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

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8.3 The Electron Transport Chain: Protein Machines as Redox-driven Proton Pumps

385

brane to proton transport across the inner

mitochondrial membrane.

At this point the facility of proton movement

through water requires further consideration.

There is the well-estabUshed perspective when

bulk water is present that protons can be passed

along a string of water molecules by a very fast

proton jump mechanism whereby a proton may

enter at one end of the string and a different

proton be given off at the other end of the

string. This was clearly demonstrated in the

1960s by the beautiful fast reaction studies of

Manfred Eigen and others. As discussed above

and in Chapter 5, when there are hydrophobic

residues present and resulting hydrophobic

hydration, proton transfer becomes lowered to

about one-fifth that of the speed of diffusion of

the water molecule

itself.

Accordingly, for the

uptake of protons from the matrix at the Qi

site,

as shown in Figure 8.21, the proximity of

CoQ

Protonation site

Qj site

Protonation site

CoQ

Protonation site

jSite

Protonation site

FIGURE 8.21. Yeast cytochrome bci stereo view of

the ubiquinone Qi site from the bottom and "waters

Thales."

AGap

becoming positively charged on oxi-

dation of ubiquinol at the Qo site opens an aqueous

access to the cytoplasmic side for proton release and

becoming negatively charged on reduction of

ubiquinone at the Qi site opens an aqueous channel

for proton uptake on the matrix

side.

The line to the

protonation site in each of the four cases goes to an

oxygen atom of Q"^. (Prepared using the crystallo-

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

Protein Data Bank, Structure File, lEZV.)

386

8. Consilient Mechanisms for Protein-based Machines of Biology

hydrophobic residues and the limited amount

of water argues, from the elastic-contractile

model protein studies, that the desired rate of

proton ingress would require an enlarged

aqueous channel of polar hydration. However,

this required enlargement of the aqueous

channel, the barrier presented by the lipid

bilayer

itself,

and the absence of water mole-

cules between hemes bt and bn in Figure 8.20

combine to ensure the stoichiometry for cou-

pling electron transfer in Complex III to

proton pumping across the inner mitochondrial

membrane.

of water molecules directed toward the matrix

side of the inner mitochondrial membrane, the

negatively charged site recruits the otherwise

hydrophobic hydration for its own hydration.

The result is an aqueous channel sufficient to

allow proton ingress in a symbolical movement

of the cusp of insolubility.

Our conclusion is that dissociation of the RIP

from the Qo site in a single step represents a

unique intersection of electron transfer and

proton translocation that simultaneously

employs both the hydrophobic and elastic con-

silient mechanisms.

8.3A.5 Complex III and the "Movable

Cusp of Insolubility''

8.3.4.5.1

Movement of Rieske Iron Protein,

Both Metaphorically and Literally, Represents

a Movable Cusp of Insolubility

On oxidation of ubiquinol at the Qo site, the

resulting positive charges raise the temperature

interval of the cusp of insolubility, as might be

symboHcally represented by shifting the central

cuspid of Figure 7.1 to that of the rightmost

cuspid. The result of hydrophobic dissociation,

due to AGap, evidences the metaphorical move-

ment of the cusp of insolubility. However, the

cusp of insolubility of the tip of the RIP literally

moves spatially from the Qo site to reside at the

cytochrome Ci site as may be considered by

examining Figures 8.14 through 8.17. Thus, as

with the y-rotor of ATP synthase considered

below, the globular domain of RIP exhibits both

Uteral and metaphorical movement of the cusp

of insolubiUty, "and the forces that... power

the molecular machines of biology drive spa-

tially localized hydrophobic protein domains

back and forth across thermodynamically

movable water-solubility-insolubility divides."

8.3.4.5.2

Reduction of Ubiquinone at the Qi

Site Effects a Metaphorical Movement of the

Cusp of Insolubility to Open Aqueous

Channel for Proton Ingress

When reduction of ubiquinone occurs at the Qi

site,

the negatively charged ubiquinone causes

an increase in AGap. During a transient

hydrophobic dissociation involving the strings

8.3.5 Complex IV: Cytochrome

c Oxidase

Crystal structure data on Complex IV devel-

oped relatively early^^'^"^ compared with the

other complexes of the electron transport

chain. Nonetheless, the understanding of mech-

anism does not rise to the same level, for

example, as that of Complex III. The following

consideration of Complex IV is less extensive

than that for Complex III above, but it contin-

ues to argue for the hydrophobic consilient

mechanism by means of the apolar-polar repul-

sive free energy of hydration, AGap, and it also

speculates on possible molecular players for

proton egress and ingress.

Complex IV (cytochrome c oxidase) uses

electrons from the product of Complex III,

ferrocytochrome c, to reduce molecular

oxygen (O2) with the result of forming water.

However, it is useful to realize that cytochrome

c oxidase is actually part of a superfamily

of heme-copper respiratory oxidases.^^ One

member of the superfamily is a ubiquinol

oxidase from E. coli,^^ In this protein-based

machine ubiquinol, QH2, replaces ferrocy-

tochrome c (cyt c^^) as an electron source.

Furthermore, ubiquinol oxidase contains no

binuclear CUA center that normally oxidizes

ferrocytochrome c in Complex IV.

The central question in the comparison,

however, becomes what molecular species in

cytochrome c oxidase replaces QH2 as the

proton source. As discussed regarding Complex

III,

QH2 was the source of both electrons to

subsequent redox centers and protons for

8.3 The Electron Transport Chain: Protein Machines as Redox-driven Proton Pumps

387

release to the cytoplasmic side of the inner

mitochondrial membrane, and ubiquinone, Q,

receives both electrons from heme bn and

protons from the matrix side of the membrane.

Because QH2 is lipid soluble, it diffuses through

the lipid layer and functions simultaneously as

proton and electron carrier to provide tight

coupling of electron transport to proton

pumping.

The following consideration of cytochrome c

oxidase reviews (1) composition, (2) structure,

(3) overall reaction, (4) the electron transfer

steps of cytochrome c oxidase, (5) status of

proton translocation and proposed aqueous

D-

and K-channels for proton ingress, (6) the

redox Bohr effect and its correlation with elec-

trochemical transduction in elastic-contractile

model proteins, and (7) possible molecular

sources of protons for translocation with an

abundant and uniquely positioned functional

side chain that exhibits interesting parallels to

the states of QH2 with, however, single rather

than double proton changes and coordination

to a metal ion required for electron transfer

capability.

Although different molecular species and

arrangements of redox centers occur in

Complex III than in Complex IV, we proceed

with the perspective that the underlying physi-

cal process is the same, that is, the operative

apolar-polar repulsive free energy of hydra-

tion,

AGap,

aspect of the hydrophobic consilient

mechanism. In this view, a change in charge due

to electron transfer to or from a redox center

changes that centers contribution to AGap in a

way that can open or close aqueous channels

for proton ingress into, and egress from, the

inner mitochondrial membrane.

83.5.1 General Structural Description of

Complex IV: Cytochrome c Oxidase

8.3.5.1.1

Composition

Bovine cytochrome c oxidase contains 13

protein subunits, summing to a molecular

weight of

200

kDa. Three of the subunits,

encoded in the mitochondrial DNA, appear

common to all species, subunits I, II and III. In

all cases the four redox centers are localized to

subunits I and II. One redox center, a binuclear

copper center,

CUA,

occurs in subunit II. The

three other redox centers are found in subunit

I; these are a heme a, a heme aa, and a single

copper ion,

CUB,

closely associated with heme

8.3.5.1.2

Molecular Structure

A cross-eye stereo view of the dimer of

Complex IV (cytochrome c oxidase) from

bovine heart mitochondria is shown in Figure

8.22. Figure

8.22A

shows the molecular struc-

ture in space-filling representation with neutral

residues in hght gray, the most hydrophobic

aromatic residues in black, other hydrophobic

residues in gray, and the charged residues in

white. With this shading, a dark hydrophobic

band surrounding the middle of the structure

positions the complex in the lipid (totally

hydrophobic) layer of the inner mitochondrial

membrane. The ribbon representation in Figure

8.22B

allows visualization of the transmem-

brane hehces within which are embedded the

redox centers of heme a, heme aa, and the

copper center,

CUB,

associated with heme aa.

The fourth redox center, CUA, resides just

outside of the lipid layer on the cytoplasmic

side of the membrane, as labeled in Figure

8.22B.

8.3.5.2 Phenomenology of Cytochrome c

Oxidation to Reduce Oxygen with

Net Proton Transport: Structural

Studies of Oxidase

8.3.5.2.1

Overall Reaction

As given, for example, by Schultz and Chan,"^^

the overall reaction of cytochrome c oxidase is

given in Equation (8.8) above. As the reduction

of one molecule of oxygen, O2, to water

requires four electrons, these are shown coming

from four molecules of ferrocytochrome c (4cyt

c^^), which become four molecules of ferricy-

tochrome c (4cyt c^^). Conversion of O2 to two

molecules of water, of course, also requires four

protons; these are indicated as 4H^ (scalar).The

fundamental purpose of the electron transport

chain, of course, is to produce an increased con-

centration of protons in the cytosol. In some as

yet not well-understood process, four protons

388

8. Consilient Mechanisms for Protein-based Machines of Biology

Cytoplasmic

side

Lipid layer

of inner

membrane

Matrix

side

Cu^

center

Lipid layer

of inner

membrane

FIGURE 8.22. Stereo view of dimer of bovine heart

Complex

IV:

cytochrome c oxidase, reduced without

oxygen and with neutral residues in light gray, aro-

matic residues in black, other hydrophobic residues

in gray, and charged residues in white. (A) Space-

filling representation showing a hydrophobic band

wherein the structure rests in the lipid bilayer. (B)

Ribbon representation with the embedded redox

centers discernible. (Prepared using the crystallo-

graphic results of Yoshikawa et

al^^

as obtained from

the Protein Data Bank, Structure File, lOCR.)

from the matrix side of the membrane become

transported to the cytoplasmic side of the

membrane.

As argued for Complex III above, shifting the

balance from hydrophobic to charged groups of

whichever sign, positive or negative, opens

aqueous access for protons into and out of the

membrane region of Complex III. This results

from an increase in AGap, the apolar-polar

repulsive free energy for hydration. Many

studies have been carried with Complex IV out

to show changes in proton uptake on changes

in redox state of the carriers, and many species

have been considered for their contribution to

proton translocation. Along with those, the

unique locations and possible states of the

imidazole side chain of histidine will again

be noted because of states that parallel those

of the ubiquinone system. Most fundamental to

the hydrophobic consilient mechanism,

however, will be the correlation of phenomena

with the elastic-contractile model proteins

that have been designed for analogous

electrochemical transduction, wherein reduc-

tion of positively charged species causes proton

uptake and increased hydrophobicity causes

8.3 The Electron Transport Chain: Protein Machines as Redox-driven Proton Pumps

389

increased electron affinity of positively charged

species. First, however, the electron-transfer

steps and the involved redox carriers are

noted.

8.3.5.2.2

Electron-Transfer Steps:

Ferrocytochrome c -^

CUA

-^ Heme a

—>

(Heme as and

CUB)

-^ O2

The series of single electron transfer steps of

Complex IV are represented in Figure 8.23A.

Ferrocytochrome c (cyt c^^), the aqueous

dif-

fusible reduction product of Complex III,

transfers a single electron to result in ferricy-

tochrome c (cyt c^^) and a reduced binuclear

copper center, (CUA)2- The single electron then

transfers to the heme a and from there to the

binuclear heme

as—CUB

center, which binds O2

between the heme iron and

CUB

coordinated by

the imidazole side chains of two histidine

residues. This process repeats for four times to

complete the reduction of O2, which on addi-

tion of four protons completes the conversion

to two molecules of water.

Cyt. c^t^ J

Heme

ubiinit II

FIGURE 8.23. Stereo view of monomer of bovine

heart Complex

IV:

cytochrome c oxidase with bound

O2.

(A) Redox centers:

CUA,

heme a, heme 33, and

CUB

with single electron transfers indicated by

arrows at left. Same orientation as in

(B) Subunits

I and II in ribbon representation, showing in subunit

II the locations of

D91

and K319 residues with D and

K channels indicated as well as the suggested

coupled residue E242. (Prepared using the crystallo-

graphic results of Yoshikawa et

al.^^

as obtained from

the Protein Data Bank, Structure File 20CC.)

390

8. Consilient Mechanisms for Protein-based Machines of Biology

8.3.5.2.3

Status of Proton Translocation

Understanding of the proton translocation has

been complicated by the need to address a

steady-state circumstance rather than to con-

sider static states. For example, in the oxidized

state in the absence of reductant, the heme-

copper binuclear center relaxes to a state that

lies outside of the catalytic cycle. With proper

consideration of the catalytic cycle according to

Wikstrom and Verkhovsky,^^ "Two protons

each are pumped during the oxidative and

reductive halves of the cycle." This impor-

tant insight has yet to be carried to the molec-

ular species involved, although an OH" ligand

for CUB[II] has been considered, as well as

earher implication of a histidine liganded to

8.3.5.2.4 Proposed Channels for

Proton Translocation

Based on crystal structure data, two channels

have been suggested for proton translocation.^"^

One channel, the K-channel identified by

residue K319, runs from the matrix side to the

dioxygen center, where O2 resides between the

iron atom of heme 33 and

CUB,

as shown in

Figure 8.23B. A second channel, the D-channel,

crosses the entire range of the lipid layer from

the matrix side to the

CUA

site.

The current perspective for proton trans-

location by Complex IV has been summarized

by Schultz and Chan"^^: "Rather, there is likely

just a chain of proton carriers through the

enzyme, and proton pumping consists of

protons hopping roughly in concert along a

chain of hydrogen bonds. The energy transduc-

tion consists of altering the orientation of the

hydrogen bonds, changing the pKa's of the

amino acid residues, and transiently removing

and restoring the osmotic barrier."

On the basis of the physical processes iden-

tified from the studies on free energy transduc-

tion by elastic-contractile model proteins

functioning by inverse temperature transitions,

the operative interaction energy that alters

"the orientation of the hydrogen bonds" and

changes "the pKa's of the amino acid residues"

is the apolar-polar repulsive free energy of

hydration,

AGap,

as developed in Chapter 5 and

reviewed above.

8.3.5.2.5

Negative Dioxygen as a Super-Qi

Site (Negatively Charged Quinone) of

Complex III

Figure

8.24B

for Complex IV exhibits "waters

of Thales" that are more nearly continuous

across the membrane than for Complex III.^^

For example, a string of water molecules con-

nects heme 83 to the matrix side of the inner

mitochondrial membrane. Such a limited string

of water molecules, however, does not neces-

sarily constitute a channel for proton transit,

particularly if they are waters of hydrophobic

hydration. Proton movement through the

elastic-contractile model protein matrix during

chemomechanical transduction by inverse tem-

perature transition is very slow,^^ even when the

contracted state is more than 60% water.

Proton movement is very slow because so much

of the water is hydrophobic hydration. The

point to be made is that water molecules,

arranged as hydrophobic hydration, are not

suitable for hydrating a proton. This same effect

results in the hydrophobic-induced pKa shifts,

for example, of Figures 5.29 through 5.32 and

5.34. Accordingly, AGap, resulting from the for-

mation of charge, disrupts hydrophobic hydra-

tion, including the incipient hydrophobic

hydration of a transient hydrophobic dissocia-

tion. Thus, the formation of charge, by the

hydrophobic consilient mechanism, is precisely

suited for activating or opening aqueous chan-

nels in protein for proton translocation.

Accordingly, by the hydrophobic consilient

mechanism, the receipt of electrons at the

dioxygen sandwiched between heme 83 and

CUB,

as shown in Figure 8.22B, creates a nega-

tively charged site that turns the incipient

channel apparent in Figure

8.23B

into an

aqueous channel suitable for proton ingress.

The result, of course, is the conversion of O2

into 2H2O. This would be the explanation

for the four scalar protons noted in Equation

(8.8).

8.3 The Electron Transport Chain: Protein Machines as Redox-driven Proton Pumps

391

A cu

FIGURE

8.24. Rhodobacter sphaeroides Complex IV:

cytochrome c oxidase. Stereo view in backbone rep-

resentation of subunits I and II showing the greater

permeation of water through the region of the Upid

layer of Complex IV than for that of Complex III in

Figure 8.20. (A) Heme redox centers at the heart of

the lipid layer. (B) "Waters of Thales" distributed at

almost all levels through the membrane region.

(Prepared using the crystallographic results of

Svensson-Ek et al.^° as obtained from the Protein

Data Bank, Structure File 1M56.)

392

8. Consilient Mechanisms for Protein-based Machines of Biology

8.3.5.3 The Redox Bohr Effect of

Complex IV Represents the Hydrophobic

Consilient Mechanism's AGap in Action

8.3.5.3.1

The Redox Bohr Effect in

Complex IV

For more than a decade it has been known and

repeatedly reaffirmed that reduction results in

proton uptake.^^"^^ In particular, two protons

are taken up on reduction and two protons are

released on oxidation. As stated by Wikstrom

and Verkhovsky,^^ "Two protons each are

pumped during the oxidative and reductive

halves of the cycle, respectively," and "with an

efficiency of two translocated charges per trans-

ferred electron in the steady state." Because

four protons add to the negative dioxygen, it

should be clear, however, that "for every elec-

tron that is transferred from cytochrome c to

cytochrome c oxidase, one proton is pumped

through the protein giving four translocated

protons...." These are the four matrix protons

of Equation (8.8).

In relation to the hydrophobic consilient

mechanism, it is relevant to note that the redox

centers are positively charged metal ions that

become less charged on the addition of the

electron and more charged on oxidation. In

general, the effect of reduction of the redox

sites,

for example, heme iron and copper

centers, is to increase hydrophobicity. Because

a change in the redox state results in proton

translocation, the protein-based machine.

Complex IV, performs electro-chemical

transduction.

8.3.5.3.2

Coherence of Phenomena for

Electro-chemical Transduction Demonstrated

in Designed Elastic-contractile Model

Protein and the Redox Bohr Effect in

Complex IV

In the case of our elastic-contractile protein-

based polymer poly(GDGFP GVGVP GV

GVP GFGVP GVGVP GVGK{NineN^}P), the

positively charged N-methyl nicotinamide

{NmeN^} becomes more hydrophobic on reduc-

tion. This causes an increase in the pKa of the

carboxylate of the aspartic acid (D) residue

by 2.5 pH units, as occurs on increasing the

hydrophobicity or oil-like character of the

polymer.^^ With the elastic-contractile protein-

based polymer, reduction causes proton uptake

and oxidation causes proton release. This is an

example of an apolar-polar repulsive free

energy,

AGap,

whereby reduction of a positively

charged species (an increase in hydrophobicity)

causes proton uptake. Thus, there exists a

coherence of phenomena for electro-chemical

transduction demonstrated in designed elastic-

contractile model proteins and in the redox

Bohr effect of Complex IV

8.3.5.3.3

Equivalence of the

Reduction/Oxidation (Redox) Bohr Effect

in Complex IV and the Original

Deoxygenation/Oxygenation Bohr Effect

in Hemoglobin

As with hemoglobin, discussed in Chapter 7, a

Bohr effect occurs with cytochrome c oxidase.

Again from the viewpoint of the hydrophobic

consilient mechanism, these phenomena are

analogous. Formation of the less polar states

on reduction of Complex IV and on forming

deoxyhemoglobin result in proton uptake,

whereas formation of the more polar oxidized

state of Complex IV and the more polar oxy-

genated state of hemoglobin result in proton

release. This is as expected from the AGap of

the comprehensive hydrophobic effect, as dis-

cussed above.

8.3.5.4 Analogy Between States of the

Metal-Ion-complexed Imidazole Side

Chain of Histidine and the

Ubiquinone/Ubiquinol System

During the transit of one electron from ferro-

cytochrome c to the (heme as-Cue) binuclear

center, one proton is transported from the

matrix side to the cytosolic side of the mem-

brane. In analogy to Complex III one suspects

that oxidation of a site with access to the

cytosolic side would release a proton to that

side,

whereas on reduction the proton would be

replenished from the matrix side. The problem

could be stated as one of identifying the groups

that would replace ubiquinol and ubiquinone of

Complex III.

The striking feature of the functional

side chains associated with the redox sites

8.3 The Electron Transport Chain: Protein Machines as Redox-driven Proton Pumps

393

of cytochrome c oxidase is the preponderance

of histidine residues, as shown in Figure

8.25. There are eight histidine residues in co-

ordination at the redox sites. (CUA)2 has two

His residues (HI 16 and H204); heme a co-

ordinates two histidines (H61 and H240)

and the (heme aa-CuB) binuclear center has

four coordinated histidines (H240, H290,

and H291 on the O2 side and H376 on the

backside).

H116

H204

H376

H61

H378

FIGURE 8.25. Complex IV: cytochrome c oxidase.

Stereo view of subunits I and II given in vine repre-

sentation to show a total of eight His residues coor-

dinated to redox sites. (A) O2 side of heme aa-Cus

binuclear center with three coordinated His residues

and

CUA

with two coordinated His residues. (B)

Backside of heme 33 with one coordinated His

residue, side view of heme a with two coordinated

His residues, and again

CUA

with two coordinated

His residues. (Prepared using the crystallographic

results of Yoshikawa et al.^^ as obtained from the

Protein Data Bank, Structure File 20CC.)

394

8. Consilient Mechanisms for Protein-based Machines of Biology

Given the dominance of His coordination of

the metal ions at the redox sites, it is difficult

not to consider the interesting properties of his-

tidine's imidazole (Im) side chain, identified in

Table 5.1. Furthermore, imidazole can exist in

three different states of protonation in analogy

to the ubiquinol/ubiquinone system except that

the three states differ by one proton for imida-

zole and two protons for ubiquinol/ubiquinone.

In particular, the three states for imidazole

are HlmH^ (imidazolium) -^ ImH (imidazole)

-^ Im" (imidazolate), and the equivalent three

states are QH2^^ ^ Q ^ Q^" for the

ubiquinol/ubiquinone system. There occurs

the important distinction, of course, that the

ubiquinone system is a two-electron-two-

proton system, whereas imidazole in associa-

tion with a metal ion would vary as a

one-electron-one-proton system as would be

fitting for the single electron transfers from

cytochrome c.

In a purely aqueous system, simple chelation

of copper by a histidine residue shifts the pKa

of the imidazole group by about 3 pH units.^"^

On the other hand, in a more hydrophobic site,

as in the inner mitochondrial membrane site of

Complex IV, it would be interesting to see

whether pKa shifts would be sufficient to access

the imidazolate state in order to pick up and

release proton as the redox state of the relevant

center changed. Another point of consideration

in this case relates to the superfamily of

heme-copper respiratory oxidases, wherein

there are ubiquinol oxidases in which ubiquinol

replaces the binuclear copper center. This raises

the question as to whether the binuclear

(CUA)2

center might be examined as replacement

for ubiquinol as a site of proton release on

oxidation.^^

8.4 ATP Synthase: The Twofold

Rotary Protein Motor of

Oxidative Phosphorylation

8.4.1 Insights into Biology's Vital

Protein-based Machine: ATP Synthase

When considering ATP synthase, this pivotal

protein-based machine of biology, what do the

phenomenological and mechanistic assertions

arising out of the data and analyses in Chapter

5 bring to the assertion of biological relevance?

It could be, perhaps, too much to expect that the

answer would be as clear-cut as the detailed

enlightenment attending the forgoing analysis

of Complex III function. Nonetheless, the

hydrophobic and elastic consiUent mechanisms

continue with demonstration, in this case, of

their capacity to predict structural relationships

and functional results. That the central rotor

of ATP synthase, the so-called y-rotor, be

hydrophobically asymmetric constitutes the

most fundamental prediction. The corollary to

this prediction is the expectation that rotor

orientation would be a predictable function

of occupancy states of the catalytic sites.

Most essential with regard to function, the

apolar-polar repulsive free energy of hydra-

tion,

AGap,

applied to the structural data would

foretell the direction of rotor rotation for both

the ATPase and synthesis modes of action. In

addition, the findings point to a number of spe-

cific experimental tests that can be carried out

to assess this assertion of the importance to

function of the hydrophobic and elastic con-

siUent mechanisms.

8.4,1.1 Mechanistic Insights That the

Assertions of This Volume Contribute

to Understanding the Function of

ATP Synthase

8.4.1.1.1

Breakdown of ATP Synthase

into its Component and Overall

Energy Conversions

ATP synthase represents the coupling of two

protein machines, one that performs chemo-

mechanical transduction and a second that

performs mechano-chemical transduction. The

net result of the coupling becomes chemo-

chemical transduction in which the input of

proton chemical energy produces the output

chemical energy to yield ATP from ADP plus

inorganic phosphate (HPO4", also indicated as

Pi).

The chemical energy output can be assessed

by its relative magnitude but opposite sign to

the heat released, approximately -8kcal/mole,

on hydrolysis of ATP to give ADP plus Pi.