Biophysical

Journal

Volume

July

Probing

the

Local

Dynamics

of

Nucleotide-Binding

Pocket

Coupled

to

the

Global

Dynamics

Myosin

versus

Kinesin

Wenjun

Zheng

and

Bernard

R.

Brooks

Laboratory

of

Computational

Biology

National

Heart

Lung

and

Blood

Institute

National

Institutes

of

Health

Bethesda

Maryland

ABSTRACT

Based

on

the

elastic

network

model

we

develop

a

new

analysis

for

protein

complexes

which

probes

the

local

dynamics

of

a

subsystem

that

is

elastically

coupled

to

a

fluctuating

environment

This

method

is

applied

to

a

comparative

dynamical

analysis

of

the

nucleotide-binding

pocket

of

two

motor

proteins

myosins

and

kinesins

In

myosins

the

observed

structural

changes

in

the

nucleotide-pocket

from

the

transition

state

to

the

rigorlike

state

are

dominated

by

the

lowest

normal

mode

that

involves

significant

movements

in

both

switch

I

and

switch

II

in

kinesins

the

measured

conformational

changes

in

the

nucleotide-pocket

are

also

dominated

by

the

lowest

mode

which

however

only

involves

large

movement

in

switch

I

We

then

compute

the

global

structural

changes

induced

by

the

nucleotide-pocket

deformations

as

described

by

the

dominant

pocket-mode

which

yield

encouraging

results

in

myosins

multiple

hinge

motions

involving

the

opening/closing

of

the

cleft

between

the

upper

and

lower

kDa

subdomains

and

the

swinging

movement

of

the

converter

are

induced

which

are

dominated

by

precisely

the

same

global

mode

that

has

been

recently

identified

by

us

as

important

to

the

dynamical

correlations

among

the

nucleotide-pocket

the

actin-binding

site

and

the

converter

in

kinesins

the

induced

global

conformational

changes

are

well

described

by

a

highly

collective

global

mode

which

hints

for

a

dynamical

pathway

spanning

from

the

nucleotide-pocket

to

the

neck-linker

via

the

helix

INTRODUCTION

Motor

proteins

are

specialized

ATPases

that

transport

cargo

by

coordinating

the

ATP

hydrolysis

with

binding

to

and

movement

along

a

filament

They

are

believed

to

be

capable

of

sensing

and

responding

to

the

presence

or

absence

of

a

g-phosphate

and

transmitting

this

information

along

a

pathway

of

increasingly

larger

conformational

changes

that

ultimately

results

in

a

force-generating

event

-LRB-

-RRB-

The

detailed

mechanism

of

force-generation

has

been

actively

investigated

-LRB-

-RRB-

The

two

best-studied

motor

proteins

myosin

and

kinesin

are

dimeric

proteins

that

contain

a

central

core

of

structural

elements

that

are

remarkably

similar

-LRB-

-RRB-

Despite

this

structural

homology

the

kinesin

motors

differ

substantially

from

the

myosins

in

their

mechanism

A

major

difference

is

the

nucleotide-dependent

interactions

of

the

motors

with

their

filament

-LRB-

actin

for

myosins

microtubule

for

kinesins

-RRB-

myosin

bound

to

ATP

is

weakly

bound

to

or

detached

from

actin

whereas

kinesin-ATP

is

strongly

bound

to

microtubules

Conversely

myosin-ADP

is

strongly

bound

to

actin

whereas

kinesin-ADP

is

weakly

bound

to

or

detached

from

microtubules

For

both

motors

the

rate-limiting

step

in

the

ATPase

cycle

is

accelerated

by

its

binding

to

its

filament

which

results

in

a

characteristic

actin

or

microtubuleactivated

ATPase

activity

whereas

binding

of

actin

causes

myosin

to

release

products

the

binding

of

microtubules

enables

hydrolysis

in

kinesin

-LRB-

-RRB-

For

myosins

the

available

crystal

structures

and

cryo-EM

results

capture

their

conformations

in

several

structural

states

with

no

nucleotide

a

transition

state

analog

or

MgADP

Submitted

March

and

accepted

for

publication

April

Address

reprint

requests

to

W.

Zheng

Tel.

E-mail

zhengwj@helix.nih.gov

by

the

Biophysical

Society

bound

to

the

nucleotide-pocket

These

states

include

transition

state

near-rigor

state

detached

state

-LRB-

-RRB-

and

rigorlike

state

-LRB-

-RRB-

The

transition

state

mimics

the

pre-power-stroke

state

compatible

with

ATP

hydrolysis

and

before

actin

binding

The

near-rigor

state

was

initially

proposed

to

reveal

the

position

of

the

lever

arm

at

the

end

of

the

power

stroke

on

release

of

MgADP

however

kinetic

evidence

showed

that

it

can

not

bind

strongly

to

actin

without

significant

structural

rearrangements

-LRB-

-RRB-

So

it

is

now

believed

to

be

a

weak-binding

state

that

occurs

shortly

after

detaching

from

actin

The

detached

state

is

argued

to

be

a

stable

ATP

state

with

unwound

helix

and

unconstrained

converter/lever

arm

-LRB-

-RRB-

The

newly

solved

crystal

structures

of

rigorlike

state

-LRB-

-RRB-

appear

to

resemble

the

strong-binding

state

that

occurs

at

the

end

of

a

power-stroke

For

kinesins

the

structural

states

have

not

been

clearly

defined

by

the

available

structures

Almost

all

the

solved

crystal

structures

are

ADP-bound

-LRB-

except

for

a

structure

-RRB-

Although

the

comparison

of

these

structures

only

revealed

relatively

small

differences

-LRB-

-RRB-

it

helps

to

identify

the

mechanical

elements

that

undergo

conformational

changes

during

the

ATPase

cycle

The

ADP-state

is

believed

to

be

a

weak-binding

state

The

strong-binding

ATP

state

still

eludes

crystallographers

and

may

need

the

binding

of

microtubules

to

stabilize

it

The

nucleotide-binding

pocket

of

both

myosins

and

kinesins

is

comprised

of

four

conserved

pieces

-LRB-

P

loop

-RRB-

-LRB-

switch

I

-RRB-

-LRB-

switch

II

-RRB-

and

-LRB-

base

-RRB-

These

regions

are

strongly

conserved

between

myosins

and

kinesins

However

the

environment

of

their

pocket

is

very

different

in

kinesins

it

is

exposed

on

the

surface

of

the

protein

rather

than

enclosed

between

two

subdomains

of

the

doi

biophysj

Zheng

and

Brooks

protein

as

in

myosins

The

switches

I

and

II

are

g-phosphate

sensors

that

engage

with

phosphate

through

hydrogen

bonding

on

ATP

binding

but

disengage

on

phosphate

release

They

are

believed

to

be

critical

for

transmitting

the

pocket

structural

changes

to

remote

sites

of

motor

proteins

and

trigger

directed

movements

In

myosins

a

salt

bridge

between

the

conserved

arginine

of

switch

I

and

the

conserved

glutamic

acid

of

switch

II

is

believed

to

stabilize

the

closed

conformation

of

myosin

motors

and

to

be

essential

for

nucleotide

hydrolysis

-LRB-

-RRB-

Such

a

salt

bridge

is

also

seen

in

some

kinesin

structures

Yun

and

co-workers

-LRB-

-RRB-

proposed

that

it

is

required

for

activation

of

the

kinesin

motors

by

the

binding

of

microtubules

The

conformational

changes

in

the

nucleotide-pocket

are

observed

to

be

significantly

correlated

with

the

global

conformational

changes

that

are

responsible

for

actin/microtubules

binding

and

ultimately

the

motor

movement

for

myosins

the

switch

I

's

opening/closing

is

associated

with

the

closing/opening

of

the

actin-binding

site

-LRB-

-RRB-

and

the

switch

II

's

opening/closing

is

associated

with

the

downward/upward

swinging

of

the

lever

arm

-LRB-

-RRB-

For

kinesins

a

closed

pocket

-LRB-

ATP-bound

-RRB-

is

associated

with

the

strong-binding

mode

of

the

microtubule-binding

site

and

the

neck-linker

being

docked

to

the

core

domain

-LRB-

-RRB-

Therefore

a

detailed

comparison

of

the

local

dynamics

of

the

nucleotide-binding

pocket

between

myosins

and

kinesins

may

reveal

their

differences

in

the

global

dynamics

that

could

hint

for

different

force-generation

mechanisms

Such

a

comparative

study

is

feasible

because

of

the

following

reasons

first

the

nucleotide-binding

pocket

is

highly

homologous

between

myosins

and

kinesins

so

a

residueto-residue

comparison

is

possible

-LRB-

this

is

not

possible

for

the

whole

motor

domain

which

lacks

such

homology

-RRB-

and

second

the

small

size

of

the

pocket

-LRB-

residues

-RRB-

as

compared

with

the

large

size

of

the

whole

motor

domain

makes

the

analysis

computationally

inexpensive

given

that

the

effective

interactions

of

coupling

between

the

nucleotide-pocket

and

the

rest

of

the

motor

domain

are

modeled

properly

Modeling

the

dynamics

of

motor

proteins

has

been

done

at

a

variety

of

resolution

levels

ranging

from

all-atom

simulations

-LRB-

-RRB-

to

identification

of

rigid-body

motions

of

subunits

during

the

hydrolysis

cycle

-LRB-

-RRB-

Full-scale

molecular

dynamics

studies

of

motor

proteins

with

all

atom

details

are

still

limited

both

by

size

and

by

timescale

The

characterization

of

observed

structural

changes

in

terms

of

rigid-body

motions

of

subunits

while

being

intuitively

appealing

is

limited

by

the

availability

and

relevance

of

crystal

structures

The

normal-modes

analysis

-LRB-

NMA

-RRB-

of

a

highly

simplified

elastic

network

model

-LRB-

ENM

-RRB-

has

been

successfully

applied

to

the

analysis

of

large-scale

protein

conformational

changes

in

several

studies

-LRB-

-RRB-

It

has

been

recently

applied

to

the

study

of

motor

proteins

-LRB-

-RRB-

In

a

recent

work

by

one

of

us

the

ENM

is

used

to

explore

the

global

conformational

changes

induced

by

deforming

the

nucleotide-binding

pocket

in

several

motor

proteins

and

interesting

differences

were

found

between

kinesins

and

myosins

in

terms

of

the

Biophysical

Journal

-LRB-

-RRB-

number

of

normal

modes

needed

for

describing

the

measured

conformational

changes

-LRB-

-RRB-

Motivated

by

these

preliminary

results

we

further

expand

and

test

this

idea

in

this

work

The

ENM

assumes

elastic

couplings

between

the

nucleotide-pocket

and

the

remaining

parts

of

the

motor

domain

-LRB-

as

environment

-RRB-

and

the

impact

of

such

elastic

couplings

on

the

local

dynamics

of

the

pocket

can

be

quantitatively

analyzed

by

effectively

integrating

out

the

environment

degrees

of

freedom

-LRB-

see

Materials

and

Methods

-RRB-

The

remaining

pocket

degrees

of

freedom

are

coupled

by

quadratic

interactions

that

include

both

direct

elastic

interactions

and

indirect

interactions

via

their

couplings

with

the

environment

The

NMA

of

this

subsystem

yields

various

modes

of

movements

to

describe

the

local

dynamics

of

the

pocket

which

can

be

validated

by

comparing

with

crystallographic

data

Furthermore

given

the

pocket

structural

change

described

by

each

pocket-mode

we

can

analyze

the

global

dynamics

coupled

to

it

by

calculating

the

global

conformational

changes

it

induces

-LRB-

-RRB-

which

helps

to

identify

plausible

dynamical

pathways

that

transmit

the

pocket

deformations

to

the

remote

parts

of

the

motor

domain

MATERIALS

AND

METHODS

Elastic

network

model

Given

the

Ca

atomic

coordinates

for

a

protein

's

native

structure

we

build

an

elastic

network

model

by

using

a

harmonic

potential

with

a

single

force

constant

C

to

account

for

pairwise

interactions

between

all

Ca

atoms

that

are

within

a

cutoff

distance

-LRB-

RC

A

-RRB-

The

energy

in

the

elastic

network

representation

of

a

protein

is

Enetwork

C

dij

dij

R

ij

c

-LRB-

-RRB-

where

dij

is

the

distance

between

the

dynamical

coordinates

of

the

Ca

atoms

i

and

j

and

dij

is

the

distance

between

Ca

atoms

i

and

j

as

given

in

the

crystal

structure

For

the

harmonic

Hamiltonian

in

Eq

we

perform

the

standard

normalmodes

analysis

-LRB-

NMA

-RRB-

After

excluding

the

six

zero-modes

corresponding

to

three

translations

and

three

rotations

the

non-zero

modes

start

from

and

the

mode

number

increases

as

the

mode

's

eigenvalue

increases

The

eigenvectors

of

the

lowest

frequency

normal

modes

are

used

to

interpret

the

protein

conformational

observed

crystallographically

-LRB-

-RRB-

The

drastic

simplification

of

representing

the

complex

protein

structure

by

an

effective

harmonic

potential

is

justified

by

a

study

by

Tirion

-LRB-

-RRB-

who

showed

that

the

use

of

a

single

spring

constant

reproduces

the

slow

dynamics

computed

from

the

normal

modes

analysis

of

all-atom

potentials

Hinsen

further

simplified

the

elastic

network

model

to

the

Ca

only

representation

-LRB-

-RRB-

Normal

mode

analysis

-LRB-

NMA

-RRB-

of

a

subsystem

coupled

to

a

flexible

environment

The

whole

protein

complex

modeled

as

a

Ca-only

elastic

network

is

divided

into

two

components

the

subsystem

which

consists

of

residues

-LRB-

Cas

-RRB-

directly

involved

in

the

functionality

-LRB-

for

example

catalytic

activity

or

ligand

binding

-RRB-

and

the

environment

which

consists

of

the

remaining

residues

We

wish

to

study

the

impact

of

the

elastic

couplings

between

the

above

two

components

on

the

local

dynamics

of

the

subsystem

Nucleotide-Pocket

Dynamics

of

Myosin

and

Kinesin

Suppose

the

elastic

energy

of

the

whole

ENM

is

given

as

follows

coordinate

root-mean-square

deviation

i.e.

RMSD

-RRB-

the

pocket

conformation

of

every

myosin/kinesin

structure

with

the

pocket

conformation

of

a

chosen

reference

structure

by

rotations

and

translations

E

xHx

xs

Hss

xs

xs

Hse

xe

xe

Hes

xs

xe

Hee

xe

Hss

Hes

Hse

Hee

-LRB-

-RRB-

where

H

stands

for

the

Hessian

matrix

of

the

ENM

which

consists

of

four

submatrices

-LRB-

Hss

Hse

Hes

Hee

-RRB-

-LRB-

s

subsystem

e

environment

-RRB-

xs

-LRB-

xe

-RRB-

is

the

displacement

vector

for

the

subsystem

-LRB-

environment

-RRB-

To

integrate

out

the

environment

degrees

of

freedom

we

set

the

gradient

xe

E

which

gives

Comparison

of

normal

modes

with

measured

structural

changes

at

the

nucleotide-pocket

Given

a

reference

structure

of

the

nucleotide-pocket

and

the

pocket-modes

we

can

project

the

measured

pocket

structural

changes

to

individual

modes

to

find

the

relevant

mode

with

significant

overlap

-LRB-

defined

as

the

generalized

cosine

between

the

mode

's

eigenvector

and

the

measured

structural

displacement

see

Ref

-RRB-

This

serves

as

a

mode-specific

test

of

the

quality

of

subsystem

NMA

in

describing

the

measured

structural

changes

-LRB-

in

both

amplitude

and

direction

-RRB-

xe

Hee

Hes

xs

Therefore

eff

E

xs

Hss

xs

xs

Hss

Hse

Hee

Hes

xs

-LRB-

-RRB-

-LRB-

-RRB-

Physically

it

is

assumed

that

the

environment

can

respond

to

the

structural

changes

in

the

subsystem

by

minimizing

the

total

energy

We

note

that

the

idea

of

partitioning

the

Hessian

matrix

into

relevant

and

irrelevant

parts

through

the

use

of

an

appropriate

unitary

transformation

was

discussed

before

by

one

of

us

-LRB-

-RRB-

For

comparison

we

can

turn

off

the

couplings

and

the

elastic

energy

of

the

isolated

subsystem

becomes

Principal

components

analysis

-LRB-

PCA

-RRB-

For

a

given

reference

pocket

structure

and

a

set

of

pocket

structures

we

do

principal

component

analysis

-LRB-

quasiharmonic

analysis

see

Ref

-RRB-

to

find

the

directions

in

configuration

space

that

best

describe

the

dominant

structural

displacements

observed

among

the

nucleotide-pocket

structures

It

consists

of

diagonalization

of

the

covariance

matrix

of

Ca

fluctuations

after

removal

of

overall

translation

and

rotation

Resulting

eigenvectors

are

directions

in

configuration

space

that

represent

collective

motions

Corresponding

eigenvalues

define

the

mean

square

fluctuation

of

the

motion

along

these

vectors

We

will

keep

the

top

two

eigenvectors

-LRB-

and

-RRB-

which

capture

the

two

most

dominant

structural

displacements

of

the

nucleotidebinding

pocket

Then

we

cluster

all

pocket

conformations

in

a

two-dimensional

plot

where

the

two-dimensional

coordinate

consists

of

the

projection

coefficients

obtained

by

projecting

the

structural

changes

from

the

reference

pocket

structure

to

and

Finally

we

calculate

the

overlap

-LRB-

see

Ref

-RRB-

of

and

with

each

pocket-mode

to

test

how

good

a

single

mode

describes

them

E

xs

Hss

xs

-LRB-

-RRB-

where

Hss

has

the

same

off-diagonal

matrix

elements

as

Hss

but

its

diagonal

elements

are

given

by

requiring

the

sum

of

each

row/column

to

be

zero

Standard

NMA

can

be

performed

for

the

harmonic

subsystem

described

by

Eq

The

eigenvectors

of

the

low-frequency

modes

-LRB-

excluding

the

six

zero-modes

-RRB-

can

be

compared

with

the

crystallographically

measured

conformational

changes

of

the

subsystem

to

assess

their

relevance

to

the

observed

structural

changes

We

can

also

compute

the

global

conformational

changes

induced

by

the

local

structural

changes

in

the

subsystem

as

given

in

Eq

which

establishes

an

important

link

between

the

local

dynamics

of

the

subsystem

and

global

dynamics

of

the

whole

protein

complex

This

allows

us

to

probe

the

dynamical

pathway

by

which

global

conformational

changes

are

triggered

by

local

deformations

of

the

subsystem

Dynamical

domains

partition

We

use

a

computational

tool

DynDom

developed

by

Hayward

-LRB-

-RRB-

for

dynamical

domains

analysis

to

analyze

the

interdomain

conformational

changes

described

by

each

global

mode

-LRB-

it

is

downloadable

from

http

-RRB-

Application

to

the

nucleotide-pocket

of

myosins

and

kinesins

Here

we

define

the

subsystem

as

the

nucleotide-binding

pocket

-LRB-

consisting

of

four

pieces

-RRB-

It

is

highly

homologous

among

all

myosins

and

kinesins

so

it

can

be

structurally

aligned

among

different

kinesins

and

myosins

The

subsystem

NMA

can

probe

the

local

dynamics

of

the

nucleotide-pocket

elastically

coupled

to

the

remaining

parts

of

the

motor

proteins

and

thereby

the

global

dynamics

coupled

with

the

local

dynamics

Crystal

structures

of

myosins

and

kinesins

The

information

of

the

crystal

structures

studied

in

this

work

is

summarized

in

Table

Calculation

of

root-mean-square

fluctuation

-LRB-

RMSF

-RRB-

Based

on

the

NMA

of

the

ENM

we

can

compute

the

root-mean-square

fluctuation

-LRB-

RMSF

-RRB-

at

position

i

-LRB-

the

Ca

position

of

residue

i

-RRB-

as

RESULTS

AND

DISCUSSION

We

will

start

with

the

analysis

of

myosins

nucleotide-pocket

dynamics

and

the

global

dynamics

it

is

coupled

to

which

is

followed

by

the

same

analysis

for

kinesins

accompanied

by

a

detailed

comparison

between

them

Myosin

's

nucleotide-pocket

dynamics

Principal

components

analysis

of

nucleotide-pocket

conformations

from

crystal

structures

qffiffiffiffiffiffiffiffiffiffi

fi

dri

-RCB-

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

vm

ia

m

a

x

y

z

lm

-LRB-

-RRB-

where

lm

and

nm

are

the

eigenvalue

and

the

eigenvector

of

mode

m

solved

eff

from

the

NMA

of

Hss

as

described

in

Eq

The

six

zero-modes

are

excluded

For

simplification

in

notation

a

uniform

factor

of

T/C

is

omitted

in

Eq

-LRB-

T

is

the

temperature

C

is

the

force

constant

in

Eq

-RRB-

We

use

Eq

to

compute

the

RMSF

per

residue

for

the

nucleotide-pocket

For

comparison

with

the

RMSF

results

we

structurally

align

-LRB-

with

minimal

We

start

with

a

principal

components

analysis

-LRB-

PCA

-RRB-

of

all

the

nucleotide-pocket

conformations

from

myosin

crystal

Biophysical

Journal

-LRB-

-RRB-

TABLE

Information

of

crystal

structures

for

myosins

and

kinesins

Name

Source

Mus

musculus

PDB

code

-LRB-

state

or

ligand

-RRB-

-LRB-

-RRB-

-LRB-

ADP-MG-ALFX

-RRB-

-LRB-

MG-ADP

-RRB-

-LRB-

MG-AMPPCP

-RRB-

-LRB-

dimer

-RRB-

and

its

mutants

-LRB-

N

-RRB-

-LRB-

T

-RRB-

-LRB-

R

-RRB-

-LRB-

N

-RRB-

-LRB-

N

-RRB-

-LRB-

N

-RRB-

-LRB-

N

-RRB-

-LRB-

N

-RRB-

-LRB-

N

-RRB-

-LRB-

T

-RRB-

-LRB-

N

-RRB-

-LRB-

T

-RRB-

and

-LRB-

D

-RRB-

and

-LRB-

N

-RRB-

-LRB-

D

-RRB-

-LRB-

T

-RRB-

-LRB-

T

-RRB-

-LRB-

T

-RRB-

-LRB-

N

-RRB-

-LRB-

R

-RRB-

-LRB-

T

-RRB-

Zheng

and

Brooks

Ncd

Ubiquitous

Kinesin

Kinesin

Fast

Kinesin

Internal

Kinesin

Myosin

II

Drosophila

melanogaster

Homo

sapiens

Rattus

norvegicus

Saccharomyces

cerevisiae

Neurospora

crassa

Homo

sapiens

Plasmodium

falciparum

Dictyostelium

discoideum

Scallop

Myosin

II

Argopecten

irradians

Smooth

muscle

myosin

Myosin

II

Myosin

V

MyoE

-LRB-

class

I

-RRB-

Gallus

gallus

Gallus

gallus

Gallus

gallus

Dictyostelium

discoideum

Myosin

states

are

T

transition

N

near-rigor

R

rigorlike

and

D

detached

We

only

keep

kinesin/myosin

structures

with

complete

coordinates

for

all

residues

in

the

nucleotide-pocket

FIGURE

Two-dimensional

clustering

of

the

nucleotide-pocket

conformations

for

-LRB-

a

-RRB-

myosins

with

reference

to

and

-LRB-

b

-RRB-

kinesins

with

reference

to

by

using

the

top

two

components

obtained

from

PCA

For

myosins

three

clusters

are

found

cluster

-LRB-

-RRB-

cluster

-LRB-

-RRB-

and

cluster

-LRB-

the

remaining

structures

-RRB-

For

kinesins

one

main

cluster

-LRB-

-RRB-

is

found

whereas

the

rest

are

not

well-clustered

-LRB-

-RRB-

For

clarity

only

some

of

the

PDB

names

are

marked

in

the

figure

structures

-LRB-

in

total

-RRB-

The

goal

is

twofold

first

to

identify

the

dominant

conformational

changes

among

them

and

second

to

cluster

those

pocket

conformations

-LRB-

see

Materials

and

Methods

-RRB-

The

PCA

is

performed

with

reference

to

a

transition

state

structure

-LRB-

PDB

-RRB-

The

observed

structural

changes

of

the

nucleotide-pocket

are

dominated

by

the

top

two

principal

components

and

which

are

used

to

cluster

those

conformations

in

a

twodimensional

plot

each

pocket

conformation

is

represented

by

two

projection

coefficients

obtained

by

projecting

the

conformational

changes

from

the

reference

structure

onto

and

-LRB-

see

Materials

and

Methods

-RRB-

Not

surprisingly

they

fall

into

two

main

clusters

corresponding

to

the

transition

state

and

the

near-rigor/detached

state

and

two

outliers

-LRB-

PDB

and

-RRB-

belonging

to

the

rigorlike

state

-LRB-

Fig.

a

-RRB-

This

is

consistent

with

the

classification

of

structural

states

-LRB-

-RRB-

and

it

supports

the

strong

correlation

between

the

nucleotide-pocket

conformation

and

the

global

conformation

of

the

myosin

motor

domain

and

justifies

the

validity

of

Biophysical

Journal

-LRB-

-RRB-

studying

the

pocket

dynamics

as

an

indirect

means

to

probe

the

global

dynamics

The

structural

changes

described

by

are

dominated

by

a

very

large

movement

of

the

switch

II

-LRB-

Fig.

a

-RRB-

which

is

observed

when

one

does

structural

comparison

between

the

near-rigor

state

structures

and

the

transition

state

structures

Historically

the

near-rigor

state

was

proposed

to

be

reached

at

the

end

of

a

power

stroke

on

release

of

MgADP

however

kinetic

evidence

showed

that

it

can

not

bind

strongly

to

actin

without

significant

structural

rearrangements

-LRB-

-RRB-

Therefore

the

near-rigor

state

is

probably

reached

from

the

strongbinding

rigor

state

instead

of

the

transition

state

during

the

working

cycle

So

a

direct

transition

from

transition

state

to

Nucleotide-Pocket

Dynamics

of

Myosin

and

Kinesin

near-rigor

state

is

probably

not

relevant

to

the

power-stroke

mechanism

The

structural

changes

described

by

simultaneously

involve

large

movements

of

P

loop

switch

I

and

switch

II

-LRB-

Fig.

b

-RRB-

This

largely

accounts

for

the

transition

from

the

transition

state

-LRB-

PDB

-RRB-

to

the

rigorlike

state

-LRB-

PDB

-RRB-

which

involves

the

opening

of

both

switch

I

and

switch

II

As

observed

by

Coureux

and

co-workers

-LRB-

-RRB-

in

the

P

loop

and

switch

I

move

apart

by

A

-LRB-

P

loop

was

used

for

structural

alignment

so

its

movement

was

not

reported

-RRB-

a

new

conformation

for

switch

II

is

stabilized

by

new

interactions

and

switch

I

conformation

follows

the

movement

of

the

upper

subdomain

relative

to

the

P

loop

and

the

N-terminal

subdomain

Similar

pocket

changes

were

observed

in

another

rigorlike

structure

-LRB-

-RRB-

in

particular

the

opening

of

switch

I

and

the

further

opening

of

switch

II

in

the

near-rigor

structure

-LRB-

PDB

-RRB-

A

transition

from

the

weak-binding

transition

state

to

the

strong-binding

rigor

state

is

believed

to

be

critical

to

the

power-stroke

generation

-LRB-

-RRB-

Effects

of

elastic

coupling

between

nucleotide-pocket

and

its

environment

We

now

examine

the

effects

of

the

elastic

coupling

between

the

nucleotide-pocket

and

its

environment

on

the

local

dynamics

of

the

pocket

We

compute

the

root-mean-square

fluctuation

-LRB-

RMSF

-RRB-

-LRB-

see

Eq

-RRB-

based

on

the

subsystem

NMA

of

the

nucleotide-pocket

in

the

absence

and

presence

of

the

elastic

coupling

respectively

-LRB-

Fig.

a

-RRB-

We

find

that

the

coupling

to

the

environment

significantly

suppresses

the

overall

RMSF

-LRB-

especially

in

that

the

two

major

peaks

in

switch

I

and

at

zero

coupling

are

sharply

reduced

-RRB-

In

the

RMSF

plot

-LRB-

Fig.

a

-RRB-

major

peaks

are

found

in

switch

I

-LRB-

peaked

at

its

N-terminal

-RRB-

switch

II

-LRB-

peaked

at

its

C-terminal

-RRB-

and

-LRB-

peaked

at

its

C-terminal

-RRB-

This

suggests

that

the

coupling

with

the

environment

significantly

affects

the

local

dynamics

of

the

nucleotide-pocket

by

sharply

reducing

its

fluctuation

nonuniformly

Comparison

of

the

measured

RMSD

with

the

computed

RMSF

in

the

nucleotide-pocket

FIGURE

Computed

RMSF

based

on

the

subsystem

NMA

for

-LRB-

a

-RRB-

-LRB-

b

-RRB-

The

line

with

plus

symbols

is

the

RMSF

at

zero

coupling

the

other

two

are

the

RMSF

in

the

presence

of

elastic

couplings

-LRB-

line

with

x-marks

indicates

real-scale

line

with

stars

indicates

rescaled

for

clarity

-RRB-

The

ranges

of

the

four

pieces

-LRB-

is

switch

I

is

switch

II

-RRB-

of

the

nucleotide-pocket

are

marked

For

comparison

we

structurally

align

the

pocket

conformation

of

every

myosin

structure

with

the

pocket

conformation

of

a

chosen

reference

structure

-LRB-

PDB

-RRB-

then

we

plot

the

RMSD

at

each

residue

in

the

pocket

-LRB-

Fig.

a

-RRB-

This

gives

the

measured

amplitude

of

conformational

changes

in

the

pocket

which

can

be

qualitatively

compared

with

the

RMSF

to

examine

if

the

latter

captures

the

observed

structure

changes

in

amplitude

namely

do

major

peaks

in

the

RMSD

match

with

the

peaks

in

RMSF

The

RMSD

plot

shows

two

interesting

features

first

large-scale

movement

in

switch

II

dominates

the

RMSD

for

pairs

between

the

transition

state

and

the

near-rigor

or

detached

state

second

several

large-scale

structural

changes

in

switches

I

II

and

P

loop

are

observed

for

pairs

between

the

transition

state

and

the

rigorlike

state

These

observations

are

also

consistent

with

the

two

principal

components

and

obtained

by

PCA

-LRB-

see

above

-RRB-

The

RMSF

shows

large

fluctuation

in

switches

I

II

and

which

is

largely

consistent

with

the

RMSD

results

-LRB-

Fig.

b

-RRB-

first

the

large

structural

changes

in

switch

I

-LRB-

peaked

at

its

N-terminal

-RRB-

and

switch

II

-LRB-

peaked

at

its

C-terminal

-RRB-

as

shown

in

the

RMSD

plot

are

qualitatively

consistent

with

similar

peaks

in

the

RMSF

plot

second

the

peak

in

P

loop

is

also

seen

at

its

third

residue

in

the

RMSF

plot

although

it

is

lower

than

in

the

RMSD

plot

and

third

the

peak

in

appears

to

be

higher

in

the

RMSF

plot

than

in

the

RMSD

plot

We

note

that

the

differences

between

the

RMSD

and

RMSF

-LRB-

in

the

P

loop

and

-RRB-

may

be

due

to

the

oversimplification

of

ENM

parameterization

and

the

lack

of

consideration

of

the

interaction

with

ligand

Despite

this

limitation

the

large

fluctuations

in

both

switch

I

and

II

are

captured

by

the

present

analysis

which

may

be

important

to

the

myosin

motor

function

Biophysical

Journal

-LRB-

-RRB-

Zheng

and

Brooks

FIGURE

Comparison

of

the

measured

RMSD

with

the

computed

RMSF

-LRB-

a

-RRB-

RMSD

with

respect

to

-LRB-

b

-RRB-

computed

RMSF

for

myosin

nucleotide-pockets

-LRB-

c

-RRB-

RMSD

with

respect

to

and

-LRB-

d

-RRB-

computed

RMSF

for

kinesin

nucleotide-pockets

The

ranges

of

the

four

pieces

-LRB-

is

switch

I

is

switch

II

-RRB-

of

the

nucleotide-pocket

are

marked

Comparison

of

pocket-modes

with

measured

conformational

changes

We

now

examine

if

individual

normal

modes

can

describe

the

observed

conformational

changes

in

the

nucleotide-pocket

We

examine

all

measured

conformational

changes

from

the

reference

pocket

structure

-LRB-

PDB

-RRB-

and

project

them

to

each

pocket-mode

solved

from

the

subsystem

NMA

Interestingly

we

find

that

the

pocket

structural

changes

from

the

transition

state

-LRB-

PDB

-RRB-

to

the

rigorlike

state

-LRB-

PDB

-RRB-

are

dominated

by

the

lowest

non-zero

mode

with

overlap

meanwhile

the

pocket

conformational

changes

from

to

the

near-rigor

state

-LRB-

PDB

-RRB-

are

not

dominated

by

any

single

mode

-LRB-

the

highest

overlap

is

with

mode

-RRB-

Similarly

we

can

also

compare

the

normal

modes

with

the

two

principal

components

and

obtained

from

PCA

-LRB-

see

above

-RRB-

We

find

similar

results

overlaps

significantly

with

mode

-LRB-

overlap

see

Fig.

b

-RRB-

whereas

is

not

dominated

by

any

single

mode

-LRB-

the

highest

overlap

is

with

mode

see

Fig.

a

-RRB-

A

comparison

between

and

mode

indicates

-LRB-

Fig.

b

-RRB-

mode

involves

large-scale

movement

in

switches

I

II

and

-LRB-

Fig.

b

-RRB-

and

it

gives

a

good

description

of

the

switch

I

and

switch

II

movement

in

although

the

movement

is

overestimated

and

the

P

loop

movement

is

underestimated

In

summary

the

observed

pocket

structural

changes

described

by

are

better

accounted

for

by

a

single

mode

than

the

one

described

by

especially

in

switch

I

and

II

This

suggests

that

a

coordinated

movement

of

both

switches

Biophysical

Journal

-LRB-

-RRB-

with

comparable

amplitude

is

dynamically

prone

to

occur

-LRB-

involving

mainly

a

single

mode

-RRB-

with

a

low-energy

barrier

whereas

the

movement

by

switch

II

alone

-LRB-

as

described

by

-RRB-

is

dynamically

more

complex

-LRB-

involving

multiple

modes

-RRB-

and

energetically

less

favorable

Global

conformational

changes

beyond

the

nucleotide-pocket

In

response

to

the

pocket

deformation

described

by

the

relevant

mode

the

subdomains

-LRB-

environment

-RRB-

around

the

pocket

will

move

accordingly

to

relax

the

strain

caused

by

the

pocket

structural

changes

We

can

calculate

the

global

conformational

changes

induced

by

the

pocket

deformation

-LRB-

see

Materials

and

Methods

-RRB-

and

project

it

to

the

low-frequency

global

modes

to

identify

the

modes

of

global

motions

induced

by

the

pocket

deformation

We

find

the

dominant

non-zero

mode

to

be

mode

-LRB-

overlap

if

excluding

six

zero-modes

-RRB-

which

was

recently

identified

as

the

dominant

mode

in

the

dynamical

correlations

among

three

functionally

critical

regions

-LRB-

the

cleft

between

the

upper

and

lower

subdomains

the

nucleotide-binding

pocket

and

the

converter

-RRB-

-LRB-

-RRB-

it

involves

simultaneous

hinge

motions

of

the

opening/closing

of

the

cleft

and

the

swinging

motion

of

the

converter

and

the

nucleotide-pocket

lies

at

its

hinge

region

-LRB-

Fig.

a

-RRB-

Therefore

the

relevant

pocket-mode

involved

in

the

local

dynamics

-LRB-

-RRB-

is

consistent

with

the

relevant

global

mode

involved

in

the

global

dynamics

-LRB-

-RRB-

in

that

the

former

can

effectively

trigger

the

latter

via

elastic

couplings

in

the

Nucleotide-Pocket

Dynamics

of

Myosin

and

Kinesin

FIGURE

Comparison

of

the

top

two

principal

components

with

the

eigenvector

of

the

dominant

pocketmode

-LRB-

a

-RRB-

First

principal

component

of

myosin

pockets

and

-LRB-

b

-RRB-

second

principal

component

of

myosin

pockets

-LRB-

c

-RRB-

First

principal

component

of

kinesin

pockets

and

-LRB-

d

-RRB-

second

principal

component

of

kinesin

pockets

Top

panel

compares

the

amplitude

whereas

the

bottom

panel

plots

the

cosine

of

the

angle

between

them

The

ranges

of

the

four

pieces

-LRB-

is

switch

I

is

switch

II

-RRB-

of

the

nucleotide-pocket

are

marked

framework

of

ENM

This

strongly

supports

the

existence

of

a

dynamical

pathway

that

transmits

the

small

deformation

at

the

nucleotide-pocket

to

the

remote

sites

of

the

myosin

motor

to

ultimately

trigger

global

motions

that

modulate

the

actinbinding

and

cause

motor

movement

This

pathway

is

clearly

revealed

by

the

present

analysis

where

the

elastic

coupling

plays

a

key

role

in

mediating

the

connection

between

the

local

dynamics

of

the

nucleotide-pocket

and

the

global

dynamics

of

the

whole

motor

Kinesin

's

nucleotide-pocket

dynamics

Comparison

of

nucleotide-pocket

conformations

between

kinesins

and

myosins

Although

myosins

and

kinesins

have

a

highly

homologous

nucleotide-binding

pocket

they

differ

significantly

in

pocket

conformation

as

revealed

by

crystallographic

studies

All

kinesins

show

a

tightly

closed

pocket

in

the

ADP

state

-LRB-

as

defined

by

P

loop-switch

II

distance

see

Ref

-RRB-

comparable

with

myosins

in

the

ATP

state

-LRB-

transition

state

-RRB-

In

contrast

switch

I

in

kinesins

is

essentially

open

although

it

is

closed

in

all

except

the

rigorlike

state

in

myosins

-LRB-

-RRB-

Evidence

from

electron

paramagnetic

resonance

shows

that

switch

I

closes

when

kinesin

binds

to

microtubules

-LRB-

-RRB-

which

is

opposite

to

the

observation

that

switch

I

opens

when

myosin

binds

to

actin

-LRB-

-RRB-

The

extent

of

openness

in

switch

I

differs

quantitatively

among

different

kinesin

structures

As

proposed

by

Song

and

co-workers

-LRB-

-RRB-

the

distance

from

the

conserved

N

of

switch

I

to

the

conserved

G

of

P

loop

is

used

to

assess

the

pocket

openness

In

PDB

structure

those

two

residues

-LRB-

and

-RRB-

are

A

apart

making

the

nucleotide-binding

pocket

very

widely

open

consistent

with

the

largest

RMSD

at

the

N-terminal

end

of

switch

I

observed

for

pair

Journal

-LRB-

-RRB-

Zheng

and

Brooks

FIGURE

Dynamical

domains

partition

for

the

global

modes

triggered

by

the

pocket

deformation

described

by

the

relevant

pocket-mode

-LRB-

a

-RRB-

Global

mode

of

describes

the

following

hinge

motions

Opening/closing

of

the

upper

subdomain

-LRB-

blue

-RRB-

versus

the

lower

subdomain

-LRB-

red

-RRB-

flipping

of

a

part

of

N-terminal

subdomain

-LRB-

yellow

-RRB-

rotation

of

converter

-LRB-

violet

-RRB-

-LRB-

b

-RRB-

The

nucleotide-pocket

conformational

changes

described

by

the

pocketmode

of

myosin

-LRB-

c

-RRB-

Global

mode

of

describes

the

following

hinge

motions

switch

I

-LRB-

cyan

-RRB-

flipping

loop

-LRB-

black

-RRB-

flipping

flipping

of

the

region

-LRB-

purple

-RRB-

tip

loops

-LRB-

and

violet

-RRB-

flipping

and

the

twisting

motion

of

the

compact

subdomain

including

helix

-LRB-

yellow

-RRB-

-LRB-

d

-RRB-

The

nucleotide-pocket

conformational

changes

described

by

the

pocket-mode

of

kinesin

In

a

and

c

the

nucleotide-pocket

residues

are

shown

as

solid

circles

-LRB-

four

levels

of

grayscale

from

dark

to

light

for

and

respectively

-RRB-

In

b

and

d

the

colors

blue

green

red

and

yellow

are

for

and

respectively

and

the

gray

trace

represents

the

pocket

conformation

after

the

displacement

The

partition

of

dynamical

domains

-LRB-

distinguished

by

different

colors

-RRB-

is

done

by

DynDom

The

hinge/bending

regions

are

colored

by

green

The

rotation

axis

for

each

pairwise

interdomain

motion

is

shown

as

an

axis

with

an

arrowhead

the

color

of

the

axis

stem

is

set

to

be

the

same

as

the

domain

fixed

for

the

structural

alignment

whereas

the

color

of

the

arrowhead

is

set

to

be

the

color

of

the

moving

domain

Biophysical

Journal

-LRB-

-RRB-

Nucleotide-Pocket

Dynamics

of

Myosin

and

Kinesin

-LRB-

Fig.

c

-RRB-

for

PDB

structure

the

corresponding

distance

-LRB-

between

and

-RRB-

is

only

A

The

narrowest

pocket

is

seen

in

PDB

structure

where

the

bulge

loop

tightens

the

entrance

of

the

active

site

further

The

switch

I

undergoes

other

large

structural

changes

too

-LRB-

in

PDB

structure

for

example

-RRB-

The

sharply

different

conformations

of

switch

I

in

kinesins

from

those

in

myosins

may

hint

for

its

different

functional

roles

Comparison

of

measured

RMSD

with

computed

RMSF

in

the

nucleotide-pocket

Principal

components

analysis

of

nucleotide-pocket

conformations

from

crystal

structures

Similar

to

the

analysis

of

myosins

we

perform

a

PCA

for

all

the

pocket

conformations

from

the

available

kinesin

structures

-LRB-

in

total

-RRB-

The

PCA

is

with

reference

to

an

ADP

state

structure

-LRB-

PDB

-RRB-

The

observed

structural

changes

in

the

nucleotide-pocket

are

dominated

by

the

top

two

principal

components

and

which

are

used

to

cluster

the

pocket

conformations

in

a

two-dimensional

plot

-LRB-

Fig.

b

-RRB-

Unlike

myosins

they

form

one

main

cluster

and

the

rest

are

spread

out

-LRB-

Fig.

b

-RRB-

This

is

consistent

with

the

lack

of

a

clear

classification

of

kinesin

structures

The

structural

changes

described

by

are

dominated

by

large

switch

I

movement

-LRB-

peaked

at

its

N-terminal

see

Fig.

c

-RRB-

which

largely

accounts

for

the

switch

I

opening

observed

in

for

example

the

conformational

changes

between

the

pair

-LRB-

-RRB-

The

structural

changes

described

by

are

also

dominated

by

large

switch

I

movement

-LRB-

peaked

at

its

second

residue

see

Fig.

d

-RRB-

which

mainly

accounts

for

the

switch

I

structural

changes

observed

in

the

conformational

changes

between

the

pair

-LRB-

-RRB-

In

-LRB-

an

ATP-like

structure

of

motor

complexed

with

AMP

PCP

see

Ref

-RRB-

switch

I

assumes

a

substantially

different

conformation

a

pseudo-b-hairpin

rather

than

a

short

loop-helixloop

as

observed

in

other

kinesin

structures

It

is

interesting

that

unlike

myosins

both

and

describe

large

structural

changes

in

switch

I

whereas

the

other

parts

including

switch

II

move

much

less

in

amplitude

The

RMSD

plot

shows

that

the

large-scale

structural

change

in

switch

I

-LRB-

peaked

at

its

N-terminal

-RRB-

dominates

the

RMSD

for

all

pairs

-LRB-

Fig.

c

-RRB-

This

is

consistent

from

the

two

principal

components

obtained

by

PCA

-LRB-

see

above

-RRB-

The

structural

comparison

study

in

Sack

et

al.

-LRB-

-RRB-

also

identified

the

switch

I

loop

-LRB-

region

-RRB-

as

the

largest

main-chain

deviations

which

primarily

consist

of

bending

of

helix

at

its

C-terminal

end

-LRB-

or

N-terminal

end

of

switch

I

loop

-RRB-

Consistent

with

the

RMSD

results

the

RMSF

also

shows

a

dominantly

large

fluctuation

in

switch

I

-LRB-

Fig.

d

-RRB-

Unlike

myosins

where

switch

I

and

switch

II

have

comparable

RMSF

switch

II

movement

is

relatively

weak

in

kinesins

The

observation

of

closed

switch

II

and

open

switch

I

in

kinesins

may

explain

the

significantly

enhanced

reduced

RMSF

of

switch

I/switch

II

in

kinesins

as

compared

with

myosins

Since

microtubule-binding

sites

are

closer

to

switch

II

than

switch

I

we

expect

such

disparity

between

them

to

persist

upon

binding

with

microtubules

which

probably

has

a

stronger

restraining

effect

on

switch

II

than

switch

I.

Comparison

of

pocket-modes

with

measured

conformational

changes

We

now

assess

how

well

the

pocket-modes

describe

the

observed

conformational

changes

of

the

nucleotide-pocket

We

examine

all

individual

conformational

changes

from

the

reference

pocket

structure

-LRB-

PDB

-RRB-

and

compare

them

with

the

pocket-modes

solved

from

the

subsystem

NMA

Similar

to

myosins

we

find

that

these

pocket

structural

changes

are

dominated

by

the

lowest

non-zero

mode

-LRB-

-RRB-

with

significant

overlap

-LRB-

Table

-RRB-

Then

we

compare

the

above

relevant

mode

with

the

two

principal

components

and

obtained

from

PCA

Both

and

overlap

significantly

with

mode

-LRB-

Table

-RRB-

TABLE

Results

of

comparing

the

subsystem

normal

modes

with

the

measured

structural

changes

in

the

nucleotide-pocket

of

myosins

-LRB-

upper

row

-RRB-

and

kinesins

-LRB-

lower

row

-RRB-

Pair

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

Mode

Overlap

Effects

of

elastic

coupling

between

nucleotide-pocket

and

its

environment

We

now

compute

the

RMSF

for

the

nucleotide-pocket

in

the

absence

and

presence

of

the

elastic

couplings

respectively

-LRB-

Fig.

b

-RRB-

Similar

to

myosins

the

coupling

to

the

environment

significantly

suppresses

the

overall

RMSF

-LRB-

especially

the

two

major

peaks

in

switch

I

and

are

sharply

reduced

-RRB-

one

dominant

peak

is

found

in

switch

I

-LRB-

peaked

at

its

N-terminal

-RRB-

with

several

much

lower

peaks

in

the

P

loop

switch

II

and

Unlike

in

myosins

the

RMSF

in

switch

I

is

suppressed

less

significantly

in

kinesins

so

it

becomes

the

dominant

peak

that

is

much

higher

than

the

others

Biophysical

Journal

-LRB-

-RRB-

Zheng

and

Brooks

A

detailed

comparison

between

and

mode

indicates

mode

involves

large-scale

movement

in

switch

I

-LRB-

peaked

at

its

N-terminal

see

Fig.

d

-RRB-

and

it

gives

a

good

description

of

the

switch

I

movement

in

both

and

-LRB-

Fig.

c

and

d

-RRB-

To

summarize

the

observed

pocket

structural

changes

are

well

described

by

a

single

mode

which

is

dominated

by

a

large

movement

in

switch

I

suggesting

that

a

large

structural

change

of

switch

I

alone

is

dynamically

prone

to

occur

with

a

low-energy

barrier

whereas

the

large

movement

by

switch

II

is

less

favorable

The

dominantly

large

movement

of

switch

I

in

kinesins

as

contrary

to

myosins

is

consistent

with

its

exposure

at

the

surface

of

the

kinesin

motor

-LRB-

in

myosins

it

is

buried

by

the

upper

and

N-terminal

subdomains

-RRB-

Furthermore

this

movement

may

be

functionally

important

Evidence

from

electron

paramagnetic

resonance

shows

that

switch

I

closes

when

kinesin

binds

to

microtubules

-LRB-

-RRB-

Another

study

by

Yun

et

al.

-LRB-

-RRB-

also

suggested

that

the

inward

movement

of

switch

I

may

accelerate

ADP

release

and

thus

serve

as

the

end-link

of

a

pathway

extending

from

microtubulebinding

helix

to

switch

I

that

modulates

the

microtubulebinding-activated

ATPase

cycle

Although

the

binding

of

the

microtubules

may

restrain

the

large

fluctuation

of

switch

I

because

switch

I

does

not

appear

to

directly

bind

to

microtubules

its

restraining

effect

is

probably

not

as

drastic

as

the

upper

subdomain

in

myosins

Therefore

the

dominantly

high

mobility/flexibility

of

switch

I

may

be

a

functionally

relevant

feature

that

distinguishes

kinesins

from

myosins

in

their

force-generation

mechanism

rather

than

an

artifact

due

to

the

lack

of

binding

of

microtubules

Meanwhile

although

in

kinesins

switch

II

has

much

weaker

fluctuation

than

switch

I

it

can

still

play

some

critical

functional

roles

such

as

sensing

the

binding

of

microtubules

that

would

cause

large

structural

changes

to

its

neighboring

loop

and

helix

Therefore

it

is

likely

that

both

switches

coordinate

dynamically

in

different

manners

to

fulfill

their

function

in

kinesin

and

myosins

Global

conformational

changes

beyond

the

nucleotide-pocket

connecting

switch

I

switch

II

with

helix

which

is

connected

to

the

neck-linker

and

it

also

involves

the

bending

motions

of

two

putative

microtubule-binding

regions

and

-LRB-

see

Ref

for

naming

scheme

of

secondary

structure

segments

of

kinesins

-RRB-

This

suggests

a

possible

dynamical

pathway

via

which

the

pocket

deformation

can

trigger

global

structural

changes

that

modulate

the

microtubule-binding

sites

and

the

neck-linker

In

particular

the

twisting

motion

may

change

the

orientation

of

the

helix

and

thereby

modulates

the

docking/undocking

of

the

neck-linker

It

is

interesting

that

this

pathway

appears

to

be

relayed

via

instead

of

the

helix

from

the

nucleotidepocket

to

the

neck-linker

We

note

that

the

region

-LRB-

another

putative

microtubule-binding

site

-RRB-

and

the

C-terminal

half

of

helix

are

not

involved

in

the

global

structural

changes

described

by

mode

Indeed

it

appears

that

these

regions

are

dynamically

frozen

-LRB-

with

reduced

fluctuation

-RRB-

in

ENM

-LRB-

-RRB-

which

seems

to

be

at

odds

with

crystallographic

data

that

shows

helix

can

move

as

a

separate

domain

effectively

sliding

over

the

back

side

of

the

central

b-sheet

-LRB-

-RRB-

It

is

likely

that

the

elastic

interactions

with

uniform

force

constant

do

not

correctly

describe

the

physical

interactions

around

the

helix

So

the

above

results

should

be

viewed

as

complimentary

to

rather

than

against

alternative

pathways

from/to

the

nucleotide-pocket

that

pass

the

region

-LRB-

-RRB-

Justification

of

flexible

environment

and

elastic

interactions

Finally

we

compute

the

global

conformational

changes

induced

by

the

pocket

deformation

described

by

the

relevant

mode

as

identified

above

We

find

that

the

induced

global

structural

changes

are

dominated

by

mode

-LRB-

overlap

if

excluding

six

zero-modes

-RRB-

Unlike

the

other

low-frequency

global

modes

describing

local

movements

this

mode

is

highly

collective

and

it

simultaneously

involves

multiple

bending/twisting

motions

as

follows

-LRB-

Fig.

c

-RRB-

bending

motions

of

region

switch

I

region

loop

and

the

tip

of

the

motor

arrowhead

-LRB-

and

-RRB-

and

the

twisting

motion

of

the

compact

subdomain

including

helix

It

is

interesting

that

this

single

mode

spans

a

pathway

of

hinge

regions

Biophysical

Journal

-LRB-

-RRB-

For

myosins

the

treatment

of

the

surrounding

subdomains

as

flexible

and

mobile

objects

that

can

respond

to

the

pocket

changes

seems

to

be

supported

by

the

observation

of

the

following

conformational

changes

In

the

PDB

structure

switch

I

follows

the

rotation

of

the

upper

subdomain

relative

to

the

P

loop

and

the

N-terminal

subdomain

Accompanied

with

the

pocket

changes

a

distortion

of

the

seven-stranded

b-sheet

that

couples

the

N-terminal

subdomain

and

the

upper

subdomain

appear

to

be

essential

to

allow

large

movement

of

the

upper

subdomain

and

switch

I

and

switch

II

to

follow

it

-LRB-

-RRB-

The

elastic-interactions-based

description

of

myosin

motor

domain

is

supported

by

our

recent

work

-LRB-

-RRB-

which

showed

that

the

ENM

indeed

gives

a

good

description

of

the

observed

conformational

changes

and

the

inter-subdomains

dynamical

correlations

Similarly

for

kinesins

for

there

to

be

a

dynamical

pathway

that

connects

the

nucleotide-pocket

with

remote

regions

of

the

motor

domain

it

seems

reasonable

to

treat

the

environment

around

the

pocket

as

flexible

and

fluctuating

rather

than

as

rigid

and

fixed

objects

However

whether

elastic

interactions

-LRB-

instead

of

irreversible

and

nonharmonic

interactions

-RRB-

are

able

to

explain

the

signal

transmission

in

a

single-domain

globular

protein

like

kinesin

is

still

controversial

The

results

of

the

present

study

are

quite

Nucleotide-Pocket

Dynamics

of

Myosin

and

Kinesin

encouraging

in

clarifying

this

controversy

although

the

ENM

with

uniform

force

constant

is

probably

not

accurate

enough

to

describe

the

movements

of

all

parts

of

kinesin

motor

it

appears

to

give

a

quantitatively

good

description

of

the

structural

changes

in

the

nucleotide-pocket

which

is

consistent

with

crystallographic

data

and

it

provides

at

least

some

qualitative

insight

into

the

possible

mechanism

by

which

the

pocket

deformation

can

be

transmitted

via

the

collective

global

motions

it

triggers

which

may

exist

in

single-domain

proteins

as

well

as

in

multidomain

proteins

After

all

single-domain

proteins

with

knobs

on

them

-LRB-

like

kinesins

-RRB-

are

not

so

different

dynamically

from

multidomain

proteins

-LRB-

like

myosins

-RRB-

and

both

can

utilize

collective

motions

to

mediate

long-range

signal

transmissions

Relations

to

functional

mechanisms

of

myosins

and

kinesins

For

myosins

the

above

results

clearly

show

that

the

relevant

nucleotide-pocket

dynamics

-LRB-

characterized

by

the

pocketmode

-RRB-

is

elastically

coupled

with

the

relevant

global

dynamics

-LRB-

described

by

the

global

mode

-RRB-

which

is

consistent

with

the

widely-hypothesized

pathways

connecting

pocket

deformations

with

actin-binding

and

force

generation

via

several

key

joints

-LRB-

-RRB-

For

kinesins

the

picture

is

more

elusive

for

the

lack

of

crystal

structures

for

the

strong-binding

state

Indeed

it

is

difficult

to

identify

a

handful

of

relevant

global

modes

simply

by

a

structural

comparison

of

the

available

crystal

structures

-LRB-

-RRB-

The

present

study

suggests

a

promising

alternative

strategy

of

finding

the

relevant

global

modes

we

first

find

the

pocket-mode

relevant

to

the

nucleotide-pocket

dynamics

and

then

use

it

to

induce

the

global

conformational

changes

-LRB-

-RRB-

This

strategy

has

indeed

generated

some

enlightening

results

a

collective

global

mode

-LRB-

-RRB-

is

revealed

from

the

induced

global

structural

changes

which

describes

multiple

bending/twisting

motions

that

involve

several

functional

sites

Further

study

is

needed

to

test

the

validity

of

this

result

The

above

results

support

the

potential

power

of

the

ENM-based

analysis

that

is

not

limited

to

the

description

of

single

hinge

motions

of

multidomain

proteins

Instead

a

collective

mode

is

able

to

encode

a

rather

complex

pattern

of

multiple

hinge

motions

that

may

account

for

the

mechanism

of

long-range

allostery

Comparison

with

the

analysis

based

on

global

modes

Second

it

is

able

to

selectively

probe

the

low-energy

dynamics

specific

to

the

chosen

subsystem

only

the

global

dynamics

coupled

with

the

local

dynamics

of

the

given

subsystem

is

probed

which

effectively

excludes

many

irrelevant

degrees

of

freedom

and

significantly

simplifies

the

task

of

finding

the

relevant

modes

-LRB-

for

example

the

global

modes

triggered

by

the

nucleotide-pocket

deformation

in

myosins

and

kinesins

-RRB-

This

is

particularly

helpful

considering

the

generally

large

size

of

the

normal-modes

spectrum

-LRB-

three

times

the

number

of

residues

-RRB-

which

poses

a

tremendous

challenge

to

researchers

to

make

sense

of

them

For

future

work

the

analysis

of

subsystem

dynamics

introduced

in

this

work

will

be

applied

to

other

protein

complexes

to

address

a

number

of

intriguing

issues

such

as

for

example

finding

dynamical

pathways

that

transmit

signals

of

ligand

binding

to

remotes

sites

comparing

functional

dynamics

of

homologous

enzymes

sharing

similar

active

site

etc.

We

will

also

work

on

the

refined

parameterization

of

the

ENM

beyond

uniform

force

constant

to

quantitatively

improve

the

results

This

work

is

supported

by

the

National

Institutes

of

Health

REFERENCES

Kull

F.

J.

and

S.

A.

Endow

Kinesin

switch

I

II

and

the

motor

mechanism

J.

Cell

Sci

Geeves

M.

A.

and

K.

C.

Holmes

Structural

mechanism

of

muscle

contraction

Annu

Rev.

Biochem

Houdusse

A.

and

H.

Sweeney

Myosin

motors

missing

structures

and

hidden

springs

Curr

Opin

Struct

Biol

Kull

F.

J.

E.

P.

Sablin

R.

Lau

R.

J.

Fletterick

and

R.

D.

Vale

Crystal

structure

of

the

kinesin

motor

domain

reveals

a

structural

similarity

to

myosin

Nature

Houdusse

A.

A.

G.

Szent-Gyorgyi

and

C.

Cohen

Three

conformational

states

of

scallop

myosin

Proc

Natl.

Acad

Sci

USA

Coureux

P.

D.

A.

L.

Wells

J.

Menetrey

C.

M.

Yengo

C.

A.

Morris

H.

L.

Sweeney

and

A.

Houdusse

A

structural

state

of

the

myosin

V

motor

without

bound

nucleotide

Nature

Reubold

T.

F.

S.

Eschenburg

A.

Becker

F.

J.

Kull

and

D.

J.

Manstein

A

structural

model

for

actin-induced

nucleotide

release

in

myosin

Nat

Struct

Biol

Holmes

K.

C.

I.

Angert

F.

J.

Kull

W.

Jahn

and

R.

R.

Schroder

Electron

cryo-microscopy

shows

how

strong

binding

of

myosin

to

actin

releases

nucleotide

Nature

Volkmann

N.

D.

Hanein

G.

Ouyang

K.

M.

Trybus

D.

J.

DeRosier

and

S.

Lowey

Evidence

for

cleft

closure

in

actomyosin

upon

ADP

release

Nat

Struct

Biol

Sack

S.

F.

J.

Kull

and

E.

Mandelkow

Motor

proteins

of

the

kinesin

family

Structures

variations

and

nucleotide

binding

sites

Eur

J.

Biochem

Yun

M.

X.

Zhang

C.

G.

Park

H.

W.

Park

and

S.

A.

Endow

A

structural

pathway

for

activation

of

the

kinesin

motor

ATPase

EMBO

J.

Wriggers

W.

and

K.

Schulten

Nucleotide-dependent

movements

of

the

kinesin

motor

domain

predicted

by

simulated

annealing

Biophys

J.

Biophysical

Journal

-LRB-

-RRB-

Compared

with

the

NMA

of

the

whole

protein

complex

where

global

modes

are

solved

and

analyzed

the

subsystem

NMA

proposed

here

has

the

following

advantages

first

it

is

computationally

more

cost-effective

it

reduces

the

analysis

of

the

complex

dynamics

of

a

large

biomolecular

system

to

the

analysis

of

a

smaller

subsystem

with

the

effects

of

the

coupling

with

its

environment

implicitly

incorporated

Minehardt

T.

J.

R.

Cooke

E.

Pate

and

P.

A.

Kollman

Molecular

dynamics

study

of

the

energetic

mechanistic

and

structural

implications

of

a

closed

phosphate

tube

in

NCD

Biophys

J.

Vale

R.

D.

and

R.

A.

Milligan

The

way

things

move

looking

under

the

hood

of

molecular

motor

proteins

Science

Atilgan

A.

R.

S.

R.

Durell

R.

L.

Jernigan

M.

C.

Demirel

O.

Keskin

and

I.

Bahar

Anisotropy

of

fluctuation

dynamics

of

proteins

with

an

elastic

network

model

Biophys

J.

Delarue

M.

and

Y.

H.

Sanejouand

Simplified

normal

mode

analysis

of

conformational

transitions

in

DNA-dependent

polymerases

the

elastic

network

model

J.

Mol

Biol

Tama

F.

and

Y.

H.

Sanejouand

Conformational

change

of

proteins

arising

from

normal

mode

calculations

Protein

Eng

Zheng

W.

and

S.

Doniach

A

comparative

study

of

motorprotein

motions

by

using

a

simple

elastic-network

model

Proc

Natl.

Acad

Sci

USA

Li

G.

and

Q.

Cui

Analysis

of

functional

motions

in

Brownian

molecular

machines

with

an

efficient

block

normal

mode

approach

myosin-II

and

Biophys

J.

Navizet

I.

R.

Lavery

and

R.

L.

Jernigan

Myosin

flexibility

structural

domains

and

collective

vibrations

Proteins

Zheng

W.

and

B.

R.

Brooks

Identification

of

dynamical

correlations

within

the

myosin

motor

domain

by

the

normal

mode

analysis

of

an

elastic

network

model

J.

Mol

Biol

Zheng

and

Brooks

Tirion

M.

M.

Large

amplitude

elastic

motions

in

proteins

from

a

single-parameter

atomic

analysis

Phys

Rev.

Lett

Hinsen

K.

Analysis

of

domain

motions

in

large

proteins

Proteins

Brooks

B.

R.

D.

Janezic

and

M.

Karplus

Harmonic

analysis

of

large

systems

J.

Comput

Chem

Levy

R.

A.

Srinivasan

W.

Olson

and

J.

McCammon

Quasiharmonic

method

for

studying

very

low

frequency

modes

in

proteins

Biopolymers

Hayward

S.

and

H.

J.

Berendsen

Systematic

analysis

of

domain

motions

in

proteins

from

conformational

change

new

results

on

citrate

synthase

and

lysozyme

Proteins

Naber

N.

T.

J.

Minehardt

S.

Rice

X.

Chen

J.

Grammer

M.

Matuska

R.

D.

Vale

P.

A.

Kollman

R.

Car

R.

G.

Yount

R.

Cooke

and

E.

Pate

Closing

of

the

nucleotide

pocket

of

kinesin-family

motors

upon

binding

to

microtubules

Science

Song

Y.

H.

A.

Marx

J.

Muller

G.

Woehlke

M.

Schliwa

A.

Krebs

A.

Hoenger

and

E.

Mandelkow

Structure

of

a

fast

kinesin

implications

for

ATPase

mechanism

and

interactions

with

microtubules

EMBO

J.

Kikkawa

M.

E.

P.

Sablin

Y.

Okada

H.

Yajima

R.

J.

Fletterick

and

N.

Hirokawa

Switch-based

mechanism

of

kinesin

motors

Nature

Biophysical

Journal

-LRB-

-RRB-

O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O O B O O B B O O O O O O O O O O O O O O O O O O B O O O O O B B O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O 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 B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O 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 B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B O O O O O O O O O O O O O O O