Urry D.W. (Ed.) What Sustains Life? : Consilient Mechanisms for Protein-Based Machines and Materials

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8.4 ATP Synthase: The Twofold Rotary Protein Motor of Oxidative Phosphorylation

395

Both protein machines of ATP synthase are

rotary motors, made possible by the mechani-

cal coupling of chemo-mechanical transduction

due to the Fo-motor to mechano-chemical

transduction of the Fi-motor. A single rotor

driven by the membranous Fo-motor in turn

drives the extramembranous Fi-motor. The

Fo-motor of yeast mitochondria, for example,

exhibits a 10-fold rotational symmetry, provid-

ing a 10-step rotary engine, whereas the Fi-

motor of all ATP synthases exhibits a threefold

rotational symmetry, resulting in a threefold

rotary engine.

8.4.1.1.2

Relevance of the Hydrophobic

Consilient Mechanism to the Fo-motor

The relevance of the Fo-motor of ATP synthase

to hydrophobicity is obvious in a v^ay that has

long been appreciated. It surprises no one that

protonation of the -COO" of aspartate or glu-

tamate to achieve the carboxyl -COOH would

facilitate solubility in a lipid bilayer. In fact,

our design for using the inverse temperature

transition in the first elastic-contractile model

protein-based machine, driven by proton chem-

ical energy, was based on the expectation that

-COOH would be more hydrophobic than

-COO".^^

To argue that the hydrophobic con-

silient mechanism is relevant to function of the

Fo-motor presents no strikingly new statement.

However, it does become possible to use values

for the Gibbs free energy of hydrophobic asso-

ciation obtained on analysis of the elastic-

contractile model proteins containing each of

the amino acid residues to provide reasonable

thermodynamic and efficiency insights for ATP

synthase.

8.4.1.1.3

Relevance of the Hydrophobic

Elastic ConsiUent Mechanism to the Fi-motor

Functioning as an ATPase: Analogy to the

Internal Combustion Rotary Engine

Analogy may be drawn between the Fi-motor

functioning in the ATPase mode, that

is,

a three-

fold chemo-mechanical rotary engine, and the

threefold rotary engine of the Mazda automo-

bile.

For the latter, localized energy (pressure-

volume) bursts produce motion by the

expansion resulting from conversion of liquid

to hot gasses on fuel ignition. Based on our view

of the hydrophobic consiHent mechanism and

specifically the apolar-polar repulsive free

energy of hydration, AGap, the analogy would

be that hydrolysis of ATP to form ADP and Pi

provides a burst of apolar-polar repulsion

directed at the most hydrophobic side of a

hydrophobically asymmetric rotor in a manner

that drives rotation.

Such an analogy could be cautioned by the

experimental finding that the ratio of ATP to

ADP

-I-

Pi at the catalytic site can be measured

as close to unity. If this were incorrectly viewed

as an equilibrium circumstance at the catalytic

site,

then one would consider the free energy

change on going from ATP to ADP -i- Pi to be

zero.

This is, however, erroneous. We know

under standard conditions that the hydrolytic

breakdown of ATP to ADP

-i-

Pi releases about

8kcal/mole of heat. Therefore, at the catalytic

site the energy resulting from the conversion of

ATP to ADP + Pi must raise the free energy of

the molecular structure. We propose that the

development of an increase of 8kcal/mole in

AGap, the apolar-polar repulsive free energy of

hydration, provides a rotational impulse by

structural deformation as required to drive the

y-rotor in the ATPase mode.

8.4.1.1.4 Relevance of the Hydrophobic

Elastic ConsiUent Mechanism to the Fi-motor

Functioning as an ATPase: Analogy to a

Three-pole DC Motor

Perhaps the better analogy, however, occurs

with a threefold symmetric electrical motor,

described by Kinosita et

al.^^

as a three-pole DC

motor. In their analogy "The rotor is a perma-

nent magnet, a static component." Rather than

being static, however, in our view the rotor and

the housing would have the capacity to store

elastic deformation. Instead of the repulsion

between like poles of a magnet, the push com-

ponent of force arises from the apolar-polar

repulsion between the most polar state attained

on formation of ADP

-H

Pi in the housing and

the most hydrophobic face of the y-rotor. Also,

instead of acting through space, the push com-

ponent of force requires an aqueous solvent

through which to function.

396

8. Consilient Mechanisms for Protein-based Machines of Biology

Thus the fundamental predictions of the

hydrophobic elastic consilient mechanism are

that the rotor would exhibit asymmetric

hydrophobicity, that different arrangements of

nucleotide analogues representing different

states of polarity at the catalytic sites would

orient the rotor, and that hydrolysis of ATP in

formation of the most polar state at a catalytic

site of the involved protein subunit(s) would

demonstrate a near-ideal elastic deformation

of the y-rotor and the protein subunit(s). Of

course, such a mechanism would exhibit high

efficiency and reversibility.

8,4.1.2 Predictions and the Demonstrated

Relevance of the Consilient Mechanisms

to the Fj-motor

8.4.1.2.1

Prediction of Hydrophobically

Asymmetric and Elastically Deformable

Rotor and Housing

Accordingly, in contrast to the obviousness of

the role of the hydrophobic consilient mecha-

nism to the Fo-motor of ATP synthase, the

relevance of the hydrophobic consilient

mechanism to the Fi-motor of ATP synthase

calls for presentation of new and otherwise

unexpected perspectives. For the hydrophobic

consilient mechanism to be a dominant factor

in the function of the Fi-motor, the primary

predictions focus on the rotor that mechani-

cally couples the two rotary engines. As noted

above, the first prediction is that the y-rotor

must be hydrophobically asymmetric within the

catalytic structure. A secondary prediction

becomes that rotor hydrophobic asymmetry

must be such that rotational orientation of the

rotor responds to the occupancy states of the

catalytic sites of the Fi-motor and that the rotor

and associated catalytic subunit(s) be capable

of nearly ideal reversible storage of deforma-

tion energy. Another important enabling pre-

diction, regarding the Fi-motor functioning as

an ATPase, is that elastic deformation arise out

of the sudden development of significant AGap

on hydrolysis of ATP to form ADP and Pi and

that this deforming force defines the direction

of rotation. Finally, the presence of the AGap on

formation of the most polar state would be

recognizable in the orientation and interac-

tions,

or lack

thereof,

of charged species

between rotor and the subunit containing the

most polar state.

8.4.1.2.2

Demonstration of an Asymmetrically

Hydrophobic Rotor by Calculation

of AGHA, Gibbs Free Energy of

Hydrophobic Association

Demonstrations of these predictions constitute

the message of this section 8.4, and its success

introduces the perspective of a conjoined

hydrophobic elastic consilient mechanism. With

the values in Table 5.3 and the crystal structure

with three different states of occupancy, empty,

ATP,

and ADP, the three sides of the rotor

can be identified and the respective Gibbs

free energies of hydrophobic association,

AGHA, have been estimated to be -20, 0, and

+9kcal/mole. The most hydrophobic face asso-

ciates with the empty site, the neutral face with

the ATP bound site, and the most polar face

with the ADP site which in the synthesis mode

would be in position to add Pj. As expected

from the magnitude of the resulting AGap for a

series of crystal structures wherein the least

polar occupancy state for the catalytic site

could be defined, the most hydrophobic side of

the rotor resides in apposition to the least polar

site.

8.4.1.2.3

Prediction and Demonstration That

the Most Hydrophobic Face of the Rotor

Hydrophobically Associates with the Most

Hydrophobic State of the Housing

On the basis of the hydrophobic consilient

mechanism, predictions of the relative

hydrophobicities of the housings at the location

of the changeable catalytic sites in order of

increasing hydrophobicity (decreasing polarity)

are ADP plus Pi, ATP, ADP, Pj when the latter

is not in position to have direct through-water

interaction with the rotor, and the empty cat-

alytic site. The empty catalytic site indeed

hydrophobically associates with the side of the

rotor found by calculation to have greatest

hydrophobicity. Furthermore, for several

dif-

ferent patterns of site occupancy available from

crystal structures, the side of the rotor deemed

most hydrophobic by the consilient hydropho-

8.4 ATP Synthase: The Twofold Rotary Protein Motor of Oxidative Phosphorylation

397

bic mechanism always aligns with the most

hydrophobic side of the rotor.

8.4.1.2.4 Prediction of the Direction of Rotor

Rotation for the ATPase and Synthesis Modes

Fortunately, a crystal structure has been

reported in which a stable analogue, ADP plus

SOf, of the most polar state, ADP plus HPO4"

, has been solved.^^ As expected for the most

potent configuration, the SOj' was nearly fully

exposed through an intervening aqueous

solvent to the y-rotor, and the very polar sulfate

was located just above the level at which the

rotor changed from a double-stranded a-helical

coiled coil at the amino-terminus of the y-chain

to a single-stranded a-helix that ultimately

ended at the carboxyl terminus of the y-chain

at the base of the Fi-motor. At this position

the apolar-polar repulsion occurring between

the polar SO4" and the hydrophobic side of the

rotor applies most directly to the amino-

terminal side of the double strand resulting in

a torque that would provide a counterclockwise

rotation for the y-rotor during function as an

ATPase. Synthesis would be achieved by a

reversal of the direction of rotation, wherein

the maximal apolar-polar repulsion would be

applied to the ADP plus Pi state and would be

relieved by formation of ATP.

8.4.1.2.5

Demonstration of an Elastically

Deformable Rotor and Housing

In the crystal structure with a (i-subunit con-

taining the sulfate analogue of the most polar

ADP plus Pi state, the y-rotor and the most polar

catalytic (i-subunit are found displaced from

each other by a mean distance of 2.9 A distance

and the y-rotor is twisted up to 20° when com-

pared with their relationship when the (3-

subunit is empty.^^ Quoting from Menz et al.,^^

"Note that interacting residues in the PE-

subunit and the y-subunit move in opposite

directions." This repulsion occurs for a configu-

ration in which the most hydrophobic side of

the y-rotor is in apposition to a slightly less polar

analogue, ADP^~ -\- S04~, of the most polar

natural occupancy state, ADP^" + HPO4", for a

catalytic (i-subunit. In our view, this displace-

ment results from a very large near-maximal

AGap available to the Fi-motor, that is, a near

maximal apolar-polar repulsive free energy of

hydration between the hydrophobic side of the

y-rotor and the very polar state, ADP

-H

SO4", of

a catalytic (3-subunit. This near-maximal repul-

sion provides an elastic deformation of rotor

and housing as required for efficient

function of the ATPase in its performance of

chemo-mechanical transduction.

8.4.1.2.6 Pattern of Charged Side Chain

Orientations Reflects Presence of a

Dominant AGap

An interesting orientation of side chains in

the housing, on the inner surface of the

(aP)3-

subunit structure, becomes rational once the

presence of an apolar-polar repulsion is recog-

nized. In particular, the negatively charged

aspartic acid residue, D315, is observed in the

crystal structure between the analogue of the

most repulsive state of the catalytic site and the

y-rotor. At this position the carboxylate of D315

is surrounded by water molecules and is bent

away from the hydrophobic side of the rotor

and toward the sulfate group with its two

negative charges yet with space for only a

few water molecules separating sulfate from

carboxylate.

Why, with the capacity to position itself at

greater distance, would the carboxylate of

D315 accept a location of higher charge-charge

repulsion? In our view, an apolar repulsion

emanating from the hydrophobic side of the y-

rotor causes it to reside in such a configuration

and as such the repulsion would effect an

element of elastic deformation in the housing

of the Fi-motor. On the other hand, residue

D316,

which is adjacent to the hydrophobic

rotor, is bent flat in the opposite direction

against the rotor where it exhibits ion pairing

and hydrogen bonding. These side chain orien-

tations reflect the AGap causing elastic defor-

mations due to the proximal hydrophobic side

of the y-rotor.

If we had not already derived AGap from

analysis of the data on elastic-contractile model

proteins, as reviewed in Chapter

with the per-

spectives presented below we would have had

to invent such a repulsive force to explain the

398

8. Consilient Mechanisms for Protein-based Machines of Biology

structural information available for the Fi-

motor of ATP synthase. Of course, AGap pro-

vides the force required to adapt the three-

pole DC motor described in Figures 5, 7, and

8 of Kinosita et al7^ to those forces available

to protein-based machines functioning in an

aqueous milieu.

8.4.2 Schematic Representation

of ATP Synthase Structure:

A Chemo-chemical Transducer

8.4.2.1 Subunits Divided into Five

Structural Classes: Membranous Rotor,

Extramembranous Rotor, Motor Housings

for Each of the Two Rotors, and Stator

Interlocking Motor Housings

As represented schematically in Figure 8.26/^

ATP synthase contains a basic set of compo-

nents that are common throughout biology.

There are two rotary motors, the membranous

Fo-motor and the extramembranous Fi-motor.

An extramembranous rotor driven by the

membranous Fo-motor couples rotations in

each motor and drives ATP synthesis in the

extramembranous Fi-motor. The effective

housings of the two rotary motors are held

fixed, one with respect to the other, by a stator

element. In this way one complete rotation in

the Fo-motor accomplishes one complete rota-

tion in the Fi-motor.

Thus,

utilizing Figure 8.26, the initial descrip-

tion of structure becomes enumeration of the

constituent protein subunits and their number

of repetitions given as a subscript for each of

the four structural components: (1) The mem-

branous protein subunits are the 10 repeats of

protein subunit c, that is, Cio. (2) The motor

housing for the membranous rotor utilizes the

a protein subunit in combination with the lipid

bilayer. (3) The extramembranous rotor is com-

prised of the

and 8 protein subunits. (4) The

motor housing for the extramembranous rotor

utilizes three a and three

protein subunits. (5)

The stator component for interlocking the two

motor housings utilizes two b protein subunits

in combination with the 5 protein subunit.

In addition, in animals mitochondrial ATP

synthase contains another eight types of sub-

units,

a number of which function in the cou-

pling of the Fo-rotor to the y-rotor.^^

8.4.2.2 Structural and Functional Roles of

Basic Protein Subunits in ATP Synthase

8.4.2.2.1

Rotor of the Fo-motor—The 10 c

Protein Subunits

The number of c protein subunits constituting

the Fo-motor depends on the species and has

been reported to vary from 9 to 14. In yeast,

it is 10, as in Figure 8.26, whereas in E. coli it

is 12. The c subunit occurs as an a-helix in a

hairpin configuration, with one side of the

hairpin forming the inner wall and the second

side of the a-helical hairpin interacting with the

housing of the Fo-motor.

8.4.2.2.2

Housing of the Fo-motor—the a

Protein Subunit and the Lipid Bilayer

As presently described, the housing of the Fo-

motor becomes the lipid bilayer and five trans-

membrane heUces of subunit a that combine to

form two half-proton channels.^^ As shown in

Figure 8.26, one half-channel spans from the

cytosol to the middle of the membrane, and the

second half-channel completes the transmem-

brane transit from middle of the lipid bilayer to

the matrix side of the membrane.

8.4.2.2.3

Rotor Driven by the Fo-motor

(Rotor of the Fi-motor)—the Single y and E

Protein Subunits

The rotor that is driven by the Fo-motor com-

prises a single y-subunit and a small e-subunit

attached to the y-subunit at a point proximal to

the base of the Fo-motor. This is called the y-

rotor. In the hydrophobic elastic consilient

mechanism, the interactions of a hydrophobi-

cally asymmetric y-rotor with the housing of the

Fi-motor with different occupancy states of the

catalytic sites constitute the basis for mechano-

chemical transduction of the Fi-motor.

8.4.2.2.4 Housing of the Fi-motor—the Three

a and Three

Protein Subunits

The housing of the Fi-motor contains the heart

of the ATP synthase function (when the y-rotor

is driven clockwise by the Fo-motor) or ATPase

8.4 ATP

Synthase:

The Twofold Rotary Protein Motor of Oxidative Phosphorylation

399

Cjo

Rotor

a subunit

+jt Stator (bj subunit)

cytosol

Lipid I

bilayer

ADP + P

FIGURE 8.26. ATP synthase: proton flow from the

cytosoUc to the matrix side of inner mitochondrial

membrane rotates upper intrinsic membrane FQ-

motor with an attached axle, which thereby is made

to rotate clockwise within the hexameric globule on

the matrix side (the Fi-motor). The latter produces

ATP from ADP and Pi to make 32 of the 36 ATPs

(==90%) resulting from glucose oxidation. The (aP)3

hexameric globule and ey stalk constitute the Fi-

motor, which when functioning separately becomes

the Fi-ATPase rotary motor. The separated extra-

membrane hexameric globule and stalk constituting

the Fi-ATPase rotary motor functions in the reverse

(counterclockwise) direction with a high efficiency

for the conversion of the energy of ATP hydrolysis,

that is, on return of ATP to ADP and Pj, to the

mechanical work of rotating a filament attached to

the stalk as shown in Figure 8.42. (Adapted with per-

mission from R.H. Fillingame, "Molecular Rotary

Motors."

Science,

286, 1687-1688, 1999.^^ Copyright

function (when driven counterclockw^ise by

hydrolysis of ATP to form ADP and Pi). The

housing of the Fi-motor is comprised of the

three ap dimers, that is,

(aP)3.

The three a-

subunits are noncatalytic with sites occupied by

ATP,

that is, aATR The p-subunits are catalytic

and have variable occupancy of their catalytic

sites.

8.4.2.2.5

The Stator of the Fo-motor-

and Two b Protein Subunits

-the 5

For the rotation of the Fo-motor to be utilized

by the Fi motor, there must be a stator that

interlocks the housings of the FQ- and Fi-

motors. Two b protein subunits arranged as

a double-stranded a-helical coiled coil fulfill

this function by attachment at one end to the

channel-containing housing of the Fo-motor

and at the other end to the 5-subunit at the

base of the threefold symmetric (aP)3

housing of the Fi-motor, as depicted in Figure

8.26. The 8-subunit would have the role of

binding the six subunits together at the base

of the housing of the Fi-motor. As such the

5-subunit constitutes part of the stator

construction.

8,4.2,3 Fj-ATPase Assembles on Raising

the Temperature by Hydrophobic

Association of an Inverse

Temperature Transition

The Fi-ATPase is composed of five different

subunits comprising eight subunits in total, with

the stoichiometry of asPsySe and constituting a

molecular weight of 371,100 kDa. The subunits

400

8. Consilient Mechanisms for Protein-based Machines of Biology

of Fi-ATPase dissociate on lowering the

temperature to 0°C, that is, they exhibit cold

denaturation.^^'^^'^^

This,

of course, indicates that

under the appropriate conditions the subunits

would assemble on raising the temperature. For

enzymatic activity, this would necessarily

include the y-rotor with its double-stranded a-

helical coiled coil within the threefold symmet-

ric (aP)3 with approximate threefold symmetry

but which looks much like an orange with six

sections. Accordingly, the Fi-ATPase is of a

nature to exhibit an inverse temperature tran-

sition of hydrophobic association/dissociation

with a Tt-value somewhere between physiolog-

ical temperature and 4°C.

Knowledge of the differential scanning

calorimetry data and the temperature of the

transition for assembly on raising the tempera-

ture would allow determination of the free

energy of hydrophobic association, the

AGHA-

would be of interest to obtain such data with

systematic increases in the number of sites occu-

pied by ATP. Based on the hydrophobic con-

silient mechanism and in analogy to forming the

more polar state by ionization of carboxyls to

form carboxylates in the elastic-contractile

model proteins, we would predict that the heat

of the inverse temperature transition would

decrease and the temperature of the transition

would rise as occupancy of the nucleotide-

binding sites progressed from being the most

hydrophobic state of empty to becoming the

most polar state with all sites containing ATP.

8.4.3 Initial Structural Information for

ATP Synthase from Electron Density

Maps and Thermodynamic Data

8.4.3.1 Overall Structure

By means of electron density maps on crystals

of yeast mitochondrial ATP synthase. Stock et

al.^^

obtained the associated

FQ-

and Fi-motors,

as demonstrated in Figure 8.27A. The Fo-rotor

was obtained in sufficient detail to identify 10 c

subunits and to locate the critical D61 residue

that undergoes protonation/deprotonation of

its carboxylate functional group. The small

white spherical dots crossing the middle of the

Fo-rotor locate the D61 residue in each subunit.

Figure

8.27B

shows only the rotating ele-

ments of ATP synthase with 10 a-helical

hairpins making up the Fo-rotor and the

double-stranded a-helical coiled coil (upper

two-thirds) of y-subunit decorated at its upper

part with the 8-subunit shown jutting out to

constitute the Y"i"<^tor (the Fi-rotor). Also

shown is the coupling component, which is

incomplete.

8.4.3.2 Three Perspectives of the Structure

of the Fo-rotor

Shown in cross-eye stereo side view in Figure

8.28 are three views of the Fo-rotor, that is, of

the rotating wheel of the Fo-motor. At this level

of resolution each residue is given as a sphere.

Furthermore, each of the 10 subunits of the

Fo-rotor is represented as a double-stranded

a-helical hairpin with the ends at the top

(cytosolic side) and the turn at the bottom

(matrix side) and with one side of the hairpin

in direct interaction with the lipid bilayer and

the other side forming the inner wall of the

rotating wheel. In Figure

8.28A

the aspartic

acid residue D61 is noted from outside. This

residue exists with its side chain as a carboxyl

(-COOH) when adjacent to the lipid bilayer,

but it releases its proton to form the carboxy-

late (-COO~) when it reaches the effective

channel when adjacent to the a-subunit.

8.4.3.3 Proton Flow (Cytosol to Matrix)

Drives Clockwise Rotation of the Fo-motor

A stereo view from the cytosolic (top) side of

the Fo-rotor is given in Figure 8.28B. From this

view the ends of the c subunits are seen. From

the matrix (bottom) side in Figure 8.28C, the

hairpin turn of the c subunits are seen. Briefly,

following FilUngame et al.,^^ a cytosolic proton

flows down a half-channel using the fourth of

five transmembrane helices of subunit a and

adds to the carboxylate of D61 that was ion

paired with arginine-210 (R210) of the fourth

transmembrane helix of subunit a. The more

hydrophobic newly protonated helix of the c

subunit rotates in a closkwise direction into the

lipid layer as the subsequent c subunit releases

its D61 proton by a second half-channel to the

8.4 ATP Synthase: The Twofold Rotary Protein Motor of Oxidative Phosphorylation

401

(ap)3 catalytic

motor housing

8 subunit

FIGURE 8.27. Stereo view of ATP synthase from the

mitochondria of yeast, neutral residues in light gray,

aromatics in black, other hydrophobics in gray, and

charged residues in white. (A) A largely complete

ATP synthase double rotary motor: Fo-motor, con-

necting rotor and Fi-motor, with only part of protein

subunits observed that couple the Fo-motor to the

rotor. (B) Fo-rotor, partial connector, and rotor

assembly of Fi-motor. (Prepared using the crystallo-

graphic results of Stock et al.^^ as obtained from the

Protein Data Bank, Structure File IQOl.)

matrix and replaces the previous c subunit by

ion pairing with the R210 at the fourth trans-

membrane helix. This completes the flow of a

single proton from the cytosol to the matrix side

of the inner mitochondrial membrane to give a

36° clockwise rotation in the FQ rotor. With

further stochastic motion the D61 carboxylate

of the newly positioned c subunit picks up

another proton from the cytosolic side of the

membrane and so on to complete the transit of

a second proton from one side to the other of

the membrane to effect a second 36° rotation in

402

8. Consilient Mechanisms for Protein-based Machines of Biology

D61

rotor

from (J

matrix

FIGURE

8.28.

Stereo view of ATP

synthase from mitochondria of

yeast, neutral residues in light

gray, aromatics in black, other

hydrophobics in gray, and

charged residues in white. (A)

Rotating wheel of Fo-motor, side

view. (B) Rotating wheel of Fo-

motor, top view (cytoplasmic

side).

Fo-motor, bottom view (matrix

side).

(Prepared using the crys-

tallographic results of Stock

et al.^^ as obtained from the

Protein Data Bank, Structure

File IQOl.)

the Fo rotor. The net direction of proton flow

and of rotation of the Fo-rotor would depend on

the frequency with which a proton enters from

one side or the other of the membrane.

8.4.3.4 Barrier to Rotation of the Fo-motor

Removed on Protonation

8.4.3.4.1

Hydrophobicity Plots, Tt and

AGHA,

of the c Subunit of Bovine ATP Synthase

The single residue Tt hydrophobicity plot for

the c subunit of bovine ATP synthase appears

in Figures 8.29A. The hydrophobic residues are

plotted with an upward deflection and the polar

residues plotted with a downward direction.

Residues D2 and K5 evidence the polar amino

terminus of the c subunit that resides at the

cytoplasmic (cytosolic) side of the inner mito-

chondrial membrane, and the polar residues at

the matrix side of the membrane, most notably

K42,

provides for polar orientation at this polar

site.

With the single additional exception of

residue E57, the remaining stretches of the c

subunit would be very hydrophobic. Of great-

est significance for proton flow, of course, is the

single ionizable carboxyl function of residue

E57.

As shown in the mean (7) residue plot of

Figure 8.29B, in the carboxylate state the c

subunit would present a barrier to movement

into the region of the lipid bilayer, but this

barrier is removed on protonation. The mean

residue plot given in terms of the Gibbs free

energy for hydrophobic association in Figure

8.29C

shows that the equilibrium for moving

into the region of the lipid bilayer would be

favored by protonation of the carboxylate to

form the carboxyl state.

As noted in the introduction of this section

8.4, this is as one would intuitively expect.

Some quantification of this in terms of the

comprehensive hydrophobic effect of the

hydrophobic consiUent mechanism follows

immediately below for the E. coli example.

8.4 ATP Synthase: The Twofold Rotary Protein Motor of Oxidative Phosphorylation

403

-150-

-100-

-50-

50H

100-

150-

200"

250-

300 •

Motor of ATP Synthase Bovine Subunit C

I U

I J III! I lllilll

-40-

-20-

0/J

•T3

(/3

OB^

80-

100-

-4H

-3-]

-2H

-1-1

2-1

i-i"i I

-|i|-|

|i |i I •!• •

H"^-binding

UlUiJlIlL

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

10 20 30 40 50 60 70

> I I

—I—T-

v/ E-

-I—I—

30 40

Residue

' I

I I

T-r-

FIGURE

8.29. Hydrophobicity plots of 1 of 10 c- becomes a small upward deflection. (B) Mean (7)

subunits of the Fo-motor of bovine ATP synthase, residue Tt plot. (C) Hydrophobicity plot in terms of

(A) Single residue Tt plot showing the hydrophobic the mean (7) residue plot of

AGHA,

the Gibbs free

sequence from residue 8 forward with the exception energy of hydrophobic association,

of very polar residue E57, which on protonation

404

8. Consilient Mechanisms for Protein-based Machines of Biology

8.4.3.4.2

Thermodynamics of Protonation

and Efficiency of Energy Conversion:

AGHA[D- -> D'] « -3.8kcal/mole

From Table 5.3 we find that the decrease in

Gibbs free energy for hydrophobic association

on protonation of the carboxylate (-COO")

of aspartate, D~, to produce the carboxyl

(-COOH) of aspartic acid,

D^,

is approximately

-3.8kcal/mole. The protonation of 10 aspartic

acid residues as required for one complete rota-

tion of the Fo-motor could be expected to

provide an energy of 38kcal/rotation, which

constitutes one complete rotation of the y-

rotor. Accordingly, by means of the Fi-motor,

one complete rotation of the y-rotor translates

into the production of 3 mole of ATP from

ADP plus Pi. Because the approximate heat

released on hydrolysis of

mol of ATP to ADP

plus Pi is 8kcal/mole, one complete rotation of

the y-rotor would produce 24kcal worth of ATP

per rotation. An energy input of 30kcal/mole

and an output energy of 24kcal per rotation

gives an efficiency maximum of about 63%.

Thus,

the value of AGHA[D- -^ D^] - -3.8

kcal/mole appears reasonable, even though it

was a value obtained from the experimental

determination of the temperature for onset of

the inverse temperature transition using the

sigmoid curve of Figure 5.10 rather than

directly measured by differential scanning

calorimetry using the difference in heat of the

inverse temperature transition for the two

states of the aspartic acid residue.

8.4.4 Crystal Structure and

Function of the Fi-motor of ATP

Synthase-Fi-ATPase

8.4.4,1 Boyer Caution About Crystal

Structure Not Being That of Active

Catalytic State

Our biochemical understanding of the mecha-

nism of ATP synthase^"^ comes in largest

measure from the pioneering work of

Boyer.^^"^^ Because of this extensive expertise

and insight, the Boyer perspective on crystal

structure data reflects the judicious critic of the

limitations of crystal structures when attempt-

ing to describe the dynamics of catalysis:

The contribution of Menz et al is welcomed as

providing essential information for the difficult

task still ahead of satisfactorily correlating structure

with events of substrate binding, covalent catalysis,

and product release. For this task, it needs to be

recognized that forms revealed by X-ray analysis

of static inhibited enzymes may not appear as

such during active catalysis, even though they

are likely representative of most intermediate

forms.^^

Even so, crystal structures provide the best

snapshots of forces in action. Crystal structures

provide an unparalleled opportunity to assess

relevance to the major protein-based machines

of biology of the free energy transduction so

dominantly displayed by elastic-contractile

model proteins (as developed in Chapter 5). If

the apolar-polar repulsive free energy of

hydration, AGap, the operative component of

the Gibbs free energy of hydrophobic associa-

tion, AGHA, is active in ATP synthase, then it

should become apparent in these snapshots.

8.4.4.2 Assembled Subunits, (ap)3 yeS, of

the Fj-ATPase

8.4.4.2.1

Structural Information

The Fi-ATPase contains five different polypep-

tide subunits, a, [3, y, 8 and e, with the stoi-

chiometry of 3:3:1:1:1, that is, aapsYiSiEi. From

crystal structure data the a- and P-subunits may

be described as the trimer,

(ap)3,

with approxi-

mate threefold symmetry, but looking much

like a peeled orange with six nearly identical

sections. A cross section of the (ap)3Y structure

at the level of the p,Y-phosphates is shown

in Figure 8.30, which, among other things,

provides visualization of the approximate

threefold symmetry despite the different occu-

pancy sites and the obviously asymmetric posi-

tion of the y-rotor. The y-subunit forms the core

of the structure residing close to the threefold

axis.

As shown in Figure 8.27B, the y-subunit

enters the upper two-thirds of the (aP)3 orange-