[H

+

in

]/[H

+

out

= 10, V

2

- V

1

=

-180 mV

∆µ = -23.3 kJ mol

-1

Energy

stored

in

a

transmembrane

electrochemical gradient is converted into the
chemical bond energy of ATP.





































)

(

3

,

2

)

(

Na

H

pNa

e

T

k

force

e

protomotiv

B

H

The membrane potential

and transmembrane ion
gradients

are

thermodynamically
equivalent.

Michell’s chemiosmotic theory

ATP Synthesis

O

H

ATP

H

HPO

ADP

2

4

2

4

3

















F

1

F

0

ATP Synthase

"The Worlds Smallest Motor"













N

P

i

nH

ATP

nH

P

ADP

It is the most

active enzyme

in the

Universe.

ADP + P

i

ATP

F

1

F

o

3 H

+

matrix

intermembrane

space

ATP synthesis with pH & 









 

+ + +

ADP

+

P

i

ATP

F

1

F

o

3

H

+

ATPase with H

+

gradient dissipated

matrix

intermembrane

space

The reaction catalyzed

by ATP synthase is fully

reversible

The complete

subunit composition

of the ATP

Synthase

was first established in

E. coli

, which has

an operon that encodes genes for all subunits.

E. coli ATPase

( cryo-electron

microscopy).

Structure of F

0

F

1

-

ATP synthase

The c subunit consists of
9–12

twin

-helices

arranged in a central
membrane-spanning array.

The a subunit consists of
5–7 membrane-spanning -

helices.

The proton channels at the
interface between the a
and c subunits.

The a subunit is connected
to F

1

by the b and 

subunits.

The  shaft and the 

subunit

connect

both

parts.

The F

1

portion alone catalyzes ATP hydrolysis, but

not ATP-synthesis.

The F

1

ATPase's size - around 50 000

atoms

The energy necessary for one revolution of the  subunit is

about three times the hydrolysis free energy of ATP.

The time scale of the ATP release or binding –

milliseconds.

The γ subunit

rotates about 100

times per second.

F

1

in E. coli consists of 5

polypeptides with stoichiometry



3

, 

3

, , , 

(named in order of

decreasing mol. weights).

 &  are arranged as a ring

of alternating subunits.

There are

three nucleotide-

binding

catalytic

sites

,

located at  interfaces but

predominantly

involving

residues of the



subunits.

Adenine nucleotides bind to

 &  subunits with

Mg

++

.

Each of the three



subunits

contains a tightly bound ATP,
but is inactive in catalysis.

The three contact levels of



with the



3



3

hexamer.

MEP – most eccentric
point

Conformational changes

during the rotation of the



shaft.

Gate 1

(controls the

admission of ATP to the

catalytic site),

Gate 2

(controls the

release of phosphate from

the catalytic site).

The power stroke

ATP binds to the catalytic site by a

rapid thermal `zippering' of

hydrogen bonds.

The top part of β rotates
about 30° toward the
bottom

part.

This

rotation closes the angle
between helices B and C.

The elastic energy stored in the β-
sheet enables it to recoil to its open
configuration at the end of the
hydroysis cycle.

The

power

stroke

During the binding process the free energy

decrease encounters only small energy barriers of
order k

B

T

A flexible binding site on the enzyme slides over

the binding surface of a fixed ligand.

Its stochastic motion is driven by biased Brownian

fluctuations.

The binding energy is converted directly into

mechanical work.

The ATP hydrolysis

Mechanical dissipation is minimal

– the bending of  is

tightly coupled mechanically to the rotation of  and the

hydrophobic sleeve holding the  shaft is nearly

frictionless.

During hydrolysis, the Binding Zipper utilizes the binding
free energy of ATP to generate

a nearly constant primary

power stroke

.

The

binding change mechanism

of energy

coupling was proposed by Paul Boyer. He shared

the Nobel prize for this model that accounts for

the existence of

3 catalytic sites

in F

1

.

Three units are working together

F

0

F

1

ATPase works in both directions

A

D

P

+

P

i

A

T

P

A

T

P

A

T

P

A

D

P

+

P

i

A

T

P

A

D

P

+

P

i

A

T

P

o

p

e

n

t

i

g

h

t

b

i

n

d

i

n

g

l

o

o

s

e

b

i

n

d

i

n

g

r

e

p

e

a

t

B

i

n

d

i

n

g

C

h

a

n

g

e

M

e

c

h

a

n

i

s

m

The H

+

ATP-ase.

The Na

+

-motive ATP-ase.

F

0

ATPase

If F

1

is removed from the

membrane

containing F

o

becomes

leaky to H

+

.

Adding back F

1

restores normal

low permeability to H

+

.

F

o

includes a

“proton channel.”

F

o

is a complex of integral membrane proteins.

Each step represents the

movement of one c subunit into,
and a second c subunit out of, an
interaction with the „a” subunit.

Ion movements across the

membrane drive rotation of the c
subunit ring in steps.

A transmembrane electrochemical

gradient provides the energy reservoir

that the motor converts into a rotary

torque.

The thermodynamic

measure of this energy

gradient is the

chemical potential

difference between the

periplasm (high ion

concentration) and the

cytoplasm (low ion

concentration)

































)

(

3

,

2

Na

H

pNa

e

T

k

B

pNa

+

= -log [Na

+

] (the sodium

analogue of pH).
 - the transmembrane electrical

potential.

It provides a

hydrophobic seal,

preventing ions from

leaking across the

membrane.

A single positive charge

on the stator located

close to the strip repels

the bound ions.

The

a-subunit

forms

2

half- channels

or proton

wires, that let H

+

pass

between the 2 membrane
surfaces.

O

OH

O

O-

+ H

+

Asp

Asp residues in the c

subunits pick up a proton
from one side of the
membrane.

They become

uncharged

and can then contact the

lipid membrane.

As the

ring of 10 c subunits rotates

, the c-subunit

carboxyls relay protons between the 2 α-subunit half-
channels.

This allows H

+

gradient-driven H

+

flux

across the membrane to drive the

rotation.

H

+

may be relayed from one

half-channel or H

+

wire to the

other only via the

carboxyl

group of a

c-subunit

.