structure . -LRB- This is reflected in different g ; Supplementary Information . -RRB- About half of these hubs are known to be important for their respective conditions -LRB- for example , Swi4 in the cell cycle ; Methods -RRB- . For the remainder with sparse annotations , their transient-hub status in a particular condition considerably augments their functional annotation -LRB- for example , Sok2 in the cell cycle -RRB- . These hubs may also relate to conditiondependent lethality , and this has clear implications for identifying specific drug targets . The defining feature of transient hubs is their capacity to change interactions between conditions . We attempted to quantify this Figure 2 Newly derived ` follow-on ' statistics for network structures . a , Transcription factor hub usage in different cellular conditions . The cluster diagram shades cells by the normalized number of genes targeted by transcription factor hubs in each condition . One cluster represents permanent hubs and the others condition-specific transient hubs . Genes are labelled with four-letter names when they have an obvious functional role in the condition , and seven-letter open reading frame names when there is no obvious role . Of the latter , gene names are red and italicised when functions are poorly characterized . Starred hubs show extreme interchange index values , I 1 . b , Interaction interchange -LRB- I -RRB- of transcription factors between conditions . A histogram of I for all active transcription 310 factors shows a uni-modal distribution with two extremes . Pie charts show five example transcription factors with different proportions of interchanged interactions . We list the main functions of the distinct target genes regulated by each example transcription factor . Note how the transcription factors ' regulatory functions change between conditions . c , Overlap in transcription factor usage between conditions . Venn diagrams show the numbers of individual transcription factors -LRB- large intersection -RRB- and pair-wise transcription factor combinations -LRB- small intersection -RRB- that overlap between the two endogenous conditions . NATURE | VOL 431 | 16 SEPTEMBER 2004 | www.nature.com/nature 2004 Nature Publishing Group letters to nature rewiring more broadly for every transcription factor in the network with the interchange index , I . This is defined so that higher values associate with transcription factors replacing a larger fraction of their interactions . Its histogram reveals a uni-modal central distribution with two groups of extreme outliers -LRB- Fig. 2b -RRB- . At one extreme -LRB- I # 10 % -RRB- , 12 transcription factors retain all interactions across multiple states . At the other end -LRB- I $ 90 % -RRB- , 27 transcription factors replace all interactions in switching conditions . Many of these are so extreme that they only regulate genes in a single condition and are inactive otherwise . These include six transient hubs of known importance for the cell cycle and stress response . Most transcription factors interchange only part of their interactions -LRB- 10 % , I , 90 % -RRB- . This group comprises most of the hubs ; surprisingly , permanent hubs interchange interactions as often as transient ones , but over a larger number of conditions . Furthermore , transcription factors in this group often regulate genes of distinct functions in different conditions , thus shifting regulatory roles . For example , the permanent hub Abf1 regulates cell growth during endogenous conditions , but refocuses to intracellular transport during stress response -LRB- in addition to its maintained core functions -RRB- . The rewiring highlighted by the interchange index allows transcription factors to be active in many conditions . Indeed , 95 of the 142 transcription factors are used in more than one process -LRB- Fig. 1b -RRB- . Specifically , within endogenous conditions 53 of 92 transcription factors overlap between cell cycle and sporulation -LRB- Fig. 2c -RRB- , and there is a similar overlap for exogenous conditions -LRB- Supplementary Information -RRB- . With so much intersection in the repertoire of active transcription factors , the precise regulation of a condition can not arise from the specificity of individual transcription factors . As others have observed24 , combinatorial transcription factor usage seems to be the key . We calculated that there are 360 unique pairwise transcription factor combinations -LRB- that is , two transcription factors regulating the same target -RRB- used in at least one condition . In contrast to individual transcription factors , only a minor proportion of pairs -LRB- 51 of 360 -RRB- participate in multiple processes and just 3 of 149 pairs overlap between endogenous conditions -LRB- Fig. 2c -RRB- . Thus far we have focused on the large dynamic changes occurring between different cellular conditions . However , dynamic transitions also take place within individual processes . Earlier , SANDY defined endogenous sub-networks by their long paths and high clustering . We can study the source of these observations by looking at the full scope of inter-regulation between transcription factors during the cell cycle -LRB- Fig. 3 -RRB- . This is possible because in a previous study13 expression-level measurements were made throughout the cell cycle and differentially expressed genes were assigned to one of five phases -LRB- early G1 , late G1 , S , G2 and M -RRB- . We then traced back from the classified genes to identify active sub-networks during each phase -LRB- Methods -RRB- . A cluster diagram -LRB- Fig. 3a -RRB- shows that most transcription factors that are active in the cell cycle operate only in a particular phase -LRB- for example , Swi4 in late G1 -RRB- . Additionally , a sizeable minority of transcription factors is ubiquitously active throughout the whole cycle . We uncover two major forms of transcription factor interregulation . In serial inter-regulation25 -LRB- Fig. 3b -RRB- , the phase-specific transcription factors regulate each other in a sequential manner to drive the cell cycle forward . In fact , we detect complete loops of interactions within the complex circuitry , and the resulting regulatory cascades undoubtedly create the long paths . We also introduce the concept of parallel inter-regulation -LRB- Fig. 3c -RRB- , in which the ubiquitous transcription factors control the phase-specific ones in a two-tiered system . This effectively provides a stable signal to aid the transition between phases . Furthermore , because about a third of ubiquitous transcription factors comprise permanent hubs , they may provide a channel of communication to relate the cell-cycle progression with house-keeping functions . Similar observations apply to sporulation -LRB- Supplementary Information -RRB- . SANDY presents an approach to examine biological network dynamics . In applying it to the yeast regulatory system , it becomes apparent that many observations made in the static state are not applicable to the condition-specific sub-networks . However , in refocusing to a dynamic perspective , we uncover substantial topological changes in network structure , and we capture the essence of the transcriptional regulatory data in a new way . Because of limitations in current data sets , we can examine this only through integrating gene-expression information . However , we anticipate future experiments to determine condition-specific interactions directly . Given the robustness of the observations to large perturbations -LRB- Methods -RRB- , we expect our approach and findings to remain valid for these new data sets . Furthermore , we anticipate that many of the concepts we have introduced could be readily transferred to other types of biological networks and complex sub-systems in multicellular organisms , such as those directing the circadian cycle26 and cellular development . A Figure 3 Transcription factor inter-regulation during the cell cycle time-course . a , The 70 transcription factors active in the cell cycle . The diagram shades each cell by the normalized number of genes targeted by each transcription factor in a phase . Five clusters represent phase-specific transcription factors and one cluster is for ubiquitously active transcription factors . Note , both hub and non-hub transcription factors are included . Transcription factor names are given in the Supplementary Information . b , Serial interregulation between phase-specific transcription factors . Network diagrams show transcription factors that are active in one phase regulate transcription factors in subsequent phases . In the late phases , transcription factors apparently regulate those in the next cycle . c , Parallel inter-regulation between phase-specific and ubiquitous transcription factors in a two-tiered hierarchy . Serial and parallel inter-regulation operate in tandem to drive the cell cycle while balancing it with basic house-keeping processes . NATURE | VOL 431 | 16 SEPTEMBER 2004 | www.nature.com/nature Methods Detailed descriptions of the methods are in the Supplementary Information and at http : / / sandy.topnet.gersteinlab.org . Data sets The transcriptional regulatory network was assembled from the results of genetic , biochemical and ChIP chip experiments9 11 . The gene-expression data were compiled from 240 microarray experiments for five conditions12 16 . We identified the following 2004 Nature Publishing Group 311 letters to nature numbers of genes with differential expression : cell cycle , 455 ; sporulation , 477 ; diauxic shift , 1,823 ; DNA damage , 1,718 ; and stress response , 866 . 27 . Yu , H. , Zhu , X. , Greenbaum , D. , Karro , J. & Gerstein , M. TopNet : a tool for comparing biological subnetworks , correlating protein properties with topological statistics . Nucleic Acids Res . 32 , 328 337 -LRB- 2004 -RRB- . 28 . Christie , K. R. et al. . Saccharomyces Genome Database -LRB- SGD -RRB- provides tools to identify and analyze sequences from Saccharomyces cerevisiae and related sequences from other organisms . Nucleic Acids Res . 32 , D311 D314 -LRB- 2004 -RRB- . Trace-back algorithm We used the following algorithm to define sections of the regulatory network used in each condition : -LRB- 1 -RRB- identify transcription factors as being ` present ' in a condition if they have sufficiently high expression levels ; -LRB- 2 -RRB- flag differentially expressed genes that appear in the regulatory network ; -LRB- 3 -RRB- mark as ` active ' the regulatory links between present transcription factors and differentially expressed genes ; and -LRB- 4 -RRB- search for any other present transcription factors that are linked to a transcription factor with an already active link and make this connection active . The last step is repeated until no more links are made active . The same procedure identifies sub-networks that are active in particular phases of cell cycle and sporulation . Supplementary Information accompanies the paper on www.nature.com/nature . Acknowledgements We thank P. Bertone , N. Domedel-Puig , E. Hovig , R. Jansen , K. Kleivi , G. Koentges , E. Koonin , B. Lenhard , A. Paccanaro , J. Rozowsky , J. Tegner , V. Trifonov , A. Todd , Y. Xia and H. Zao for comments on the paper . N.M.L. thanks the Anna Fuller Fund and the MRC LMB Visitor 's Program . M.M.B. acknowledges financial support from the Cambridge Commonwealth Trust , Trinity College , Cambridge and the MRC LMB . M.G. is supported by the NSF and NIH . Competing interests statement The authors declare that they have no competing financial interests . Correspondence and requests for materials should be addressed to N.M.L. , M.M.B. , S.A.T. & M.G. -LRB- sandy@bioinfo.mbb.yale.edu -RRB- . SANDY This extends the methodology used by the TopNet software tool27 and it evaluates each sub-network with the following : -LRB- 1 -RRB- standard statistics , including global measures of topology -LRB- k in , k out , l , and c -RRB- 6 and local motif occurrence -LRB- SIM , MIM and FFL -RRB- 4 ; -LRB- 2 -RRB- follow-on statistics , including permanent and transient hub identification , interchange index -LRB- I -RRB- and counting the overlap in transcription factor usage -LRB- individual and pairs -RRB- across multiple conditions . -LRB- Hubs are transcription factors in the top 30 % , by number of target genes , in at least one condition . The number of target genes is normalized to measure the relative influence of a transcription factor hub in a particular process . -RRB- In all cases , regulatory functions are obtained from the Saccharomyces Genome Database28 and are current as of June 2004 ; and -LRB- 3 -RRB- a comparison of observations and random expectation by simulating sub-graphs that are similar in size to each sub-network , and calculating standard and follow-on statistics for them . Simulated sub-graphs sample the same number of differentially expressed genes and trace through the static network . We also tested the sensitivity of our observations to noise by randomly perturbing the static networks by 30 % -LRB- random addition , deletion and replacement of interactions -RRB- , tracing back from the original differentially expressed genes and then recalculating the statistics . Received 15 January ; accepted 24 June 2004 ; doi : 10.1038 / nature02782 . 1 . Jeong , H. , Tombor , B. , Albert , R. , Oltvai , Z. 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The small world inside large metabolic networks . Proc . R. Soc . Lond . B 268 , 1803 1810 -LRB- 2001 -RRB- . 21 . Yu , H. , Greenbaum , D. , Xin Lu , H. , Zhu , X. & Gerstein , M. Genomic analysis of essentiality within protein networks . Trends Genet . 20 , 227 231 -LRB- 2004 -RRB- . 22 . Martinez-Antonio , A. & Collado-Vides , J. Identifying global regulators in transcriptional regulatory networks in bacteria . Curr . Opin . Microbiol . 6 , 82 489 -LRB- 2003 -RRB- . 23 . Madan Babu , M. & Teichmann , S. A. Evolution of transcription factors and the gene regulatory network in Escherichia coli . Nucleic Acids Res . 31 , 1234 1244 -LRB- 2003 -RRB- . 24 . Pilpel , Y. , Sudarsanam , P. & Church , G. M. Identifying regulatory networks by combinatorial analysis of promoter elements . Nature Genet . 29 , 153 159 -LRB- 2001 -RRB- . 25 . Simon , I. et al. . Serial regulation of transcriptional regulators in the yeast cell cycle . Cell 106 , 697 708 -LRB- 2001 -RRB- . 26 . Ueda , H. R. et al. . A transcription factor response element for gene expression during circadian night . Nature 418 , 534 539 -LRB- 2002 -RRB- . ... . Long-lasting self-inhibition of neocortical interneurons mediated by endocannabinoids Alberto Bacci , John R. Huguenard & David A. Prince Department of Neurology and Neurological Sciences , Stanford University School of Medicine , Stanford , California 94305 , USA ... . Neocortical GABA-containing interneurons form complex functional networks responsible for feedforward and feedback inhibition and for the generation of cortical oscillations associated with several behavioural functions1 ,2 . We previously reported that fast-spiking -LRB- FS -RRB- , but not low-threshold-spiking -LRB- LTS -RRB- , neocortical interneurons from rats generate a fast and precise selfinhibition mediated by inhibitory autaptic transmission3 . Here we show that LTS cells possess a different form of self-inhibition . LTS , but not FS , interneurons undergo a prominent hyperpolarization mediated by an increased K1-channel conductance . This self-induced inhibition lasts for many minutes , is dependent on an increase in intracellular -LSB- Ca21 -RSB- and is blocked by the cannabinoid receptor antagonist AM251 , indicating that it is mediated by the autocrine release of endogenous cannabinoids . Endocannabinoid-mediated slow self-inhibition represents a powerful and long-lasting mechanism that alters the intrinsic excitability of LTS neurons , which selectively target the major site of excitatory connections onto pyramidal neurons ; that is , their dendrites4 7 . Thus , modulation of LTS networks after their sustained firing will lead to long-lasting changes of glutamatemediated synaptic strength in pyramidal neurons , with consequences during normal and pathophysiological cortical network activities . We obtained whole-cell recordings from fast-spiking and LTS interneurons in layer Vof rat somatosensory neocortical slices . Cells were characterized electrophysiologically by their firing behaviours as described previously8 -LRB- Fig. 1a , c , insets ; see also Methods -RRB- . All biocytin-filled LTS interneurons contained cholecystokinin -LRB- CCK -RRB- -LRB- n 7 ; Supplementary Fig . S1 -RRB- , whereas FS cells were CCKnegative -LRB- n 4 ; Supplementary Fig . S1 -RRB- , indicating that we sampled a homogeneous non-FS cell population . Although LTS interneurons lack GABAergic autaptic transmission3 , we found a unique form of slow self-inhibition -LRB- SSI -RRB- in NATURE | VOL 431 | 16 SEPTEMBER 2004 | www.nature.com/nature 312 2004 Nature Publishing Group

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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