Noise

Propagation

in

Gene

Networks

Juan

M.

Pedraza

et

al.

Science

-LRB-

-RRB-

DOI

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Downloaded

from

on

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REPORTS

In

contrast

the

autocorrelation

of

the

intrinsic

noise

-LRB-

-RRB-

decays

rapidly

tintrinsic

G

min

tcorr

-LRB-

Fig.

-RRB-

Thus

the

observed

slow

fluctuations

do

not

result

from

intrinsic

noise

they

represent

noise

extrinsic

to

CFP

expression

-LRB-

see

supporting

online

text

-RRB-

The

concentration

of

a

stable

cellular

factor

would

be

expected

to

fluctuate

with

a

time

scale

of

the

cell

cycle

period

-LRB-

-RRB-

For

instance

even

though

intrinsic

fluctuations

in

production

rates

are

fast

the

difference

between

the

total

amounts

of

YFP

and

CFP

in

the

symmetric

branch

experiments

has

an

autocorrelation

time

of

ttotal

T

min

-LRB-

-RRB-

A

similar

time

scale

may

well

apply

to

other

stable

cellular

components

such

as

ribosomes

metabolic

apparatus

and

sigma

factors

As

such

components

affect

their

own

expression

as

well

as

that

of

our

test

genes

extrinsic

noise

may

be

self-perpetuating

These

data

indicate

that

the

single-cell

GRF

can

not

be

represented

by

a

single-valued

function

Slow

extrinsic

fluctuations

give

the

cell

and

the

genetic

circuits

it

comprises

a

memory

or

individuality

-LRB-

-RRB-

lasting

roughly

one

cell

cycle

These

fluctuations

are

substantial

in

amplitude

and

slow

in

time

scale

They

present

difficulty

for

modeling

genetic

circuits

and

potentially

for

the

cell

itself

In

order

to

accurately

process

an

intracellular

signal

a

cell

would

have

to

average

its

response

for

well

over

a

cell

cycle

a

long

time

in

many

biological

situations

This

problem

is

not

due

to

intrinsic

noise

in

the

output

noise

that

fluctuates

rapidly

but

rather

to

the

aggregate

effect

of

fluctuations

in

other

cellular

components

There

is

thus

a

fundamental

tradeoff

between

accuracy

and

speed

in

purely

transcriptional

responses

Accurate

cellular

responses

on

faster

time

scales

are

likely

to

require

feedback

from

their

output

-LRB-

-RRB-

These

data

provide

an

integrated

quantitative

characterization

of

a

genetic

element

at

the

single-cell

level

its

biochemical

parameters

together

with

the

amplitude

and

time

scale

of

its

fluctuations

Such

systems-level

specifications

are

necessary

both

for

modeling

natural

genetic

circuits

and

for

building

synthetic

ones

The

methods

introduced

here

can

be

generalized

to

more

complex

genetic

networks

as

well

as

to

eukaryotic

organisms

-LRB-

-RRB-

References

and

Notes

M.

A.

Savageau

Biochemical

Systems

Analysis

-LRB-

AddisonWesley

Reading

MA

-RRB-

M.

Ptashne

A

Genetic

Switch

Phage

Lambda

and

Higher

Organisms

-LRB-

Cell

Press

and

Blackwell

Science

Cambridge

MA

ed

-RRB-

H.

H.

McAdams

L.

Shapiro

Science

-LRB-

-RRB-

E.

H.

Davidson

et

al.

Science

-LRB-

-RRB-

S.

S.

Shen-Orr

R.

Milo

S.

Mangan

U.

Alon

Nature

Genet

-LRB-

-RRB-

J.

E.

Ferrell

Jr.

E.

M.

Machleder

Science

-LRB-

-RRB-

M.

B.

Elowitz

S.

Leibler

Nature

-LRB-

-RRB-

T.

S.

Gardner

C.

R.

Cantor

J.

J.

Collins

Nature

-LRB-

-RRB-

A.

Becskei

B.

Seraphin

L.

Serrano

EMBO

J.

-LRB-

-RRB-

N.

Rosenfeld

M.

B.

Elowitz

U.

Alon

J.

Mol

Biol

-LRB-

-RRB-

F.

J.

Isaacs

J.

Hasty

C.

R.

Cantor

J.

J.

Collins

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

K.

S.

Koblan

G.

K.

Ackers

Biochemistry

-LRB-

-RRB-

P.

J.

Darling

J.

M.

Holt

G.

K.

Ackers

J.

Mol

Biol

-LRB-

-RRB-

R.

J.

Ellis

Trends

Biochem

Sci

-LRB-

-RRB-

M.

Mirasoli

J.

Feliciano

E.

Michelini

S.

Daunert

A.

Roda

Anal

Chem

-LRB-

-RRB-

Materials

and

methods

are

available

as

supporting

material

on

Science

Online

P.

Cluzel

M.

Surette

S.

Leibler

Science

-LRB-

-RRB-

G.

Lahav

et

al.

Nature

Genet

-LRB-

-RRB-

I.

B.

Dodd

et

al.

Genes

Dev

-LRB-

-RRB-

B.

J.

Meyer

R.

Maurer

M.

Ptashne

J.

Mol

Biol

-LRB-

-RRB-

J.

A.

Shapiro

Annu

Rev.

Microbiol

-LRB-

-RRB-

M.

B.

Elowitz

A.

J.

Levine

E.

D.

Siggia

P.

S.

Swain

Science

-LRB-

-RRB-

P.

S.

Swain

M.

B.

Elowitz

E.

D.

Siggia

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

J.

M.

Raser

E.

K.

O'Shea

Science

-LRB-

-RRB-

E.

M.

Ozbudak

M.

Thattai

I.

Kurtser

A.

D.

Grossman

A.

van

Oudenaarden

Nature

Genet

-LRB-

-RRB-

W.

J.

Blake

M.

K

rn

C.

R.

Cantor

J.

J.

Collins

Nature

-LRB-

-RRB-

H.

H.

McAdams

A.

Arkin

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

J.

Paulsson

Nature

-LRB-

-RRB-

J.

L.

Spudich

D.

E.

Koshland

Jr.

Nature

-LRB-

-RRB-

P.

S.

Swain

J.

Mol

Bio

-LRB-

-RRB-

We

thank

Z.

Ben-Haim

R.

Clifford

S.

Itzkovitz

Z.

Kam

R.

Kishony

A.

J.

Levine

A.

Mayo

R.

Milo

R.

Phillips

M.

Ptashne

J.

Shapiro

B.

Shraiman

E.

Siggia

and

M.

G.

Surette

for

helpful

discussions

M.B.E.

is

supported

by

a

CASI

award

from

the

Burroughs

Wellcome

Fund

the

Searle

Scholars

Program

and

the

Seaver

Institute

U.A.

and

M.B.E.

are

supported

by

the

Human

Frontiers

Science

Program

P.S.S.

acknowledges

support

from

a

Tier

II

Canada

Research

Chair

and

the

Natural

Sciences

and

Engineering

Research

Council

of

Canada

N.R.

dedicates

this

work

to

the

memory

of

his

father

Yasha

-LRB-

Yaakov

-RRB-

Rosenfeld

Supporting

Online

Material

Materials

and

Methods

SOM

Text

Figs

to

References

and

Notes

Movies

to

October

accepted

February

science

Noise

Propagation

in

Gene

Networks

Juan

M.

Pedraza

and

Alexander

van

Oudenaarden

Accurately

predicting

noise

propagation

in

gene

networks

is

crucial

for

understanding

signal

fidelity

in

natural

networks

and

designing

noise-tolerant

gene

circuits

To

quantify

how

noise

propagates

through

gene

networks

we

measured

expression

correlations

between

genes

in

single

cells

We

found

that

noise

in

a

gene

was

determined

by

its

intrinsic

fluctuations

transmitted

noise

from

upstream

genes

and

global

noise

affecting

all

genes

A

model

was

developed

that

explains

the

complex

behavior

exhibited

by

the

correlations

and

reveals

the

dominant

noise

sources

The

model

successfully

predicts

the

correlations

as

the

network

is

systematically

perturbed

This

approach

provides

a

step

toward

understanding

and

manipulating

noise

propagation

in

more

complex

gene

networks

The

genetic

program

of

a

living

cell

is

determined

by

a

complex

web

of

gene

networks

The

proper

execution

of

this

program

relies

on

faithful

signal

propagation

from

one

gene

to

the

next

This

process

may

be

hindered

by

stochastic

fluctuations

arising

from

gene

expression

because

some

of

the

components

in

these

circuits

are

present

at

low

numbers

which

makes

fluctuations

in

concentrations

unavoidable

-LRB-

-RRB-

Additionally

reaction

rates

can

fluctuate

because

of

stochastic

variation

in

the

global

pool

of

housekeeping

genes

or

because

of

fluctuations

in

environmental

conditions

that

affect

all

genes

For

example

fluctuations

in

the

number

of

available

polymerases

or

in

any

factor

that

alters

the

cell

growth

rate

will

change

the

reaction

rates

for

all

genes

Recent

Department

of

Physics

Massachusetts

Institute

of

Technology

Cambridge

MA

USA

To

whom

correspondence

should

be

addressed

E-mail

avano@mit.edu

experimental

studies

-LRB-

-RRB-

have

made

substantial

progress

identifying

the

factors

that

determine

the

fluctuations

in

the

expression

of

a

single

gene

However

how

expression

fluctuations

propagate

from

one

gene

to

the

next

is

largely

unknown

To

address

this

issue

we

designed

a

gene

network

-LRB-

Fig.

-RRB-

in

which

the

interactions

between

adjacent

genes

could

be

externally

controlled

and

quantified

at

the

single-cell

level

This

synthetic

network

-LRB-

-RRB-

consisted

of

four

genes

of

which

three

were

monitored

in

single

Escherichia

coli

cells

by

cyan

yellow

and

red

fluorescent

proteins

-LRB-

CFP

YFP

and

RFP

-RRB-

The

first

gene

lacI

is

constitutively

transcribed

and

codes

for

the

lactose

repressor

which

down-regulates

the

transcription

of

the

second

gene

tetR

that

is

bicistronically

transcribed

with

cfp

The

gene

product

of

tetR

the

tetracycline

repressor

in

turn

downregulates

the

transcription

of

the

third

gene

reported

by

YFP

The

fourth

gene

rfp

is

under

SCIENCE

VOL

MARCH

Downloaded

from

on

May

REPORTS

pffiffiffiffiffi

Fig.

-LRB-

A

to

C

-RRB-

Coefficient

of

variation

h

i

Cii

of

the

expression

in

genes

to

as

a

function

of

IPTG

concentration

in

the

steady

state

-LRB-

D

to

F

-RRB-

Correlation

between

the

expression

levels

of

genes

and

and

and

and

respectively

The

solid

lines

are

predictions

from

the

Langevin

model

-LRB-

-RRB-

the

control

of

the

lambda

repressor

promoter

PL

which

is

a

strong

constitutive

promoter

Because

this

gene

is

not

part

of

the

cascade

this

reporter

was

used

to

evaluate

the

effect

of

global

fluctuations

This

cascade

was

used

to

measure

how

fluctuations

in

an

upstream

gene

-LRB-

tetR

reported

by

CFP

-RRB-

transmit

downstream

-LRB-

and

are

reported

by

YFP

-RRB-

The

inducers

isopropyl-b-D-thiogalactopyranoside

-LRB-

IPTG

-RRB-

and

anhydrotetracycline

-LRB-

ATC

-RRB-

bind

to

and

inhibit

the

repression

of

the

lactose

and

tetracycline

repressors

respectively

and

were

used

to

tune

respectively

the

expression

of

the

upstream

gene

and

the

coupling

between

the

two

genes

We

assayed

the

response

of

single

cells

to

various

amounts

of

inducers

by

using

automated

fluorescence

microscopy

In

each

experimental

run

the

level

of

the

three

fluorescent

reporters

was

quantified

for

individual

cells

Figure

shows

that

the

average

signal

of

the

upstream

gene

displayed

a

sigmoidal

response

to

changes

in

the

concentration

of

IPTG

in

the

growth

media

In

response

the

average

signal

of

the

downstream

gene

-LRB-

Fig.

-RRB-

behaved

inversely

and

decreased

sharply

at

larger

IPTG

concentrations

The

enhanced

sensitivity

of

the

YFP

response

compared

to

the

CFP

response

when

IPTG

is

varied

demonstrates

the

utility

of

cascades

for

generating

steep

switches

-LRB-

-RRB-

However

the

average

expression

alone

does

not

capture

the

population

behavior

because

the

expression

of

most

cells

is

quite

different

from

the

average

-LRB-

Fig.

-RRB-

Even

for

a

fixed

IPTG

concentration

the

fluctuations

in

gene

expression

resulted

in

a

broad

distribution

that

reflects

the

interaction

between

the

upstream

and

downstream

genes

To

quantify

the

expression

fluctuations

and

the

degree

of

correlation

between

different

genes

we

computed

the

correlation

MARCH

VOL

SCIENCE

Downloaded

from

on

May

Fig.

-LRB-

A

-RRB-

A

schematic

design

of

the

network

-LRB-

B

and

C

-RRB-

Average

CFP

and

YFP

expression

as

a

function

of

IPTG

concentration

in

the

steady

state

Each

experimental

data

point

was

obtained

from

single-cell

measurements

The

solid

lines

are

fits

obtained

from

the

Langevin

model

-LRB-

-RRB-

-LRB-

D

-RRB-

Scatter

plot

of

the

fluorescence

levels

for

the

entire

population

at

-LSB-

IPTG

-RSB-

mM

This

corresponds

to

the

points

marked

by

the

arrows

in

-LRB-

B

-RRB-

and

-LRB-

C

-RRB-

The

red

lines

indicate

the

average

CFP

and

YFP

expression

REPORTS

of

the

upstream

gene

i

is

varied

For

example

the

main

term

in

the

transmitted

intrinsic

noise

from

gene

to

gene

-LRB-

Fig.

-RRB-

is

proportional

to

the

squared

logarithmic

gain

H

-LRB-

Fig.

inset

-RRB-

The

pronounced

peak

in

H

occurs

at

an

IPTG

concentration

for

which

the

response

of

the

downstream

gene

is

most

sensitive

to

changes

in

the

upstream

signal

Consistently

the

downstream

fluctuations

reach

a

maximum

at

this

concentration

-LRB-

Fig.

-RRB-

-LRB-

-RRB-

The

last

component

of

the

noise

reflects

the

effect

of

the

global

fluctuations

It

includes

the

direct

effect

on

the

gene

the

transmitted

effect

from

the

upstream

genes

-LRB-

Fig.

-RRB-

and

the

effect

of

the

correlated

transmission

which

depends

on

the

interactions

The

latter

illustrates

the

main

difference

between

transmitted

intrinsic

and

transmitted

global

noise

The

different

intrinsic

noise

sources

are

uncorrelated

whereas

the

global

fluctuations

arise

from

the

same

sources

-LRB-

Fig.

-RRB-

This

means

that

the

transmitted

global

noise

-LRB-

Fig.

purple

arrows

-RRB-

does

not

simply

add

to

the

direct

global

noise

-LRB-

Fig.

red

arrows

-RRB-

Because

both

fluctuations

came

from

the

same

sources

correction

terms

arise

that

depend

on

the

strength

-LRB-

and

sign

-RRB-

of

the

interaction

-LRB-

-RRB-

In

Fig.

these

different

noise

components

are

shown

for

gene

The

intrinsic

component

-LRB-

Fig.

green

line

-RRB-

varies

as

the

inverse

of

the

square

root

of

the

mean

resulting

in

increased

noise

at

higher

IPTG

concentrations

The

transmitted

intrinsic

component

-LRB-

Fig.

blue

line

-RRB-

corresponds

roughly

to

the

square

of

the

logarithmic

gain

-LRB-

Fig.

inset

-RRB-

times

the

noise

in

the

upstream

gene

-LRB-

Fig.

-RRB-

-LRB-

-RRB-

The

global

noise

component

-LRB-

Fig.

red

line

-RRB-

is

not

constant

but

rather

shows

the

modulation

as

explained

above

Thus

the

main

features

of

the

noise

in

this

gene

are

determined

by

the

network

interactions

rather

than

by

its

own

intrinsic

noise

characteristics

The

effect

of

modulating

the

global

noise

is

also

demonstrated

by

the

behavior

of

the

correlations

between

noninteracting

genes

-LRB-

Fig.

E

and

F

-RRB-

A

global

fluctuation

that

raises

the

expression

of

RFP

will

also

raise

the

expression

of

YFP

and

CFP

An

increased

CFP

expression

will

result

in

a

decreased

YFP

expression

by

an

amount

that

depends

on

the

interaction

between

gene

and

gene

and

hence

will

vary

with

IPTG

-LRB-

-RRB-

This

can

be

seen

in

the

expression

for

the

correlations

-LRB-

-RRB-

A

consequence

of

this

modulation

is

that

the

correlations

and

display

qualitatively

similar

behavior

as

IPTG

is

varied

-LRB-

Fig.

D

and

F

-RRB-

This

indicates

that

is

dominated

by

the

global

noise

that

is

transmitted

from

gene

to

gene

Similarly

the

correlation

is

dominated

by

the

global

noise

transmitted

from

gene

to

gene

and

therefore

displays

a

different

behavior

compared

to

and

-LRB-

-RRB-

We

directly

quantified

the

intrinsic

and

extrinsic

noise

for

genes

to

as

a

function

Fig.

-LRB-

A

-RRB-

A

sketch

of

the

propagation

of

the

fluctuations

showing

how

the

two

sources

of

noise

intrinsic

and

global

can

result

in

many

components

-LRB-

B

-RRB-

The

logarithmic

gain

is

obtained

as

the

negative

of

the

slope

in

log-log

space

of

the

mean

expression

of

YFP

as

a

function

of

mean

CFP

expression

-LRB-

Inset

-RRB-

The

square

of

as

a

function

of

IPTG

-LRB-

C

-RRB-

Noise

in

the

downstream

gene

-LRB-

Fig.

-RRB-

decomposed

into

the

different

sources

of

noise

The

total

noise

-LRB-

black

-RRB-

is

the

result

of

the

intrinsic

noise

in

this

gene

-LRB-

green

-RRB-

the

transmitted

noise

from

the

intrinsic

fluctuations

in

upstream

genes

-LRB-

blue

-RRB-

and

the

global

noise

-LRB-

red

-RRB-

Cij

from

the

fluorescence

levels

bFi

bFj

Fi

in

individual

cells

The

brackets

bI

denote

averaging

over

all

cells

in

the

population

and

the

indices

i

and

j

refer

to

the

gene

number

as

defined

in

Fig.

Because

each

cell

is

characterized

by

three

different

expression

values

-LRB-

and

-RRB-

the

statistical

properties

of

this

network

are

summarized

by

the

three

self-correlations

and

and

the

three

cross-correlations

and

The

self-correlation

is

identical

to

the

square

of

the

coefficient

of

variation

hi

which

is

defined

as

the

standard

deviation

of

the

expression

distribution

normalized

to

the

mean

expression

These

six

correlations

were

plotted

as

a

function

of

the

IPTG

concentration

-LRB-

Fig.

-RRB-

The

correlations

behave

in

a

nonintuitive

manner

For

example

the

noise

properties

of

the

upstream

gene

reflected

in

-LRB-

Fig.

-RRB-

are

very

different

from

those

of

the

downstream

gene

reflected

in

-LRB-

Fig.

-RRB-

even

though

both

genes

are

repressed

by

a

single

upstream

repressor

-LRB-

Fig.

-RRB-

The

correlations

and

are

also

dependent

on

IPTG

concentration

-LRB-

Fig.

E

and

F

-RRB-

Because

RFP

is

not

part

of

the

cascade

one

might

expect

a

correlation

that

is

independent

of

IPTG

To

clarify

these

issues

we

developed

a

stochastic

model

that

allows

for

a

systematic

interpretation

of

the

data

in

terms

of

the

different

components

of

the

noise

The

coefficients

of

variations

and

correlations

bFi

Fj

jbFi

bFj

can

be

derived

from

the

model

analytically

enabling

a

direct

fit

to

the

entire

experimental

data

set

-LRB-

-RRB-

Our

model

is

based

on

the

Langevin

approach

-LRB-

-RRB-

in

which

the

deterministic

differential

equations

describing

the

dynamics

of

the

system

are

modified

by

adding

stochastic

terms

-LRB-

-RRB-

that

reflect

the

two

sources

of

noise

intrinsic

fluctuations

due

to

low

numbers

of

molecules

and

global

fluctuations

in

cellular

components

that

change

the

reaction

rates

for

all

genes

Using

the

resulting

expressions

-LRB-

-RRB-

for

the

correlations

we

can

decompose

the

noise

in

each

gene

into

three

components

intrinsic

noise

in

that

specific

gene

transmitted

intrinsic

noise

from

the

upstream

genes

and

global

noise

modulated

by

the

network

-LRB-

Fig.

-RRB-

The

intrinsic

noise

-LRB-

Fig.

green

arrows

-RRB-

arises

mostly

from

low

copy

numbers

of

mRNAs

-LRB-

-RRB-

The

second

noise

component

the

transmitted

intrinsic

noise

-LRB-

Fig.

blue

arrows

-RRB-

includes

the

transmitted

fluctuations

of

each

of

the

upstream

genes

in

the

network

and

depends

on

three

factors

the

intrinsic

noise

for

that

upstream

gene

the

effect

of

temporal

averaging

-LRB-

-RRB-

which

depends

on

the

lifetimes

of

the

proteins

and

the

susceptibility

of

the

downstream

gene

to

the

upstream

one

We

characterize

this

susceptibility

through

the

logarithmic

gain

Hji

-LRB-

-RRB-

-LRB-

Fig.

-RRB-

The

logarithmic

gain

reflects

how

the

average

expression

of

the

downstream

gene

j

changes

as

the

expression

SCIENCE

VOL

MARCH

Downloaded

from

on

May

REPORTS

of

the

IPTG

concentration

-LRB-

Fig.

A

and

B

-RRB-

by

measuring

the

correlation

between

CFP

and

YFP

in

constructs

in

which

both

reporters

were

driven

by

the

same

promoter

-LRB-

-RRB-

The

total

noise

was

generally

dominated

by

extrinsic

fluctuations

The

experimentally

obtained

intrinsic

and

extrinsic

noise

of

genes

and

was

consistent

with

the

predictions

of

the

model

To

probe

the

predictive

power

of

the

stochastic

model

we

used

it

to

predict

the

noise

and

correlations

as

the

coupling

between

genes

and

was

altered

by

adding

ATC

to

the

growth

media

-LRB-

-RRB-

We

compared

these

predictions

to

experimental

results

As

an

example

and

are

shown

in

Fig.

C

and

D.

Both

and

display

rich

behavior

as

a

function

of

both

the

IPTG

and

ATC

concentrations

As

is

seen

in

Fig.

a

small

perturbation

to

the

network

can

transform

a

maximum

in

the

curve

-LRB-

Fig.

black

-RRB-

into

a

step

-LRB-

red

-RRB-

or

even

a

minimum

-LRB-

green

-RRB-

These

features

were

faithfully

predicted

by

the

model

-LRB-

Fig.

-RRB-

Similarly

the

model

correctly

predicts

correlation

-LRB-

Fig.

E

and

F

-RRB-

and

the

other

correlations

-LRB-

-RRB-

These

experiments

demonstrate

that

the

stochastic

model

is

not

only

descriptive

but

also

has

predictive

power

and

can

therefore

be

used

as

a

design

tool

for

synthetic

circuits

Our

results

show

that

the

noise

in

a

gene

affects

expression

fluctuations

of

its

downstream

genes

This

transmitted

noise

can

be

calculated

from

the

interactions

between

upstream

and

downstream

genes

as

quantified

by

the

logarithmic

gains

Thus

it

is

not

necessary

to

have

low

numbers

of

molecules

to

have

large

fluctuations

because

noise

could

be

transmitted

from

upstream

genes

We

show

that

the

noise

has

a

correlated

global

component

that

is

modulated

by

the

network

Thus

even

in

a

network

where

all

components

have

low

intrinsic

noise

fluctuations

can

be

substantial

and

the

distributions

of

expression

levels

depend

on

the

interactions

between

genes

Measuring

the

correlation

between

a

constitutive

gene

and

a

gene

embedded

in

a

network

provides

a

sensitive

probe

for

correlated

sources

of

noise

This

would

have

been

difficult

to

reveal

by

monitoring

single

genes

-LRB-

-RRB-

or

two

copies

of

the

same

gene

-LRB-

-RRB-

Our

results

highlight

the

importance

of

including

stochastic

effects

in

the

study

of

regulatory

networks

This

will

be

necessary

for

understanding

faithful

signal

propagation

in

natural

networks

-LRB-

-RRB-

as

well

as

for

designing

noise-tolerant

synthetic

circuits

-LRB-

-RRB-

References

and

Notes

C.

V.

Rao

D.

M.

Wolf

A.

P.

Arkin

Nature

-LRB-

-RRB-

E.

M.

Ozbudak

et

al.

Nature

Genet

-LRB-

-RRB-

M.

B.

Elowitz

A.

J.

Levine

E.

D.

Siggia

P.

S.

Swain

Science

-LRB-

-RRB-

W.

J.

Blake

M.

Kaern

C.

R.

Cantor

J.

J.

Collins

Nature

-LRB-

-RRB-

J.

M.

Raser

E.

K.

O'Shea

Science

-LRB-

-RRB-

Materials

and

methods

are

available

as

supporting

material

on

Science

Online

M.

Thattai

A.

van

Oudenaarden

Biophys

J.

-LRB-

-RRB-

P.

B.

Chock

E.

R.

Stadtman

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

A.

Goldbeter

D.

E.

Koshland

Jr.

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

J.

E.

Ferrell

Jr.

E.

M.

Machleder

Science

-LRB-

-RRB-

We

fitted

the

analytical

results

to

all

means

noises

and

correlations

simultaneously

To

test

the

resulting

parameters

-LRB-

table

-RRB-

we

conducted

Monte

Carlo

simulations

of

the

network

using

Gillespie

's

stochastic

simulation

algorithm

-LRB-

-RRB-

The

results

from

the

Langevin

model

are

consistent

with

these

simulations

T.

B.

Kepler

T.

C.

Elston

Biophys

J.

-LRB-

-RRB-

J.

Hasty

et

al.

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

N.

G.

van

Kampen

Stochastic

Processes

in

Physics

and

Chemistry

-LRB-

North-Holland

Amsterdam

-RRB-

The

interaction

between

two

genes

is

determined

by

the

rate

of

synthesis

from

the

downstream

gene

as

a

function

of

the

concentration

of

upstream

proteins

-LRB-

yi

-RRB-

this

will

be

called

the

transfer

function

Assuming

that

the

interactions

are

Hill-type

repressions

the

parameters

for

the

transfer

function

-LRB-

-RRB-

for

the

repression

between

genes

and

can

be

obtained

from

the

two

means

up

to

the

conversion

constants

from

fluorescence

counts

to

protein

numbers

To

match

the

notation

in

previous

studies

-LRB-

-RRB-

we

define

the

logarithmic

gain

corresponding

to

y

fj

y

genes

i

and

j

as

Hji

j

yj

g

yi

i

jyi

where

gj

is

the

i

j

decay

rate

of

gene

j

and

the

overbar

denotes

the

steady

state

average

The

global

and

plasmid

noise

are

characterized

by

the

parameters

hG

and

hN

respectively

-LRB-

-RRB-

Subscripts

to

correspond

to

genes

lacI

cfp

yfp

and

rfp

-LRB-

Fig.

-RRB-

hi

int

denotes

the

intrinsic

noise

in

gene

i

In

this

notation

the

total

noise

in

genes

to

is

given

by

h

h

int

h

G

h

h

j

h

G

N

Fig.

-LRB-

A

and

B

-RRB-

Experimentally

determined

intrinsic

and

extrinsic

noise

as

a

function

of

IPTG

-LRB-

-RRB-

The

solid

lines

represent

predictions

by

the

stochastic

model

-LRB-

A

-RRB-

Two

copies

of

the

lac

promoter

are

driving

CFP

and

YFP

-LRB-

B

-RRB-

Two

copies

of

the

tet

promoter

are

driving

CFP

and

YFP

The

model

parameters

used

are

those

in

table

except

for

the

basal

transcription

which

was

adjusted

to

the

measured

value

-LRB-

-RRB-

-LRB-

C

and

E

-RRB-

Coefficient

of

variation

and

correlation

as

a

function

of

IPTG

concentration

in

the

steady

state

for

different

levels

of

ATC

The

solid

lines

are

guides

to

the

eye

Each

experimental

data

point

was

obtained

from

single-cell

measurements

-LRB-

-RRB-

-LRB-

D

and

F

-RRB-

Predictions

for

and

from

the

Langevin

model

given

the

parameters

obtained

previously

-LRB-

-RRB-

h

h

int

h

int

h

int

h

G

j

j

h

j

N

h

h

int

h

h

G

N

MARCH

VOL

SCIENCE

Downloaded

from

on

May

REPORTS

The

expressions

for

the

correlations

are

j

h

int

j

h

int

h

j

j

j

G

h

j

N

J.

Paulsson

Nature

-LRB-

-RRB-

M.

A.

Savageau

Biochemical

Systems

Analysis

-LRB-

AddisonWesley

Reading

MA

-RRB-

The

expression

for

the

transmitted

noise

in

can

not

be

rewritten

as

the

transmission

of

the

total

steady-state

noise

in

gene

only

-LRB-

-RRB-

J.

Paulsson

M.

Ehrenberg

Q.

Rev.

Biophys

-LRB-

-RRB-

L.

H.

Hartwell

et

al.

Nature

-LRB-

suppl

-RRB-

-LRB-

-RRB-

J.

Hasty

D.

McMillen

J.

J.

Collins

Nature

-LRB-

-RRB-

D.

T.

Gillespie

J.

Phys

Chem

-LRB-

-RRB-

Duplicated

measurements

are

averaged

The

error

bars

reflect

the

standard

deviation

of

run-to-run

differences

and

the

error

within

each

measurement

as

determined

by

bootstrapping

We

thank

T.

S.

Gardner

J.

J.

Collins

R.

Lutz

and

H.

Bujard

for

their

kind

gift

of

plasmids

M.

Thattai

A.

Becskei

and

H.

Lim

for

helpful

discussions

and

suggestions

and

B.

Kaufmann

for

his

help

with

the

initial

constructs

Supported

by

NSF

CAREER

grant

no

and

NIH

grant

no

Supporting

Online

Material

Materials

and

Methods

Figs

to

Tables

and

References

and

Notes

December

accepted

February

science

h

j

h

G

N

h

j

h

j

G

N

RNA-Dependent

Cysteine

Biosynthesis

in

Archaea

Anselm

Sauerwald

Wenhong

Zhu

Tiffany

A.

Major

Herve

Roy

Sotiria

Palioura

Dieter

Jahn

William

B.

Whitman

John

R.

Yates

Michael

Ibba

Dieter

Several

methanogenic

archaea

lack

cysteinyl

transfer

RNA

-LRB-

tRNA

-RRB-

synthetase

-LRB-

CysRS

-RRB-

the

essential

enzyme

that

provides

Cys-tRNACys

for

translation

in

most

organisms

Partial

purification

of

the

corresponding

activity

from

Methanocaldococcus

jannaschii

indicated

that

tRNACys

becomes

acylated

with

O-phosphoserine

-LRB-

Sep

-RRB-

but

not

with

cysteine

Further

analyses

identified

a

class

II

type

O-phosphoseryl-tRNA

synthetase

-LRB-

SepRS

-RRB-

and

Sep-tRNA

CystRNA

synthase

-LRB-

SepCysS

-RRB-

SepRS

specifically

forms

Sep-tRNACys

which

is

then

converted

to

Cys-tRNACys

by

SepCysS

Comparative

genomic

analyses

suggest

that

this

pathway

encoded

in

all

organisms

lacking

CysRS

can

also

act

as

the

sole

route

for

cysteine

biosynthesis

This

was

proven

for

Methanococcus

maripaludis

where

deletion

of

the

SepRS-encoding

gene

resulted

in

cysteine

auxotrophy

As

the

conversions

of

Sep-tRNA

to

Cys-tRNA

or

to

selenocysteinyl-tRNA

are

chemically

analogous

the

catalytic

activity

of

SepCysS

provides

a

means

by

which

both

cysteine

and

selenocysteine

may

have

originally

been

added

to

the

genetic

code

The

translation

of

cysteine

codons

in

mRNA

during

protein

synthesis

requires

cysteinyltRNA

-LRB-

Cys-tRNACys

-RRB-

Cys-tRNACys

is

normally

synthesized

from

the

amino

acid

cysteine

and

the

corresponding

tRNA

isoacceptors

-LRB-

tRNACys

-RRB-

in

an

adenosine

triphosphate

-LRB-

ATP

-RRB-

dependent

reaction

catalyzed

by

cysteinyltRNA

synthetase

-LRB-

CysRS

-RRB-

Genes

encoding

CysRS

cysS

have

been

detected

in

hundreds

of

organisms

encompassing

all

three

living

domains

-LRB-

-RRB-

The

only

exceptions

are

certain

methanogenic

archaea

the

completed

genome

sequences

of

which

encode

no

open

reading

frames

-LRB-

ORFs

-RRB-

with

obvious

homology

to

known

cysS

sequences

-LRB-

-RRB-

Because

of

the

discovery

Department

of

Molecular

Biophysics

and

Biochemistry

and

of

Chemistry

Yale

University

New

Haven

CT

USA

of

Cell

Biology

The

Scripps

Research

Institute

La

Jolla

CA

USA

of

Microbiology

University

of

Georgia

Athens

GA

USA

of

Microbiology

The

Ohio

State

University

Columbus

OH

USA

of

Microbiology

Technische

Universitat

Braunschweig

Braunschweig

Germany

To

whom

correspondence

should

be

addressed

E-mail

soll@trna.chem.yale.edu

that

the

genomes

of

a

number

of

methanogenic

archaea

either

lack

cysS

-LRB-

Methanocaldococcus

jannaschii

Methanothermobacter

thermautotrophicus

and

Methanopyrus

kandleri

-RRB-

or

can

dispense

with

it

-LRB-

Methanococcus

maripaludis

-RRB-

the

formation

of

Cys-tRNACys

in

these

organisms

has

been

a

much

studied

and

increasingly

contentious

topic

-LRB-

-RRB-

A

noncognate

aminoacyl-tRNA

synthetase

EaaRS

-LRB-

-RRB-

and

a

previously

unassigned

ORF

-LRB-

-RRB-

were

variously

implicated

in

Cys-tRNACys

formation

Recent

studies

failed

to

provide

conclusive

support

for

either

of

these

routes

leaving

the

mechanism

of

Cys-tRNACys

formation

still

in

doubt

-LRB-

-RRB-

Previous

investigations

of

archaeal

CystRNACys

biosynthesis

have

been

hampered

by

the

significant

levels

of

noncognate

tRNA

routinely

cysteinylated

and

detected

by

conventional

filter

binding

assays

This

problem

was

circumvented

with

a

more

stringent

assay

of

Cys-tRNACys

formation

gel-electrophoretic

separation

of

uncharged

tRNA

from

aminoacyltRNA

-LRB-

aa-tRNA

-RRB-

and

subsequent

detection

of

the

tRNA

moieties

by

sequence-specific

probing

-LRB-

-RRB-

Given

that

M.

jannaschii

is

a

SCIENCE

VOL

Fig.

Acid

urea

gel

electrophoresis

and

Northern

blot

analysis

of

total

M.

maripaludis

tRNA

charged

with

M.

maripaludis

SerRS

dialyzed

M.

jannaschii

M.

maripaludis

CysRS

and

M.

jannaschii

SepRS

in

the

presence

of

amino

acids

-LRB-

AA

-RRB-

phosphoserine

or

a

M.

jannaschii

cell-free

extract

filtrate

-LRB-

-RRB-

Half

of

each

tRNA

sample

was

deacylated

by

mild

alkaline

hydrolysis

-LRB-

OH

-RRB-

The

blots

were

probed

with

oligonucleotides

complementary

to

M.

maripaludis

tRNACys

-LRB-

A

-RRB-

and

M.

maripaludis

tRNASec

-LRB-

B

-RRB-

Total

M.

maripaludis

tRNA

charged

with

dialyzed

or

undialyzed

M.

maripaludis

DcysS

cellfree

extract

-LRB-

-RRB-

in

the

presence

of

amino

acids

and

or

Sep

and

NasS

-LRB-

C

-RRB-

The

blot

was

analyzed

with

oligonucleotides

complementary

to

M.

maripaludis

tRNACys

MARCH

Downloaded

from

on

May

strict

anaerobe

and

considering

that

earlier

aerobic

purification

erroneously

identified

prolyl-tRNA

synthetase

-LRB-

-RRB-

we

used

anaerobic

conditions

for

all

procedures

unless

otherwise

indicated

When

these

procedures

were

used

to

monitor

acylation

of

total

M.

maripaludis

tRNA

by

an

undialyzed

M.

jannaschii

cell-free

extract

-LRB-

-RRB-

tRNACys

was

charged

with

an

amino

acid

that

gave

rise

to

the

same

mobility

shift

-LRB-

-RRB-

exhibited

by

standard

M.

maripaludis

Cys-tRNACys

generated

by

M.

maripaludis

CysRS

-LRB-

-RRB-

-LRB-

Fig.

lanes

and

-RRB-

Further

optimization

of

the

reaction

at

this

stage

showed

that

and

ATP

were

also

required

for

the

successful

formation

of

charged

tRNACys

When

the

S

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

genevariation
stochasticity
genecircuits
avano lab