Evolutionarily

Conserved

Pathways

of

Energetic

Connectivity

in

Protein

Families

Steve

W.

Lockless

et

al.

Science

-LRB-

-RRB-

DOI

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REPORTS

The

following

surface

areas

buried

between

domains

in

the

Fn-III

Fn-III

and

structures

-LRB-

-RRB-

were

calculated

with

XPLOR

-LRB-

-RRB-

with

a

probe

radius

Fn-III

Fn-III

Fn-III

Fn-III

Fn-III

and

-LRB-

molecule

B

-RRB-

J.

M.

Leong

P.

E.

Morrissey

R.

R.

Isberg

J.

Biol

Chem

-LRB-

-RRB-

L.

H.

Saltman

Y.

Lu

E.

M.

Zaharias

R.

R.

Isberg

ibid

-LRB-

-RRB-

R.

D.

Bowditch

et

al.

ibid

-LRB-

-RRB-

S.-I

Aota

M.

Nomizu

K.

M.

Yamada

ibid.

p.

T.

P.

Ugarova

et

al.

Biochemistry

-LRB-

-RRB-

T.

A.

Jones

and

M.

Kjeldgaard

Methods

Enzymol

-LRB-

-RRB-

J.

M.

Casasnovas

T.

Stehle

J.

Liu

J.

Wang

T.

A.

Springer

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

Single-letter

abbreviations

for

the

amino

acid

residues

are

as

follows

A

Ala

D

Asp

G

Gly

L

Leu

N

Asn

P

Pro

R

Arg

T

Thr

and

W

Trp

R.

R.

Isberg

Y.

Yang

D.

L.

Voorhis

J.

Biol

Chem

-LRB-

-RRB-

We

thank

S.

M.

Soltis

and

the

staff

at

the

Stanford

Synchrotron

Radiation

Laboratory

-LRB-

SSRL

-RRB-

for

help

with

xenon

derivatization

and

data

collection

M.

J.

Bennett

A.

J.

Chirino

L.

M.

Sanchez

D.

E.

Vaughn

and

A.

P.

Yeh

for

discussions

and

help

with

crystallographic

software

S.

Matthews

for

intimin

coordinates

P.

D.

Sun

for

coordinates

W.

I.

Weis

for

helpful

discussions

about

C-type

lectin

structures

and

W.

I

Weis

J.

M.

Leong

and

members

of

the

Bjorkman

lab

for

critical

reading

of

the

manuscript

coordinates

have

been

deposited

in

the

PDB

-LRB-

PDB

code

-RRB-

June

accepted

September

Evolutionarily

Conserved

Pathways

of

Energetic

Connectivity

in

Protein

Families

Steve

W.

Lockless

and

Rama

Ranganathan

For

mapping

energetic

interactions

in

proteins

a

technique

was

developed

that

uses

evolutionary

data

for

a

protein

family

to

measure

statistical

interactions

between

amino

acid

positions

For

the

PDZ

domain

family

this

analysis

predicted

a

set

of

energetically

coupled

positions

for

a

binding

site

residue

that

includes

unexpected

long-range

interactions

Mutational

studies

confirm

these

predictions

demonstrating

that

the

statistical

energy

function

is

a

good

indicator

of

thermodynamic

coupling

in

proteins

Sets

of

interacting

residues

form

connected

pathways

through

the

protein

fold

that

may

be

the

basis

for

efficient

energy

conduction

within

proteins

Many

cellular

processes

depend

on

the

sequential

establishment

of

protein-protein

interactions

that

underlies

the

propagation

of

information

through

a

signaling

system

The

interaction

of

one

protein

with

another

can

be

thought

of

as

an

energetic

perturbation

to

each

binding

surface

that

distributes

through

the

three-dimensional

structure

to

cause

specific

changes

in

protein

function

-LRB-

-RRB-

The

structural

basis

for

this

process

is

largely

unknown

but

large-scale

mutagenesis

has

begun

to

define

some

basic

principles

of

energy

parsing

in

proteins

Studies

of

the

interaction

of

human

growth

hormone

with

its

receptor

show

that

binding

energy

is

not

smoothly

distributed

over

the

interaction

surface

instead

a

few

residues

comprising

only

a

small

fraction

of

the

interaction

surface

account

for

most

of

the

free-energy

change

-LRB-

-RRB-

Similarly

high-affinity

interaction

of

K

channel

pores

with

peptide

scorpion

toxins

buries

residues

on

the

toxin

molecule

but

most

of

the

binding

energy

depends

on

only

two

amino

acid

positions

-LRB-

-RRB-

Thus

protein

interaction

surfaces

contain

functional

epitopes

or

hot

spots

of

binding

energy

that

are

generally

not

predictable

from

the

atomic

structure

In

addition

a

large

body

of

evidence

sugHoward

Hughes

Medical

Institute

and

Department

of

Pharmacology

University

of

Texas

Southwestern

Medical

Center

Harry

Hines

Boulevard

Dallas

TX

USA

To

whom

correspondence

should

be

addressed

Email

rama@chop.swmed.edu

gests

that

the

change

in

free

energy

at

a

protein

interaction

surface

propagates

through

the

tertiary

structure

in

a

seemingly

arbitrary

manner

Studies

addressing

mechanisms

of

substrate

specificity

in

serine

proteases

show

that

many

sites

distantly

positioned

from

the

active

site

contribute

to

a

determination

of

the

energetics

of

catalytic

residues

-LRB-

-RRB-

The

conversion

of

trypsin

to

chymotrypsin

specificity

required

a

large

set

of

simultaneous

mutations

many

at

unexpected

positions

Similarly

mutations

introduced

during

maturation

of

antibody

specificity

have

been

shown

to

occur

at

sites

that

are

distant

in

tertiary

structure

from

the

antigenbinding

site

despite

substantial

increases

in

binding

energy

-LRB-

-RRB-

An

important

step

in

understanding

the

problem

of

energy

distribution

in

proteins

is

the

full-scale

mapping

of

energetic

coupling

between

amino

acid

positions

Thermodynamic

mutant

cycle

analysis

-LRB-

-RRB-

a

technique

that

measures

the

energetic

interaction

of

two

mutations

provides

a

direct

method

to

systematically

probe

such

relations

of

protein

sites

However

practical

considerations

limit

this

technique

to

small-scale

studies

precluding

a

full

mapping

of

all

energetic

interactions

on

a

complete

protein

We

report

a

study

that

uses

evolutionary

data

for

a

protein

family

to

measure

energetic

coupling

between

positions

on

a

multiple

sequence

alignment

-LRB-

MSA

-RRB-

Evolution

of

a

protein

fold

is

the

result

of

large-scale

random

mutagenesis

with

selection

constraints

imposed

by

function

The

theory

described

below

is

based

on

two

hypotheses

that

derive

from

the

empirical

observation

of

sequence

evolution

The

lack

of

evolutionary

constraint

at

one

position

should

cause

the

distribution

of

observed

amino

acids

at

that

position

in

the

MSA

to

approach

their

mean

abundance

in

all

proteins

and

deviances

from

the

mean

values

should

quantitatively

represent

conservation

In

addition

the

functional

coupling

of

two

positions

even

if

distantly

positioned

in

the

structure

should

mutually

constrain

evolution

at

the

two

positions

and

these

should

be

represented

in

the

statistical

coupling

of

the

underlying

amino

acid

distributions

-LRB-

-RRB-

Two

definitions

guide

the

development

of

statistical

parameters

used

in

our

analysis

-LRB-

i

-RRB-

Conservation

at

a

given

site

in

a

MSA

is

defined

as

the

overall

deviance

of

amino

acid

frequencies

at

that

site

from

their

mean

values

and

-LRB-

ii

-RRB-

statistical

coupling

of

two

sites

i

and

j

is

defined

as

the

degree

to

which

amino

acid

frequencies

at

site

i

change

in

response

to

a

perturbation

of

frequencies

at

another

site

j

This

definition

of

coupling

does

not

require

that

the

overall

conservation

of

site

i

change

upon

perturbation

at

j

but

only

that

the

amino

acid

population

be

rearranged

Therefore

we

describe

a

site

by

a

vector

of

binomial

probabilities

of

individual

amino

acid

frequencies

instead

of

the

scalar

multinomial

probability

of

the

overall

amino

acid

distribution

-LRB-

-RRB-

This

approach

uniquely

represents

all

changes

in

an

amino

acid

distribution

regardless

of

conservation

at

a

given

site

For

an

evolutionarily

well

sampled

MSA

where

additional

sequences

do

not

significantly

change

the

distribution

at

sites

the

probability

of

any

amino

acid

x

at

site

i

relative

to

that

at

another

site

j

is

related

to

the

statistical

free

energy

separating

sites

i

and

j

for

amino

acid

x

-LRB-

Gx

-RRB-

by

the

mann

distribution

-LRB-

-RRB-

Px

i

Px

j

Gi

j

x

e

kT

-LRB-

-RRB-

where

kT

is

an

arbitrary

energy

unit

-LRB-

-RRB-

The

probability

of

any

amino

acid

x

at

site

i

-LRB-

P

x

-RRB-

is

given

by

the

binomial

probability

of

i

the

observed

number

of

x

amino

acids

given

its

mean

frequency

in

all

proteins

-LRB-

Fig.

-RRB-

-LRB-

-RRB-

The

full

distribution

of

amino

acids

at

a

site

i

can

then

be

characterized

by

a

element

vector

of

Px

for

all

x

-LRB-

Px

-RRB-

If

we

take

i

i

SCIENCE

VOL

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Downloaded

from

on

May

REPORTS

as

site

j

a

hypothetical

site

where

all

amino

acids

are

found

at

their

mean

frequencies

in

the

MSA

as

a

reference

state

for

all

sites

we

can

use

Eq

to

transform

Px

into

a

vector

of

i

statistical

energies

that

represents

the

evolutionary

constraint

at

site

i

We

then

define

an

overall

empirical

evolutionary

conservation

parameter

-LRB-

Gstat

-RRB-

for

site

i

G

stat

i

kT

x

ln

Px

i

x

P

MSA

-LRB-

-RRB-

which

amounts

to

taking

the

magnitude

of

the

vector

of

amino

acid

statistical

energies

for

site

i

-LRB-

-RRB-

To

test

the

theory

we

chose

the

PDZ

domain

family

as

a

model

system

for

the

analyses

described

below

PDZ

domains

are

a

Fig.

Statistical

coupling

for

a

single

site

in

the

PDZ

domain

family

-LRB-

A

-RRB-

Examples

of

amino

acid

distributions

for

two

PDZ

domain

sites

before

-LRB-

black

bars

-RRB-

and

after

-LRB-

gray

bars

-RRB-

a

kT

perturbation

at

position

The

distribution

at

position

changes

very

little

upon

perturbation

at

position

despite

high

overall

conservation

and

the

distributin

at

position

changes

significantly

-LRB-

B

-RRB-

A

full

mapping

of

Gstat

for

PDZ

position

i

j

for

all

other

positions

in

the

fold

family

Only

a

small

set

of

coupled

positions

distributed

throughout

the

primary

sequence

emerge

above

noise

-LRB-

C

through

F

-RRB-

Mapping

of

the

data

in

-LRB-

B

-RRB-

on

the

tertiary

structure

of

a

representative

member

of

the

fold

family

Four

views

are

shown

each

successively

rotated

by

from

the

first

of

the

statistical

coupling

pattern

for

perturbations

at

PDZ

position

over

the

entire

PDZ

domain

Coupled

positions

describe

energetic

interactions

at

sites

spatially

close

to

and

distant

from

the

point

of

perturbation

The

color

scale

ranges

from

blue

-LRB-

kT

-RRB-

to

red

-LRB-

kT

-RRB-

OCTOBER

VOL

SCIENCE

Downloaded

from

on

May

Fig.

A

statistical

energy

function

describing

evolutionary

conservation

-LRB-

A

-RRB-

A

comparison

of

amino

acid

distributions

-LRB-

-RRB-

in

unique

eukaryotic

proteins

from

the

Swiss-Prot

database

-LRB-

black

bars

-RRB-

and

members

of

the

PDZ

family

-LRB-

gray

bars

-RRB-

Examples

of

amino

acid

distributions

in

-LRB-

B

-RRB-

moderately

conserved

and

-LRB-

C

-RRB-

weakly

conserved

positions

-LRB-

POS

-RRB-

in

the

PDZ

family

-LRB-

gray

bars

-RRB-

in

comparison

to

the

Swiss-Prot

mean

distribution

-LRB-

black

bars

-RRB-

There

is

a

difference

in

scale

between

-LRB-

B

-RRB-

and

-LRB-

C

-RRB-

-LRB-

D

-RRB-

The

statistical

energy

-LRB-

G

stat

-RRB-

representing

evolutionary

conservation

is

plotted

against

the

primary

structure

position

-LRB-

E

and

F

-RRB-

A

colorimetric

mapping

of

G

stat

on

the

tertiary

structure

of

a

representative

member

of

the

PDZ

fold

family

-LSB-

made

with

GRASP

-LRB-

-RRB-

-RSB-

-LRB-

F

-RRB-

is

rotated

in

relation

to

-LRB-

E

-RRB-

and

the

color

scale

for

the

energy

function

ranges

from

blue

-LRB-

kT

-RRB-

to

red

-LRB-

kT

-RRB-

The

yellow

stick

model

shows

the

peptide

ligand

bound

at

the

interaction

site

of

the

PDZ

domain

REPORTS

family

of

small

evolutionarily

well

represented

protein

binding

motifs

for

which

four

high-resolution

structures

of

distantly

related

members

exist

-LRB-

-RRB-

The

structures

are

quite

similar

-LRB-

root

mean

square

deviation

in

C

atoms

of

-RRB-

although

the

average

sequence

identity

between

pairs

of

domains

is

only

and

in

many

cases

is

indistinguishable

from

random

sequence

identity

We

used

structure-based

alignment

techniques

to

generate

a

MSA

of

eukaryotic

PDZ

domains

-LRB-

-RRB-

Overall

amino

acid

distributions

for

all

proteins

and

for

PDZ

domains

alone

differed

only

slightly

a

fact

that

derives

from

the

large

sequence

divergence

of

this

fold

family

-LRB-

Fig.

-RRB-

Distributions

at

sites

that

represent

moderately

conserved

kT

-LSB-

position

Gstat

kT

-LRB-

Fig.

-RRB-

-RSB-

and

weakly

conserved

-LSB-

position

kT

-LRB-

Fig.

-RRB-

-RSB-

Gstat

kT

positions

show

that

even

moderate

conservation

skewed

the

mean

amino

acid

distribution

significantly

and

lack

of

conservation

was

correlated

with

distributions

closer

to

the

mean

Using

Eq

we

calculated

Gstat

for

all

sites

on

the

PDZ

domain

alignments

These

data

plotted

on

the

primary

structure

show

a

dispersed

pattern

that

describes

the

overall

conservation

profile

of

the

fold

family

-LRB-

Fig.

-RRB-

The

same

data

plotted

on

a

representative

three-dimensional

structure

of

a

member

of

the

family

show

that

this

pattern

simplifies

into

a

rough

description

of

the

protein

interaction

surface

of

the

fold

-LRB-

Fig.

E

and

F

-RRB-

For

example

the

groove

on

the

surface

of

the

PDZ

domain

that

contains

the

co-crystallized

peptide

ligand

-LRB-

-RRB-

-LRB-

Fig.

-RRB-

emerges

as

the

most

conserved

portion

of

the

protein

family

This

finding

is

consistent

with

the

intuitive

expectation

that

a

proper

measure

of

conservation

should

be

able

to

map

functionally

important

sites

on

a

protein

-LRB-

-RRB-

To

measure

the

functional

coupling

of

sites

we

performed

an

experiment

in

which

the

statistical

energy

vector

at

a

given

site

i

was

measured

for

two

conditions

-LRB-

i

-RRB-

the

full

MSA

-LRB-

Gstat

-RRB-

or

-LRB-

ii

-RRB-

a

selected

subset

of

the

i

MSA

representing

a

perturbation

of

the

amistat

no

acid

frequencies

at

another

site

j

-LRB-

Gi

j

-RRB-

The

magnitude

of

the

difference

in

these

two

energy

vectors

gives

a

statistical

coupling

energy

-LRB-

Gstat

-RRB-

between

sites

i

and

j

i

j

G

stat

i

j

kT

x

ln

Px

j

i

x

P

MSA

j

ln

Px

i

x

P

MSA

-LRB-

-RRB-

which

quantitatively

represents

the

degree

to

which

the

probability

of

individual

amino

acids

at

i

is

dependent

on

the

perturbation

at

j

-LRB-

-RRB-

A

systematic

calculation

of

Gstat

at

i

j

all

sites

i

for

a

given

site

j

gives

the

fullscale

mapping

of

statistical

coupling

for

position

j

over

all

protein

sites

We

chose

one

functionally

important

site

in

the

PDZ

domain

family

as

a

test

case

for

the

perturbation

analysis

The

PDZ

domain

family

is

divided

into

distinct

classes

on

the

basis

of

target

sequence

specificity

class

I

domains

bind

to

peptide

ligands

of

the

form

S/T-X-V/I-COO

and

class

II

domains

bind

to

sequences

of

the

form

F/Y-X-V/A-COO

-LRB-

-RRB-

An

important

determinant

of

ligand

specificity

is

domain

position

-LRB-

-RRB-

which

appears

to

select

the

identity

of

the

antepenultimate

peptide

position

In

class

I

domains

a

histidine

at

this

position

hydrogen

bonds

to

the

serine

or

threonine

hydroxyl

of

the

characteristic

recognition

motif

-LRB-

-RRB-

To

examine

the

full

pattern

of

energetic

connectivity

for

PDZ

position

we

made

a

perturbation

to

the

amino

acid

distribution

at

this

site

by

extracting

the

subset

of

the

MSA

that

contains

only

histidine

at

this

position

The

statistical

energetic

consequence

of

this

perturbation

is

a

change

at

position

from

the

full

MSA

We

illustrate

statistical

coupling

to

position

through

two

examples

Position

is

highly

conserved

in

all

PDZ

domains

showing

a

distribution

that

is

virtually

exclusive

for

leucine

isoleucine

or

valine

-LRB-

Fig.

top

-RRB-

but

is

largely

unaffected

by

the

perturbation

at

position

Consequently

this

position

displays

a

low

coupling

kT

kT

-RRB-

energy

-LRB-

Gstat

with

respect

to

position

In

contrast

the

distribution

at

position

changes

for

several

amino

acids

upon

perturbation

at

position

-LRB-

Fig.

bottom

-RRB-

resulting

in

significant

kT

statistical

coupling

-LRB-

Gstat

kT

-RRB-

A

full

primary

sequence

mapping

of

statistical

coupling

for

PDZ

position

shows

that

most

positions

in

the

fold

family

were

not

coupled

to

the

perturbed

site

instead

only

a

small

set

of

statistical

couplings

emerged

from

noise

-LRB-

Fig.

-RRB-

Mapping

the

data

on

the

PDZ

domain

tertiary

structure

shows

that

the

coupled

sites

fall

into

three

classes

-LRB-

Fig.

C

through

F

-RRB-

A

small

set

of

residues

-LSB-

-RSB-

are

in

the

immediate

environment

of

position

a

finding

consistent

with

expected

local

propagation

of

energy

from

a

site

of

perturbation

In

addition

Fig.

Mutant

cycle

analysis

at

PDZ

sites

predicted

to

be

thermodynamically

coupled

by

statistical

analysis

was

expressed

as

a

fusion

protein

with

EGFP

and

binding

of

TMR-labeled

peptide

ligands

was

followed

by

the

measurement

of

fluorescence

resonance

energy

transfer

efficiency

The

inset

in

-LRB-

B

-RRB-

shows

protein

and

a

class

I

binding

peptide

-LRB-

-RRB-

An

an

example

of

a

binding

isotherm

for

wild-type

average

and

standard

deviation

of

five

measurements

are

shown

for

each

ligand

concentration

tested

-LRB-

solid

circles

-RRB-

with

the

smooth

curve

showing

a

fit

to

the

Hill

equation

Using

this

binding

energy

assay

we

carried

out

double

mutant

cycle

analysis

for

mutations

at

PDZ

position

-LRB-

-RRB-

and

at

a

set

of

statistically

coupled

and

uncoupled

positions

-LRB-

A

-RRB-

and

-LRB-

B

-RRB-

show

a

comparison

of

statistical

coupling

-LRB-

G

stat

-RRB-

and

mutational

coupling

-LRB-

G

mut

-RRB-

with

sites

categorized

in

three

groups

those

sites

that

are

statistically

coupled

and

near

to

position

-LSB-

-RSB-

those

sites

that

are

statistically

coupled

but

distant

from

position

-LSB-

-RSB-

and

those

that

are

statistically

uncoupled

-LSB-

-RSB-

The

energy

units

-LRB-

kT

and

kT

-RRB-

are

different

for

the

two

analyses

and

can

not

be

quantitatively

compared

-LRB-

-RRB-

In

each

graph

the

horizontal

line

depicts

the

error

in

kT

or

kT

-LRB-

C

-RRB-

A

scatterplot

of

mutational

coupling

energies

and

statistical

coupling

energies

-LRB-

D

-RRB-

Thermodynamic

mutant

cycle

analysis

between

mutations

at

PDZ

position

-LRB-

-RRB-

and

mutations

at

ligand

positions

at

the

directly

interacting

position

-LRB-

-RRB-

and

at

the

COOH-terminal

position

-LRB-

-RRB-

SCIENCE

VOL

OCTOBER

Downloaded

from

on

May

REPORTS

other

interaction

surface

residues

implicated

in

target

sequence

recognition

-LSB-

-RSB-

emerged

as

coupled

This

result

suggests

energy

propagation

through

bound

substrate

and

would

be

an

expected

consequence

of

cooperative

interaction

of

binding

site

residues

Finally

we

observed

unexpected

coupling

at

long

range

from

sites

in

the

core

and

on

the

opposite

side

of

the

PDZ

domain

-LSB-

-RSB-

To

determine

how

statistical

coupling

patterns

are

related

to

physical

energetic

coupling

of

sites

we

used

the

technique

of

thermodynamic

mutant

cycle

analysis

-LRB-

-RRB-

to

measure

mutational

coupling

energies

for

position

for

one

PDZ

domain

-LSB-

the

third

PDZ

domain

from

-LRB-

-RRB-

-RSB-

and

compared

these

data

to

the

statistical

predictions

In

the

mutant

cycle

method

the

energetic

effect

of

one

mutation

is

measured

for

two

conditions

-LRB-

i

-RRB-

the

wild-type

background

-LRB-

-RRB-

or

-LRB-

ii

-RRB-

the

background

of

a

second

mutation

-LRB-

-RRB-

The

difference

in

these

two

energies

gives

the

coupling

energy

-LRB-

-RRB-

between

the

two

mutations

If

does

not

have

the

same

effect

in

-RRB-

then

tions

and

-LRB-

is

nonzero

and

indicates

thermodynamic

coupling

of

the

two

mutations

To

follow

energetic

coupling

we

developed

an

equilibrium

binding

energy

assay

based

on

fluorescence

resonance

energy

transfer

between

green

fluorescent

protein

-LRB-

GFP

-RRB-

PDZ

domain

fusion

proteins

and

tetramethylrhodamine

-LRB-

TMR

-RRB-

labeled

interacting

peptides

-LRB-

-RRB-

Figure

-LRB-

inset

-RRB-

shows

a

binding

isotherm

for

interaction

of

a

wildtype

protein

and

a

TMRlabeled

class

I

peptide

demonstrating

that

this

assay

is

capable

of

high-resolution

mapping

of

binding

energies

Using

this

assay

we

measured

coupling

energies

for

a

mutation

at

position

-LSB-

-LRB-

-RRB-

-RSB-

against

mutations

at

a

set

of

PDZ

domain

positions

and

two

peptide

positions

-LRB-

-RRB-

The

mutations

chosen

were

designed

to

test

a

range

of

statistical

couplings

on

the

PDZ

domain

including

a

set

of

sites

that

are

not

significantly

statistically

coupled

Statistical

energies

at

coupled

sites

whether

spatially

near

to

or

distant

from

position

are

in

fact

well

correlated

to

the

thermodynamic

coupling

through

mutagenesis

-LRB-

Fig.

-RRB-

statistically

uncoupled

sites

display

mutational

coupling

energies

near

to

noise

Thus

patterns

of

statistical

energetic

coupling

for

a

protein

site

are

likely

to

describe

the

thermodynamic

energetic

connectivity

for

that

position

The

statistical

analysis

for

perturbation

at

position

indicated

that

other

binding

site

positions

-LSB-

and

-RSB-

are

energetically

coupled

and

suggested

the

possibility

of

propagated

coupling

through

the

substrate

peptide

-LRB-

Fig.

B

and

C

-RRB-

Indeed

mutations

at

the

peptide

position

directly

interacting

with

PDZ

position

-LSB-

-LRB-

-RRB-

-RSB-

and

at

the

position

carrying

the

terminal

carboxylate

-LSB-

-LRB-

-RRB-

-RSB-

were

also

thermodynamically

coupled

to

the

mutation

-LRB-

Fig.

-RRB-

With

regard

to

the

process

of

energy

propagation

in

proteins

the

overall

mapping

of

coupling

shows

that

residues

interacting

at

long

range

are

connected

by

a

set

of

juxtaposed

coupled

residues

These

residues

form

a

pathway

of

energetic

connectivity

linking

these

positions

-LRB-

Fig.

-RRB-

For

example

PDZ

position

couples

through

the

substrate

peptide

to

the

floor

of

the

binding

site

-LRB-

position

-RRB-

to

position

within

the

core

of

the

protein

and

to

position

on

the

opposite

face

from

the

ligand-binding

pocket

Although

residues

composing

the

pathway

occur

in

some

cases

along

secondary

structure

elements

-LRB-

residues

and

fall

along

one

face

of

a

helix

-RRB-

the

pathway

as

a

whole

is

an

inherent

property

of

the

tertiary

structure

As

an

independent

study

we

examined

patterns

of

statistical

coupling

for

a

MSA

of

POZ

domains

a

fold

family

that

mediates

homo

and

hetero-oligomerization

of

ion

channel

subunits

and

transcription

factors

-LRB-

-RRB-

A

perturbation

at

a

position

at

the

interaction

surface

-LSB-

-RSB-

shows

a

pattern

of

statistical

coupling

that

forms

a

sterically

connected

path

-LSB-

-RSB-

that

connects

the

oligomerization

interface

with

the

opposing

protein

surface

through

four

aromaticaromatic

interactions

-LRB-

-RRB-

two

of

which

are

fully

buried

in

the

core

of

the

protein

-LRB-

Fig.

C

and

D

-RRB-

Position

which

forms

one

end

of

the

pathway

has

been

implicated

in

the

binding

of

K

channel

subunits

to

the

POZ

domain

of

Shaker-class

K

channels

these

subunits

confer

properties

of

rapid

stimulusdependent

channel

inactivation

-LRB-

-RRB-

The

apparent

energetic

connectivity

between

two

POZ

protein

interaction

surfaces

may

represent

a

mechanism

of

subunit

dependent

Fig.

Pathways

of

physical

connectivity

through

the

core

underlie

long-distance

propagation

of

energetic

coupling

in

two

fold

families

Sections

through

the

protein

core

of

PDZ

and

POZ

domains

show

that

like

at

the

protein

surface

energetically

coupled

positions

in

the

interior

for

perturbations

at

-LRB-

A

-RRB-

PDZ

position

and

at

-LRB-

C

-RRB-

POZ

position

are

mostly

surrounded

by

uncoupled

positions

The

color

scale

is

the

same

as

in

Fig.

-LRB-

B

-RRB-

and

-LRB-

D

-RRB-

show

stereo

images

of

the

pattern

of

energetic

coupling

for

these

two

positions

superimposed

on

ribbon

models

of

representative

members

of

PDZ

or

POZ

fold

families

respectively

A

continuous

pathway

of

van

der

Waals

interaction

connects

distantly

coupled

sites

through

the

interior

of

each

domain

The

pathway

is

composed

of

residues

in

several

secondary

structure

elements

and

is

therefore

an

inherent

property

of

the

tertiary

structure

The

figure

was

prepared

with

Molscript

-LRB-

-RRB-

GLRender

-LRB-

-RRB-

Povray

-LRB-

-RRB-

and

-LRB-

-RRB-

OCTOBER

VOL

SCIENCE

Downloaded

from

on

May

REPORTS

regulation

of

K

channel

activity

The

ability

to

efficiently

propagate

energy

through

tertiary

structure

is

a

fundamental

property

of

many

proteins

and

is

the

physical

basis

for

key

biological

properties

such

as

allostery

and

signal

transmission

The

coupled

pathways

may

represent

conduits

along

which

energy

distributes

through

a

protein

structure

to

generate

these

functional

features

Protein

interaction

modules

such

as

the

PDZ

and

POZ

domains

are

known

to

play

key

roles

as

organizing

centers

for

multiprotein

signaling

complexes

in

which

proteins

are

assembled

into

functional

macromolecular

units

-LRB-

-RRB-

In

addition

to

this

established

role

in

cellular

scaffolding

the

finding

of

energetically

coupled

pathways

within

these

domains

raises

the

possibility

that

the

interaction

modules

may

also

act

as

conductors

of

signaling

In

the

PDZ

domain

evidence

for

such

a

role

comes

from

the

finding

that

interaction

of

the

guanylate

kinase

domain

of

the

multi-PDZ

protein

with

depends

on

the

binding

of

target

peptides

to

the

PDZ

domains

-LRB-

-RRB-

As

with

any

thermodynamic

mapping

the

approach

described

here

can

identify

couplings

but

it

does

not

itself

reveal

the

physical

mechanism

of

the

energetic

coupling

Nevertheless

the

arrangement

of

coupled

residues

into

ordered

pathways

through

the

core

of

the

PDZ

and

POZ

protein

folds

suggests

that

one

mechanism

may

be

simple

mechanical

deformation

of

the

structure

along

coupled

pathways

Given

the

evolutionary

basis

of

the

statistical

analysis

we

infer

that

these

pathways

of

energetic

connectivity

have

emerged

early

in

the

evolution

of

the

protein

folds

and

much

like

the

atomic

structure

are

fundamentally

conserved

features

of

the

domain

families

With

growing

sequence

data

for

evolutionarily

distant

genomes

the

mapping

of

energetic

connectivity

for

many

fold

families

should

be

a

realistic

goal

J.

M.

Holt

and

G.

K.

Ackers

FASEB

J.

-LRB-

-RRB-

J.

Monod

J.

Wyman

J.-P

Changeux

J.

Mol

Biol

-LRB-

-RRB-

K.

M.

Perry

J.

J.

Onuffer

M.

S.

Gittelman

L.

Barmat

C.

R.

Matthews

Biochemistry

-LRB-

-RRB-

D.

W.

Pettigrew

et

al.

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

V.

J.

LiCata

and

G.

K.

Ackers

Biochemistry

-LRB-

-RRB-

G.

J.

Turner

et

al.

Proteins

-LRB-

-RRB-

E.

Freire

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

S.

Atwell

M.

Ultsch

A.

M.

De

Vos

J.

A.

Wells

Science

-LRB-

-RRB-

T.

Clackson

and

J.

A.

Wells

ibid

-LRB-

-RRB-

J.

A.

Wells

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

Biotechnology

-LRB-

-RRB-

P.

Hidalgo

and

R.

MacKinnon

Science

-LRB-

-RRB-

S.

A.

Goldstein

D.

J.

Pheasant

C.

Miller

Neuron

-LRB-

-RRB-

R.

Ranganathan

J.

H.

Lewis

R.

MacKinnon

ibid

-LRB-

-RRB-

P.

Stampe

L.

Kolmakova-Partensky

C.

Miller

Biochemistry

-LRB-

-RRB-

L.

Hedstrom

Biol

Chem

-LRB-

-RRB-

L.

Hedstrom

L.

Szilagyi

W.

J.

Rutter

Science

-LRB-

-RRB-

J.

J.

Perona

L.

Hedstrom

W.

J.

Rutter

R.

J.

Fletterick

Biochemistry

-LRB-

-RRB-

P.

A.

Patten

et

al.

Science

-LRB-

-RRB-

P.

J.

Carter

G.

Winter

A.

J.

Wilkinson

A.

R.

Fersht

Cell

-LRB-

-RRB-

G.

Schreiber

and

A.

R.

Fersht

J.

Mol

Biol

-LRB-

-RRB-

E.

Neher

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

The

multinomial

probability

for

all

amino

acids

gives

the

probability

of

randomly

observing

a

given

amino

acid

distribution

at

a

site

but

is

degenerate

given

the

redistribution

of

amino

acids

with

a

similar

mean

frequency

For

example

consider

a

site

that

displays

a

distribution

of

Ala

Asp

and

Ile

in

the

overall

alignment

and

changes

to

Ala

Asp

and

Ile

upon

perturbation

at

another

site

Because

the

mean

frequency

of

Asp

and

Ile

is

nearly

identical

-LRB-

Fig.

-RRB-

the

multinomial

probability

of

these

two

distributions

is

the

same

although

the

significant

reorganization

of

chemical

character

suggests

that

these

positions

are

indeed

coupled

Description

of

the

site

as

vectors

of

individual

amino

acid

probabilities

accounts

for

all

such

cases

because

each

amino

acid

distribution

maps

to

a

unique

vector

R.

C.

Tolman

The

Principles

of

Statistical

Mechanics

-LRB-

Dover

New

York

-RRB-

For

conventional

statistical

mechanical

systems

at

equilibrium

the

temperature

-LRB-

T

-RRB-

of

an

ensemble

is

proportional

to

the

mean

velocity

of

state

transitions

and

defines

the

fundamental

energy

unit

kT

where

k

is

Boltzmann

's

constant

-LRB-

-RRB-

Sites

on

a

MSA

can

be

seen

as

individual

statistical

mechanical

systems

that

represent

discrete

states

in

an

overall

state

space

of

amino

acid

frequencies

The

temperature

-LRB-

T

-RRB-

of

an

ensemble

of

such

systems

is

again

related

to

the

mean

transition

rates

between

states

but

the

energy

unit

in

such

a

system

-LRB-

kT

-RRB-

is

not

necessarily

related

to

that

for

conventional

mechanical

systems

Each

position

in

a

MSA

can

be

described

as

a

vector

of

individual

amino

acid

frequencies

Each

element

is

transformed

into

a

probability

for

that

amino

acid

with

the

binomial

density

function

P

x

N

pnx

n

x

N

n

x

x

px

N

nx

References

and

Notes

N

is

the

total

number

of

sequences

nx

is

the

number

of

sequences

with

amino

acid

x

and

px

is

the

mean

frequency

of

amino

acid

x

in

all

proteins

To

determine

px

we

created

histograms

of

amino

acids

for

all

entries

-LRB-

as

of

October

-RRB-

in

the

Swiss-Prot

database

of

eukaryotic

nonredundant

proteins

and

calculated

the

mean

values

-LRB-

Fig.

-RRB-

Because

all

structural

and

functional

information

has

been

scrambled

in

this

analysis

the

frequencies

of

amino

acids

should

represent

that

which

is

expected

without

any

functional

evolutionary

constraint

Stirling

's

approximation

was

used

for

the

evaluation

of

large

factorials

-LRB-

-RRB-

For

visualization

and

analysis

statistical

energies

were

arbitrarily

scaled

by

for

compatibility

with

GRASP

and

output

in

Microsoft

Excel

format

or

were

written

to

a

Protein

Data

Bank

file

of

a

representative

member

of

the

fold

family

Mapping

of

statistical

energies

onto

tertiary

structures

was

done

with

GRASP

-LRB-

-RRB-

In

evaluating

statistical

coupling

distributions

at

sites

before

and

after

perturbation

were

normalized

for

comparison

D.

A.

Doyle

et

al.

Cell

-LRB-

-RRB-

J.

H.

Cabral

et

al.

Nature

-LRB-

-RRB-

D.

L.

Daniels

A.

R.

Cohen

J.

M.

Anderson

A.

T.

Brunger

Nature

Struct

Biol

-LRB-

-RRB-

Eukaryotic

PDZ

domains

were

collected

from

the

nonredundant

database

of

protein

sequences

with

PSI-BLAST

-LRB-

-RRB-

-LRB-

e

score

-RRB-

four

PDZ

domains

with

known

structures

-LSB-

-LRB-

-RRB-

M.

Socolich

and

R.

Ranganathan

unpublished

data

-RSB-

were

used

in

initial

searches

Alignments

were

created

with

PILEUP

-LRB-

Genetics

Computer

Group

Madison

WI

-RRB-

followed

by

structure-based

manual

alignment

-LRB-

-RRB-

O.

Lichtarge

H.

R.

Bourne

F.

E.

Cohen

J.

Mol

Biol

-LRB-

-RRB-

Z.

Songyang

et

al.

Science

-LRB-

-RRB-

C.

P.

Ponting

C.

Phillips

K.

E.

Davies

D.

J.

Blake

Bioessays

-LRB-

-RRB-

Single-letter

abbreviations

for

the

amino

acid

residues

are

as

follows

A

Ala

C

Cys

D

Asp

E

Glu

F

Phe

G

Gly

H

His

I

Ile

K

Lys

L

Leu

M

Met

N

Asn

P

Pro

Q

Gln

R

Arg

S

Ser

T

Thr

V

Val

W

Trp

X

any

amino

acid

and

Y

Tyr

The

numbering

scheme

for

both

PDZ

and

POZ

domains

used

is

consistent

with

that

reported

for

the

structures

used

for

mapping

statistical

energies

-LRB-

-RRB-

A

final

concentration

of

nM

enhanced

green

fluorescent

protein

-LRB-

EGFP

-RRB-

PDZ

fusion

protein

in

storage

buffer

-LRB-

-RRB-

was

used

for

peptide

titrations

Ligand

peptides

were

synthesized

with

an

TMR

adduct

and

were

freshly

diluted

from

a

single

batch

of

M

frozen

aliquots

for

binding

measurements

For

all

measurements

we

used

the

binding

peptide

-LRB-

or

mutants

thereof

as

indicated

-RRB-

co-crystallized

in

the

original

structure

determination

-LRB-

-RRB-

Energy

transfer

was

followed

by

quenching

of

fluorescence

at

nm

-LRB-

corrected

for

peptide

fluorescence

-RRB-

Transfer

efficiencies

measured

for

four

or

five

peptide

concentrations

covering

a

log-order

range

around

the

dissociation

constant

were

used

for

each

binding-energy

calculation

each

individual

measurement

was

made

three

to

five

times

Data

were

fit

to

the

Hill

equation

-LRB-

Origin

MicroCal

Software

Northampton

MA

-RRB-

Site-directed

mutagenesis

on

the

rat

third

PDZ

domain

-LRB-

residues

through

-RRB-

was

carried

out

with

standard

polymerase

chain

reaction

based

techniques

Domains

were

expressed

as

COOH-terminal

fusions

with

EGFP

-LRB-

-RRB-

using

the

pRSET-B

vector

-LRB-

Invitrogen

-RRB-

in

Escherichia

coli

-LSB-

strain

-LRB-

-RRB-

Stratagene

-RSB-

Cultures

-LRB-

ml

-RRB-

in

Terrific

broth

were

grown

to

an

optical

density

-LRB-

nm

-RRB-

of

at

C

induced

for

hours

with

M

isopropyl

D-thiogalactopyranoside

and

harvested

Cells

were

lysed

with

B-PER

-LRB-

Pierce

Rockford

IL

-RRB-

cleared

supernatants

were

batch-bound

to

a

bed

volume

of

Ni

nitrilotriacetic

acid

agarose

beads

-LRB-

Qiagen

Valencia

CA

-RRB-

prewashed

in

binding

buffer

-LRB-

mM

tris

at

pH

mM

NaCl

and

mM

imidazole

-RRB-

and

washed

with

column

volumes

of

binding

buffer

and

eluted

with

elution

buffer

-LRB-

mM

tris

at

pH

M

NaCl

and

mM

imidazole

-RRB-

The

protein

was

dialyzed

overnight

into

storage

buffer

-LRB-

mM

tris

at

pH

mM

NaCl

and

mM

dithiothreitol

-RRB-

at

C

and

used

immediately

for

binding

assays

or

flash

frozen

and

stored

at

C

for

later

use

A.

Kreusch

P.

J.

Pfaffinger

C.

F.

Stevens

S.

Choe

Nature

-LRB-

-RRB-

L.

Aravind

and

E.

V.

Koonin

J.

Mol

Biol

-LRB-

-RRB-

V.

J.

Bardwell

and

R.

Treisman

Genes

Dev

-LRB-

-RRB-

N.

V.

Shen

X.

Chen

M.

M.

Boyer

P.

J.

Pfaffinger

Neuron

-LRB-

-RRB-

S.

K.

Burley

and

G.

A.

Petsko

Science

-LRB-

-RRB-

S.

Sewing

J.

Roeper

O.

Pongs

Neuron

-LRB-

-RRB-

A.

S.

Fanning

and

J.

M.

Anderson

J.

Clin

Invest

-LRB-

-RRB-

R.

V.

Schillace

and

J.

D.

Scott

ibid.

p.

R.

Ranganathan

and

E.

M.

Ross

Curr

Biol

-LRB-

-RRB-

S.

Tsunoda

et

al.

Nature

-LRB-

-RRB-

J.

E.

Brenman

et

al.

J.

Neurosci

-LRB-

-RRB-

A.

Nicholls

K.

Sharp

B.

Honig

Proteins

-LRB-

-RRB-

S.

F.

Altschul

et

al.

Nucleic

Acids

Res

-LRB-

-RRB-

R.

Doolittle

Methods

Enzymol

-LRB-

-RRB-

R.

Heim

and

R.

Y.

Tsien

Curr

Biol

-LRB-

-RRB-

P.

J.

Kraulis

J.

Appl

Crystallogr

-LRB-

-RRB-

L.

Esser

unpublished

material

D.

Bacon

and

W.

F.

Anderson

J.

Mol

Graphics

-LRB-

-RRB-

E.

A.

Merrit

and

M.

E.

P.

Murphy

Acta

Crystallogr

-LRB-

-RRB-

We

thank

M.

Wall

for

help

with

figures

N.

Grishin

for

advice

regarding

manual

sequence

alignments

A.

Pertsemlidis

for

help

with

parsing

the

Swiss-Prot

database

and

L.

Aravind

for

communication

of

data

before

publication

We

are

indebted

to

C.

F.

Stevens

for

teaching

and

important

discussions

R.R.

is

a

recipient

of

the

Burroughs-Wellcome

Fund

New

Investigator

Award

in

the

Basic

Pharmacological

Sciences

and

is

an

Assistant

Investigator

of

the

Howard

Hughes

Medical

Institute

April

accepted

September

SCIENCE

VOL

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