Molecular

Systems

Biology

Article

number

doi

Citation

Molecular

Systems

Biology

EMBO

and

Nature

Publishing

Group

All

rights

reserved

Programming

gene

expression

with

combinatorial

promoters

Robert

Sidney

Cox

Michael

G

and

Michael

B

Division

of

Biology

California

Institute

of

Technology

Pasadena

CA

USA

Department

of

Microbiology

and

Infectious

Diseases

University

of

Calgary

Calgary

Alberta

Canada

and

Department

of

Applied

Physics

California

Institute

of

Technology

Pasadena

CA

USA

Corresponding

author

Division

of

Biology

and

Department

of

Applied

Physics

California

Institute

of

Technology

M/C

Pasadena

CA

USA

Tel.

626 395 8871

Fax

626 395 5972

E-mail

melowitz@caltech.edu

Received

accepted

Promoters

control

the

expression

of

genes

in

response

to

one

or

more

transcription

factors

-LRB-

TFs

-RRB-

The

architecture

of

a

promoter

is

the

arrangement

and

type

of

binding

sites

within

it

To

understand

natural

genetic

circuits

and

to

design

promoters

for

synthetic

biology

it

is

essential

to

understand

the

relationship

between

promoter

function

and

architecture

We

constructed

a

combinatorial

library

of

random

promoter

architectures

We

characterized

promoters

in

Escherichia

coli

each

containing

up

to

three

inputs

from

four

different

TFs

The

library

design

allowed

for

multiple

and

boxes

and

we

observed

varied

promoter

strength

over

five

decades

To

further

analyze

the

functional

repertoire

we

defined

a

representation

of

promoter

function

in

terms

of

regulatory

range

logic

type

and

symmetry

Using

these

results

we

identified

heuristic

rules

for

programming

gene

expression

with

combinatorial

promoters

Molecular

Systems

Biology

November

doi

Subject

Categories

metabolic

and

regulatory

networks

synthetic

biology

Keywords

combinatorial

promoter

logic

gate

signal

integration

synthetic

biology

transcription

regulation

This

is

an

open-access

article

distributed

under

the

terms

of

the

Creative

Commons

Attribution

License

which

permits

distribution

and

reproduction

in

any

medium

provided

the

original

author

and

source

are

credited

This

license

does

not

permit

commercial

exploitation

or

the

creation

of

derivative

works

without

specific

permission

Introduction

In

many

promoters

gene

expression

is

regulated

in

response

to

two

or

more

transcription

factors

-LRB-

TFs

-RRB-

A

classic

example

is

the

lac

operon

where

promoter

activity

depends

on

both

the

repressor

LacI

-LRB-

Jacob

and

Monod

-RRB-

and

the

activator

CRP

-LRB-

Zubay

et

al

-RRB-

Such

combinatorial

regulation

of

gene

expression

underlies

diverse

cellular

programs

-LRB-

Ptashne

-RRB-

including

responses

to

environmental

conditions

-LRB-

Ligr

et

al

-RRB-

and

multicellular

development

Combinatorial

promoters

with

multiple

TF

binding

sites

or

operators

can

facilitate

the

integration

of

multiple

signals

For

example

a

synthetic

combinatorial

promoter

responding

to

LuxR

and

l

cI

was

recently

used

to

construct

a

genetic

pulse

generator

-LRB-

Basu

et

al

-RRB-

a

band-pass

filter

and

a

bulls-eye

pattern

formation

system

-LRB-

Basu

et

al

-RRB-

Furthermore

circuits

containing

combinatorial

promoters

are

predicted

to

generate

robust

oscillations

-LRB-

Hasty

et

al

Atkinson

et

al

-RRB-

or

to

create

sign-sensitive

filters

signal

averaging

and

response

acceleration

or

delay

-LRB-

Mangan

and

Alon

-RRB-

Bacterial

promoters

typically

occupy

a

region

of

bp

or

less

surrounding

the

start

site

-LRB-

-RRB-

of

transcription

approximately

from

positions

to

This

sequence

includes

the

EMBO

and

Nature

Publishing

Group

primary

binding

sites

for

the

polymerase

the

and

boxes

-LRB-

Hawley

and

McClure

-RRB-

additional

upstream

-LRB-

Chan

and

Busby

Ross

et

al

-RRB-

and

downstream

-LRB-

Kammerer

et

al

Haugen

et

al

-RRB-

regulatory

sequences

along

with

operators

for

activator

and/or

repressor

TFs

-LRB-

Busby

and

Ebright

Browning

and

Busby

-RRB-

Operators

within

this

region

enable

bound

TFs

to

directly

contact

and

recruit

the

polymerase

-LRB-

activation

-RRB-

or

to

sterically

block

polymerase

contact

with

the

and

boxes

-LRB-

repression

-RRB-

The

type

and

arrangement

of

these

regulatory

sequences

and

operators

within

the

promoter

region

specify

the

promoter

architecture

Genome

sequencing

and

annotation

reveal

the

identity

and

placement

of

the

TF

operators

in

natural

promoters

-LRB-

Collado-Vides

et

al

Gralla

and

Collado-Vides

Salgado

et

al

-RRB-

In

these

and

related

works

the

distributions

of

TF

operators

in

Escherichia

coli

have

highlighted

trends

in

the

operator

positions

relative

to

the

polymerase

box

sequences

For

example

it

was

found

that

activator

operators

occur

principally

around

whereas

repressor

operators

were

clustered

from

to

These

studies

proposed

that

activation

is

effective

only

on

promoters

with

low

unregulated

activity

such

as

in

promoters

containing

a

weak

box

The

effective

repression

of

a

promoter

defined

as

the

ratio

of

Molecular

Systems

Biology

Programming

gene

expression

RS

Cox

III

et

al

expression

in

on

and

off

states

was

expected

to

be

highest

for

promoters

of

strong

unregulated

activity

These

results

indicated

that

repression

and

activation

are

most

effective

at

different

promoter

locations

and

on

different

intrinsic

promoter

strengths

The

potential

diversity

of

promoter

architecture

and

functionality

is

large

when

one

considers

the

many

known

mechanisms

by

which

proteins

and

DNA

interact

Here

we

focus

on

the

simplest

promoter

architectures

regulated

by

multiple

TFs

and

ask

what

types

of

regulation

functions

are

possible

Classical

descriptions

of

gene

networks

have

used

Boolean

logic

to

describe

combinatorial

regulation

-LRB-

Kauffman

Thomas

and

D'Ari

-RRB-

However

because

the

output

of

a

promoter

is

not

a

binary

function

of

the

concentrations

of

its

regulators

-LRB-

Setty

et

al

Atsumi

and

Little

Guido

et

al

Mayo

et

al

-RRB-

a

range

of

non-Boolean

logical

phenotypes

are

possible

Recent

theoretical

descriptions

of

transcriptional

logic

-LRB-

Buchler

et

al

Bintu

et

al

Hermsen

et

al

-RRB-

have

focused

on

the

effects

of

explicit

TF

TF

contacts

and

operator

overlap

but

it

is

not

known

whether

such

interactions

are

necessary

to

generate

diverse

phenotypes

To

better

understand

natural

promoter

function

and

to

improve

the

design

of

new

promoters

for

synthetic

biology

applications

-LRB-

Hasty

et

al

Endy

Sprinzak

and

Elowitz

-RRB-

we

report

a

synthetic

library-based

approach

for

construction

and

analysis

of

modular

combinatorial

promoters

Here

we

varied

the

placement

affinity

and

sequence

of

known

operators

-LRB-

Supplementary

Table

-RRB-

allowing

us

to

determine

the

range

of

functions

encoded

by

the

simplest

combinatorial

promoters

This

approach

reveals

fundamental

features

of

the

relationship

between

promoter

architecture

and

function

active

only

in

the

presence

of

the

corresponding

inducers

L

-LRB-

-RRB-

arabinose

-LRB-

Lara

-RRB-

and

lactone

-LRB-

VAI

-RRB-

respectively

The

repressors

TetR

and

LacI

are

inactivated

by

the

inducers

anhydrotetracycline

-LRB-

aTc

-RRB-

and

isopropyl

-LRB-

IPTG

-RRB-

respectively

Consequently

induction

of

each

factor

-LRB-

AraC

LuxR

LacI

or

TetR

-RRB-

is

expected

to

increase

a

target

promoter

's

activity

These

four

TFs

bind

specifically

to

well-defined

operators

are

dispensable

and

can

be

induced

by

small

molecules

without

disrupting

normal

cellular

processes

For

each

position

-LRB-

distal

core

and

proximal

-RRB-

we

designed

unregulated

and

operator-containing

units

These

sequences

varied

the

affinity

location

and

orientation

of

operators

-LRB-

Figure

-RRB-

The

design

also

allowed

for

variable

and

boxes

to

encourage

diverse

expression

levels

The

units

of

each

type

were

assembled

by

randomized

assembly

ligation

-LRB-

Materials

and

methods

-RRB-

to

generate

a

plasmid

library

containing

approximately

independent

assemblies

and

providing

fivefold

coverage

of

the

possible

promoters

We

transformed

the

plasmid

library

into

E.

coli

strain

expressing

LacI

TetR

AraC

and

LuxR

We

then

sequenced

a

set

of

randomly

chosen

transformants

and

found

correctly

assembled

promoters

-LRB-

Supplementary

Information

-RRB-

We

determined

of

these

promoters

to

be

unique

Within

this

set

out

of

the

possible

units

were

represented

at

least

once

Thus

the

randomized

assembly

ligation

method

produced

a

diverse

set

of

correctly

assembled

promoters

Library

functions

We

measured

the

expression

of

the

sequenced

transformants

in

each

of

combinations

of

the

four

chemical

inducers

-LRB-

Figure

Materials

and

methods

Supplementary

Information

-RRB-

The

library

showed

five

decades

of

variation

in

promoter

activity

-LRB-

Supplementary

Figure

-RRB-

Promoters

of

high

unregulated

activity

contained

strong

and

boxes

although

the

presence

of

consensus

box

sequences

did

not

predict

unregulated

promoter

activity

-LRB-

Supplementary

Figure

-RRB-

Of

the

unique

promoters

produced

measurable

expression

in

at

least

one

of

the

conditions

and

changed

expression

by

a

factor

of

or

more

Of

these

clones

were

found

to

respond

to

a

single

inducer

and

responded

by

more

than

twofold

to

two

inducers

No

promoters

were

found

to

respond

more

than

twofold

to

three

or

four

inducers

or

to

decrease

expression

to

less

than

half

in

the

presence

of

an

inducer

-LRB-

anti-induction

-RRB-

All

of

the

dual-input

promoters

measured

increased

their

activity

monotonically

in

response

to

the

inducer

concentrations

both

singly

and

in

combination

Overall

the

promoter

library

exhibited

a

diverse

set

of

behaviors

across

the

conditions

How

does

promoter

architecture

constrain

function

For

each

promoter

we

compared

the

architecture

-LRB-

Supplementary

Information

-RRB-

with

the

measured

response

-LRB-

Supplementary

Information

-RRB-

We

found

no

significant

regulation

without

the

presence

of

a

corresponding

operator

-LRB-

Supplementary

Information

-RRB-

The

relationship

between

sequence

and

phenotype

revealed

several

rules

relating

promoter

architecture

to

promoter

function

which

we

describe

below

EMBO

and

Nature

Publishing

Group

Results

Combinatorial

library

design

and

assembly

We

developed

an

efficient

method

for

assembling

promoters

from

modular

components

The

method

uses

three

classes

of

synthetic

duplex

DNA

units

with

compatible

cohesive

ends

These

units

correspond

to

the

bp

region

upstream

of

the

box

-LRB-

distal

-RRB-

the

region

between

the

and

boxes

-LRB-

core

-RRB-

and

the

region

downstream

of

the

box

-LRB-

proximal

-RRB-

In

this

scheme

an

arbitrary

promoter

can

be

assembled

from

any

combination

of

proximal

core

and

distal

units

The

internal

overhangs

determine

each

unit

's

placement

in

the

promoter

-LRB-

Figure

-RRB-

We

assayed

promoter

activity

using

a

bacterial

luciferase

reporter

cassette

on

a

low

copy

plasmid

-LRB-

Figure

and

C

-RRB-

Here

we

report

all

promoter

activities

in

terms

of

arbitrary

luminescence

units

-LRB-

ALU

-RRB-

We

incorporated

operators

for

two

activators

and

two

repressors

The

activator

AraC

-LRB-

Ogden

et

al

Schleif

-RRB-

regulates

arabinose

metabolism

in

E.

coli

whereas

LuxR

activates

luminescence

genes

in

Vibrio

fischeri

-LRB-

Fuqua

et

al

-RRB-

The

repressor

LacI

-LRB-

Jacob

and

Monod

Setty

et

al

-RRB-

controls

the

metabolism

of

lactose

in

E.

coli

whereas

TetR

represses

the

tetracycline

resistance

genes

in

transposon

-LRB-

Beck

et

al

Skerra

-RRB-

The

two

activators

are

Molecular

Systems

Biology

Programming

gene

expression

RS

Cox

III

et

al

distal

core

proximal

tcgagtacaacgtcgtgttagctgccttttagcaattttatccatagacttgtgagcgctcacaatt

tataattcgtgcaatTtttaaacctgtaggatcgtacaggt

g

catgttgcagcacaatcgacggaaaatcgttaaaataggtatctgaacactcgcgagtgttaa

atattaagcacgttaAaaatttggacatcctagcatgtcca

cctag

AraC

operator

LacI

Os

operator

distal

core

LuxR

operator

proximal

AraC

LacI

KAN

luxCDABE

LuxR

TetR

Lara

aTc

-LRB-

ALU

-RRB-

Figure

Random

assembly

ligation

generates

a

diverse

promoter

library

Promoters

can

be

assembled

out

of

modular

sequence

units

-LRB-

A

-RRB-

The

assembled

sequence

of

an

example

promoter

The

overhangs

of

each

unit

are

shown

in

red

The

RNA

polymerase

boxes

-LRB-

and

-RRB-

are

highlighted

in

yellow

and

the

predicted

start

site

of

transcription

-LRB-

-RRB-

is

capitalized

Operator

colors

are

consistent

throughout

the

figure

-LRB-

B

-RRB-

Steps

in

promoter

assembly

and

ligation

into

the

luciferase

reporter

vector

promoters

are

assembled

by

mixed

ligations

using

or

cohesive

ends

and

then

ligated

into

a

luciferase

reporter

plasmid

-LRB-

C

-RRB-

Luminescence

measurements

in

inducer

conditions

-LRB-

each

of

four

inducers

as

indicated

-RRB-

for

the

promoter

shown

in

-LRB-

A

-RRB-

The

output

levels

determine

promoter

logic

Note

that

this

promoter

does

not

respond

to

LuxR

regulation

at

the

distal

region

-LRB-

D

-RRB-

The

unique

units

used

in

the

library

contain

operators

responsive

to

the

four

TFs

-LRB-

indicated

by

color

-RRB-

in

the

regions

distal

core

and

proximal

-LRB-

Sequences

in

Supplementary

Table

-RRB-

The

promoter

fragments

corresponding

to

-LRB-

A

-RRB-

are

boxed

in

red

IPTG

VAI

distal

core/proximal

Induced

activity

-LRB-

ALU

-RRB-

Induced

activity

-LRB-

ALU

-RRB-

the

repressed

SIGs

exhibited

higher

regulatory

ranges

up

to

r

-LRB-

Table

I

-RRB-

Activated

SIGs

AraC

proximal

AraC

core

LuxR

core

LuxR

proximal

Activation

ceiling

AraC

distal

LuxR

distal

Uninduced

activity

-LRB-

ALU

-RRB-

Uninduced

activity

-LRB-

ALU

-RRB-

Figure

Activation

functions

at

distal

and

is

attenuated

by

intrinsic

promoter

strength

-LRB-

A

-RRB-

Measurements

of

promoters

activated

at

distal

operators

These

promoters

respond

only

to

LuxR

-LRB-

solid

triangles

-RRB-

or

AraC

-LRB-

open

triangles

-RRB-

induction

Some

promoters

fail

to

respond

even

though

they

contain

a

functional

operator

-LRB-

points

on

the

solid

line

-RRB-

The

activation

ceiling

-LRB-

red

dashed

line

-RRB-

represents

the

maximal

observed

activation

and

does

not

depend

on

the

unregulated

expression

level

-LRB-

B

-RRB-

Promoters

containing

operators

at

core

-LRB-

squares

-RRB-

or

proximal

-LRB-

circles

-RRB-

do

not

respond

to

induction

Single-input

gates

The

simplest

promoters

termed

single-input

gates

-LRB-

SIGs

-RRB-

responded

to

a

single

inducer

-LRB-

Figures

and

-RRB-

For

these

switch-like

gates

we

defined

the

regulatory

range

r

as

the

ratio

of

the

induced

to

uninduced

activity

Within

this

group

activated

SIGs

showed

regulatory

ranges

up

to

r

whereas

EMBO

and

Nature

Publishing

Group

Activated

expression

level

was

independent

of

unregulated

activity

-LRB-

Figure

-RRB-

The

best-activated

SIGs

-LRB-

highest

r

-RRB-

occurred

at

promoters

with

low

expression

in

the

unregulated

state

Activation

was

ineffective

for

promoters

with

unregulated

activity

above

approximately

ALU

which

is

lower

than

the

strongest

promoter

activity

measured

This

activation

ceiling

was

the

same

for

both

AraC

and

LuxRactivated

promoters

These

results

show

that

activation

is

limited

by

the

absolute

expression

level

and

is

most

effective

on

promoters

of

low

intrinsic

activity

consistent

with

previous

suggestions

-LRB-

Busby

and

Ebright

Gross

et

al

-RRB-

Activation

functioned

only

at

the

distal

position

-LRB-

Figure

-RRB-

in

accordance

with

previous

studies

of

AraC

and

LuxR

-LRB-

Collado-Vides

et

al

Egland

and

Greenberg

-RRB-

We

found

neither

inducible

activation

nor

inducible

repression

by

LuxR

or

AraC

at

core

or

proximal

-LRB-

Figure

-RRB-

In

such

promoters

the

typical

induction

response

was

only

for

LuxR

and

for

AraC

regulation

Some

of

the

strongest

activated

SIGs

-LRB-

Table

I

-RRB-

had

additional

activator

operators

at

core

or

proximal

sites

along

with

a

functional

operator

at

distal

We

found

that

activator

binding

to

core

and

proximal

Molecular

Systems

Biology

Programming

gene

expression

RS

Cox

III

et

al

distal

Repressed

activity

-LRB-

ALU

-RRB-

Repressed

activity

-LRB-

ALU

-RRB-

LacI

TetR

background

core

LacI

TetR

background

proximal

Repressed

activity

-LRB-

ALU

-RRB-

LacI

TetR

background

Unrepressed

activity

-LRB-

ALU

-RRB-

Unrepressed

activity

-LRB-

ALU

-RRB-

Unrepressed

activity

-LRB-

ALU

-RRB-

Figure

Repression

is

effective

at

all

three

positions

following

the

trend

coreXproximalXdistal

Measurements

of

repressed

single-input

promoters

Responses

are

colored

according

to

the

repressor

LacI

-LRB-

filled

-RRB-

or

TetR

-LRB-

open

-RRB-

Each

promoter

contains

a

single

operator

located

at

distal

-LRB-

A

-RRB-

core

-LRB-

B

-RRB-

or

proximal

-LRB-

C

-RRB-

positions

Single-input

activities

are

plotted

in

the

induced

-LRB-

unregulated

-RRB-

versus

uninduced

-LRB-

repressed

-RRB-

states

In

some

promoters

operators

do

not

effectively

repress

the

promoter

-LRB-

points

located

near

solid

black

line

-RRB-

Luciferase

detection

limits

are

shown

with

gray

dashed

lines

Table

I

SIG

promoters

TF

Uninduced

-LRB-

ALU

-RRB-

TetR

Expression

Induced

-LRB-

ALU

-RRB-

Regulatory

range

-LRB-

r

-RRB-

ID

distal

TTGACA

TTGACA

TTGACA

TTGACA

TTGACA

TTGACA

TTGACT

TTGACA

TTGACA

TTGACA

TTTACT

TTTACA

TAGACA

TAGACT

Genotypea

core

GATACT

GATACT

GATACT

TAGAGT

TAGATT

GATACT

GATACT

TATAAT

GATACT

GATACT

GATAAT

TATAAT

GATACT

GATAAT

proximal

LacI

LuxR

AraC

a

The

genotype

refers

to

the

three

units

that

make

up

each

promoter

and

the

and

polymerase

boxes

Here

con

tet

lac

ara

and

lux

refer

to

no

operator

and

TetR

LacI

AraC

and

LuxR

operators

In

each

case

the

number

refers

to

the

operator

variant

Full

sequences

for

each

unit

are

available

in

Supplementary

Table

Functional

operators

are

highlighted

in

bold

did

not

on

average

strongly

affect

the

maximal

promoter

activity

-LRB-

Supplementary

information

Supplementary

Figure

-RRB-

These

results

show

that

AraC

and

LuxR

have

neither

positive

nor

strong

negative

regulatory

effects

on

gene

expression

at

the

core

and

proximal

regions

Repressed

SIGs

In

contrast

to

activation

repression

occurred

effectively

at

all

three

positions

-LRB-

Figure

-RRB-

However

we

found

a

clear

trend

between

operator

location

and

repression

Repression

was

most

effective

at

core

-LRB-

Figure

-RRB-

followed

by

proximal

-LRB-

Figure

-RRB-

and

then

distal

-LRB-

Figure

-RRB-

Within

this

trend

we

found

that

the

promoters

of

low

unregulated

activity

were

less

sensitive

to

operator

position

This

result

shows

that

repression

is

effective

at

all

three

positions

with

relative

strength

following

the

rule

coreXproximalXdistal

As

with

activation

the

expression

level

in

the

repressed

state

was

not

determined

by

the

unregulated

level

Examples

Molecular

Systems

Biology

of

completely

repressed

expression

were

observed

at

every

level

of

unregulated

promoter

activity

-LRB-

Figure

-RRB-

In

fact

some

repressed

SIGs

exhibited

the

highest

activities

observed

-LRB-

ALU

-RRB-

upon

induction

-LRB-

Table

I

-RRB-

Within

the

limits

of

detection

the

effective

repression

-LRB-

r

-RRB-

tended

to

increase

with

unregulated

expression

level

Strikingly

the

SIG

showing

the

strongest

regulation

-LRB-

r

Table

I

-RRB-

had

only

a

single

TetR

operator

at

the

core

region

Furthermore

a

single

repression

site

at

any

of

the

three

positions

was

often

enough

to

repress

the

promoter

below

the

detection

limit

-LRB-

Figure

-RRB-

In

general

multiple

operators

were

not

more

effective

at

repression

than

single

operators

We

found

nine

LacI-regulated

and

six

TetR-regulated

SIGs

containing

multiple

repressor

operators

Of

these

only

one

LacI-regulated

-LRB-

Table

I

-RRB-

and

one

TetR-regulated

-LRB-

Table

I

-RRB-

promoter

produced

higher

regulation

than

corresponding

promoters

containing

a

single

operator

These

results

show

that

operator

position

is

more

important

than

operator

multiplicity

for

achieving

strong

regulation

with

repressors

EMBO

and

Nature

Publishing

Group

Programming

gene

expression

RS

Cox

III

et

al

Dual-input

logic

We

next

considered

dual-input

gates

as

logic

functions

of

their

two

input

inducers

Because

of

the

continuous

nature

of

the

output

levels

in

each

input

state

Boolean

logic

does

not

accurately

represent

the

space

of

possible

functions

For

example

in

a

recent

study

the

natural

lac

promoter

increased

activity

by

a

factor

of

when

induced

by

cAMP

alone

by

a

factor

of

when

induced

by

IPTG

alone

and

by

a

factor

of

when

induced

by

both

simultaneously

-LRB-

Setty

et

al

-RRB-

This

intermediate

behavior

could

be

described

as

either

AND-like

or

OR-like

depending

on

the

activity

threshold

chosen

To

describe

such

intermediate

logic

phenotypes

we

introduced

a

three-dimensional

parameterization

for

the

space

of

promoter

functions

In

this

scheme

we

represented

the

promoter

functions

with

three

numerical

parameters

that

quantify

dynamic

range

logic

type

and

asymmetry

of

inputs

-LRB-

Materials

and

methods

-RRB-

As

before

r

is

the

ratio

of

the

maximum

to

minimum

promoter

activity

The

parameter

l

quantifies

the

logical

behavior

of

the

promoter

from

pure

OR

-LRB-

l

-RRB-

to

pure

AND

logic

-LRB-

l

-RRB-

Finally

the

parameter

a

quantifies

the

asymmetry

of

the

gate

with

respect

to

its

two

inducers

At

a

the

gate

responds

identically

to

either

inducer

whereas

at

a

the

promoter

responds

to

one

input

only

-LRB-

pure

SIG

-RRB-

These

parameters

span

the

full

range

of

observed

phenotypes

and

have

intuitive

interpretations

They

also

represent

relative

promoter

activities

rather

than

absolute

levels

making

them

less

sensitive

to

the

choice

of

reporter

growth

media

or

other

experimental

conditions

Therefore

they

form

an

ideal

quantitative

representation

for

the

phenotypic

behavior

of

these

promoters

Within

this

logic-symmetry

space

the

positive

monotonic

response

of

promoters

to

their

inputs

restricts

promoter

logic

to

the

triangular

region

shown

in

Figure

The

corners

of

this

region

include

three

Boolean

logic

functions

the

switch-like

SIG

-LRB-

l

a

-RRB-

along

with

the

canonical

binary

gates

AND

-LRB-

l

a

-RRB-

and

OR

-LRB-

l

a

-RRB-

The

symmetric

SLOPE

gate

-LRB-

l

a

-RRB-

exhibits

logic

intermediate

between

AND

and

OR

The

asymmetric

asym-AND

-LRB-

l

a

-RRB-

asym-OR

-LRB-

l

a

-RRB-

and

asym-SLOPE

-LRB-

l

a

-RRB-

gates

Inputs

describe

idealized

logic

functions

intermediate

between

SIG

and

AND

SIG

and

OR

and

SIG

and

SLOPE

respectively

-LRB-

Figure

-RRB-

This

representation

provides

qualitative

categories

for

the

different

types

of

logic

displayed

by

monotonic

dual-input

promoters

We

identified

dual-input

gates

-LRB-

Materials

and

methods

-RRB-

Each

defined

a

point

-LRB-

r

a

l

-RRB-

in

the

logical

phenotype

space

-LRB-

Figure

-RRB-

revealing

a

range

of

functional

behaviors

AsymAND

and

SIG-like

gates

exhibited

strong

regulation

up

to

r

The

AND

and

asym-SLOPE

gates

were

regulated

up

to

r

whereas

the

SLOPE

gates

were

regulated

up

to

r

Notably

we

found

no

gates

exhibiting

strong

OR

or

asym-OR

logic

functions

However

one

class

of

dual-input

promoters

-LRB-

discussed

below

-RRB-

exhibited

asym-SLOPE

logic

approaching

an

asym-OR

response

-LRB-

-RRB-

Thus

we

observed

a

wide

distribution

of

promoter

logic

types

The

library

contained

two

classes

of

dual-input

gates

The

repressor

repressor

-LRB-

RR

-RRB-

promoters

contained

operators

for

the

repressors

LacI

and

TetR

whereas

the

activator

repressor

-LRB-

AR

-RRB-

promoters

responded

to

the

activator

AraC

and

one

of

the

repressors

Due

to

the

relative

scarcity

of

LuxR-activated

promoters

we

did

not

find

LuxR-regulated

AR

promoters

in

the

characterized

promoter

set

-LRB-

Figure

-RRB-

These

two

classes

of

dual-input

gates

exhibited

differing

but

overlapping

distributions

of

logical

phenotypes

Comparison

of

AR

and

RR

promoter

phenotypes

-LRB-

Figure

-RRB-

revealed

that

each

has

a

preference

for

different

logical

categories

although

both

produced

strong

asym-AND

gates

The

RR

promoters

produced

the

strongest

symmetric

-LRB-

AND

and

SLOPE

-RRB-

gates

whereas

the

AR

promoters

generated

the

strongest

asym-SLOPE

gates

This

shows

that

RR

promoters

produced

both

symmetric

and

asymmetric

logic

while

AR

promoters

produced

only

asymmetric

logic

Mathematical

model

of

repressor

interaction

To

better

understand

the

variety

of

symmetric

and

asymmetric

logic

observed

for

the

RR

promoter

class

we

employed

a

AR-promoters

RR-promoters

Activity

SIG

Asymmetry

-LRB-

a

-RRB-

Regulation

-LRB-

r

-RRB-

Asym-OR

Asym-SLOPE

OR

SLOPE

Asymmetry

-LRB-

a

-RRB-

Asym-AND

AND

Logic

-LRB-

l

-RRB-

More

OR

more

AND

Logic

-LRB-

l

-RRB-

More

OR

more

AND

Figure

Dual-input

gates

exhibit

diverse

functions

in

logic-symmetry

space

Promoter

response

phenotypes

can

be

represented

by

their

asymmetry

a

-LRB-

y-axis

-RRB-

logic

type

l

-LRB-

x-axis

-RRB-

and

regulatory

range

r.

-LRB-

A

-RRB-

Diagram

showing

the

space

of

allowed

logical

phenotypes

with

the

locations

of

ideal

logic

gates

indicated

The

SIG

responds

completely

to

one

inducer

and

not

at

all

to

the

other

The

SLOPE

gate

represents

an

intermediate

logical

function

between

AND

and

OR

whereas

the

asymmetric

gates

are

intermediate

between

SIG

and

the

corresponding

symmetric

gate

Intermediate

logical

behavior

is

represented

between

these

ideal

locations

The

logic-symmetry

parameterization

is

defined

in

the

Materials

and

methods

Points

outside

of

the

dashed

triangle

are

not

accessible

if

promoters

respond

monotonically

to

each

input

-LRB-

B

-RRB-

The

logical

phenotypes

of

dual-input

promoters

-LRB-

r

-RRB-

AR

promoters

are

shown

as

purple

circles

RR

promoters

are

shown

as

gold

disks

The

diameter

of

each

disk

is

proportional

to

the

logarithm

of

its

regulatory

range

r.

EMBO

and

Nature

Publishing

Group

Molecular

Systems

Biology

Programming

gene

expression

RS

Cox

III

et

al

simple

model

of

promoter

activity

in

the

presence

of

two

repressors

-LRB-

Materials

and

methods

-RRB-

In

this

model

and

o

represent

the

strength

of

repression

at

the

stronger

operator

the

weaker

operator

and

the

repressor

repressor

interaction

respectively

-LRB-

Bintu

et

al

-RRB-

When

the

repressors

do

not

interact

with

each

other

o

whereas

for

exclusive

interactions

-LRB-

only

one

repressor

can

bind

at

a

time

-RRB-

o

Cooperative

interactions

would

correspond

to

The

logic

parameter

l

was

tightly

coupled

to

the

model

interaction

parameter

o

-LRB-

Materials

and

methods

-RRB-

A

plot

of

a

and

l

as

parameterized

functions

of

the

microscopic

model

parameters

-LRB-

Supplementary

Figure

-RRB-

showed

that

RR

promoters

with

o

ranging

from

-LRB-

exclusive

interaction

-RRB-

to

-LRB-

independent

interaction

-RRB-

can

produce

any

logic

function

in

the

right

half

-LRB-

-RRB-

of

the

phenotype

space

triangle

SIG

AND

SLOPE

asym-AND

and

asym-SLOPE

In

particular

exclusive

interaction

-LRB-

o

-RRB-

approached

pure

AND

logic

-LRB-

l

-RRB-

whereas

independent

interaction

-LRB-

o

-RRB-

always

resulted

in

SLOPE-like

logic

-LRB-

l

-RRB-

Conversely

we

found

that

an

asymOR

gate

would

require

extremely

high

cooperative

interaction

-LRB-

o

-RRB-

whereas

an

ideal

OR

gate

would

require

infinite

cooperativity

Therefore

the

range

of

logic

functions

displayed

by

the

library

RR

promoters

-LRB-

Figure

-RRB-

falls

within

the

spectrum

of

noncooperative

interactions

-LRB-

-RRB-

This

model

demonstrates

that

a

variety

of

logic

functions

can

be

achieved

without

explicit

protein

protein

cooperativity

RR

promoters

Dual

repression

can

be

either

symmetric

or

asymmetric

-LRB-

Figure

-RRB-

with

either

repressor

dominant

-LRB-

Figure

-RRB-

As

with

the

SIGs

even

the

strongest

RR

promoters

could

be

fully

repressed

exhibiting

effective

repression

up

to

r

RR

promoter

logic

was

always

AND-like

or

SLOPE-like

-LRB-

pl

-RRB-

indicating

that

there

were

no

instances

of

strong

cooperative

interaction

between

the

repressors

-LRB-

-RRB-

In

three

cases

mutation

of

a

repressor

operator

resulted

in

almost

completely

asymmetric

-LRB-

a

-RRB-

SIG

logic

-LRB-

Figure

top

of

LacI

Architecture

LacI/TetR

genotype

distal

TTGACA

TTGACA

TTGACA

TTGACA

TTGACA

TTGACA

TTGACA

TTGACA

TTGACT

TTGACA

triangle

-RRB-

In

other

cases

the

repression

was

more

balanced

-LRB-

-RRB-

producing

symmetric

AND

and

SLOPE

responses

Thus

RR

promoters

displayed

a

large

range

of

dual-input

regulatory

logic

including

AND

SLOPE

asym-SLOPE

and

asym-AND

gates

In

principle

the

logic

phenotype

displayed

by

a

promoter

could

depend

on

the

inducer

concentrations

used

Therefore

we

chose

three

RR

promoters

-LRB-

Figure

clones

and

-RRB-

and

measured

their

responses

to

combinations

of

inducer

concentrations

-LRB-

Supplementary

Information

-RRB-

As

expected

all

three

promoters

increased

their

activity

monotonically

with

increasing

concentrations

of

each

inducer

As

shown

in

Supplementary

Figure

inducer

concentrations

primarily

affected

r

and

a

whereas

the

logic

parameter

l

was

less

dependent

-LRB-

Supplementary

Information

-RRB-

The

most

ANDlike

gate

-LRB-

-RRB-

had

the

highest

variation

in

logic

-LRB-

l

to

l

-RRB-

whereas

the

most

SLOPE-like

-LRB-

-RRB-

exhibited

the

narrowest

range

-LRB-

l

to

l

-RRB-

These

results

imply

that

r

and

a

depend

strongly

on

input

concentration

whereas

for

l

independent

-LRB-

SLOPE

-RRB-

logic

is

more

robust

than

exclusive

regulation

-LRB-

AND

-RRB-

The

repressor

operator

location

trend

coreXproximalX

distal

explains

the

combinatorial

promoter

behaviors

shown

in

Figure

For

RR

promoters

the

position

of

the

operators

determined

whether

LacI

or

TetR

was

dominant

We

found

only

one

clear

exception

to

this

trend

-LRB-

Figure

clone

-RRB-

where

TetR

acting

at

proximal

slightly

dominates

LacI

acting

at

core

Symmetric

repression

occurred

for

several

architectures

such

as

with

a

TetR

at

core

and

two

LacI

operators

one

at

distal

and

the

other

at

proximal

-LRB-

Figure

-RRB-

In

all

other

asymmetric

cases

core

dominated

proximal

and

distal

while

proximal

dominated

distal

RR

promoter

architectures

with

operators

at

proximal

and

distal

produced

the

largest

range

of

logic

behaviors

including

AND

SLOPE

asym-AND

and

asymSLOPE

RR

promoters

with

operators

at

the

core

and

proximal

positions

produced

only

AND

and

asym-AND

logic

Of

the

seven

RR

promoters

exhibiting

strong

AND-like

logic

-LRB-

-RRB-

five

had

operators

at

core

and

proximal

Finally

RR

promoter

TetR

AraC

Architecture

AraC

TetR

genotype

TAGACA

TAGACA

TAGACA

TAGAGT

TAGATT

TATAAT

Input

Output

IPTG

aTc

proximal

Input

Output

Lara

aTc

Clone

Clone

-LRB-

Arbitrary

luminescence

units

-RRB-

core

TAGAGT

TAGAGT

GATACT

TAGAGT

TATAAT

GATACT

GATACT

GATACT

GATACT

TATAAT

AraC/LacI

genotype

TAGACT

TAGACA

TAGACA

TAGACT

TAGACT

TAGACT

TATAAT

TATAAT

TAGAAT

TATAAT

GATACT

GATAAT

Lara

IPTG

Figure

Combinatorial

promoter

architecture

reveals

rules

for

programming

gene

expression

The

architecture

and

function

of

several

dual-input

promoters

The

architecture

of

each

promoter

-LRB-

colored

according

to

Figure

-RRB-

is

shown

with

its

functional

operators

and

and

boxes

-LRB-

A

-RRB-

RR

promoters

respond

to

both

LacI

and

TetR

The

fourth

induction

column

-LRB-

IPTG

aTc

-RRB-

corresponds

to

the

unregulated

state

-LRB-

B

-RRB-

AR

promoters

respond

to

AraC

and

one

of

the

two

repressors

as

indicated

Here

the

third

column

-LRB-

IPTG/aTc

Lara

-RRB-

corresponds

to

the

unregulated

state

Molecular

Systems

Biology

EMBO

and

Nature

Publishing

Group

Programming

gene

expression

RS

Cox

III

et

al

architectures

with

operators

at

core

and

distal

produced

the

most

asymmetric

logic

functions

-LRB-

e.g.

Figure

-RRB-

the

repressor

acting

at

core

was

always

strongly

dominant

These

results

show

that

repressor

dominance

in

combinatorial

promoters

follows

the

trend

coreXproximalXdistal

and

that

close

operator

proximity

is

consistent

with

AND-like

logic

Operator

proximity

Independent

regulators

generate

SLOPE-like

logic

Operator

proximity

increases

competitive

interactions

making

the

logic

more

AND-like

For

both

activation

and

repression

the

activity

of

the

promoter

in

the

regulated

-LRB-

activated/repressed

-RRB-

state

is

not

determined

by

the

activity

in

the

unregulated

state

-LRB-

Rule

-RRB-

Intuitively

activation

has

higher

r

when

the

unregulated

activity

is

low

and

repression

has

higher

r

when

the

unregulated

activity

is

high

Furthermore

as

predicted

by

recent

theoretical

work

-LRB-

Bintu

et

al

-RRB-

repression

is

able

to

achieve

extremely

high

levels

of

regulation

-LRB-

-RRB-

whereas

activated

regulation

is

moderately

strong

-LRB-

-RRB-

These

limits

apply

to

both

SIGs

-LRB-

Figures

and

-RRB-

and

dual-input

promoters

-LRB-

Figure

-RRB-

AR

promoters

are

a

special

case

and

exhibit

a

trade-off

increasing

the

unregulated

activity

increases

the

regulatory

range

-LRB-

r

-RRB-

at

the

expense

of

greater

asymmetry

-LRB-

a

-RRB-

For

example

compare

the

first

and

last

promoter

in

Figure

Rules

and

summarize

the

operator

position

and

multiplicity

effects

for

both

activators

and

repressors

The

repression

trend

-LRB-

Rule

-RRB-

has

been

previously

reported

for

promoters

regulated

by

LacI

-LRB-

Lanzer

and

Bujard

Elledge

and

Davis

-RRB-

The

authors

of

the

first

paper

proposed

a

mechanistic

model

involving

two

competing

effects

core

and

proximal

sites

more

effectively

block

polymerase

binding

whereas

core

and

distal

sites

bind

to

repressor

more

rapidly

-LRB-

are

more

accessible

-RRB-

as

the

polymerase

initiation

complex

clears

the

and

boxes

We

confirmed

the

operator

location

trend

for

SIGs

regulated

by

LacI

and

TetR

alone

and

found

that

this

heuristic

also

holds

for

RR

promoters

of

both

repressors

Of

course

differences

in

operator

affinity

repressor

concentration

and

repressor

structure

can

overcome

these

rules

We

compared

Rules

and

with

the

distribution

of

known

E.

coli

operators

compiled

from

natural

promoters

in

the

database

RegulonDB

-LRB-

Salgado

et

al

Figure

-RRB-

In

agreement

with

analysis

made

on

earlier

versions

of

the

database

-LRB-

Collado-Vides

et

al

Gralla

and

Collado-Vides

-RRB-

we

found

that

activator

operators

are

most

common

in

the

distal

region

-LRB-

Figure

-RRB-

whereas

repressor

operators

cluster

around

all

three

promoter

regions

-LRB-

Figure

-RRB-

Figure

shows

the

operator

density

of

the

promoters

that

are

recognized

by

the

polymerase

subunit

The

small

regulatory

effect

observed

for

activator

operators

in

the

core

and

proximal

regions

-LRB-

Rule

-RRB-

appears

consistent

with

the

general

scarcity

of

natural

activator

sites

in

these

regions

Similarly

the

density

of

repressor

operators

found

in

promoters

is

significantly

enriched

for

core

sites

over

distal

and

proximal

locations

consistent

with

the

repressor

operator

location

trend

-LRB-

Rule

-RRB-

The

sufficiency

of

one

operator

for

repressing

promoter

activity

up

to

five

orders

of

magnitude

-LRB-

Rule

-RRB-

raises

the

classic

question

of

why

natural

promoters

are

so

often

regulated

by

redundant

operators

-LRB-

Collado-Vides

et

al

-RRB-

Our

study

used

high

concentrations

of

repressors

in

the

range

of

mM

-LRB-

Lutz

and

Bujard

-RRB-

paired

with

strong

operators

-LRB-

Supplementary

Table

-RRB-

At

lower

repressor

concentrations

and

operator

affinities

the

presence

of

multiple

binding

sites

can

increase

the

effective

repression

r

through

looping

-LRB-

Vilar

and

Leibler

Becker

et

al

-RRB-

cooperativity

-LRB-

Oehler

et

al

Ptashne

Rosenfeld

et

al

-RRB-

or

even

without

explicit

TF

TF

interactions

-LRB-

Bintu

et

al

-RRB-

Molecular

Systems

Biology

AR

promoters

Among

AR

promoters

-LRB-

Figure

-RRB-

repression

always

dominated

activation

-LRB-

-RRB-

The

AR

promoters

were

regulated

by

AraC

in

combination

with

LacI

or

TetR

and

exhibited

regulation

up

to

r

In

all

cases

the

activator

functioned

from

the

distal

region

whereas

the

repressor

functioned

at

core

or

proximal

We

found

one

AR

promoter

that

approached

symmetric

response

-LRB-

r

a

l

Figure

-RRB-

The

three

most

AND-like

-LRB-

-RRB-

promoters

of

this

class

had

the

repressor

operator

at

the

core

The

most

OR-like

-LRB-

smallest

l

-RRB-

promoter

exhibited

asym-SLOPE

logic

-LRB-

r

a

l

Figure

-RRB-

with

the

repressor

operator

at

proximal

Therefore

we

found

AR

promoters

are

well

represented

by

asym-AND

when

the

repressor

acts

as

core

and

asym-SLOPE

when

the

repressor

acts

at

proximal

The

AR

promoters

also

confirmed

our

previous

result

relating

activation

to

intrinsic

promoter

activity

the

higher

the

unregulated

activity

of

an

AR

promoter

-LRB-

IPTG/aTc

Lara

-RRB-

the

smaller

the

change

upon

activator

induction

-LRB-

compare

the

last

two

columns

in

Figure

-RRB-

When

the

unregulated

activity

exceeded

the

activation

ceiling

the

AR

promoter

did

not

respond

to

AraC

induction

at

all

resulting

in

SIG-like

behavior

-LRB-

e.g.

Figure

-RRB-

This

result

indicates

that

AR

promoters

will

depend

on

both

inputs

only

when

the

unregulated

promoter

activity

is

below

the

activation

ceiling

Discussion

Combinatorial

synthesis

of

synthetic

promoters

as

described

here

permits

systematic

analysis

of

promoter

architecture

and

rapid

identification

of

promoters

that

implement

specific

functions

The

spectrum

of

promoter

functions

observed

in

this

library

highlights

several

heuristic

rules

for

promoter

design

Limits

of

regulation

Gene

expression

can

be

regulated

over

five

orders

of

magnitude

Regulated

promoter

activity

is

independent

of

unregulated

activity

As

a

result

effective

repression

tends

to

increase

with

unregulated

activity

whereas

activation

tends

to

decrease

Activation

is

limited

by

an

absolute

level

of

expression

at

around

the

level

of

the

strongest

unregulated

promoter

activities

Repressor

operator

location

The

effectiveness

of

repression

depends

on

the

operator

location

with

coreXproximalX

distal

Dual-repression

may

be

symmetric

or

asymmetric

with

the

dominant

repressor

predicted

by

operator

locations

One

is

enough

Full

repression

is

possible

with

a

single

operator

between

and

at

high

repressor

concentrations

Activators

function

only

upstream

of

-LRB-

distal

-RRB-

and

have

little

positive

or

negative

effect

downstream

at

core

or

proximal

Repression

dominates

activation

producing

asymmetric

logic

EMBO

and

Nature

Publishing

Group

Programming

gene

expression

RS

Cox

III

et

al

Relative

operator

density

-LRB-

-RRB-

Repressors

60 80 100 120

140 160 180 200

Activators

distal

core

proximal

remote

remote

Activators

Repressors

No

of

operators

No

of

operators

Operator

center

-LRB-

bp

-RRB-

Figure

The

distribution

of

operator

locations

in

natural

promoters

reflects

functional

trends

of

synthetic

promoters

Operator

locations

are

as

annotated

in

RegulonDB

-LRB-

Salgado

et

al

-RRB-

Distributions

of

repressor

-LRB-

A

-RRB-

and

activator

-LRB-

B

-RRB-

operators

as

found

in

E.

coli

promoters

The

number

of

operators

centered

at

each

position

relative

to

the

start

site

of

transcription

-LRB-

-RRB-

is

plotted

-LRB-

C

-RRB-

The

density

of

operators

found

in

promoters

is

broken

down

into

three

promoter

regions

distal

core

and

proximal

as

well

as

regions

upstream

-LRB-

remote

-RRB-

and

downstream

-LRB-

remote

-RRB-

of

the

promoter

The

density

is

shown

as

the

fraction

of

sites

in

each

position

weighted

by

the

relative

size

-LRB-

bp

-RRB-

of

each

region

These

effects

can

also

increase

the

steepness

of

response

to

repressor

concentration

-LRB-

Ptashne

-RRB-

or

engender

exceptions

to

the

dominance

of

repression

-LRB-

Rule

-RRB-

Finally

the

presence

of

multiple

operators

might

increase

the

mutational

plasticity

of

promoter

functions

-LRB-

Mayo

et

al

-RRB-

Rule

provides

insight

for

both

AR

and

RR

promoters

operators

at

the

neighboring

sites

will

tend

to

generate

more

AND-like

logic

-LRB-

higher

l

-RRB-

than

non-neighboring

sites

-LRB-

i.e.

distal

and

proximal

-RRB-

In

AR

promoters

repression

at

core

produces

more

AND-like

logic

than

at

proximal

This

effect

can

be

understood

intuitively

for

RR

promoters

if

operators

are

closely

spaced

binding

of

one

repressor

can

inhibit

the

binding

of

the

other

Removing

one

repressor

has

two

conflicting

effects

it

increases

expression

due

to

its

reduced

occupancy

but

it

simultaneously

decreases

expression

by

allowing

binding

of

the

other

repressor

This

makes

the

overall

logic

more

AND-like

In

terms

of

the

mathematical

model

AND-like

-LRB-

-RRB-

RR

promoters

correspond

to

strong

balanced

repression

-LRB-

-RRB-

and

exclusive

interaction

-LRB-

-RRB-

The

library

described

here

represents

a

starting

point

for

systematic

investigation

of

the

functional

repertoire

of

prokaryotic

promoters

These

simple

promoters

can

not

include

all

the

complex

effects

found

in

natural

promoters

including

those

dependent

on

DNA

bending

or

specific

protein

protein

interactions

Nevertheless

they

provide

a

view

of

what

is

possible

with

the

simplest

genetic

elements

and

interactions

Within

this

context

the

heuristics

described

above

allow

the

design

of

particular

promoter

functions

controlled

by

arbitrary

TF

regulators

The

assembly

method

allows

for

construction

of

any

specific

promoter

Other

promoter

architectures

could

be

generated

with

this

method

to

provide

more

diverse

logic

phenotypes

or

to

explore

regulatory

DNA

in

eukaryotic

organisms

-LRB-

Ligr

et

al

-RRB-

For

example

the

lac

promoter

architecture

regulated

by

a

distal

activator

and

multiple

repressor

operators

-LRB-

including

upstream

sites

-RRB-

can

exhibit

phenotypes

not

found

in

our

library

such

as

asym-OR

-LRB-

Mayo

et

al

-RRB-

In

another

case

a

synthetic

activator

activator

-LRB-

AA

-RRB-

promoter

has

been

constructed

which

exhibits

near-symmetric

SLOPE

logic

-LRB-

Joung

et

al

-RRB-

Tandem

promoters

are

expected

to

generate

additive

logic

functions

more

closely

representing

OR

logic

and

in

fact

many

natural

promoters

are

found

in

tandem

Molecular

Systems

Biology

60 80 100 120

140 160 180 200

Operator

center

-LRB-

bp

-RRB-

repeats

-LRB-

Collado-Vides

et

al

-RRB-

If

our

heuristic

rules

apply

to

natural

combinatorial

promoters

we

may

begin

to

elucidate

complicated

functions

by

inspection

of

these

non-coding

DNA

sequences

In

this

regard

effective

parameterizations

of

logic

such

as

the

one

shown

in

Figure

can

provide

a

more

intuitive

understanding

of

the

computations

performed

by

promoters

Materials

and

methods

Reagents

All

inducers

and

chemicals

were

purchased

from

Sigma

Concentrations

-LRB-

unless

otherwise

stated

-RRB-

were

mg/ml

kanamycin

mg/ml

ampicillin

mM

IPTG

ng/ml

anhydrotetracycline

-LRB-

aTc

-RRB-

L

-LRB-

-RRB-

arabinose

-LRB-

Lara

-RRB-

and

mM

lactone

-LRB-

VAI

-RRB-

LB

growth

media

-LRB-

Lennox

-RRB-

was

used

for

all

experiments

All

ligation

reactions

were

carried

out

with

U

of

DNA

ligase

-LRB-

Invitrogen

-RRB-

and

mg/ml

BSA

-LRB-

Invitrogen

-RRB-

in

ml

of

ligase

buffer

-LRB-

Invitrogen

-RRB-

at

Randomized

assembly

ligation

Promoters

were

constructed

by

total

synthesis

and

ligation

Each

promoter

was

constructed

from

three

duplex

DNA

fragments

comprising

the

distal

core

and

proximal

regions

An

overhanging

phosphorylated

G

on

the

downstream

end

of

distal

is

compatible

with

a

phosphorylated

overhanging

C

on

the

upstream

end

of

core

Likewise

an

overhanging

phosphorylated

AA

on

the

downstream

end

of

core

is

compatible

with

an

overhanging

phosphorylated

TT

on

the

upstream

end

of

proximal

The

terminal

ends

of

the

fully

assembled

promoters

had

mutually

incompatible

XhoI

and

BamHI

bp

overhangs

which

remained

unphosphorylated

A

total

of

duplex

units

-LRB-

Supplementary

Table

-RRB-

were

annealed

out

of

PAGE-purified

synthetic

DNA

oligonucleotides

-LRB-

University

of

Calgary

DNA

synthesis

and

sequencing

center

-RRB-

at

mM

in

ligase

buffer

All

duplex

units

were

mixed

together

in

equal

nM

proportions

and

ligated

for

week

then

cloned

into

bacterial

luciferase

reporter

plasmid

-LRB-

Bjarnason

et

al

-RRB-

We

purified

the

plasmids

using

the

Qiagen

Plasmid

Midi

kit

and

transformed

the

library

into

strain

-LRB-

reference

-LRB-

Riley

et

al

-RRB-

containing

the

native

ara

operon

the

LacI

and

TetR-overexpressing

cassette

-LRB-

Lutz

and

Bujard

-RRB-

and

the

medium-copy

plasmid

which

constitutively

expresses

LuxR

-RRB-

We

picked

clones

and

chose

randomly

for

sequencing

-LRB-

Bjarnason

et

al

-RRB-

and

functional

characterization

Luminescence

measurements

The

library

was

assayed

in

inducer

conditions

corresponding

to

all

saturating

combinations

of

the

four

inducers

VAI

IPTG

Lara

and

aTc

Cells

were

grown

in

plates

to

stationary

phase

-LRB-

h

at

EMBO

and

Nature

Publishing

Group

Programming

gene

expression

RS

Cox

III

et

al

-RRB-

and

inoculated

into

triplicate

plates

containing

LB

media

antibiotics

and

each

inducer

combination

These

were

grown

at

for

h

in

the

dark

Luminescence

measurements

were

obtained

using

a

Tecan

Safire

plate

reader

-LRB-

ms

integration

default

settings

-RRB-

To

determine

the

background

we

took

the

median

measurements

of

nonfunctioning

clones

in

each

condition

All

data

reported

are

the

median

of

triplicate

measurements

To

assess

the

luminescent

crosstalk

between

neighboring

wells

we

inoculated

a

constitutively

bright

clone

into

every

other

row

and

column

of

a

plate

-LRB-

total

wells

-RRB-

and

measured

it

continuously

during

growth

over

h

These

data

were

used

to

compute

the

horizontal/vertical

-LRB-

-RRB-

and

diagonal

-LRB-

-RRB-

neighbor

crosstalk

We

assumed

-LRB-

linear

-RRB-

crosstalk

of

the

form

O

AX

where

O

is

the

observed

data

A

the

actual

luminescence

of

each

well

and

X

the

crosstalk

matrix

We

computed

A

OX

for

combinations

-LRB-

-RRB-

and

then

took

the

total

variance

of

all

empty

wells

as

a

metric

This

metric

reached

a

minimum

of

horizontal/vertical

and

diagonal

crosstalk

This

was

a

very

small

effect

compared

to

other

sources

of

error

-LRB-

below

-RRB-

and

only

resulted

in

an

appreciable

difference

for

wells

neighboring

the

very

brightest

clones

-LRB-

ALU

-RRB-

The

vector

background

level

-LRB-

ALU

-RRB-

was

subtracted

from

all

data

points

We

set

each

datum

to

a

minimum

level

of

corresponding

to

ms.

To

assess

the

plate-to-plate

variation

we

calculated

the

standard

error

between

triplicates

and

divided

by

the

mean

We

found

an

average

replicate

error

of

To

assess

day-to-day

error

we

measured

one

set

of

clones

on

two

consecutive

days

and

computed

standard

relative

errors

by

a

linear

fit

of

the

second

day

's

data

to

the

first

-LRB-

-RRB-

Similarly

we

computed

the

well-to-well

error

on

the

same

plate

by

identifying

clones

with

the

same

sequence

genotype

and

doing

a

linear

fit

between

them

-LRB-

-RRB-

Together

these

data

provide

an

upper

limit

of

on

repeatability

Specifically

l

quantifies

the

logic

type

ranging

from

a

perfect

AND

-LRB-

-RRB-

l

-RRB-

to

a

perfect

OR

-LRB-

-RRB-

l

-RRB-

The

parameter

a

quantifies

the

asymmetry

with

respect

to

the

two

inputs

ranging

from

perfectly

symmetric

-LRB-

-RRB-

a

-RRB-

to

the

completely

asymmetric

SIG

-LRB-

and

-RRB-

a

-RRB-

SLOPE

theorem

separation

of

variables

in

combinatorial

gene

regulation

Consider

a

dual-input

promoter

regulated

by

two

TFs

X

and

Y

-LRB-

we

use

x

and

y

to

represent

their

respective

activities

-RRB-

If

these

TFs

regulate

the

promoter

independently

with

single-input

functions

s

-LRB-

x

-RRB-

and

t

-LRB-

y

-RRB-

the

variables

of

the

regulation

function

p

-LRB-

x

y

-RRB-

separate

p

-LRB-

x

y

-RRB-

s

-LRB-

x

-RRB-

t

-LRB-

y

-RRB-

Suppose

-LRB-

without

loss

of

generality

-RRB-

that

regulator

X

is

dominant

Then

the

four

logical

output

states

of

the

promoter

are

p

p

p

p

The

arrows

signify

the

high

-LRB-

m

-RRB-

and

low

-LRB-

k

-RRB-

states

of

the

promoter

with

respect

to

each

input

-LRB-

e.g.

induced

and

uninduced

respectively

-RRB-

The

logic

parameters

of

the

promoter

are

then

by

definition

r

p

a

p

l

p

r

r

pffiffiffiffiffiffiffiffiffiffi

p

p

p

p

Considering

the

logic

parameter

l

the

separation

of

variables

requires

that

sffiffiffiffiffiffiffiffiffiffiffiffi

p

s

t

s

t

p

r

l

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

s

t

p

p

p

s

t

s

t

-RRB-

l

Promoter

function

analysis

To

calculate

the

expression

levels

for

dual-input

promoters

-LRB-

or

SIGs

-RRB-

we

first

identified

the

two

-LRB-

one

-RRB-

primary

inducers

of

each

promoter

We

then

averaged

the

luminescence

data

over

the

four

-LRB-

eight

-RRB-

background

conditions

Standard

errors

were

computed

from

these

values

and

the

median

of

the

triplicate

measures

gave

the

four

-LRB-

two

-RRB-

expression

levels

of

the

gate

We

then

computed

the

regulatory

ratio

r

defined

as

the

maximum

expression

level

divided

by

the

minimum

The

error

in

regulation

-LRB-

Table

I

-RRB-

was

computed

from

the

relative

errors

for

each

state

For

SIGs

with

expression

levels

-LRB-

off

-RRB-

and

-LRB-

on

-RRB-

the

error

in

r

is

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Dr

r

We

identified

SIGs

and

dual-input

promoters

from

their

sequences

-LRB-

Supplementary

Information

-RRB-

Functional

activator

operators

were

found

at

distal

and

functional

repressor

operators

occurred

at

all

three

positions

With

one

exception

-LRB-

discussed

in

Supplementary

Information

-RRB-

significant

-LRB-

-RRB-

regulation

by

a

TF

occurred

only

with

one

or

more

corresponding

operators

in

the

promoter

sequence

The

presence

of

an

operator

did

not

always

guarantee

regulation

nonfunctioning

SIGs

lie

on

the

diagonal

lines

of

Figures

and

and

dual-input

promoters

responding

to

only

one

input

occur

at

the

apex

-LRB-

-RRB-

of

the

triangle

in

Figure

Therefore

separation

of

variables

regardless

of

the

TF

regulation

functions

implies

that

the

promoter

logic

is

always

SLOPE

or

asymSLOPE

-LRB-

or

in

the

case

that

one

of

the

regulators

is

nonfunctional

SIG

-RRB-

The

converse

is

not

generally

true

but

it

does

hold

for

the

model

of

dual

repression

discussed

below

Model

of

RR

promoter

logic

We

employed

a

previously

defined

model

of

RR

promoter

activity

under

dual

repression

-LRB-

Bintu

et

al

-RRB-

P

A

Logic-symmetry

space

In

addition

to

the

regulation

r

the

two-input

gates

displayed

a

variety

of

relative

expression

levels

For

the

dual-input

promoters

we

defined

four

measured

response

values

-LRB-

-RRB-

such

that

As

repression

always

dominated

activation

for

AR

promoters

corresponded

to

the

activator-induced

state

and

corresponded

to

the

repressor-induced

state

Similarly

for

RR

promoters

corresponded

to

the

expression

level

when

the

weaker

repressor

is

induced

and

to

the

induction

of

the

stronger

To

represent

the

range

of

logical

functionality

we

defined

the

three

phenotypic

parameters

-LRB-

r

a

l

-RRB-

in

terms

of

these

response

values

r

log

log

log

log

l

a

log

r

log

r

The

maximal

promoter

activity

is

A

and

the

normalized

repressor

concentrations

-LRB-

-RRB-

range

from

to

Here

and

represent

the

effectiveness

of

each

repressor

at

excluding

polymerase

from

the

promoter

The

term

o

represents

interactions

between

repressors

corresponds

to

competitive

binding

o

represents

exclusive

binding

and

represents

cooperative

binding

When

o

the

repressors

are

said

to

act

independently

We

solved

for

the

three

logic-symmetry

parameters

-LRB-

r

a

l

-RRB-

in

terms

of

the

three

microscopic

parameters

-LRB-

o

-RRB-

log

r

a

log

r

log

l

log

r

By

the

SLOPE

theorem

independent

interaction

-LRB-

o

-RRB-

produces

SLOPE-like

logic

-LRB-

l

-RRB-

The

converse

is

also

true

here

when

l

RR

promoters

-LRB-

-RRB-

are

regulated

by

the

two

repressors

independently

-LRB-

o

-RRB-

log

-RRB-

log

-RRB-

o

Molecular

Systems

Biology

EMBO

and

Nature

Publishing

Group

Programming

gene

expression

RS

Cox

III

et

al

For

symmetric

RR

promoters

-LRB-

c

-RRB-

a

-RRB-

the

independently

interacting

RR

promoter

is

an

ideal

SLOPE

gate

-LRB-

a

l

-RRB-

When

the

interaction

is

symmetric

but

dependent

-LRB-

-RRB-

the

logic

l

is

described

by

l

log

c

log

o

For

exclusive

interaction

-LRB-

o

-RRB-

the

logic

depends

only

on

the

operator

strength

c

As

c

grows

large

the

logic

approaches

pure

AND

-LRB-

l

-RRB-

l

c

In

the

opposite

extreme

pure

OR

logic

-LRB-

l

-RRB-

is

only

approached

in

the

limit

logc

o

l

logc

o

RegulonDB

analysis

Following

prior

analysis

of

TF

binding

sites

-LRB-

Collado-Vides

et

al

-RRB-

we

examined

E.

coli

regulatory

promoter

sequences

from

RegulonDB

-LRB-

Salgado

et

al

-RRB-

Operator

binding

sites

for

activators

and

repressors

in

each

promoter

were

identified

The

TF

operators

annotated

as

dual

were

removed

from

this

list

For

each

operator

we

determined

the

middle

of

the

annotated

binding

sequence

calculated

the

distance

to

the

annotated

transcription

start

and

calculated

the

number

of

repressor

and

activator

operators

centered

at

each

base

pair

in

the

region

-LRB-

bp

total

-RRB-

These

distributions

were

plotted

as

histograms

for

activators

and

repressors

-LRB-

Figure

and

B

-RRB-

We

also

calculated

the

distribution

of

operators

for

promoters

recognized

by

-LRB-

Figure

-RRB-

In

this

histogram

the

relative

fraction

at

each

region

was

weighted

by

its

length

in

bp

This

weighting

was

necessary

to

observe

the

enrichment

of

repressor

operator

density

in

the

core

region

Supplementary

information

Supplementary

information

is

available

at

the

Molecular

Systems

Biology

website

-LRB-

-RRB-

Acknowledgements

We

thank

Aaron

White

for

help

with

library

design

and

construction

Mercedes

Paulino

for

help

preparing

figures

and

Carla

Davidson

for

plasmid

Avidgor

Eldar

contributed

to

the

logic-symmetry

space

formalism

T

Irie

D

Morris

P

Sternberg

E

Winfree

G

Anderson

J

Locke

H

Garcia

R

Kishony

U

Alon

and

C

Dalal

provided

helpful

discussions

We

thank

W

Kim

C

Vizcarra

G

Seelig

and

J

Kim

for

technical

assistance

RSC

was

partially

supported

by

the

National

Physical

Science

Consortium

and

Sandia

National

Laboratory

MGS

is

supported

as

an

Alberta

Heritage

Foundation

for

Medical

Research

-LRB-

AHFMR

-RRB-

Scientist

and

Canada

Research

Chair

in

Microbial

Gene

Expression

This

work

was

supported

by

NIH

-LRB-

grants

to

MBE

and

to

the

Center

for

Modular

Biology

-RRB-

HFSP

the

Packard

Foundation

and

the

Caltech

Center

for

Biological

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activator
gene expression
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synthetic biology
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