The dynamics of actin and myosin association and the crossbridge

Biochem.

J.

(1991) 274,

1-14

(Printed

in

Great

Britain)

REVIEW

ARTICLE

The

dynamics

of

actin

and

myosin

association

and

the

crossbridge

model

of

muscle

contraction

Michael

A.

GEEVES

Department

of

Biochemistry,

School

of

Medical

Sciences,

University

of

Bristol,

Bristol

BS8

1TD,

U.K.

INTRODUCTION

The

production

of

mechanical

force

in

muscle

is

believed

to

be

the

result

of

a

dynamic

interaction

between

the

proteins

in

two

sets

of

interdigitating

filaments,

the

thick

myosin

and

thin

actin

filaments

(Fig.

1).

In

the

cycling

crossbridge

model

of

muscle

contraction,

myosin

heads

project

from

the

surface

of

the

thick

filament

and

form

crossbridges

with

actin

of

the

thin

filament.

Hydrolysis

of

ATP

by

myosin

then

drives

a

cycle

of

interaction

between

the

actin

and

myosin

which

tends

to

move

the

two

filaments

past

each

other

[1,2].

Early

studies

of

the

properties

of

the

isolated

actin

and

myosin

concentrated

on

the

mechanism

of

ATP

hydrolysis

by

myosin

(and

its

proteolytic

subfragments

SI

and

HMM,

Fig.

1)

and

the

activation

of

the

ATPase

by

actin.

The

essential

features

of

this

mechanism

were

well

established

by

the

mid-1970s

and

have

been

reviewed

extensively

[3-5].

The

details

of

the

mechanism

have

been

revised

[6-10]

but

the

principal

events

remain

unchanged.

More

recent

work

has

concentrated

on

attempts

to

correlate

the

events

of

the

ATP

hydrolysis

mechanism

with

the

mechanism

of

force

generation.

The

cycling

crossbridge

model

is

a

mechanical

model,

the

crossbridge

is

a

physical

link

between

the

two

filaments

and

force

is

generated

by

a

change

in

the

structure

of

the

crossbridge,

usually

conceptualized

as

a

change

in

the

angle

at

which

the

myosin

head

binds

to

the

thin

filament.

The

true

nature

of

this

change

in

structure

remains

elusive

and

its

definition

remains

the

principle

aim

of

work

in

the

field.

The

definition

of

this

structural

change

will

require

contributions

from

many

different

sources

and

ultimately

will

provide

the

high-resolution

structures

of

the

individual

molecular

components,

their

organization

in

the

muscle

and

the

way

in

which

the

structures

change

on

a

millisecond

time

scale.

These

aims

are

still

some

way

from

being

realized.

This

review

will

consider

the

information

available

from

studies

of

the

dynamics

of

the

interaction

between

actin

and

myosin

in

solution

and

how

these

studies

can

help

to

focus

on

where

to

look

for

these

structural

changes.

HISTORICAL

BACKGROUND

The

first

major

advance

in

correlating

the

events

of

the

enzymic

breakdown

of

ATP

with

the

proposed

crossbridge

cycle

came

from

the

transient-kinetic

studies

of

Lymn

&

Taylor

[11]

using

purified

actin

and

myosin.

They

were

able

to

explain

two

earlier

apparently

paradoxical

observations.

In

the

absence

of

ATP,

actin

binds

to

myosin

very

tightly

(Kr

-8

107

M-1)

and

the

presence

of

ATP

reduces

the

association

constant

to

<

104

M-1.

However

the

ATPase

rate

of

myosin

is

low

(0.1

s-1)

and

actin

accelerates

this

even

though

the

two

proteins

are

largely

dissociated.

The

extent

of

acceleration

is

dependent

upon

actin

concentration

and

ionic

strength

but

can

be

as

much

as

200-fold.

Lymn

&

Taylor

were

able

to

show

that

these

steady

state

observations

were

compatible

with

a

transient

interaction

be-

tween

actin

and

myosin.

Their

principal

observations

were

as

follows.

In

the

absence

of

actin,

ATP

binds

rapidly

to

myosin

(second

order

rate

constant

2

x

10

M-1

s-1)

and

is

hydrolysed

to

ADP

and

phosphate

at

>

100

s-I

but

slow

release

of

the

products

limits

the

turnover

to

0.1

s-

.

On

addition

of

ATP

to

actomyosin

the

two

proteins

rapidly

dissociate,

and

then

ATP

is

hydrolysed

on

myosin

at

the

same

rate

as

in

the

absence

of

actin.

Lymn

&

Taylor

proposed

that

actin

rebinds

to

the

myosin

products

complex

at

this

point

and

promotes

the

release

of

products

from

myosin.

Rebinding

of

ATP

to

actomyosin

then

dissociates

the

two

proteins

once

more.

The

model

therefore

requires

a

cycle

of

attachment

and

detachment

between

actin

and

myosin

for

each

ATP

hydrolysed

and

this

is

precisely

the

type

of

mechanism

which

is

required

by

the

cycling

crossbridge

model

of

contraction

proposed

earlier.

The

original

model

of

Lymn

&

Taylor

is

shown

in

Fig.

2,

and

the

biochemical

model

is

redrawn

in

more

detail in

Fig.

3(a).

In

drawing

the

biochemical

model

and

the

crossbridge

cycle

side

by

side

as

Lymn

&

Taylor

were

able

to

do,

two

additional

features

of

the

model

became

apparent;

the

force-generating

event

is

associated

with

the

loss

of

the

products

of

the

ATPase

reaction

from

the

myosin

active

site

and

therefore

the

actomyosin

complex

represents

a

ground

state

at

the

end

of

the

ATPase

cycle.

Secondly,

if

the

force-generating

event

is

a

structural

change

such

as

a

change

in

the

angle

of

attachment

of

myosin

to

actin

(as

proposed

in

the

models

of

A.

F.

Huxley

&

H.

E.

Huxley

[1,2])

then

a

recovery

stroke

is

required

during

the

detached

part

of

the

cycle

(which

in

the

Lymn

&

Taylor

model

was

located

as

part

of

the

hydrolysis

step).

It

is

important

to

emphasize

that

these

two

features

of

the

model

did

not

come

from

any

experimental

data

but

were

implicit

in

the

model

devised

to

accommodate

the

experimental

findings.

The

next

major

development

in

correlating

events

of

the

actomyosin

ATPase

reaction

with

a

crossbridge

model

came

from

the

work

of

Eisenberg

and

his

collaborators.

Stein

et

al.

[12]

showed

that

although

ATP

reduced

the

affinity

of

Sl

for

actin

more

than

1000-fold,

detachment

followed

by

hydrolysis

and

reattachment

was

not

an

obligatory

pathway.

Hydrolysis

of

ATP

by

acto

SI

without

dissociation

was

possible

at

high

protein

concentration.

The

work

of

Greene

&

Eisenberg

[13]

on

the

equilibrium

interaction

between

actin

and

myosin

subfragment

1

established

that

myosin

and

myosin

nucleotide

complexes

formed

two

classes

of

complexes

with

actin;

those

which

bound

actin

strongly

(M,

M

ADP,

K,,,

>

105

M-1)

and

those

which

bound

actin

weakly

(M-ATP,

and

M

ADP-P,

K,,s

<

105

M-1).

In

the

weak

complexes,

actin

was

in

rapid

equi-

Vol.

274

Abbreviations

used:

SI,

myosin

subfragment

1;

HMM,

heavy

meromyosin;

ATPyS,

adenosine

5'-[y-thio]triphosphate;

AMP-PNP,

adenosine

5'-[fiy-imido]triphosphate;

FRET,

fluorescence

energy

transfer;

mant,

N-methylanthraniloyl;

Tm,

tropomyosin;

Tn,

troponin;

in

equations

A,

N,

and

M

refer

to

actin,

nucleotide

and

myosin

(or

its

subfragments)

respectively.

I

M.

A.

Geeves

Thick

filament

(a)

(b)

S~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I%"

|

Lig

h

It

chaiins

D>ISS

I

i

.

I

LMM

HMM

Fig.

1.

The

principal

proteins

of

muscle

(a)

Diagram

of

overlapping

thick

and

thin

filaments

at

the

centre

of

a

sarcomere

of

relaxed

muscle.

For

clarity,

the

lateral

separation

of

the

filaments

has

been

drawn

greater

than

in

vivo,

and

the

M-line

structure

omitted.

The

thin

filament

is

a

1

,sm

long

polymer

of

actin,

which

is

a

single-

polypeptide,

globular

protein

of

Mr

42000.

The

crystal

structure

of

monomeric

actin

in

a

complex

with

DNAase

I

has

recently

been

solved

to

<

0.3

nm

resolution

[109a]

and

the

orientation

of

the

monomer

in

the

filament

has

been

proposed

[109b].

Associated

with

the

thin

filament

are

the

control

proteins

troponin

and

tropomyosin

which

interact

with

calcium

to

regulate

the

interaction

of

actin

with

myosin.

The

thick

filament

is

a

bipolar

polymer

of

myosin.

Myosin

is

an

Mr

520000

protein

and

consists

of

six

polypeptide

chains,

two

identical

heavy

chains

and

four

light

chains

(from

[56]

with

permission).

(b)

Myosin

is

insoluble

at

physiological

ionic

strength

and

therefore

biochemical

studies

use

proteolytic

fragments

of

myosin.

Heavy

meromyosin

(HMM)

has

a

short

tail

and

two

globular

heads

with

all

of

the

light

chains

intact

(Mr

340000).

Subfragment

1

(S1)

is

the

globular

head

group

with

one

or

two

light

chains

per

head

(Mr

115000).

Both

HMM

and

Sl

retain

the

ATPase

activity

and

the

actin-binding

properties

of

the

parent

myosin.

The

thick

filament

is

assembled

by

the

tails

of

the

myosin

packing

together

parallel

to

the

filament

axis

with

the

tails

pointing

towards

the centre

of

the

filament.

librium

between

bound

and

free

states.

In

the

strong

complexes,

free

actin

was

only

in

slow

exchange

with

bound

actin.

The

effect

of

this

on

the

Lymn

&

Taylor

model

was

to

add

the

vertical

equilibrium

arrows

in

Fig.

3

[14,15].

This

model

implies

that

force

generation

is

associated

with

the

transition

from

the

weakly

bound

actin

to

the

strongly

bound

actin

which

occurs

during

this

product

dissociation

step,

as

in

the

Lymn

&

Taylor

model.

Eisenberg

&

Greene

called

the

weak

state

a

900

crossbridge

and

the

strong

state

a

450

crossbridge

to

emphasize

the

corres-

pondence

between

the

solution

model

and

the

rotating

cross-

bridge

model.

This

assignment

makes

a

fundamental

difference

to

the

recovery

stroke

of

the

crossbridge

which

in

the

Lymn

&

Taylor

model

occurs

during

detachment.

In

the

Eisenberg

&

Greene

model

the

crossbridge

must

return

to

a

weak

binding

(900)

state

before

it

can

detach,

i.e.

the

force-generating

event

is

reversed

before

the

crossbridge

detaches.

This

can

clearly

present

problems

for

the

efficient

production

of

mechanical

energy

by

the

cycle,

as

was

pointed

out

by

the

authors

when

the

model

was

first

proposed.

Their

suggestion

for

avoiding

this

was

that

the

reversal

of

the

power

stroke

did

occur

but

that

it

was

a

rapid

process

and

the

following

detachment

was

also

a

very

fast

step.

Thus

the

lifetime

of

this

'negatively

strained

crossbridge'

was

very

short

and

therefore

contributed

little

to

the

overall

force

produced

in

the

cycle.

Goody

&

Holmes

[16]

reviewed

the

interaction

between

myosin,

actin

and

nucleotide,

and

emphasized

the

competitive

nature

of

the

binding

of

actin

and

nucleotide

to

myosin.

They

pointed

out

that

the

tighter

a

nucleotide

or

nucleotide

analogue

bound

to

myosin,

the

weaker

the

interaction

between

actin

and

the

myosin

-

nucleotide

complex.

Further,

they

suggested

that

myosin

nucleotide

complexes

could

be

classified

as

a

continuum

between

those

possessing

weak

and

strong

actin-binding

proper-

ties

and

this

could be

accounted

for

by

a

two-step

association

reaction

between

actin

and

myosin-

nucleotide

complexes.

In

this

model,

actin

binds

initially

to

form

the

'attached

state'

(A

in

eqn.

1)

in

which

the

actin

is

relatively

weakly

bound

and

is

in

rapid

equilibrium

with

free

actin.

This

complex

can

then

be

isomerized

to

the

'rigor-like'

complex

(R)

in

which

actin

is

tightly

bound

and

the

nucleotide

is

correspondingly

more

weakly

bound

(at

low

concentrations

of

nucleotide

the

nucleotide

can

subsequently

dissociate).

KI

K11

KN

A+M

N=A-M*N=A

M*N=AM+N

(1)

A

state

R

state

At

the

time

this

idea

was

proposed

there

was

some

kinetic

evidence

for

more

than

one

acto

S1

complex

in

the

presence

of

ADP

[17,18],

in

the

presence

of

ATP

[19]

and

in

the

presence

of

adenosine

5'-[/Jy-imido]triphosphate

('AMP-PNP')

[20].

Geeves

1991

2

Dynamics

of

muscle

contraction

(a)

(4)

(3)

E

(b)

A-M-D-P

(3)

±A

M-D-P

(1)

(2)

(4)

Do

A-M

-D,P

+ATI

(1)

M*T

-(2

(2)

Fig.

2.

The

Lyme-Taylor

1111

model

of

the

actomyosin

ATPase

and

the

crossbridge

cycle

(a)

Contractile

cycle

for

a

single

crossbridge.

Actin

sites

which

are

suitably

orientated

to

interact

with

a

crossbridge

are

indicated

by

circles.

(b)

Steps

in

the

chemical

mechanism

for

ATP

hydrolysis

by

actomyosin.

Binding

of

ATP

and

dissociation

of

actin

is

shown

as

a

single

step

because

actin

dissociation

is

very

fast

following

substrate

binding.

Goody

&

Gutfreund

[21]

drew

this

evidence

together

and

proposed

a

detailed

biochemical

model

of

the

actomyosin

ATPase.

The

model,

referred

to

as

the

'3G'

model,

is

shown

in

Fig. 3

drawn

at

right

angles

to

the

way

it

was

drawn

in

the

original

form

in

order

to

emphasize

the

correspondence

with

the

previous

models.

In

this

model,

myosin-nucleotide

complexes

bind

actin

in

a

two-step

reaction

and

the

isomerization

from

the

attached

A-M

-N

to

the

A

M

-N

state

represents

the

trans-

formation

from

a

weakly

to

a

strongly

attached

state

as

defined

by

Eisenberg

&

Greene.

Whether

a

particular

myosin

-

nucleotide

complex

is

classified

as

weak

or

strong

actin-binding

state

simply

depends

upon

the

value

of

the

equilibrium

constant

KII.

If

KII

>

1

then

the

A

*

M

*

N

state

predominates

and

the

myosin

-

nucleotide

is

strong

actin-binding;

if

KII

<

1

then

the

A-M

-

N

state

predominates

and

it

is

a

weak

actin-binding

complex.

It

was

suggested

that

the

value

of

K,

was

103-104

M-1,

independent

of

the

occupancy

of

the

myosin

nucleotide-binding

site.

As

the

ATPase

reaction

progresses

the

predominant

state

of

the

acto

-

S

1

nucleotide

complex

alternates

between

the

strongly

and

weakly

attached

states.

In

the

absence

of

nucleotide

the

rigor

state

predominates

(KII

=

200)

and

on

binding

ATP,

K,I

is

reduced

to

<

0.01

and

the

weakly

attached

state

predominates

as

in

the

Eisenberg

&

Greene

model.

As

ATP

is

hydrolysed

and

the

products

are

sequentially

released,

the

actomyosin

progress-

ively

reverts

to

the

strongly

attached

rigor-like

state

and

in

doing

so

can

generate

mechanical

force

between

the

two

proteins.

Geeves

et

al.

[21]

went

on

to

discuss

how

the

transition

from

the

attached

to

the

rigor-like

state

could

be

coupled

to

force

generation.

M

-

M-T

i

M-D.P

MD

M

A-M,-

i

A-M-T

A-M.D.P

iA.MD-i

A-M

%v

_

J

f

Weak

binding

Strong

binding

states

states

M

M-T

M-D-P

M-D

M

Detached

'states

'

'

i i

t

1

Attached

(A)

A-M

A-M.T

,

A-M.D.P

A-MD

A-M

states

|

1

1

1

1

1

Rigor-like

(R)

AM

iA-M-T

iAM-D-P

A-MD

A-M

states

Lymn

&

Taylor

(1971

)

Eisenberg

&

Greene

(1980)

Geeves

et

al.

(1984)

Fig.

3.

Biochemical

models

of

the

actomyosin

ATPase

mechanism

(a)

A

redrawing

of

the

Lymn-Taylor

[11]

model.

In

the

original

model

the

order

of

product

release

was

not

specified;

the

AMD

and

MD

states

are

added

here

for

completeness

and

to

emphasize

the

correspondence

with

the

two

other

models.

(b)

The

model

of

Eisenberg

&

Greene

[14].

This

model

allows

for

all

myosin

nucleotide

states

to

interact

with

actin

and

classifies

these

as

weak

(K.

<

l0

M-1)

or

strong

(K.

>

105

M-1)

actin-

binding

states.

In

addition

it

allows

for

the

possibility

of

hydrolysis

of

ATP

by

myosin

whilst

the

actin

remains

attached.

(c)

The

model

of

Geeves,

Goody

&

Gutfreund

[21].

This

is

similar

to

(b),

but

each

myosin

nucleotide

complex

binds

to

actin

in

two

steps.

The weak

or

strong

definition

of

(b)

depends

upon

whether

the

A

or

the

R

state

predominates

for

a

given

nucleotide.

Vol.

274

(b)

(c)

3

M.

A.

Geeves

The

difference

between

this

model

and

the

one

proposed

by

Eisenberg

&

Greene

is

relatively

small,

but

the

implications

for

the

nature

of

the

actin-myosin

interaction

are

more

far-reaching.

This

model

suggests

that

the

conformational

change

which

results

in

force

generation

is

not

a

unique

feature

of

a

particular

actomyosin

nucleotide

complex

but

is

common

to

all

such

complexes.

It

suggests

that

the

actomyosin

rigor

complex

is

a

ground

state

and

ATP

is

required

to

dissociate

actin

from

this

complex.

Hydrolysis

of

ATP

then

allows

the

return

to

the

rigor-

like

state.

The

route

taken

through

the

different

complexes

available

to

any

given

crossbridge

will

depend

on

the

con-

centration

of

available

actin

sites,

the

relative

rates

of

specific

steps

and

the

mechanical

strain

experienced

by

the

crossbridge.

In

1984,

when

the

3G

model

was

proposed,

no

directed

observation

of

the

two

step

binding

reaction

had

been

made.

Before

discussing

the

model

further

it

is

therefore

appropriate

to

consider

the

more

recent

biochemical

evidence

on

actin-myosin

interaction.

EVIDENCE

OF

TWO-STEP

BINDING

OF

ACTIN

TO

S1

IN

SOLUTION

Direct

evidence

of

two

acto

-Sl

complexes

from

pressure

jump

The

most

convenient

monitor

of

actin-myosin

interactions

has

been

the

use

of

light

scattering,

which

is

approximately

linearly

related

to

the

concentration

of

actomyosin

complex

formed

[22,23].

Its

use

in

equilibrium

measurements.

has

been

limited

because

its

sensitivity

is

restricted

to

protein

concentrations

>

5

/tM.

However,

this

signal

has

found

wide

use

in

stopped-flow

kinetic

studies

and

has

been used

to

define

the

rate

of

association

between

actin

and

myosin

and

myosin;nucleotide

complexes

[20,22-26].

Most

of

these

studies

were

consistent

with

a

single-

step

binding

reaction

A+

M

A-

M,

although

many

authors

reported

evidence

of

a

more

complex

reaction;

in

particular

the

rate

of

association

of

actin

with

myosin

(or

myosin

*

nucleotide)

was

slower

than

expected

for

a

diffusion-controlled

reaction.

Equilibrium

perturbation

studies

provide

an

alternative

means

of

studying

association/dissociation

reactions

and

Geeves

&

Gutfreund

[18]

demonstrated

that

increases

in

hydrostatic

pressure

weakened

the

interaction

between

actin

and

myosin

subfragment

1.

They

were

therefore

able

to

use

rapid

pressure

perturbations

to

measure

the

rate

of

the

association

of

both

SI

and

SI

-

ADP

with

actin.

The

measured

rates

were

compatible

with

the

earlier

stopped-flow

studies

but

analysis

of

the

con-

centration

dependence

of

the

pressure-induced

amplitudes

was

not

compatible

with

a

single

step

binding

reaction.

Fluorescent

reporter

groups

covalently

attached

to

proteins

can

provide

a

sensitive

monitor

of

protein-ligand

interactions

and

the

presence

of

a

reactive

thiol

(Cys-374)

on

actin

has

made

such

modifications

routine

[24,27-31].

The

fluorescence

of

a

pyrene

group

covalently

attached

to

Cys-374

is

quenched

by

70

%

when

actin

binds

to

myosin

or

its

subfragments

(S1,

HMM

[27,31]).

The

use

of

this

label

has

greatly

increased

the

ease

and

accuracy

with

which

the

affinity

of

actin

for

myosin

and

myosin-nucleotide

complexes

can

be

measured

by

fluorescence

titration.

Criddle

et

al.

[31]

used

this

label

to

measure

the

rate

and

equilibrium

of

actin

binding

to

SI

and

showed

that

the

presence

of

the

label

had

no

measurable

effect

on

the

actin-SI

interaction.

Using

this

label,

Coates

et

al.

[32]

were

able

to

observe

two

pressure-induced

relaxations

in

solutions

of

acto

SI

in

the

absence

of

any

nucleotide

(Fig.

4).

The

fast

relaxation

was

always

complete

in

the

pressure

release

time

(200

/,s)

and

its

amplitude

increased

as

the

protein

concentration

increased

(i.e.

as

the

fraction

of

the

actin

bound

to

SI

increased).

The

rate

of

the

second

relaxation

was

linearly

dependent

on

protein

concen-

tration

and

its

amplitude

decreased

at

high

protein

concentrations.

This

relaxation

could

also

be

observed

by

light

scattering.

No

pressure-induced

relaxation

was

observed

with

actin

alone;

therefore

the

two

relaxations

must

represent

two

relaxations

of

the

acto

*

SI

complex.

These

experimental

findings

were

interpreted

in

terms

of

the

following

model

in

which

step

2

is

a

pressure-sensitive

transition

(i.e.

increases

in

pressure

results

in

a

reduction

in

K2)

and

pyrene

fluorescence

monitors

step

2

only.

1

2

A

+

M

=

A-M

A-M

(2)

Thus

an

increase

in

pressure

will

reduce

K2

and

lead

to

a

decrease

of

the

overall

affinity

of

actin

for

S1.

At

low

protein

concentrations

therefore,

an

increase

in

pressure

will

result

in

dissociation

of

a

fraction

of

the

acto

SI

complex.

On

pressure

release

a

rapid

re-equilibration

of

A-M

and

A

*

M

will

be

observed

by

fluorescence

followed

by

the

reassociation

of

free

actin

which

can

be

observed

by

both

light

scattering

and

fluorescence.

However,

at

infinitely

high

protein

concentration

increases

in

pressure

will

cause

no

dissociation

of

the

two

proteins

but

will

still

perturb

the

first-order

isomerization

step.

An

important

feature

of

the

model

is

that

the

two

complexes

shown

are

distinct

and

stable.

Consideration

of

the

temperature

dependence

of

k+1

led

Coates

et

al.

[32]

to

suggest

that

this

is

not

a

diffusion-controlled

step

and

therefore

A-M

is

not

a

collision

complex.

A

preceding

step

therefore

probably

exists

which

involves

formation

of

the

collision

complex

and

this

then

becomes

the

A-M

state

with

the

formation

of

specific

protein-protein

interaction

sites.

As

this

collision

complex

is

not

observed

directly

and

is

expected

to

be

a

minor

component

in

any

equilibrium

or

kinetic

experiments,

the

formation

of

the

A-M

state

will

be

treated

as

a

single

event

(i.e.

K1

=

KO

K'1

where

Ko

and

K,

are

the

equilibrium

constants

of

the

collision

complex

formation

and

the

isomerization

to

A-M

steps

respectively).

Thus

the

simplest

model

required

to

fit

the

pressure

jump

data

identifies

two

principle

steps

in

the

association

of

SI

and

actin,

and

K1

and

K2

of

eqn.

2

are

equivalent

to

KI

and

KII

in

eqn.

(1).

A

prediction

of

this

model

is

-that

the

formation

of

any

acto

-SI

-

nucleotide

complex

which

only

occupies

the

weakly

attached

state

(A-M

or

A-M

*

N)

would

not

quench

the

fluorescence

of

the

pyrene

label.

This

prediction

of

the

model

allows

the

generality

of

the

two-step

binding

model

to

be

tested

and

such

experiments

are

discussed

below.

Measurements

of

K,,

in

the

presence

of

nucleotides

The

3G

model

predicts

that

for

acto

-SI

in

the

presence

of

ATP,

the

only

significantly

occupied

state

with

actin

bound

is

the

A-M

-

T

(high

pyrene

fluorescence)

state.

In

principle

this

can

be

tested

by

following

the

change

in

pyrene

fluorescence

when

nucleotide

is

added

to

acto

-SI

under

conditions

where

no

dissociation

of

the

two

proteins

occurs,

i.e.

at

high

protein

concentration.

In

practice

the

experiment

is

more

complex

because

a

sufficiently

high

protein

concentration

cannot

be

achieved

experimentally.

Using

very

low

ionic

strength

to

increase

the

affinity

of

actin

for

S1,

Geeves

et

al.

[33]

showed

that

addition

of

ATP

to

acto

*SI

produces

30%

dissociation

of

acto

-SI

as

judged

by

the

changes

in

light

scattering

(Fig.

5).

The

dissociation

is

only

transient

because

under

these

conditions

the

steady-state

ATP

hydrolysis

is

rapid

and

the

proteins

reassociate

as

the

ATP

concentration

falls.

Monitoring

of

the

pyrene

fluorescence

signal

showed

that

the

signal

change

was

the

same

as

that

expected

for

complete

dissociation

of

the

two

proteins.

This

indicated

that

in

the

presence

of

ATP

<

1

%

of

the

bound

actin

was

in

the

low

fluorescence

rigor-like

state,

establishing

a

value

of

<

0.01

for

KII

as

predicted

in

the

3G

model.

The

assignment

of

the

fluorescence

change

to

the

isomerization

step

alone

then

allows

a

simple

experiment

to

determine

the

1991

4

Dynamics

of

muscle

contraction

41

c

a

4,

4,

0

X(]

r

60-

U,

C-

40

-

20

p

Time

1.;

1.0

0.8.

N

E

2L

E4

0.6

F

0.4[

0.2

0

0

5

10

[pA]

+

[S1

]

(AM)

15

20

5

10

15

20

[pA]

+

[S1]

(AM)

Fig.

4.

Pressure-induced

changes

in

the

fluorescence

of

a

solution

of

pyrene-labelled

actin

and

S1

(a)

A

solution

of

acto

-

SI

was

exposed

to

100

atm

pressure

and

allowed

to

equilibrate.

At

the

small

arrow

the

pressure

was

returned

to

1

atm

within

200

,us.

A

best

fit

single

exponential

(4.1,

13.6

and

50.5

s-1

respectively)

is

superimposed

on

the

slow

relaxation.

The

solutions

were

(i)

2.7

/M-pyr-

actin,

2.4

/Mm-S1,

(ii)

2.6

/tM-pyr-actin,

4.8

,uM-Sl,

(iii)

5.0

/IM-pyr-actin,

15.9

,pM-SI

in

a

pH

7

buffer,

ionic

strength

0.13

M,

20

'C.

In

the

model

of

eqn.2

in

the

text

the

fast

relaxation

is

defined

by:

I/T,

=

k+22

k-2

and

the

slower

relaxation

by:

1/72

=

k+j-([A]+[M])+k-1/(l

+K2)

where

the

bar

indicates

equilibrium

concentrations

and

the

ratio

of

the

two

amplitudes

is

defined

in

terms

of

the

equilibrium

constants:

amp1

1

(l+K2)

amp2

=

+

K1([AJ

+

[M])

K

amp2

42

K2

Plots

of

1

/T2

and

the

ratio

of

the

two

amplitudes

against

protein

concentration

are

shown

in

(b)

and

(c)

respectively.

fraction

of

bound

actin

in

the

two

states

for

any

given

nucleotide.

In

such

an

experiment

addition

of

nucleotide

to

acto

-SI

under

conditions

where

no

dissociation

occurs

produces

a

fluorescence

change

which

can

then

be

directly

related

to

the

fraction

of

the

bound

actin

in

the

two

states

A-M

N

and

A

M

N.

Such

an

approach

was

exploited

by

Geeves

&

Jeffries

[34]

and

a

summary

of

their

results

is

included

in

Table

1.

The

experiment

was

simple

to

perform

in

the

case

of

ADP

as

no

significant

dissociation

of

the

proteins

occurred.

For

the

other

nucleotide

analogues

a

more

complex

approach

was

necessary

in

order

to

correct

for

the

fraction

of

the

actin

which

dissociated

from

Sl.

The

results

of

Geeves

&

Jeffries

[34]

support

the

principal

Vol.

274

(b)

0

0

0

0

(c)

0

0

0

0

0

/

U

w

I

I

z

I

v

_

5

1)

M.

A.

Geeves

2)

C.)

C

0)

U)

0)

0

Fig.

5.

Light

scattering

and

fluorescence

changes

in

pyrene-acto.

Si

on

addition

of

a

small

excess

of

ATP

Curves

labelled

A:

addition

of

10

M-ATP

to

5

/LM-pyrene-actin

and

a

small

excess

(6

IM)

of

SI

(reaction

chamber

concentration).

The

light

scattering

showed

a

rapid

decrease

consistent

with

>

90

%

dissociation

of

actin

from

S1.

This

was

followed

by

reassociation,

as

the

ATP

was

hydrolysed,

back

to

the

original

level.

The

broken

line

represents

the

signal

expected

for

complete

dissociation

of

acto

S1.

The

fluorescence

signal

shows

the

same

features.

Note

that

the

light

scattering

signal

has

been

inverted

to

emphasize

the

similarities

in

the

form

of

the

two

signals.

Curves

labelled

B:

addition

of

75

/M-

ATP

to

5

/SM-actin

and

50

/LM-Sl

.

The

light

scattering

now

shows

a

rapid

decrease

but

with

only

300%

of

the

amplitude

seen

in

(A)

followed

by

reassociation

as

before.

The

fluorescence

signal

has

the

same

amplitude

as

in

A.

The

length

of

the

steady

state

and

the

rate

of

the

reassociation

reaction

differ

in

A

and

B

because

of

the

different

ATPase

rates

in

the

two

experiments.

Reaction

conditions:

pH

7.0,

ionic

strength

0.012

M,

20

'C.

In

both

cases

the

solutions

were

mixed

at

the

small

arrow

(1)

200

ms

after

the

recorder

was

triggered.

From

[33]

with

permission.

equilibrium

proposal

of

the

3G

model

in

that

the

two

acto

*Sl

states

have

been

identified

and

the

ATP

causes

the

predominant

bound

state

to

switch

from

the

R

state

in

the

absence

of

nucleotide

to

the

A

state.

As

the

ATP

is

hydrolysed

and

the

products

are

sequentially

released

the

acto

SI

complex

pro-

gressively

reverts

to

the

rigor-like

low

fluorescence

A-M

or

A

-

M

N

state.

No

direct

information

is

available

on

the

acto

Sl

ADP

Pi

state,

as

addition

of

Pi

to

acto

*SI

-

ADP

results

in

minimal

binding

of

phosphate

to

the

complex

[17].

In

principle

the

acto

SI

ADP

-P

state

could

be

significantly

occupied

during

the

steady

state,

but

at

physiological

ionic

strength

the

affinity

of

actin

for

S1

ADP

P1

is

too

weak

for

actin

to

remain

bound.

At

low

ionic

strength

the

affinity

of

actin

for

Sl

nucleotide

complexes

is

greatly

increased,

but

the

rate

of

the

hydrolysis

step

Table

1.

Variation

in

the

value

of

K.

with

nucleotide

analogue

and

ionic

strength

Ionic

strength

(M)

Nucleotide

0.01

0.1

0.3

0.5

None

ADP

Pyrophosphate

ATP

ATPyS

ADP

+

vanadate

nd

>

20

2.3

280*

74t

40*

10

2.5

nd

10-2

All

values

from

[34],

except

*

from

[32]

and

t

from

[93]

becomes

sufficiently

slow

for

S1

ATP

to

be

a

major

component

of

the

steady

state

[36-38].

Kinetic

studies

The

pressure

perturbation

studies

in

the

absence

of

nucleotide,

described

above,

have

provided

kinetic

information

on

the

transition

between

the

two

attached

states

of

acto

SI

in

addition

to

the

equilibrium

measurements

[32].

Similar

studies

in

the

presence

of

nucleotide

in

combination

with

stopped

flow

measurements

have

defined

the

rate

of

the

transition

in

the

presence

of

ADP

and

ATP

[19,33,40].

A

summary

of

the

rate

and

equilibrium

constants

which

have

been

measured

for

steps

I

and

II

in

the

3G

model

is

provided

in

Table

2

and

they

are

discussed

below.

In

the

pressure-jump

experiment

in

the

absence

of

nucleotide

the

observed

rate

of

the

fast

relaxation

(attributed

to

k+i

+

k

II)

was

complete

in

the

pressure

release

time

(200

Its)

under

all

the

conditions

used.

This

limits

the

rate

of

the

transition

to

>

2000

s-i.

Thus

the

transition

between

the

two

attached

states

is

a

fast

equilibrium

process

in

the

absence

of

nucleotide.

It

is

also

fast

in

the

presence

of

ATP.

The

maximum

rate

of

the

ATP-induced

dissociation

of

rabbit

skeletal

acto

S1

is

too

fast

to

measure

at

ambient

temperatures

by

conventional

rapid

flow

methods.

It

has

been

measured

(120

s-1

[41])

for

arterial

myosin

and

estimated

as

1500

s-1

for

other

'slow'

myosins

[42].

The

rate

for

skeletal

myosin

can

however

be

measured

directly

at

temperatures

below

1

'C.

Millar

&

Geeves

[19]

were

able

to

measure

the

rate

over

the

range

-

15

to

0

'C

by

using

ethylene

glycol

solvents

to

prevent

freezing.

This

allowed

them

to

extrapolate

to

the

maximum

rate

at

20

°C

as

5000

s-I

and

this

was

assigned

to

a

protein

isomerization

which

preceded

dissociation

of

actin.

In

a

subsequent

study

ATPyS

was

used

in

place

of

ATP

[33]

as

it

has

been

shown

to

have

a

similar

affinity

for

S1

and

acto

*

S1

as

has

ATP

yet

the

maximum

rate

of

the

ATPyS-induced

dissociation

of

actin

was

one-tenth

of

that

of

ATP

[43].

This

allowed

the

isomerization

rate

to

be

measured

over

the

range

0-20

°C

and

demonstrated

the

validity

of

the

method

used

to

estimate

the

rate

of

the

reaction

for

ATP

from

studies

below

0

°C.

The

ATP-induced

dissociation

experiment

was

also

repeated

but

using

the

pyrene

signal

to

monitor

the

reaction.

This

demonstrated

that

the

event

monitored

by

pyrene

fluorescence

occurred

at

the

same

rate

as

the

isomerization

which

limited

the

rate

of

actin

dissociation

and

so

the

rate

of

A

M

T

-.A-M

T

was

assigned

to

5000

s-

.

The

significance

of

this

result

is

in

relation

to

the

requirement

of

both

the

3G

and

Eisenberg

models

for

a

reversal

of

the

weak-

to-strong

isomerization

before

detachment

of

the

crossbridge

takes

place.

The

rate

of

5000

s-1

in

solution

means

that

if

the

rate

of

reversal

of

the

A-to-R

transition

is

similar

in

an

unstrained

crossbridge

then

such

a

reversal

followed

by

detachment

can

occur

in

less

than

1

ms.

Thus,

even

if

the

isomerization

is

directly

Table

2.

Rate

and

equilibrium

constants

for

the

two-step

binding

of

actin

to

myosin-nucleotide

complexes

The

values

quoted

are

those

appropriate

for

pH

7,

20

°C,

ionic

strength

of

0.15 M.

The

experiments

to

define

the

constants

are

described

in

the

text.

Nucleo-

K,

k,1

k-I

k+11

k

-l

tide

(M-')

(M-1.

S-1) (S-1)

K11

(s-1)

(s-1)

None

5

x

104

ATP

103-104

ADP

5

x

104

2x

106

>

2x

106

4x

104

40

200

2000

>

500

102

50

2

10

4

10

5000

0.4

1991

6

Dynamics

of

muscle

contraction

coupled

to

force

generation,

the

lifetime

of

the

negatively

strained

crossbridge

will

not

be

significant.

In

marked

contrast

to

the

previous

two

rate

measurements

the

rate

of

the

isomerization

between

A-M

-D

and

A-

M

-D

has

been

measured

as

4

s-'.

ADP

binding

to

acto

SI

has

been

shown

to

be

a

rapid

equilibrium

reaction

with

Kr,

=

104

M-1,

and

a

dissociation

rate

constant

of

500

s-1

[25,44].

However,

the

change

in

pyrene

fluorescence

observed

on

adding

ADP

to

acto

SI,

under

conditions

where

no

dissociation

of

actin

takes

place,

was

4

s-1

[40].

This

allowed

the

assignment

of

the

rate

of

A-M

D

A

M

D

as

4

s-

.

This

rate

is

substantially

below

the

maximum

steady-state

actomyosin

ATPase

rate

in

solution

(and

the

ATPase

rate

of

a

rapidly

contracting

muscle

fibre)

and

therefore

little

flux

through

this

transition

will

take

place

during

rapid

turnover.

Furthermore

the

rate

of

ADP

dissociation

from

A-M

-D

has

been

estimated

to

be

2

s-1

([40];

see

later

discussion),

therefore

the

A-M

D

state

cannot

be

significantly

occupied

during

rapid

ATP

turnover.

This

contrasts

with

the

view

of

Sleep

&

Hutton

[17]

who

showed,

using

isotope

exchange

studies,

that

two

acto

Sl

ADP

states

existed

during

ATP

turnover,

only

one

of

which

could

be

readily

formed

by

incubating

ADP

with

acto

-SI

(A

*

M

D).

The

experimental

data

suggest

that

the

second

com-

plex

is

present

during

ATP

turnover

at

50

times

the

concentration

of

A-

M

*D

or

that

the

equilibrium

constant

is

50

in

favour

of

A-

M

D

or

a

combination

of

the

two.

Sleep

&

Hutton

went

on

to

discuss

the

possibility

that

A-

M

-

D

was

not

on

the

main

ATPase

pathway.

The

data

of

Geeves

[40]

and

Geeves

&

Jeffries

[34]

suggest

a

value

of

10

for

K2

but

at

the

low

ionic

strengths

used

by

Sleep

&

Hutton

this

becomes

>

20,

allowing

the

possibility

that

A-M

-

D

is

the

second

state

identified

by

Sleep

&

Hutton.

However

these

more

recent

data

suggest

that

at

high

turnover

rates

and

physiological

ionic

strength,

it

is

A-M

D

which

is

not

on

the

main

ATPase

pathway

as

the

dissociation

of

ADP

from

this

complex

or

its

isomerization

to

A

M

D

is

slower

than

the

turnover

rate.

This

need

not

be

the

case

when

the

turnover

rate

is

substantially

reduced,

such

as

occurs

in

a

muscle

which

is

prevented

from

shortening.

Under

these

isometric

conditions

the

ATPase

is

considerably

reduced

and

is

comparable

to

the

rate

of

the

transition

of

A-M

-

D

to

A-

M

-

D,

to

the

rate

of

loss

of

ADP

from

A-M

*

D

and

the

detachment

of

actin

from

A-M

D.

The

slow

rate

of

detachment

of

actin

from

this

complex

is

unusual

and

suggests

that

if

the

rate

is

similar

in

the

intact

muscle

then

this

complex

could

have

a

role

in

allowing

tension

to

be

maintained

without

rapid

hydrolysis

of

ATP;

i.e.

it

is

in

some

ways

comparable

to

the

catch

crossbridges

of

molluscan

muscle

[39,39a],

albeit

on

a

much

faster

time

scale.

[The

catch

state

of

molluscan

muscle

is

a

contraction

state

which

is

maintained

with

a

low

level

of

energy

expenditure

and

is

thought

to

operate

through

a

long-lived

force-holding

attached

crossbridge.

There

is

evidence

that

this

is

a

long-lived

actomyosin

-

ADP

state

[116]

and

if

this

is

correct

then

both

actin

and

ADP

must

detach

slowly

from

the

complex.

The

conversion

of

this

state

to

the

normal

actomyosin

-

ADP

state

with

a

fast

rate

of

ADP

dissociation

would

then

be

influenced

by

both

calcium

and

myosin

light

chain

phosphorylation.

Any

relationship

between

this

catch

actomyosin

*

ADP

state

and

the

A-M

-

D

state

has

not

been

investigated.

Although

the

properties

of

the

two

states

are

similar

their

lifetimes

must

differ

by

several

orders

of

magnitude.]

THE

IMPLICATIONS

OF

THE

TWO-STEP

BINDING

MODEL

The

detailed

solution

studies

discussed

so

far

lend

support

to

the

3G

model

of

actin

and

myosin

interactions

in

that

two-step

association

of

actin

with

myosin

and

myosin

nucleotide

complexes

have

been

identified

and

the

equilibrium

constant

of

the

isomerization

step

depends

upon

the

bound

nucleotide

in

the

manner

proposed.

I

want

now

to

turn

to

the

implications

and

predictions

of

this

model

for

force

generation

in

muscle.

The

most

widely

accepted

model

for

force

generation

in

muscle

is

the

cycling

crossbridge

model

(shown

in

its

simplest

form

in

Fig.

2).

In

this

model,

force

generation

is

the

result

of

a

cyclical

interaction

between

myosin

heads

and

actin

driven

by

ATP.

The

nature

of

the

structural

change

remains

undefined;

it

may

involve

only

the

actin-myosin

interface

such

that

the

two

proteins

roll

past

each

other,

a

gross

change

in

shape

or

size

of

a

single

myosin

head

or

it

could

involve

both

the

myosin

head

and

the

S2

fragment

as

in

the

model

of

Harrington

[45].

What

is

clear

is

that

the

structural

change

which

takes

place

has

to

be

sufficient

for

the

generation

of

the

mechanical

force

and

to

account

for

the

4-10

nm

axial

displacement

of

the

crossbridge

required

by

transient

mechanical

measurements

[46].

The

force-generating

(or

force-holding)

state

thus

created

has

to

have

a

lifetime

long

enough

to

account

for

the

level

of

force

produced

in

a

non-shortening

(isometric)

muscle

and

yet

have

a

lifetime

short

enough

to

allow

for

the

rapid

shortening

of

a

muscle

under

zero

load.

The

most

straight-

forward

possibility

is

that

the

lifetime

of

this

force-maintaining

state

is

dependent

upon

the

mechanical

condition

of

the

crossbridge,

i.e.

the

lifetime

of

the

force-holding

state

is

strain-

dependent;

the

higher

the

strain

the

longer

the

lifetime.

In

the

3G

model

the

structural

transition

(to

the

force-holding

state)

is

clearly

correlated

with

the

transition

from

the

associated

state

(A)

to

the

rigor-like

state

(R).

It

was

discussed

in

the

original

paper

how

this

transition

may

be

coupled

directly

or

indirectly

with

the

force-generating

event.

The

indirect

route

can

be

envisaged

as

the

structural

change

in

the

myosin

head

not

generating

force

itself

but

allowing

some

other

event

(such

as

S2

melting

in

Harrington's

model)

to

occur.

The

indirect

model

still

requires

some

coupling

of

the

state

of

the

myosin

head

with

the

state

of

the

force-generating

element,

and

in

the

absence

of

any

clear

evidence

for

how

this

coupling

might

occur

it

is

simpler

for

the

purposes

of

this

discussion

to

consider

the

direct

mechanism

alone;

i.e.

the

A-to-R

transition

is

the

force-generating

event

and

therefore

the

properties

ascribed

to

the

force-generating

event

above

must

apply

equally

to

the

A-to-R

transition.

This

transition

must

therefore

involve

a

structural

change

sufficient

to

account

for

the

mechanical

properties

of

the

crossbridge.

Two

other

conditions

can

be

identified

which

are

required

for

this

transition

to

be

the

force-generating

event.

First,

the

transition

must

be

coupled

to

the

release

of

products

of

the

ATPase

reaction,

i.e.

no

acceleration

of

the

release

of

products

can

occur

without

formation

of

the

R

state.

Secondly,

the

transition

in

the

organized

system

must

be

sensitive

to

mechanical

strain

and

parameters

which

affect

the

transition

must

also

affect

force

generation.

The

relationship

between

the

A-to-R

transition

and

these

three

conditions

will

be

considered

in

the

next

sections.

Structural

change

All

versions

of

the

cycling

crossbridge

model

of

contraction

require

at

least

two

structural

states

of

the

actomyosin

complex

with

the

transition

between

the

two

states

being

referred

to

as

the

'

power

stroke'

or

the

'force-generating

event'.

A

brief

review

of

the

possible

structural

changes

in

the

actomyosin

crossbridge

appeared

in

[47]

and

the

principal

structural

changes

discussed

are

shown

in

Fig.

6.

That

article

was

prompted

by

neutron-

scattering

data

that

suggest

that

any

deformation

of

the

myosin

head

shape

can

involve

no

more

than

20

%

of

the

mass

of

the

head

and

therefore

limits

the

form

of

any

structural

change

[48].

Structural

studies

of

myosin

and

actomyosin

have

so

far

been

limited

to

the

resolution

achieved

with

the

electron

microscope

and,

as

with

the

neutron-scattering

data,

no

evidence

of

a

gross

change

in

the

structure

of

the

myosin

head

has

been

obtained

Vol.

274

7

M.

A.

Geeves

(b)

(c)

(f)

Fig.

6.

Schematic

illustration

of

different

ways

of

producing

an

axial

shift

of

4-12

nm

of

the

rod

end

of

the

myosin

head

(M)

on

actin

(A)

during

the

contractile

cycle

of

muscle

The

black

helices

(T)

represent

tropomyosin

strands.

(a)

Swing

about

the

actin-myosin

interface;

(b)

roll

of

the

myosin

head

(roll

axis

indicated

by

R--R);

(c)

simple

axial

translation;

(d)

distributed

shear

along

the

myosin

head;

(e)

swing,

but

leaving

a

small

head

domain

(p)

unchanged;

(f)

privoting

one

major

domain

of

the

head

(D1)

relative

to

another

domain

(D2).

Squire

[47]

discussed

these

models

and

concluded

that

there

were

good

grounds

for

eliminating

models

(c),

(d)

and

(f),

leaving

models

(a)

and

(e)

as

possible

and

(b)

as

possible

but

unlikely.

Note

that

a

modified

form

of

(a)

could

involve

movement

of

a

rigid

myosin

head

firmly

attached

to

a

domain

of

the

actin

molecule

that

itself

moves

relative

to

the

rest

of

the

actin

filament.

From

[47]

with

permission.

Under

conditions

where

the

actin

is

strongly

attached

to

SI

and

the

R

state

predominates

then

the

two

residues

were

estimated

to

be

6

nm

apart.

Yet,

under

conditions

where

the

actin

is

weakly

attached

the

distance

is

reduced

to

<

3

nm,

suggesting

some

major

rearrangement

of

the

two

proteins.

These

distances

were

calculated

on

the

assumption

that

only

a

single

acto

-S1

complex

is

present

in

each

of

the

experiments.

If

more

than

one

complex

is

present

then

the

estimated

distance

represents

an

average

value.

It

would

be

of

interest

to

measure

the

distance

under

conditions

where

the

pyrene

signal

suggests

equal

occupancy

of

the

two

states.

The

kinetic

models

of

Fig.

3

do

not

give

any

direct

structural

information

on

the

nature

of

the

transition

between

the

two

actomyosin

states.

The

transition

could

represent

a

structural

change

in

the

myosin

head,

in

the

actin,

in

the

actomyosin

interface

or

a

combination

of

all

three

and

still

be

compatible

with

the

proposed

models.

However,

specific

kinetic

models

do

incorporate

a

relationship

between

the

nucleotide-binding

site

and

the

actin-binding

site

which

has

structural

implications.

For

example,

the

discussion

of

Goody

&

Holmes

[16]

on

the

reciprocal

nature

of

the

nucleotide

and

actin

binding

to

myosin

requires

communication

between

the

two

binding

sites.

The

kinetic

definition

of

actomyosin

*

nucleotide

states

does

provide

thermo-

dynamic

information

on

the

transition

between

states

which

can

set

limits

on

the

type

of

structural

change

involved.

Solution

studies

can

also

provide

information

on

the

feasibility

of

isolating

a

particular

state

for

detailed

structural

analysis.

One

problem

with

attempting

to

find

a

structure

of

actomyosin

other

than

the

stable

rigor

complex

is

that

such

states

may

be

very

short

lived.

Even

if

it

is

possible

to

define

conditions

where

the

weakly

bound

acto

Sl

ATP

is

the

predominant

species

in

solution

it

may

be

in

very

rapid

equilibrium

with

other

states

and

the

structural

analysis

could

sample

the

minority

species

disproportionately.

The

kinetic

studies

have

shown

that

when

nucleotide

binds

to

acto

SI

then

the

fluorescence

of

a

pyrene

group

covalently

attached

to

Cys-374

on

actin

senses

the

nucleotide

binding.

FRET

studies

have

shown

that

in

the

rigor

complex

Cys-374

of

actin

is

some

4

nm

away

from

the

nucleotide

binding

site

on

SI

[30].

Cys-374

is

therefore

unlikely

to

be

sensing

the

proximity

of

the

nucleotide

directly.

In

addition,

both

ADP

and

ATP

are

in

rapid

equilibrium

with

the

rigor-like

complex

at

a

rate

which

is

consistent

with

a

diffusion-limited

reaction

[19,25]

but

the

nucleotide-induced

change

in

pyrene

fluorescence

occurs

at

5000

s-1

for

ATP

and

4

s-'

for

ADP.

These

observations

suggest

that

the

pyrene

is

not

monitoring

the

nucleotide

binding

itself

but

a

nucleotide-induced

change

in

the

conformation

of

the

acto

*

SI

nucleotide

complex

which

is

communicated

from

the

nucleotide

binding

site

to

the

acto

*

SI

interface.

The

pyrene

is

therefore

not

monitoring

some

very

local

perturbation

affecting

only

its

own

environment.

[35,49].

Other

probes

of

the

structure

of

myosin

and

actomyosin,

fluorescence

energy

transfer

(FRET)

[30],

chemical

cross-linking

[50],

proteolytic

susceptibility

[51],

and

spectroscopic

probes

on

either

the

protein

or

nucleotide

[7,8,10,52,53,66]

have

revealed

changes

in

myosin

on

nucleotide

binding

and

in

the

acto

*SI

interface

between

rigor

and

weakly

attached

crossbridges.

These

approaches

can

be

sensitive

to

small,

local

changes

in

structure

and

are

therefore

not

inconsistent

with

the

absence

of

a

gross

structural

change.

Several

recent

reviews

have

discussed

the

detailed

structural

aspects

of

myosin,

actomyosin

and

the

crossbridge

[55,57,58].

One

approach

which

has

shown

evidence

of

a

substantial

conformational

change

in

acto

*

SI

is

the

use

of

FRET

to

measure

the

distance

between

Cys-374

on

actin

(the

same

site

as

labelled

by

pyrene)

and

Cys-177

on

the

alkali

1

light

chain

of

S1

[59,60].

Table

3.

Molar

volume

changes

for

reaction

of

biochemical

interest

Values

are

taken

from

[131].

Molar

volume

change

(cm3/mol)

Phosphate

ionization

(pK7)

Tris

ionization

Hydrogen

bond

formation

Myosin

filament

elongation

Microtubule

elongation

Chymotrypsin

denaturation

Myoglobin

denaturation

Acto

SI

isomerization

-24.0

+

1.0

+1.0

-280

-50

-43

-100

-80

to

-

100

1991

8

Dynamics

of

muscle

contraction

In

a

complementary

study

a

fluorescent

probe

on

the

ribose

of

ATP

[2'(3')-O-(N-methylanthraniloyl)-ATP,

abbreviated

to

mant-ATP]

has

been

used

to

probe

the

relationship

between

actin

and

nucleotide

binding

to

myosin

S1

[62].

These

studies

have

shown

that

the

binding

of

'mant'

nucleotides

to

S1

induces

a

2-3-fold

enhancement

of

mant

fluorescence,

but

the

mere

binding

of

nucleotide

to

acto

S1

does

not

induce

the

fluorescence

change.

The

fluorescence

change

monitors

a

conformational

change

in

the

complex

which

occurs

at

the

same

rate

and

to

the

same

extent

as

the

conformational

change monitored

by

the

pyrene

signal

on

actin.

As

the

same

transition

is

perturbing

the

environment

of

two

fluorescent

probes

which

are

4

nm

apart,

the

transition

is

not

the

result

of

a

small

local

rearrangement.

As

discussed

in

the

previous

section,

the

isomerization

of

acto

S5

can

be

perturbed

by

a

change

in

hydrostatic

pressure

both

in

the

absence

of

nucleotide

and

in

the

presence

of

ADP.

The

pressure-induced

change

in

the

equilibrium

constant

for

transition

(KII)

suggests

a

volume

change

of

80-120

cm3

mol-I

[32].

This

is

a

large

volume

change,

as

is

evident

from

comparison

with

the

volume

changes

listed

in

Table

3.

This

implies

that

the

conformational

change

results

in

a

structural

change

equivalent

to

the

exposure

to

the

solvent

of

either

four

buried

charged

groups,

four

buried

methyl

groups,

the

deprotonation

of

four

carboxyl

groups

or

a

combination

of

these

three.

The

volume

change

is

similar

to

that

observed

for

denaturation

of

small

proteins.

Thus,

the

fluorescence

signals

from

both

pyrene

and

mant

nucleotides

and

the

volume

changes

suggest

that

the

protein

isomerization

is

a

major

reorganization

of

the

structure

of

acto

*

SI

and

this

transition

can

take

place

in

the

presence

or

absence

of

nucleotide.

Changes

in

solvent

composition

can

result

in

the

destabilization

of

the

rigor-like

state

in

favour

of

the

attached

state.

Increases

in

ionic

strength

or

the

presence

of

organic

solvent

reduce

the

equilibrium

constant

of

the

transition

in

the

absence

of

nucleotide

or

in

the

presence

of

ADP

[32,34,63].

Table

1

documents

the

observed

values

of

KII

over

a

range

of

ionic

strengths

in

the

absence

of

nucleotide

and

in

the

presence

of

ADP.

Interestingly,

both

increases

in

ionic

strength

and

the

presence

of

organic

solvent

reduced

the

estimate

of

the

volume

change

of

the

reaction

[63].

Large

volume

changes

in

solution

normally

result

from

changes

in

hydration

shells

around

the

reacting

species.

Thus

the

presence

of

large

concentrations

of

either

ions

or

organic

molecules

could

produce

a

significant

amount

of

order

in

the

bulk

solvent,

reducing

the

free

energy

released

when

water

is

removed

from

the

hydration

shell

of

the

protein.

It

has

been

established

that

at

least

one

(and

probably

more

than

one)

conformational

change

takes

place

in

Sl

when

nucleotide

binds

even

in

the

absence

of

actin

[8,10,52,61,64,65].

Clearly

there

is

some

relationship

between

the

affinity

of

a

nucleotide

for

S1

and

the

ability

of

that

nucleotide

to

dissociate

actin

from

the

rigor

complex

(Table

4).

However,

the

relationship

between

the

conformational

changes

induced

in

SI

by

nucleotide

and

the

isomerization

of

the

acto

-S1

complex

discussed

here

is

Table

4.

Affinity

of

nucleotide

analogues

for

Si

and

acto

*S1

Affinity

of

Affinity

of

Affinity

of

N

for

M

N

for

A-M

A

for

M

N

(M-1)

(M-1)

(M-')

ATP*

1011

0.5x

103

ATPySt

107

1

x

103

AMP-PNPt

107

0.5

x

103

ADP§

106

5

x

103

References:

*[3,19],

t[33,52],

t[20],

§[401.

Vol.

274

<

10,

105

106

not

understood.

If

the

A-to-R

transition

is

a

change

in

the

conformation

of

S1

alone

then

studies

of

the

conformation

of

SI

and

SI

nucleotide

complexes

are

sufficient

to

define

the

molecular

changes

responsible

for

force

generation.

Indeed,

Shriver

&

Sykes

[7]

proposed

such

a

model

based

on

studies

of

SI

in

the

absence

of

actin.

Most

proteins

undergo

conformational

changes

when

a

ligand

binds

so

it

is

important

to

distinguish

between

small

local

changes

in

conformation

which

may

be

a

part

of

the

ligand

recognition/docking

process

and

a

major

conformation

change

in

which

information

is

transmitted

to

other

parts

of

the

molecule.

The

experimental

work

supporting

the

model

of

Shriver

[61]

and

Shriver

&

Sykes

[7]

suggested

that

both

temperature

and

nucleotides

can

be

used

to

manipulate

the

SI

conformation,

so

it

should

be

possible

to

test

how

the

different

conformations

interact

with

actin.

One

implication

in

the

original

Lymn

&

Taylor

model

was

that

the

conformational

change

that

takes place

in

the

myosin

head

during

the

power

stroke

is

reversed

when

actin

is

detached.

At

the

time,

the

only

significant

event

known

to

occur

during

the

detached

part

of

the

cycle

was

the

hydrolysis

step

and

so

it

was

reasonable

to

suggest

the

hydrolysis

step

as

the

reversal

of

the

conformational

change

which

results

in

the

power

stroke.

The

later

models

do

not

necessarily

attach

any

specific

significance

to

the

conformational

changes

occurring

when

actin

is

detached.

In

the

absence

of

direct

structural

evidence

we

have

only

indirect

information

to

guide

our

prejudices.

A

significant

observation

is

that the

transition

in

acto

Sl

occurs

with

a

significant

volume

change.

We

have

so

far

failed

to

find

any

evidence

of

a

significant

volume

change

on

either

ADP

or

AMP-PNP

binding

to

SI

in

the

absence

of

actin

(M.

A.

Geeves,

unpublished

work).

The

evidence

discussed

so

far

supports

the

view

that

a

major

conformational

change

takes

place

in

the

acto

-

Sl

complex

and

this

conformational

change

is

sensitive

to

the

nucleotide

bound

to

SI.

There

is

no

information

on

where

in

the

structure

this

change

takes

place

except

that

the

change

perturbs

the

en-

vironment

of

probes

attached

to

both

actin

and

nucleotide,

and

changes

the

distance

between

a

point

on

actin

and

a

point

on

the

myosin

light

chain.

The

values

of

KII

given

in

Table

1

define

the

fraction

of

an

actin-bound

S1

nucleotide

complex

in

the

two

states

A

and

R.

For

example,

addition

of

ADP

to

acto

Sl

in

0.3

M-KCI

will

result

in

30

%

of

the

complex

occupying

the

A

state.

Further

exploration

of

the

effect

of

solvent

conditions

on

KI,I

particularly the

nature

of

the

anion

used

and

the

presence

of

organic

solvent

[63],

may

be

able

to

increase

this

to

>

50

%.

The

ability

to

define

the

state

of

actin-bound

myosin

bound

may

be

useful

if

coupled

to

the

structural

methods

mentioned

earlier

(electron

microscopy,

FRET,

cross-linking

probes,

proteolysis

probes,

spectroscopic

probes

and

scattering

measurements).

The

relationship

between

the

isomerization

of

acto

*

S1

and

product

release

In

order

for

the

3G

model

to

account

for

the

steady-state

ATPase

behaviour

of

acto

*

S1

and

to

allow

the

coupling

of

the

ATPase

reaction

to

force

generation,

the

mere

binding

of

actin

to

a

myosin-product

complex

should

not

accelerate

the

release

of

products

from

SI.

Only

the

formation

of

the

R

state

(A

M

N)

should

accelerate

the

release

of

products.

This

was

implied

in

the

3G

model

by

stating

that

KI

was

independent

of

the

presence

of

nucleotide

on

S1

and,

for

this

to

be

true,

thermodynamic

balance

requires

that

the

binding

of

nucleotide

to

M

is

the

same

as

to

A-M.

The

thermodynamic

argument

only

applies

to

the

equi-

librium

constants,

not

to

the

rate

constants.

The

formation

of

the

A-M

state

could

increase

both

the

rate

of

binding

of

nucleotide

and

its

rate

of

release.

Little

direct

information

is

available

on

the

rate

of

product

dissociation

from

the

A-M

state,

as

this

state

is

difficult

to

isolate,

but

the

equilibrium

constants

which

have

been

9

M.

A.

Geeves

Attached

Low

force

\O

QOC

-IN

(a)

A

state

Low

force

(b)

Attached

High

force

#l

Detached

R

state

A-M-D-P

High

force

A-M-D

A-M

ATP

Detached

crossbridge

Fig.

7.

Relationship

between

the

'3G'

model

in

solution

and

the

mechanical

crossbridge

cycle

in

muscle.

(a)

The

simple

crossbridge

cycle

which

consists

of

three

mechanical

states.

The

detached

crossbridge

attaches

to

actin

rapidly

and

reversibly

to

form

the

'low

force'

crossbridge.

The

transition

from

the

low-force

to

the

high-force

state

is

shown

diagrammatically

as

a

change

in

the

angle

at

which

the

attached

crossbridge

binds

to

actin

and

which

occurs

with

the

stretching

of

an

elastic

element

shown

as

a

spring

in

the

S2

segment

of

the

crossbridge.

Binding

of

ATP

to

the

high-force

crossbridge

results

in

essentially

irreversible

detachment

of

the

crossbridge

from

actin.

(b)

The

'3G'

solution

model

is

redrawn

to

emphasize

the

correspondence

between

the

states

identified

in

solution

and

the

three

states

of

the

mechanical

cycle.

For

simplicity

only

those

states

which

are

thought

to

be

significantly

occupied

are

included.

The

detached

M

and

M-D

states

are

thought

to

be

rarely

occupied,

the

A-

M

T

state

is

transiently

occupied

each

time

ATP

binds

but

has

a

very

short

lifetime,

and

the

A-M

state

is

in

rapid

equilibrium

with

the

A-M

state

([A

M]/[A-M]

>

100).

measured

(see

above

and

Table

4)

are

consistent

with

little

change

in

affinity

of

nucleotide

for

M

and

A-M.

In

the

case

of

the

interaction

of

acto

*

SI

with

ADP,

all

of

the

rate

and

equilibrium

constants

have

been

estimated.

As

shown

in

Table

2,

KI

is

identical

in

the

presence

and

absence

of

ADP

and

therefore

the

affinity

of

ADP

for

M

and

A-M

must

be

the

same.

The

rate

of

ADP

dissociation

from

A-M

cannot

be

measured

directly,

but

in

a

complex

series

of

experiments

it

was

shown

that

ADP

dissociates

from

A-M

*

D

at

a

rate

which

is

not

significantly

faster

than

the

rate

at

which

it

dissociates

from

M

*

D

(2

s-I

[40]).

The

fluorescent

ADP

analogue

mant-ADP

can

be

displaced

from

its

complexes

with

S1

and

acto

-S

by

the

addition

of

a

large

excess

of

ATP.

The

observed

rates

of

mant-ADP

release

from

M,

A-M

and

A-

M

were

0.2,

0.5

and

400

s-

respectively

[62],

confirming

this

interpretation.

In

the

case

of

ATP

the

experiment

can

in

principle

be

done

by

displacing

isotopically

labelled

ATP

from

A-M

-T

at

very

low

ionic

strength.

The

experiment

has

been

performed

by

Barman,

Travers

and

their

colleagues

[65]

using

the

cold

chase

method.

The

interpretation

of

the

results

is

complicated

by

the

observation

that

the

SI

1

ATP

state

formed

immediately

on

release

of

actin

from

the

ternary

complex

is

not

the

same

as

that

formed

on

mixing

ATP

with

S1

[9,65].

The

cold

chase

experiments

do

however

show

that

the

ATP

bound

to

A-M

-

T

is

bound

tightly

with

a

dissociation

rate

constant

of

<

5

s-1.

The

myosin

product

complex

of

most

interest

is

the

complex

with

both

ADP

and

Pi

bound.

This

unfortunately

is

not

readily

formed

by

the

addition

of

Pi

to

acto-

S1

ADP

as

little

evidence

of

P1

binding

can

be

found.

Indeed,

calculations

suggest

a

binding

constant

of

>

1

M

for

P1

to

be

appropriate

[21].

In-

formation

on

the

binding

of

P1

comes

from

isotope

exchange

studies

during

hydrolysis

of

ATP.

Incubation

of

labelled

Pi

with

acto

SI

in

the

presence

of

unlabelled

ATP

can

lead

to

the

formation

of

labelled,

protein-bound

ATP

[17].

These

experiments

were

discussed

above

and

led

to

the

first

suggestion

of

two

acto

S1

ADP

complexes,

one

of

which

cannot

readily

be

formed

by

incubating

actin,

SI

and

ADP

together

but

which

can

bind

phosphate.

In

the

3G

model

this

state

could

be

A-M

D,

which

will

bind

Pi

with

an

affinity

similar

to

that

of

M

D.

We

have

made

some

preliminary

observations

which

suggest

that

Pi

can

bind

to

acto

Sl

ADP

at

high

pressure,

conditions

which

increase

the

concentration

of

A-M

-

D,

but

the

interpretation

of

these

experiments

is

complex

and

requires

confirmation

by

further

studies.

To

summarize,

the

data

available,

though

not

complete,

are

consistent

with

nucleotide

and

Pi

binding

to

A-M

with

an

affinity

similar

to

that

for

free

SI

and

with

the

fact

that

acceleration

of

the

release

of

products

of

the

ATPase

reaction

requires

the

formation

of

the

rigor-like

state.

The

relationship

between

the

isomerization

of

acto.Sl

and

force

generation

Studies

of

the

crossbridge

cycle

in

contracting

muscle

and

the

coupling

of

the

mechanical

events

to

the

biochemical

events

in

actomyosin

have

been

reviewed

several

times

recently

[76-78,117,118]

and

no

attempt

will

be

made

here

to

consider

all

of

this

evidence.

Only

those

experiments

which

bear

directly

on

the

interaction

between

actin

and

myosin

as

studied

in

solution

will

be

considered

in

detail.

At

its

simplest

level

the

mechanical

cycle

can

be

considered

as

a

three-step

cycle,

as

shown

in

Fig.

7(a).

Each

of

these

three

states

will

consist

of

a

subset

of

particular

myosin

or

actomysin

nucleotide

states.

There

is

general

agreement

that

the

detached

crossbridge

is

predominantly

a

mixture

of

M

*

ATP

and

M

ADP

*

P1

(i.e.

there

is

little

occupancy

of

the

M

and

M

*

D

states)

and

these

states

are

in

rapid

equilibrium

with

the

attached

low-force

state.

The

transition

from

the

low-

force

state

to

the

high-force

state

is

the

key

event,

the

details

of

which

have

not

been

resolved.

The

binding

of

ATP

to

the

high-

force

crossbridge

results

essentially

in

irreversible

detachment.

In

the

3G

model

there

is

an

obvious

correlation

between

the

three

principal

solution

states

and

the

three

states

of

the

mechanical

model.

This

assignment

implies

that

all

A-M

N

states

have

the

same

mechanical

properties.

This

may

be

true,

but

a

subtle

change

in

the

mechanical

properties

may

occur

as

the

nature

of

the

myosin-bound

nucleotide

changes.

The

available

energy

is

maximum

for

the

A-M

D

P

to

A

M

D

P

transition

when

coupled

with

the

loss

of

phosphate

which

traps

the

crossbridge

in

the

high-force

state.

The

3G

model

has

been

redrawn

in

Fig

7(b)

to

emphasize

the

correspondence

with

the

mechanical

model.

The

properties

of

the

A-to-R

state

transition

in

solution

have

been

described

above.

Significantly,

Coates

et

al.

[32]

pointed

out

that

this

transition

was

inhibited

by

increased

ionic

strength,

by

the

presence

of

ethylene

glycol

and

by

increases

in

hydrostatic

pressure.

The

data

in

Table

I

show

that

the

transition

is

sensitive

1991

lo

)

Dynamics

of

muscle

contraction

to

the

nucleotide

bound

to

myosin.

If

the

A-to-R

transition

occurs

id

the

contracting

fibre

and

is

coupled

to

the

force-

generating

event

(as

shown

in

Fig.

7),

then

these

same

treatments

would

be

expected

to

inhibit

force

generation.

There

is

evidence

to

support

this

in

most

cases.

Experiments

on

muscle

fibres

which

are

equivalent

to

those

which

can

be

readily

performed

in

solution

have

been

made

possible

by

the

development

of

the

use

of

skinned

muscle

fibres.

These

are

single

muscle

fibres

(or

small

bundles

of

such

fibres)

with

the

outer

membrane

chemically

[119]

or

mechanically

[120]

removed.

The

composition

of

the

solution

surrounding

the

crossbridges

can

therefore

be

readily

exchanged.

The

more

recent

development

of

photolabile

precursors

of

nucleotides

and

other

molecules

of

interest

(calcium,

inositol

trisphosphate)

has

allowed

kinetic

as

well

as

equilibrium

studies

to

be

made

on

such

fibres

[79-84].

Two

approaches

to

the

study

of

the

effect

of

nucleotide

or

other

factors

such

as

the

presence

of

ethylene

glycol,

on

the

mechanical

properties

of

the

crossbridge

have

been

made.

In

the

first,

nucleotide

is

added

to

a

muscle

fibre

in

a

mechanical

and

biochemical

equilibrium

state

such

as

rigor.

In

the

second,

the

muscle

fibre

is

perturbed

during

a

steady-state

contraction.

A

muscle

goes

into

rigor

in

the

absence

of

nucleotide

and

will

hold

a

fixed

tension

with

no

expenditure

of

energy.

The

addition

of

ethylene

glycol,

ADP

or

the

nucleotide

analogue

AMP-PNP

to

rigor

fibres

has

been

shown

to

induce

a

reversible

decline

in

the

measured

tension

(or

a

rightwards

shift

in

the

length-tension

relationship)

for

a

variety

of

muscle

types

[70,115,121].

In

complementary

experiments

the

extent

of

nucleotide

binding

to

the

crossbridges

increased

as

the

rigor

fibre

was

stretched

[115,127].

Marston

et

al.

[115]

suggested

that

these

effects

were

compatible

with

a

perturbation

of

the

equilibrium

between

the

low-

and

high-force

states

of

the

crossbridge,

nucleotide

or

ethylene

glycol

favouring

the

low-force

state.

In

a

complex

system

such

as

a

muscle

fibre

it

is

dangerous

to

extrapolate

too

readily

between

the

isolated

pure

proteins

in

solution

and

the

complex

mechanochemical

interactions

present

in

the

organized

system.

However,

while

these

effects

cannot

be

attributed

solely

to

the

influence

of

ADP,

AMP-PNP

and

ethylene

glycol

on

the

A-to-R

transition

in

fibres,

the

effects

are

in

the

expected

direction

and

are

of

the

order

of

magnitude

expected

from

solution

studies.

If

solution

studies

could

be

extrapolated

directly

to

single

muscle

fibres

then

a

10

MPa

pressure

rise

would

be

predicted

to

induce

a

small

(<

1

%)

decline

in

rigor

tension.

This

is

rather

small

to

be

detected

and

in

fact

the

observed

tension

changes

in

a

rigor

fibre

are

dominated

by

the

effects

of

pressure

on

the

length

of

an

elastic

element

in

series

with

the

crossbridge

[110].

Such

effects

on

the

elastic

element

can

also

be

seen

in

the

active

muscle,

but

in

this

case

the

effects

are

small

compared

to

the

effect

on

the

crossbridge

itself.

Studies

of

the

effect

of

pressure

on

these

elastic

elements

will

provide

information

on

the

structural

nature

of

the

elements;

however,

these

considerations

are

not

central

to

the

current

argument

and

will

not

be

discussed

here.

In

a

steady-state

contraction,

muscle

is

calcium-activated,

is

hydrolysing

ATP

and

is

generating

a

steady

active

tension.

If

the

crossbridges

are

independent

force-generating

elements

then

tension

is

directly

proportional

to

the

number

of

crossbridges

in

the

high-force

state.

A

perturbation

of

the

crossbridge

cycle

which

changes

the

fraction

of

crossbridges

in

the

high-force

state

will

therefore

change

the

measured

tension.

The

effects

of

ionic

strength,

hydrostatic

pressure

and

the

addition

of

ADP

or

P1

on

the

steady

active

tension

have

been

reported.

Several

studies

have

shown

that

the

level

of

isometric

tension

in

an

actively

contracting

muscle

fibre

is

sensitive

to

the

ionic

strength

of

the

bathing

solution

[68,69,1

1

1].

In

a

complementary

series

of

experiments

Gulati

&

Babu

[1

12]

demonstrated

that

the

effect

of

ionic

strength

could

not

be

attributed

to

changes

in

the

fibre

lattice

and

concluded,

therefore,

that

the

reduction

in

isometric

force

was

due

to

effects

on

the

crossbridge

cycle.

The

75

0

reduction

in

isometric

force

observed

in

frog

fibres

over

a

range

of

KCI

concentrations

from

0

to

0.2

M

has

both

the

direction

and

the

order

of

magnitude

expected

for

the

effect

of

KCI

on

K,

as

shown

in

Table

1.

However,

it

is

known

that

in

solution

ionic

strength

has

marked

effects

on

nucleotide

binding

to

both

myosin

and

actomyosin,

on

the

interaction

between

actin

and

myosin

in

the

presence

and

absence

of

nucleotide,

and

on

the

rate

of

the

ATP

hydrolysis

step.

Any

of

these

effects

could

lead

to

a

change

in

the

isometric

force

by

perturbing

one

or

more

steps

of

the

mechanical

cycle.

The

application

of

hydrostatic

pressure

to

an

isometrically

contracting

muscle

fibre

produced

a

reversible

depression

of

tension

of

0.8

%

per

MPa

pressure

rise

over

the

range

0.1-10

MPa.

(This

effect

has

since

been

observed

on

the

tetanic

tension

of

small

bundles

of

intact

electrically

stimulated

fibres

[71]

and

similar

results

were

originally

reported

on

whole

muscles

in

the

1930s

[73,74].)

Subsequent

studies

on

the

influence

of

ADP

and

Pi

on

the

observed

amplitude

of

the

pressure

effect

[75],

on

the

effect

of

pressure

on

the

equatorial

X-ray

scattering

[1

13]

and

on

the

time

scale

of

tension

recovery

following

a

rapid

release

of

high

pressure

[110]

support

the

contention

that

pressure

is

perturbing

a

crossbridge

event.

Once

again,

the

direction

and

size

of

the

pressure

effect

is

compatible

with

the

effect

of

pressure

on

the

A-to-R

transition

in

solution.

Evidence

for

two

states

of

the

actomyosin

nucleotide

complex

in

muscle

comes

from

studies

of

Pi

binding.

Isotope

exchange

studies

using

either

32P

or

180

have

shown

that

Pi

binds

to

an

actomyosin

ADP

complex

(and

is

incorporated

into

protein-

bound

ATP)

more

readily

in

a

skinned

muscle

fibre

during

an

isometric

contraction

than

in

a

rigor

or

relaxed

muscle

[67,122,128].

This

has

been

interpreted,

like

the

equivalent

experiments

with

purified

proteins

in

solution

[17],

as

demon-

strating

the

presence

of

an

additional

actomyosin

-

ADP

com-

plex

which

is

only

present

at

significant

concentrations

during

a

steady-state

contraction.

Addition

of

P1

to

a

contracting

isometric

muscle

results

in

a

reversible

depression

of

the

isometric

tension

by

up

to

500%

[123].

In

kinetic

studies

the

observed

rate

of

the

tension

decline

following

rapid

release

of

P1

from

caged

P1

is

faster

than

the

turnover

rate

of

the

ATPase

reaction

and

shows

evidence

of

saturation

at

high

Pi

concentrations

[125,126].

This

has

been

interpreted

in

terms

of

a

two-step

binding

reaction;

Pi

initially

binds

to

an

actomyosin

-

ADP

crossbridge

and

then

an

isomerization

of

the

complex

occurs

which

results

in

a

lower

isometric

force.

This

isomerization

could

correspond

to

a

reversal

of

the

A-M

D-Pi

to

A-M-D

Pi

transition

in

the

3G

model.

Preliminary

studies

of

the

rate

of

tension

recovery

in

single

skinned

muscle

fibres

following

a

rapid

release

of

10

MPa

pressure

show

that

the

rates

of

the

observed

tension

changes

have

similar

P1

dependence

to

those

seen

in

the

caged

P1

experiments.

Addition

of

millimolar

concentrations

of

ADP

to

an

iso-

metrically

contracting

muscle

increases

tension

by

up

to

300%

[123,124].

The

data

are

compatible

with

a

model

where

ADP

competes

with

ATP

for

the

force-holding

crossbridge

and

thereby

increases

the

lifetime

of

the

high-force

state

(i.e.

ADP

inhibits

step

3).

Pate

&

Cooke

[114]

have

modelled

such

a

system

in

detail

for

a

crossbridge

cycle

excluding

actomyosin

isomerization

steps.

The

introduction

of

such

steps

in

Fig.

7(b)

should

not

affect

that

interpretation

significantly.

The

influence

of

increased

hydrostatic

pressure

on

isometric

tension

is

less

in

the

presence

of

ADP

(6.5

%

per

10

MPa)

and

greater

in

the

presence

of

P1

(13

%)

than

in

control

measurements

Vol.

274

I

I

M.

A.

Geeves

(8.0

%).

This

result

can

be

understood

by

considering

the

effect

of

pressure

on

a

first

order

equilibrium

constant,

K

(or

the

ratio

between

two

complexes

in

a

steady

state).

The

relationship

between

pressure

change

(AP)

and

the

change

in

the

equilibrium

constant

(AK)

is

defined

by

AK

AV-AP

K

R-T

where

A

V

is

the

molar

volume

change

for

the

reaction

and

R

is

the

gas

constant.

If

K

=

[Y]/[X]

then

the

change

in

[Y]

is

maximal

when

K

=

1.

In

solution

the

volume

change

of

the

A-to-R

transition

is

100

cm3

mol-

1,

which

means

KII

decreases

by

a

factor

of

2

at

10

MPa.

If

the

8

0

drop

in

tension

were

due

solely

to

a

2-fold

reduction

in

ratio

of

high-force

to

low-force

crossbridges

(HF/LF),

then

it

can

be

shown

that

KII

in

the

fibre

is

10.5.

The

value

of

KII

would

be

13

in

the

presence

of

ADP

and

5.7

in

the

presence

of

Pi.

Thus

the

data

are

consistent

with

P.

decreasing

and

ADP

increasing

the

ratio

of

HF/LF

bridges

and

thereby

altering

the

pressure

sensitivity

of

the

A-to-R

transition.

These

calculations

are

meant

for

illustrative

purposes

rather

than

suggesting

that

these

are

the

real

values

in

the

muscle

fibre.

Many

control

experiments

need

to

be

performed

before

the

effects

of

pressure

can

be

solely

attributed

to

effects

on

KII

in

the

fibre.

The

experimental

data

quoted

above

do

not

amount

to

a

strong

case

to

support

the

model

of

Fig.

7.

What

they

do

show

is

that

there

is

evidence

of

two

mechanical

states

of

the

attached

crossbridge

which

are

in

a

steady-state

equilibrium.

Additionally,

there

is

some

evidence

that

treatments

which

reduce

KII

in

solution

also

perturb

the

equilibrium

between

the

two

attached

mechanical

states.

The

data,

although

in

most

cases

preliminary,

are

sufficient

for

the

model

to

be

given

serious

consideration

when

attempting

to

interpret

mechanical

and

biochemical

data

from

intact

muscle

fibres.

The

information

presented

here

does

not

address

directly

the

fundamental

question

of

how

the

biochemical

and

mechanical

events

are

coupled

in

the

crossbridge

nor

does

it

define

the

nature

of

the

structural

change

in

the

crossbridge.

However,

the

model

in

solution

and

its

extension

to

the

crossbridge

cycle

in

fibres

does

provide

a

framework

which

can

define

in

biochemical

terms

when

the

A-to-R

transition

takes

place.

This

information

can

be

used

in

conjunction

with

structural

and

mechanical

studies

to

define

the

relationship

between

the

structural,

mechanical

and

biochemical

state

of

the

crossbridge.

UNRESOLVED

PROBLEMS

AND

FUTURE

PROSPECTS

The

detailed

experimental

evidence

on

the

interaction

between

actin

and

SI

in

solution

discussed

in

this

review

is

consistent

with

the

3G

model

proposed

in

1984.

However,

it

is

clear

that

the

phosphate-release

step

remains

the

key

to

understanding

the

relationship

between

the

actomyosin

ATPase

and

the

force-generating

mechanism,

as

was

identified

some

15

years

ago

[3,23].

And

although

the

use

of

isotope

exchange

methods,

with

both

32P

and

180

[17,67],

have

provided

a

method

of

probing

this

step,

the

almost

irreversible

nature

of

this

event

in

solution

means

that

we

still

have

little

direct

information

on

the

relationship

between

phosphate

release

and

acto

SI

interaction.

These

steps

are

more

accessible

in

the

intact

muscle

fibre

where

the

coupling

of

the

ATPase

to

force

generation

results

in

a

higher

occupancy

of

the

states

involved

in

phosphate

release.

The

experimental

approach

to

the

actomyosin

ATPase

in

muscle

is

quite

different

and

beyond

the

scope

of

this

discussion.

However,

the

ability

of

a

solution

model

to

account

for

experimental

observations

in

the

intact

system

must

be

the

ultimate

test

of

the

model.

There

are

several

major

problems

in

extrapolating

from

any

study

of

purified

acto

-SI

in

solution

to

the

intact

muscle

fibre,

some

of

which

have

been

discussed

in

recent

reviews

of

studies

of

the

intact

system

[76-78].

The

principal

problems

are

how

the

three-dimensional

lattice

geometry

of

the

proteins

in

the

muscle

fibre

and

the

presence

of

mechanical

strain

affect

the

rate

and

equilibrium

constants

measured

in

solution.

These

questions

can

only

be

addressed

in

the

intact

system

and

increasingly

sophisticated

methods

are

being

applied

to

the

problem,

i.e.

photogeneration

of

nucleotides,

Ca2+

and

other

effectors

such

as

IP3

[79-84];

mechanical,

temperature

and

hydrostatic

pressure

perturbations

of

muscle

fibres

[71,75,85-89];

and

in

vitro

motility

assays

[90,91].

These

studies

have

shown

that

in

outline

the

events

of

the

ATPase

mechanism

remain

the

same

as

in

solution,

but

as

these

studies

progress

the

questions

asked

become

questions

of

detail,

not

of

overall

principle.

The

challenge

to

the

solution

biochemist

is

to

keep

pace

with

the

advances

made

in

understanding

the

intact

system.

For

many

years

SI

was

con-

sidered

an

adequate

model

of

the

myosin

ATPase

and

pure

actin

a

good

model

of

the

activated

thin

filament

(actin

-

troponin

tropomyosin

in

the

presence

of

calcium).

However,

when

modelling

the

co-operative

behaviour

of

the

intact

muscle,

small

differences

in

detail

can

make

major

changes

to

the

behaviour

of

the

system.

It

is

known

that

the

presence

of

tropomyosin

and

troponin

(Tm/Tn)

on

the

thin

filament

even

in

the

presence

of

calcium

produce

changes

in

the

affinity

of

actin

for

SI

and

SI

l

nucleotide

complexes

[92,93]

and

changes

in

the

maximum

ATPase

of

acto

S1

[94,95].

We

do

not

yet

know

at

which

steps

of

the

overall

mechanism

Tm/Tn

exert

their

effects.

There

is

evidence

that

Tm/Tn

influence

the

actin-binding

steps

both

in

the

presence

and

absence

of

calcium

[96,97]

and

the

effects

on

the

ATPase

could

be

a

result

of

modifying

the

P1

release

rate

or

the

A-to-R

transition

[98,99].

In

a

similar

way

there

is

little

evidence

to

suggest

that

there

is

any

co-operative

interaction

between

the

two

S1

heads

in

myosin

(or

HMM)

in

the

way

in

which

the

heads

interact

with

nucleotide.

However

few

experiments

have

addressed

the

question

of

inter-

action

between

the

heads

in

binding

to

actin.

The

theoretical

problem

of

comparing

the

affinity

of

two

SI

molecules

with

a

single

HMM

molecule

has

been

discussed

[100],

and

calculations

based

on

the

measured

affinities

of

SI

and

HMM

suggest

that

the

two

heads

of

HMM

bind

more

weakly

than

two

S1

heads

[16,101].

The

differences

in

behaviour

of

the

two

heads

may

not

be

significant

in

the

rigor

state

where

binding

is

very

tight,

but

in

the

presence

of

nucleotide

(where

KII

is

smaller)

these

effects

could

become

more

important.

Some

studies

of

actomyosin

interactions

in

muscle

in

the

presence

of

pyrophosphate

have

been

interpreted

in

terms

of

co-operative

binding

of

myosin

heads

to

actin

[102,103].

It

is

possible

that

when

both

heads

of

HMM

have

ATP

bound

and

only

weak

binding

to

actin

takes

place

(i.e.

the

A*

M

-

N

or

R

state

is

not

occupied)

then

only

one

head

of

HMM

is

likely,

statistically,

to

bind

to

actin

at

a

time,

but

once

one

head

binds

in

the

A

*

M

*N

state

the

probability

of

the

second

head

binding

is

greatly

enhanced;

i.e.

the

binding

is

co-operative

during

a

kinetic

cycle.

The

probability

of

two

heads

binding

simultaneously

will

depend

upon

the

lifetime

of

the

A

M

N

state

and

this

could

be

significantly

longer

in

an

isometrically

contracting

muscle

(low

ATPase

rate)

compared

to

a

shortening

muscle

(high

ATPase

rate).

Such

considerations

may

not

be

significant

in

solution,

but

in

studies

of

the

intact

system

such

co-operative

behaviour

of

the

two

heads

could

become

of

increasing

importance.

The

use

of

fluorescent

reporter

groups

on

proteins

and

on

nucleotides

should

make

these

problems

experimentally

ap-

proachable.

The

pyrene

label

on

actin

will

give

a

signal

for

each

myosin

head

which

forms

a

rigor-like

bond

irrespective

of

the

behaviour

of

the

second

head

[27,31]

and

the

same

should

be

true

1991

12

Dynamics

of

muscle

contraction

for

mant

nucleotides.

This

will

allow

the

degree

of

attached

and

rigor-like

binding

states

to

be

identified

for

HMM

in

the

presence

of

various

nucleotides

and

nucleotide

analogues.

Similarly,

the

mant

and

pyrene

signals

in

conjunction

with

fluorescent

probes

of

the

state

of

the

troponin-tropomyosin

complex

[104,105]

should be

able

to

delineate

the

relationship

between

the

acto

*

SI

isomerization

discussed

here,

the

nucleotide

dissociation

rate

and

the

state

of

the

actin

tropomyosin

co-operative

unit.

The

major

goal

of

understanding

the

generation

of

mechanical

force

in

terms

of

the

behaviour

of

the

individual

protein

components

remains

out

of

reach,

but

the

development

of

methods

which

can

be

used

in

the

muscle

fibre

as

well

as

on

the

isolated

proteins

will

bring

the

goal

much

closer.

The

use

of

photolabile

nucleotides

has

made

significant

contributions

in

the

last

5

years

and

will

continue

to

do

so.

The

use

of

perturbation

methods

in

solution

and

in

muscle

fibres

is

now

beginning

to

contribute.

Spectroscopic

probes

which

can

be

used

in

the

muscle

fibre

have

been

used

for

some

time,

but

problems

of

specificity

of

labelling

and

of

labels

modifying

protein

behaviour

have

limited

the

exploitation

of

this

approach.

However

the de-

velopment

of

a

new

generation

of

labels

such

as

the

mant

nucleotides

[106]

and

the

potential

of

exchanging

labelled

proteins

into

muscle

fibres

[107,108]

promise

to

remove

these

limitations.

These

developments

should

provide

the

framework

for

an

understanding

of

the

relationship

between

the

myosin

ATPase

and

force

development.

And

finally,

the

publication

of

the

atomic

structure

of

actin

[109a,109b],

and

the

successful

appli-

cation

of

molecular

genetic

methods

to

both

actin

[129]

and

myosin

fragments

[130]

bring

us

to

the

point

where

we

can

begin

to

ask

questions

about

the

mechanism

of

force

generation

at

the

atomic

level.

I

would

like

to

thank

H.

Gutfreund,

P.

Knight

and

N.

Millar

for

detailed

comments

on

this

manuscript.

The

author

is

a

Royal

Society

University

Research

Fellow

and

this

work

was

additionally

supported

by

The

Wellcome

Trust

and

the

European

Economic

Community.

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