REDOX POTENTIALS OF
THE CHARGE - PAIR MODEL OF
BIOENERGETICS

Thesis for the Degree of Ph. D.
MICHIGAN STATE UNIVERSITY
PHILLIP WILLIAM SINGER
1977

 

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thesis entitled

REDOX POTENTIALS OF
THE CHARGE-PAIR MODEL OF
BIOENERGETICS

presented by

PHILLIP WILLIAM SINGER

has been accepted towards fulfillment
of the requirements for

PH.D. . BIOPHYSICS
degree in

 

 

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ABSTRACT

REDOX POTENTIALS OF THE CHARGE-PAIR
MODEL OF BIOENERGETICS

By
Phillip William Singer

The theory of redox potentials in the charge-pair
model of bioenergetics is deve10ped for two specific ver-
sions. the original model and a new model. In both models
the midpoint potentials are found to depend upon the
phosphate potential, uncoupler concentration. and upon
any other ion which may be coupled to the electron trans-
fer process. The phosphate potential dependence of the
original pair model is found to differ from experimen-
tal data, while the new pair model is generally. but not
completely. in agreement. The new pair model also incor-
porates the "proton in the membrane” concept of Williams.
The implications of these results for the pair theory and
bioenergetica are discussed, and it is shown that features
of both the reverse electron transport and the two cyto-

chrome theories are incorporated in the pair model.

REDOX POTENTIALS OF
THE CHARGE-PAIR MODEL OF
BIOENERGETICS

By
Phillip William Singer

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements for
the degree of

DOCTOR OF PHILOSOPHY

Department of Biophysics
1977

ACKNOWLEDGMENTS

This research was supported by funds from the col-
leges of Osteopathic Medicine. Human Medicine, and Natural
Science. Thanks are given to Drs. Rosenberg. Mahanti. and
Iien for their helpful comments. Special thanks are due
to Dr. Gator Kemeny. for showing faith in me above and
beyond the call of duty.

Table.g£ Content;

LIST OP TABLE 0 I O O O O O O O 0 O 0
LIST OF FIGURES . . . . . . . . . . .

Is INTRODUCTION e e e e e e e e e e e
A. Statement 0: th. PrOblem e e e

1. Nucleotide Transport . .
2. Exchange Reactions . . .
a. Chemical theory . . . . .

. Chemiosmotic Theory . . .
5. Proton in the lembrane .
6. Simple Pair Model . . . .

II. IITOCHONDRIAL MIDPOINT POTENTIALS

A. Introduction . . . . . . . . .
B. Experimental Techniques . . .

3. Introduction to Mitochondria . . . .
C. Introduction to Electron-Transfer Chains
D. Introduction to Uncouplers . . . . . . .
E. Introduction to Energy Coupling Theories

C. Summary of Experimental Observations
1. Phosphate Potential Induced Shift
2e Uncouplsr Effect. e e e e e e e e

III. OVERVIEW OF THE ANSVERS TO THE PROBLEM

A. EffCCts e e e e e

B. lass 3 theories - Something is missing

1. Chemiosmotic Explanation

C. Introduction to Classl
D. Class 2 Theories:
1. Marbach and Vignais . . .
2e DeVault s 3 e e e e e e e
3e Wilson e e e e e e e e e

IVA. THE PAIR ‘ODEL O O I O C O C O O O

A. The Complete Iodel and Calculations

B. New Pair Model and Calculations
C. New Pair Model - Discussion .
1. Phosphate Potential . . .

iii

2. Reversed Electron Transport Theory
and 2 theories
[013/ [red] changes

vi

“DOMIJRJDDHr he

iv

2. Uncoupler Effects . . . . . . . .
D. Comparison with Other Models . . . . .

V. FURTHER SPECULATIONS AND SUGGESTIONS FOR
mERIst O O C C O O O O O O O C I O O O

A. Real vs. Apparent Redox Shifts . . . .
B. Semi-Reversed Electron Transfer Theory
C. Phosphate Potential Dependence . . . .
De Uncoupler EffeCts e e e e s e e e e 0
Es ConCJJAflionB e e e e e e e e e e e e 0
APPENDIX I O O O O O O O O O O O O O O O O O I
APPENDIX II 0 O O O O O O O O O O O O O O O 0
APPENDIX III C O O O O I O O O I 0 O O O O O 0

LI 8! or REFERMCES . O O . O O C O O O C C O 0

69
69

71
7

75
77
80
33
86

LIST OF TABLES

Table 1: Midpoint potential changes in cytochromes
with increasing phosphate potential . . . . . 62a

Table 2: Table of Experiments with Redox Shifts . . . 80

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE
FIGURE
FIGURE
FIGURE

FIGURE
FIGURE

13

2:

3:

#3

5|

6:

7:
8:

98

103
11:

LIST OF FIGURES

Diagram of the original chemiosmotic
hyPOtheai.eeeeeeeeeeeeeee

Diagram of the revised chemiosmotic
hyPOthesiaeeeeeeeeeeeeeee

Diagram of the basic features of
the pair theory . . . . . . . . . . . .

Relationship between the midpoint
potentials of cytochromes‘b and
'53 and the phosphate potential . . . . .

pH dependence of the midpoint potential
Ofcyt.2t...............

Fundamental scheme of the Class 2 theories
DeVault's mechanism of energy coupling . .
Wilson's scheme of energy coupling . . . .
Steps in the original pair model
process for coupling oxidative
phosphorylation to the electron
trmsferchain.............

Diagram of the modified pair theory . . .

lhb

15b

17b

21b

26b
38b
39b
42b

48b
56b

Method of computation of midpoint potentials 78b

vi

I. INTRODUCTION
A. Statement‘gf the Problem

For all of its complicated mechanisms and unknown
details. the central problem of mitochondrial bioenergetics
can be stated quite simply. In the mitochondrion the fol-
lowing two chemical reactions occur:

14.1 8H2 +1502 =- s+n20

I.A.2 Pi + ADP = ATP + 320
where 8H2 is a substrate, such as succinate. These two
reactions are coupled together in a process termed oxida-
tive phosphorylation. resulting in the transfer of energy
from substrate to ATP (33). The central problems of bio-
energetics is to explain how these two reactions are cou-

pled together.

The object of this thesis is to apply one coupling
theory, the paired moving charge theory, to the measure-
ment of the midpoint potentials of certain electron car-
riers, and relate the results to the experimental data
concerning shifts in these potentials. A secondary ob-
jective is to discuss these data in terms of other theories,
and evaluate the relative merits of these theories. To
do this, we must first discuss some background material

1

2

and set a frame of reference for the later discussions.

B. Introduction 32 Mitochondria

Mitochondria are located in the cytOplasm of aerobic
eucaryotic cells. They have two membranes. referred to
as the ”inner” and ”outer” membranes. The outer membrane
encloses the organelle, while the inner membrane contains
many inward folds called cristae. The material inside the
inner membrane is called the matrix (23.33).

Located along the inner membrane are the electron
transfer chains, which contain the electron carriers.

Each chain is a complete unit, containing all the material
needed to transfer electrons from substrate to oxygen.

The electron carriers in the chain include flavin-linked
dehydrogenases. which remove the electrons from the sub-
strate and transfer them to some as yet unknown carrier;
cytochromes. containing iron as part of a heme group: non-
heme iron proteins, containing iron but not as part of a
heme; and capper proteins(33).

On the inner surface of the inner membrane is a struc-
ture known as the F1 complex. It is the principal ATP-
synthetase of the mitochondrion. As the electron flows
through the electron transfer chain, the F1 complex is
activated, and ATP is produced. Although the evidence is
in some doubt, it appears that the F1 complex is also in-
volved in ATP hydrolysis (23.33.53).

3
C. Introductionltg Electron Transfer Chains

The term ”electron transfer chain" dates back to the
20’s. when it was believed there was a simple linear or-
der to the sequence of oxidations and reductions (33.53).
Today. it appears more probable that the electron-transfer-
ring molecules are arranged in four complexes. which facili-
tate the transfer of electrons from sources of low redox
potential to sinks of high potential; the energy difference
being transferred to the F1 complex (22.53.80). Thus.
rather than the picture of a simple assembly line. with
electrons as an input. H20 an output. and ATP produced
somewhere in between. we have a picture of four machines.
with electrons as one of their raw materials. and energi-
zation of the F1 complex as the main product of three of
them.

Complex I transfers electrons from NADH to ubiquinone.
energizing P1 in the process. It contains FMN and a non-
heme iron. among other electron carriers. Complex II trans-
fers electrons from succinate to ubiquinone. but does not
energize F1.' It contains RAD and a nonheme iron. and pro-
bably other electron carriers. The next two complexes com-
bine to transfer electrons from ubiquinone to oxygen. each
energizing F1. Complex III contains the y’andlg cyto-
chromes. and a non-heme iron. Complex IV is linked to
complex III by 8.2 cytochrome. and contains the'g cyto-

chromes and several non-heme cOppers (33).

h
D. Introduction.tg Uncouplers

Before we discuss theories of energy coupling we will
mention a few facts about uncoupling. Certain chemicals.
such as 2.“ dinitrOphenol. or FCCP. completely block ATP
synthesis while enhancing electron transfer. This effect
is called uncoupling. Other chemicals. such as oligomycin.
block both phosphorylation and electron transport and
are known as inhibitors. Still other drugs block only
electron transport within a complex. such as rotenone
in complex I. antimycin in III. and cyanide in IV (2“. 52).

Until such time as a definite theory of energy
coupling is known. uncoupling will necessarily remain a
mystery. In the mean time. we can discuss mechanisms for
the dissipation of energy. and temporarily ignore how
this dissipation is mechanistically related to energy
coupling. As might be expected. the nature of this dissi-
pation is controversial.

Three models have been proposed to explain uncoupling.
The oldest. inspired by the chemical theory. is that the
uncoupler reacts with the chemical intermediate. apprOpri-
ating the high-energy bond which was intended for ATP (9).
Later. the chemiosmotic theory inspired a model in which
the uncoupler collapses the transmembrane proton gradient.
dissipating any energy stored therein (#2). In yet another
model the energy is converted into mechanical energy by

the transport of the uncoupler across the membrane (3.25.61).

5
The evidence. both for and against these models. is

indecisive. The strongest evidence supports the chemica-
motic model. and consists of the fact that the measured
proton gradient is in fact reduced by uncoupling agents
(2h. 58). Furthermore. the correlation between a drug's
effectiveness in increasing conductivity in artificial
membranes. presumably by increased proton conduction. and
in uncoupling. is high (21. 60).

However. it is not certain that these events are the
primary step. rather than a secondary side effect. in the
uncoupling process. Wilson has observed that the pH for
optimum uncoupling does not coincide with the pH for cpti-
mum conductivity in artificial membranes. uncouples sub-
mitochondrial particles (24).

The chemical model explains these proton effects in
terms of a "proton pump” driven by the high-energy inter-
mediate (68). The uncoupler is postulated to react with this
intermediate. thus shifting the equilibrium of the pump
reactions. If this is true. then the pump reactions
should be titratable. and indeed a titration effect has
been found (#0). Following up on this. Nicholle and Wen-
ner have shown that this effect can be derived from a
general kinetic analysis of uncoupling. which is indepen-
dent of any specific mechanism.(h5). Consequently. nothing
definite can be concluded.

A Some studies have shown that complete uncoupling occurs

at concentrations of less than one uncoupler molecule per

6
phosphorylation site (#0. 59). This suggests that the trans-
port model is incorrect. However. this argument overlooks
the possibility that one uncoupler molecule may be transa
ported through more than one phosphorylation site (4).
We will return to this point in our discussion of the pair

model.
B. Introduction.§g Energy Coupling Theories

Considering that the exact mechanism of energy coupling
is unknown. there is a surprising amount known about oxida-
tive phosphorylation. enough to put some severe constraints
on possible theories. We can see what these constraints
are by looking again at the overall reaction:

I.E.l Pi + ADP a ATP + H20
In solution. at physiological pH's. this reaction would
have the form:

I.E.2 Pi’ + ADP"’ a ATP”" + 320
However. species such as ATP"" cannot exist in membranes:
the species must be protonated (29). Since these protons
are attached to oxygen. we can represent this symbolically
by writing Pi-Ofilfor Pi. and ADP-HO for ADP. where the H€
is the proton gained or lost in the reaction. For simpli-
city however. we will normally write just Pi. ADP. and ATP

when there is no danger of confusion.

1. Nucleotide Trgpspogt
The fact that the form of the reactants in the mem-

is?

 

 

7

brane must be different from their form in solution should
alert us to the fact that there is a complicated mechanism
involved in transporting the chemicals to the P1 complex.
Two transport systems are known; one transports Pi into the
F1 complex and the other exchanges an internal ATP for an
external ADP. This means that reactant concentrations at
the reaction site are carrier limited. rather than being
diffusion limited as in typical chemical reactions. An
exact model consequently will have the phosphorylation
reaction dependent upon the carrier systems. However.
we can assume as a first approximation that the carrier
mechanisms and the phosphorylation mechanism are indepen-
dent (13. 63. 6O). Since the same substances are involved
in both mechanisms. this may appear to be a drastic assump-
tion. Its usefulness. however. has been well tested; this
assumption has been made in virtually all energy coupling
theories preposed to date (13).

The picture we shall use of these two systems. then.
is the following. External nucleotides diffuse through
the outer membrane of the mitochondrion. Next. the carrier
systems transport the nucleotides into the matrix space.
Finally. they diffuse to the F1 complex. where the phos-
phorylation reaction occurs.

While the mechanism of respiratory control is un-
.known. we do know some of the parameters involved. The
most important one is the ADP concentration. When the

ADP concentration is low. the respiratory rate is also

8

very low. Adding ADP causes the rate to increase. until
all the ADP has been phosphbrylated. Low ADP concentra-
tions are referred to as State U mitochondria. while ac-
tively phosphorylating mitochondria are said to be in
State 3. from a terminology proposed by Chance (9).

Besides ADP. ATP and Pi are also involved in respira-
tory control. although they are of lesser importance. and
their role is not as easily described. It is convenient
to have a single statistic relating these three terms. and
the statistic commonly used is the term

1.13.3 P a (ATP)/(Pi)-(ADP)
P is commonly called the ”Phosphate potential". a bit of
a misnomer (81). since it is actually only the logarithmic
term in a possible potential expression. such as either
the overall chemical potential of eq. I.E.l
I.E.u ”MPWK "/40093AG‘P=AGP + RTE“?

or the electrical potential in a coupled redox reaction.

The important point is to observe that unless the Pi
and the ATP/ADP transport systems are in thermodynamic equil-
ibrium with the F1 complex and the outside solution. the
phosphate potential of the reaction environment and the
external solution will not be identical. Since there is
no 5 priori reason to assume that they are equal. and
since some experimental evidence suggests that they are
not equal (17. 56). any theoretical predictions based upon
phosphate concentrations at the F1 complex cannot be ex-

pected to agree exactly with experimental measurements

made in solution.

2. Exchange Reactions

There is also a fair amount known about the intermediate
steps in the phophorylation reaction. Isotope studies have
shown that the following exchange reactions take place in
the mitochondrion. where the labeled species have been marked

with an asterisk:

I.E.5 ATP + HO*H. a ADP + P0*H

I.E.6 ADP-P + Pi" = ADP-P '+ Pi

I.E.7 A*DP + ADP-P a A*DP-P + ADP

I.E.8 ADP-OP + H20* 8 ADP-0*P + H20

I.E.9 P-O'H 1+ H036 = P—OH + HO*fi:

The fact that these reactions are blocked by uncouplers

or inhibitors is usually taken to mean that they are di-
rectly involved in the phosphorylation process (7. 31. 33).
It will be seen that matters are actually a little more
complicated than this.

Eq. I.E.5 indicates that the oxygen bridge between
the last two phosphates in ATP comes from ADP and not
from Pi. Eq. I.E.6 and I.E.7 are the individual steps
in the overall reaction I.E.5. Eq. I.E.8 and I.E.9 are
not as easily explained; they are less sensitive to un-
couplers than I.E.5 and their kinetics are faster (7).
Consequently they cannot be justified by simple rever-
sal of oxidative phosphorylation: they must be explained

10
in terms of specific. rapid. intermediate steps in the
overall reaction scheme. Thus. they can be used to
check particular coupling models for completeness.

Eq. I.E.l is written in an energetically unfavorable
direction. We have explained that it is able to proceed
as written because energy from the electron transfer chain
drives it forward. The stoichiometry introduces another
constraint upon possible energy coupling models. for
the number of electrons transferred through a complex
per ATP molecule synthesized is 2 and not 1. To further
complicate matters. the electron carriers in the electron
transfer chain all appear to transfer one electron at a
time. Thus. in a given complex. the electron transfer
step which energizes the P1 complex must either involve
two carriers acting simultaneously. or. if only one car-
rier is involved. it must energize the F1 complex in i
step increments (23. 33). This 2e'/ATP ratio will be

seen to be a most confounding fact.

3. Chemi l Thgggy

Theories of coupling can be divided into two classes.
chemical and non-chemical. Historically. the chemical
theory came first. others being preposed as its short-
comings appeared. Nevertheless. the chemical theory has
remained popular. possibly because its logical structure
cannot be refuted by any empirical observation (1). This

will become more apparent later on.

 

 

11

Lipmann. in 19h6 (38) appears to have been the first
to formulate the chemical theory. The names Slater. Chance.
and Lehninger are the most prominent among those who have
adOpted it. The gist of the chemical hypothesis is that
in the respiratory chain a "high energy" chemical inter-
mediate is formed.. This intermediate is the key ingre-
dient in ATP production.

Before describing the chemical hypothesis we must
describe some symbolism which we will use throughout this
thesis. The usual way to write oxidized and reduced states
of a chemical species A is by

on & Ared
or. if ionized. by their valence:
5+8 & A+(a-1)
The latter notation is suitable only for ions. In addition.
neither notation provides the information really desired.
namely. the electron balance. Therefore. we introduce the
following notation for an oxidized and a reduced species:
A() e A(e)
We can then write a reaction scheme for the chemical theory.
exactly as it appears in a famous biochemistry text (33).
I.E.10 A(e) + I + B() = A()-I + B(e) I

I.E.11 A()-I + E a A() + E'~I
I.E.12 ENI + Pi =3 I + E~Pi
I.E.13 ErVPi + ADP = E + ATP

Here A & B.are the relevant electron carriers. I is an in-

termediate. and E is the F1 ATPase.

12

This sample scheme illustrates the typical problems
encountered in reconciling the partial reactions. The
scheme. as written. indicates a stoichiometry of 1e'/ATP
rather than 2. This means that eq. I.E.IO must be re-
placed by something like

I.E.lll 2A(e) + I + 2130 a 2A()-I + 2130
Unfortunately. this is a very unlikely reaction. as the
A's are fixed in the membrane. and it is very improba-
ble that they are precisely arranged so that one I can
simultaneously bind with both Ais. Consequently. a bet-
ter try at improving eq. I.E.10 is:

I.E.15 2A(e) + I + 2B() 2 2A() + 23(e) + 1’“
which ignores the detailed mechanism. but still allows
for some reasonable possibilities. Eq. I.E.11 must now
be changed to

I.E.16 I‘“ + E = E~VI
and the rest can remain unchanged.

Now that we have the electrons balanced we can try to
get the water exchanges correct. Eq. I.E.12 & I.E.13 are
not written as involving protons. This is because in hy-
drolysis reactions in aqueous solution. H20 as a reactant
or productis often ignored. since the amount of water
present does not affect the final equilibrium.. The cor-
rect way to write I.E.12 and I.E.13 is:

I.E.17 E-I + PiO‘ + H+ a I + E-POH
I.E.18 E-POH + ADPOH = E + ATP + H20

13

I.E.9 may now be explained as the reversal of I.E.17
and I.E.18. Its relative sensitivity to uncouplers can
be explained by postulating E-I or I to be the species
affected by uncouplers. Its rapid kinetics can be ex-
plained by postulating I.E.15 or I.E.16 to be the rate
determining step for oxidative phosphorylation.

No combination of these steps. however. can rational-
ize I.E.8. Comparison with I.E.5. the overall phosphoryla-
tion reaction. indicates that in I.E.8 the oxygen atom be-
comes attached to the wrong molecule. ADP instead of Pi.
Consequently. I.E.8 cannot lie on the ”main path” of oxi-
dative phosphorylation: it must represent a side reaction
(6. 31). Its significance for the reaction mechanism is
that a preposed mechanism must allow for this side reac-
tion.

The reason for developing the chemical theory the
hard way was to show the importance of precisely defining
the steps in an energy coupling scheme. Most of our ar-
guments can be applied to theories other than the chemi-
cal. And having explored the pitfalls. we can survey
other theories with more confidence.

The evidence for the chemical theory is indirect.
First. this sort of mechanism is used for other biochem—
ical phosphorylations. Second. the theory provides a
reference frame which has led to the identification of
other compounds and reactions. all of which are consis-

tent with this model (31). The evidence against the chem-

14

ical theory is also indirect. In 30 years I has yet to
be isolated. and every pr0posed candidate has proven to be
something else.

4. Chemiosmotic Theogy

The first serious challenger to the chemical hypo-
thesis was the chemiosmotic hypothesis of Mitchell (41).
Mitchell noted that isolated cytochromes cannot phosphoryl-
ate: indeed. an intact membrane appears to be necessary.
He also noted that the overall oxidative phosphorylation
stoichiometry indicates an overall transfer of protons.
If the reaction components are suitably arranged in the
membrane a proton gradient will result. Mitchell pos-
tulated that this gradient is responsible for oxidative
phosphorylation.

Let us take another look at the endergonic compo-
nent of oxidative phosphorylation:

I.E.i ADP + Pi = ATP + 320

Obviously. if the 320 concentration can be made small
enough. the reaction will tend towards ATP production.
Just as obviously. this is no mean feat in an aqueous
environment. Mitchell has explained how the proton gra-

dient could accomplish this task.

To begin with. Mitchell postulated that the active
site of the F1 complex is hydrOphobic. Without water
present the equilibrium will drive the reaction into ATP

production. Almost immediately. however. the water pro-

FIGURE 1

Diagram of the original chemiosmotic hypo-
thesis. with the electron transport chain
producing a proton gradient. and the phos-
phorylation reaction using this gradient
as a source of energy.

14a

 

 

I'Hv

 

(inc.

I-I'é—

 

 

 

RDP* P3.

 

/ \

Rm </

DTP

 

 

\/

Fleur: l

Han\m I / ou‘
/ + e...
\W

I
g"
I
I

15
duced would stOp the reaction. unless there is a mechanism
for getting rid of it. This is where the proton gradient
comes in.

The proton gradient will tend to drive protons across
the membrane. The membrane is postulated to be so construc-
ted that these protons pass near the active site. with the _
protons abstracting an OH” from the water molecule (Figure
1). An OH' from the other side of the membrane takes care
of the rest of the water molecule. The water molecule is
thus removed from the active site. which can now produce
more ATP (34).

This. at least. was the original formulation. The
novelty of the approach led to attempts to see if respira-
tion did in fact produce a proton gradient. The result
was that two protons are transferred per ATP. instead of
the single proton which Fig. 1 predicts (43). Mitchell
got the stoichiometry correct by introducing a new scheme.
Fig. 2. where an intermediate molecule I has been intro-
duced. I binds to another molecule X. and together they
transport two protons and one oxygen molecule across the
membrane. X and I formally play the same role in the
chemiosmotic theory which the high-energy intermediate
plays in the chemical theory. meaning that an experimen-
tal result in one theory can be immediately translated into
the other (1).

There have been several other suggestions advanced to

FIGURE 2
Diagram of the revised chemiosmotic hypothesis.

15a

 

 

 

 

 

 

 

 

 

Etc.
H’f PM»
Punp
GDP 1- P;
+ T
a H ~\ *
New
X3 10’ x- 1

I-I.O

 

Fiqwe D.

BTI’
H30

 

‘N

 

16
explain how a proton gradient may form ATP and H20 from
Pi and ADP. One suggestion is that two protons attack Pi'
to form species of the form FORE. which then attack ADPO'
(42). This is the only suggestion we are aware of which
specifically incorporates the exchange reactions. Another.
less specific prOposal. is that a transmembrane potential
somehow is involved: the sum of the energy in the proton
gradient is often lumped together with the electrical ener-
gy and called the "proton motive force” (58).

Although the chemiosmotic theory has replaced the
chemical theory as the favored theory among bioenergeti-
cists. there has been enough evidence collected to indi-
cate that the chemiosmotic hypothesis is not entirely
correct. Kinnally and Tedeschi have estimated the pro-
ton motive force available under certain experimental
conditions and concluded that it is not sufficient to
drive the observed phosphorylation (30). And Good et.
al. have done kinetic studies on chlorOplasts and found
that one obtains phosphorylation before the chlorOplast
has had time to build up a proton gradient (47).

5. Proton ig 1:333 Membggpe

Related to the chemiosmotic theory. and preceding
it chronologically. is the "proton in the membrane”
theory of Williams (72-74). Like the other theories.
it has never been specified enough to be put in more than

qualitative terms. but in those terms it is simple enough.

17
The theory is that any protons transferred by the electron
transfer chain function by first accumulating in.the F1
complex. where they form a highly acidic environment.
Then the reaction I.E.1 can proceed easily. since it is
well known that ester hydrolysis is catalyzed by acids.
although for ATP the specific mechanism is uncertain (72).

6. Sipple Pair Model
The pair theory originated with the observation that

charges can exist in a membrane only when paired to an
apposite charge (29). Denoting an electron by e'. this means
that we cannot talk about e’ by itself. but only as parts

of an e"-p+ pair. where p+ is a positive charge (Figure 3A).
We can then diagram the transfer of an electron between

two hypothetical cytochromes. X and Y.by Figure 3B.

The pairing is primarily electrostatic in nature.
rather than being a chemical bond. As the pair is trans-
ferred. we postulate that the electron e’ passes from a
region of low dielectric constant to one of high dielec-
tric constant. with p+ doing the apposite. The dielectric
constant is. of course. a convenient macroscOpic parameter
of the internal membrane structure: an average over the
short and long range interactions of the membrane with the
pair.

Under these assumptions. the electrostatic energy of
the pair resides mainly with the electron before the cross-

ing and with the positive charge afterwards. In this man-

FIGURES 3A & 3B ,
Diagram of the basic features of the pair theory.
I and Y are two hypothetical cytochromes. A) The
pairing of two charges associated with a cyto-
chrome. B) Transfer of the pair to a second cyto-
chrome. with energy transfer.

AZV region of low dielectric constant.
.fi? region of high dielectric constant.

17a

 

 

 

 

18
ner energy may be transferred from the electron to the
positive charge without having to postulate high energy
intermediates (28).

Before moving on. let us compare the four theories to
see what distinguishes them from one another. In the chemi-
cal theory. energy is stored in chemical bonds. and if the
membrane-bound enzymes could be extracted. the reactions
could proceed as well in solution as in the mitochondrion.
In the chemiosmotic theory energy is stored in concentra-
tion gradients. The membrane is essential. but only to main-
tain the gradient. William's theory has the energy stored
in local concentrations. The membrane is used to contain
the concentration. much as a reaction vessel does. The pair
theory has the energy stored in pairs. with the membrane

being used to direct the motion of these pairs.

II. MITOCHONDRIAL MIDPOINT POTENTIALS
A. Introduction

While the ADP concentration is known to be a control-
ling element in respiratory control. the molecular mechanism
remains a mystery. Late in the '60s several groups sug-
gested that control was achieved through electron carriers
in the chain changing their midpoint potentials (ll. 15.

65. 66).. Britten Chance's.research group then attempted
to measure the relationship between redox potentials and
respiratory control. They discovered that the midpoint:
potentials of certain cytochromes were affected by ATP (10).

B. Espegimegtgl tgghnigues

The measurement of midpoint potentials involves a num-
ber of steps. but is fairly straightforward (8. 20. 78. 80).
First. the intact mitochondria. or submitochondrial parti-
cles. are extracted. Next. they are suspended in a suitable
medium. buffered to maintain the pH. and placed in a reac-
tion vessel designed for simultaneous measurement of spec-
tra and potentials. To control the reaction rate. the mea-
surements are usually performed anaerobically. To establish
anaerobic conditions oxygen is removed by bubbling in agron.
Finally..the apprcpriate redox mediators are added. and the

19

20
system is ready for measuring.

The concentrations of the oxidized and reduced species
are measured spectroscopically. The redox potential is
followed by inserting a platinum electrode and measuring
its potential relative to a calomel electrode with a high
impedance potentiometer.

It happens that. because the actural electron carrier
is a metal atom embedded in a cytochrome which is itself
embedded in a membrane. the electrode does not react with
the cytochromes. Thus. the potential that is actually
measured is that of a mediator molecule M. which is capa-

ble of reacting with both (12).

at electrode: l(‘e) :3 M() + e'

at cytochrome: A(e) + M) $3 A() + Ne)

 

net reaction: A(e) F’— A() + c”

This will theoretically give the correct result in all

cases.. However. a check of the equilibrium relationship:

A()-u(e)/A(e)-n() = K
or

M()/M(e) = (l/K)-(A()/l(e))
reveals that when I is at its midpoint. A will be far from
its midpoint unless Kris close to 1. implying that the mid-
point potentials are equal.“ If A is far from its midpoint.
then the ratio A()/A(e) is either much less than. or much
greater than 1: which implies that either A() or A(e) is

21
very small. The measurement of these small quantities is
difficult and Open to a number of experimental artifacts.
This means that. in practice. the mediator must be close
to the cytochrome in midpoint potential for accurate re-

sults (12).

C. Summgzy‘gf Egperimegtal Obsegvgtions

l. Phosphate Potential Igduged Shifi

Figure 4 shows the experimentally observed redox
behavior of cytochromes 2t and'g3. Notice that increasing
the so-called "phosphate potential”. (ATP)/(ADP)°(Pi). of
the system results in a shift.in the observed midpoint
potential V°. and that the direction of this chift can be
positive or negative depending on the cytochrome in ques-
tion. The magnitude of the shift varies as i h P“ with
a slaps of from 40 to 60 mV/phosphate potential unit.

The direction of the shifts has not received the atten-
tion which it deserves. The midpoint potential is related
to the standard free energy by the equation: I

II.C.1 AGO. a -nFV°
Thus. increasing the midpoint potential of a redox system
is equivalent to decreasing the standard free energy of the
system.. At the midpoint. the standard free energy is the
free energy. Naively applying this to cytochrome‘pt implies
that adding ATP dissipates free energy from cytochrome'bt.

Since this is unacceptable. we are forced to conclude

FIGURE 4
Relationship between the midpoint potentials of cyto-
chromes pt and 33. and the phosphate potential.
a) cytochrome pt. b) cytochrome 53. (After 75).

21a

 

 

 

III,

 

 

 

 

L01 P s;

 

B)

<‘-"——'*

 

 

 

F
J

v

V

Fiqure, '4-

22

that the midpoint potentials as they are measured are not
simple functions of the ”true" standard free energies of
the cytochromes. While none of the theories put forth to
explain the shifts state this point explicitly. it is re-
cognized implicitly. One group of theories suggest that
there is a second form of the cytochrome present. with a
different midpoint potential.. This second form is indis-
tinguishable spectroscOpically from the usual form. but
measureable electrically. In this theory. some average
of the two frame is measured electrically. with ATP causing
the ratio of the two forms to vary (16. 54. 55, 57. 79).
Another theory suggests that one does not measure cyto-
chrome Pt or|ga at all electrically. but only cytochrome
a. (32. 67). Adding ATP to the system will then result in
reversed electron transport according to the equations:

II.c.2 br°d+ 30" + ADP + Pi = b°"+ 93”“ + ATP
and

11.0.3 fed + £31 + ADP + Pi . «:0x + £13?“ + up
respectively. The midpoint potential calculated by mis-
takenly applying the Nernst equation to the measurements
is off by essentially 1; in P. the positive sign applying
to cytochromelpt and the negative sign to cytochrome‘g3.

In summary. we will mention what we feel to be the
strongest points made by either side. The two cytochrome
theory has argued that if reverse electron transport is

the cause of the shifts. then all electron carriers be-

23
tween cytochromes Pt and.g on the one hand. and between
cytochromes g3 and g,on the other hand. should show the
same shift (35). In return. the reverse electron trans-
fer advocates argue that it is an amazing coincidence that
the signs of the shifts should be exactly that predicted
by their theory (32).

2. Upcoupler Effects

Bohme and Cramer (5) have reported that uncouplers
lower the midpoint potential of plant mitochondria cyto-
chrome pé. The data of Wilson and Dutton (76) for cyto-
chrome‘bt also show this effect. although they prefer to
interpret it differently. The data of the.gpcytochromes
are ambiguous (49. 71. 77).

Bohme and Cramer (5) explain their uncoupler effect
as resulting from a change in the local dielectric con-
stant. this change being induced by the binding of the
uncoupler. This leaves the phosphate potential shifts
unexplained. Similarly. the phosphate potential theories
make no effort to explain uncoupler shifts. instead re-
garding an uncoupler as a drug which sets the phosphate
potential equal to zero. In short. no theory fully ex-
plains all the data. Using the pair model. we shall now
attempt to explain both effects..

III. OVERVIEW OF THE ANSWERS TO THE PROBLEM

If all chemical species are in equilibrium with one
another we may describe the system by classical thermodyna-
mics. For a perfect gas mixture. the chemical potential
of a species 1 is given by (14):

III.1 p1 a )4? + RT. log (i).
where: ,u1 a chemical potential of species i
p2 = standard chemical potential of species
i. a constant depending only of how the
standard state is defined.

R a gas constant

T. 2 Absolute temperature

(1)

concentration of species i (we will often
drOp the bracket notation when it is clear
that concentrations are meant.)
If this perfect gas mixture undergoes a chemical reac-
tion. then the chemical potentials are related by
III.2 Z J’s/u; =0

where the are defined as the coefficients in the reaction

formula

Vi/l-l. *va/ugi"” 2 Vsfli-t see +Vnfin.

being positive if they appear on the left and negative if
on the right. If we substitute III.1 into III.2 we find

IVA/m. : Zn (ft-(+81 mm)

.Vi
111.3 ZVg/uzzyyif +RTLJIIDT :0
2n

25
Which can be put into the form V
111.u A6 = AG" +RTlm-ITDI] "

If the reaction is at equilibrium,.mflm is equal to
the equilibriumconstant K. Substituting into III.h we find
111.5 AGO = 411 log K
The difference between gas phase reactions and solu-
tion reactions is that the chemical species no longer obey
the Ideal gas law and we must replace concentrations by ac-
tivities in order to remain theoretically correct. However.
as the argument of Appendix I shows, our purposes will be
satisfied if we make the approximation of using concentra-
tions instead of activities.
In a redor reaction the free energy released is equal
to the work done in transferring the electrons. Thus
III.6 AG 2 -nFV-’
where n is the number of electrons transferred per mole,
V‘is the electrical potential. and F is Faraday's constant.
In reaction steps of the electron transfer chain, n equals
one. Finally. we substitute III.6 into 111.4 and find
ALG - - nFV V
a AG° 4- RT 1n-n—D1] i

111.7. I a YO - (RT/nF) lanEAJy‘
where V0 = - AGO/n? .
To keep the signs consistent we have to agree on how we

shall write the reaction equation. Without going into a

26

long discussion about sign conventions. we simply state that

the usual convention leaves 111.? looking like

RT
III.8 V 3 V0 + F_'1n Cpxidized species]

 

[reduced species)
for an electron transfer reaction written as
111.9 A(e) a A() + e'
If the reaction is reversed, YO becomes negative.
Thus far, our argument has been perfectly general. Any
explanation of a shift must therefore arise from 111.7, and
that leaves only three classes of possibilities:

1) V° changes

2) [oxidized species
[reduced species changes

3) there is something overlooked in the system.

 

It is more convenient to discuss these classes in reverse

order, beginning with class 3).

LEW

One point which our discussion has ignored thus far
is the influence of pH in the redox measurements. We have
been able to do this because the experiments we wish to ex-
plain are done in buffered media. However, as Figure 5
shows, the midpoint potential of cytochrome byis strongly'
dependent on the pH. It also shows that the high-poten-
tial form 3* is unaffected by pH. Fortunately, these ef-
fects can be explained in a way applicable to all classes

FIGURE 5
pH dependence of the midpoint potential of cytochrome
b .

26a

165

200

 

v.9) ”o \

 

9“

Figure 5

27
of theories (20).

This explanation is that for many biomolecules. in-
cluding the cytochromes. the pK of the reduced form is lar-
ger than that of the oxidized form. This means that at
physiological pfifs the oxidized form will be unprotonated,
while the reduced form will be protonated. Then one can
write the reactions

111.1.1 pun-H. =20 + 11"
from.which one can write a Nernst expression:

111.1.2 v . v°+ (am/r) mffgfi] [EU/[guys];

=- v° + (RT/P)ln [3*] + (RT/F)lngcb(W[b(e)-RJ}
Allowing one to define the midpoint potential as:
111.1.3 v°' =- v°- (RT/Hpfl

This does not explain the lack of pH.dependence of the
high-potential form. Proponents of the class 1 a 2 theories
say this indicates that there is a second form of the cyto-
chrome, with a different pK. The class 3 advocates, how-
ever. reply that it merely shows how the cytochrome inter-
acts with the proton gradient of the chemiosmotic theory.

As was the case with the exchange reactions, the data can-

not distinguish between the two leading alternatives.

B..glggg‘3 theories - Something is missing
1. Chemiosmotic explanations

We can now move on to specific models. Since the

m sifim'

28

most natural subdivision is between the class 3 theories
and the class 1 & 2 theories. we will first discuss the
class 3 theories. We begin by specifically considering
one of our tacit assumptions. This assumption is that we
may ignore the possible presence of an electric field.
Since redox potentials are actually measurements of elec-
tronic chemical potentials, in electrical units, the pre-
sence of an electrical field does affect the redox poten-
tial. If there is an electric field present, something

causes it to change. and the observer is not aware of

3% "er-1mm

this, the change in the electric field would appear to the
observer to be a change in the midpoint potential.

Fortunately. the possible sources of electric fields
in membranes are few. Indeed, the only biological source
of an electric field is the transmembrane potential. To
be responsible for the redox shifts, it would have to vary
with the phosphate potential. A» riori. there is no rea-
son why it should. This is, however, Mitchell's original
interpretation of the effect (#2).

We may refer to Mitchell's model as the chemiosmotic
interpretation. It relates the midpoint potential to the
transmembrane potential by

111.3.1 v° = v3 + 7C?
where ‘f/ is the transmembrane potential and x is a fudge
factor describing how far the cytochrome is inside the mem-

brane (and hence how much of it is affected by either side's

29
potential) Uncoupling, in this version of the chemiosmo-
tic theory, destroys the membrane potential; ATP. by ener-
gizing the system, increases the potential. Depending on
the sign of;x:, and on how Y’ depends on B, one can have
the midpoint potential increase or decrease.

While this was a reasonable argument when it was pro-
posed, knowledge of the relationships between the electron
carriers and the inner membrane has improved since then,
and the theory is no longer viable. Thus, while one could
speculate in 1970 that cytochrome oxidase was embedded in
the membrane. we now know that it extends into the aqueous
phase. Yet cytochromes g.and‘g3 show a shift while cyto-
chrome g_does not. Moreover, there is no evidence of any
differences in membrane relationships between cytochromes
pt and 2k. yet one shows a shift and the other does not.
Finally. this theory suggests that most electron carriers
should show a shift. while the Opposite is the case. In
brief, the chemiosmotic explanation is not correct, and

we must look elsewhere for a complete explanation.

2. Reversed electron transport theogy

Let us now be very specific to see what, besides the
membrane potential. could be missing from our equations.
We have a mediator M, and only M,.reacting at the electrode.
We also have cytochrome b,reacting with the mediator. The
equations are

IIIOBOZ ”(8) a M() + e-

30
III.B.3 bfie) + H() a M(e) + b()
with
111.3.» x a [mu] [p0] / [:10] [men
The redox potential measured at the electrode is
111.3.5 vm .. mg + (Rs/r)1n|§:()]/[n(e)]
New 111.3.3 is the sum of the two half-reactions
111.3.6 ye) - y) + e"
III.B.7 l() + e’ - M(e)
Note that 111.3.7- is the reverse of 111.3.2. Thus A03,
the free energy of III.B.3, is just
III.B.8 463 :- AG6+ AG? a 4:26 - 4G2
From III.A.5:
111.3.9 as; a 4:11.11:
From III.B.#:
[nun/Emu] =- (l/KHL‘QUJ/bhfl)
Thus:
v. =- w; + (RT/r) 1n <1/K)<[2<)]/[1(e)]>
111.3.10 v, . v; - (RT/P)ln x + (RT/F) ln[_b_()]/[b(e)]
But, from III.A.7 and III.A.8
111.3,11 v; =- -AGg/F . v: . —AG§/P
Plugging 111.3.11. 111.3.8. and 111.3.9 into 111.3.10.
v; = 4563/? -49‘3/1 + (RT/F) 1n[p_()]/[fg(e)]
a -AG§/F 4163/1 +Acg/r
+ (RT/F) lnfig()]/E13(e)]
111.13.12 a vg+ (RT/F) 1n[g()]/[p(e)]

Consequently. what we measure is exactly what we desire.

«OI

31

The only other possible complication is to add addi-
tional reactants to the system. We know that cytochrome
g reacts with b:

III.B.13 20 + _c_(e) =- me) + 20

Repeating the above calculation on the system III.B.Z,
III.B.3. and III.B.13 yields

111.3.11: v a v3 + (RT/F)ln[g()]/[g(e)]

m
The final complication is to include ATP synthesis,

:ij i

replacing III.B.13 with
111.3.15 ye) + 20 + Pi + ADP . 130+ 3(e) + m

‘I f RITA—Cm”!

where-we have ignored the water. Again. III.B.12 can be
derived. However, III.B.lh must now be modified. Rather
than derive the new equation, we will change III.B.3 and
derive the corresponding result for‘p. This makes our
system

111.3.2 ’ Me) a M() + e"

111.13.16 n() + ch) a ate) 4- _c_()

111.3.15 2(a) + 90 + Pi + we a y) + g(e) + m
The same argument as before readily yields

111.3.11: Vm . v§+ (RT/F) ln[g()]/Eg(e)]
But now, when we try to express Vb in terms of‘b the com-
plication arises. For, instead of eq. III.B.B we have

III.B.17. 4615 :- A66 -AG° +156p

where -Gp is the free energy of ATP formation.

Once again. we substitute into eq. III.B.ih:

rm = v: + (RT/F)1n. LEN)! [ATP]
K‘_ e i

32

O
v1m a Vc+(RT/F)ln i”?

+ (RT/F) 1nL12()]/[p(e)] - (RT/F)ln x
a v: + 11, (AG: ”sag +1.56; ) + (RT/F)ln[b()]/[J;(e)]

1
+ (RT/Fun WW

1113.18 :3 vg + (RT/F)1n[2( )]/Lb(e)]+ ‘11; (AGE "‘ RI ”filmifip]

which clearly depends upon the logarithm of the phosphate
potential.

This is the explanation of the redox shifts put for-
ward by Slater (51) and also championed by Wikstrom (68).

1,?“ ““thm

It has been presented here in some detail to indicate exactly
how the phosphate potential dependence enters in. The phos-
phate potential dependent redox shift is explained as an
artifact caused by the mediator not reacting directly with~
the cytochrome measured spectroscopically. The uncoupler
effect is then explained by postulating that it sets the
effective phosphate potential to zero.

Before discussing this theory further we must illus-
trate another possible effect, that of the short circuit.
Suppose we add eq. III.B.3 to the system of III.B.Z.
III.B.15 and III.B.16. Then the electron need not go
through the energy transducing machinery to get from'g
toig: it can travel via the mediator. If we add up the
equations we discover that the net reaction is

III.B.19 Pi + ADP = ATP
or ATP hydrolysis.

33
This result should not be surprising. The electron

transfer system and the ATP synthesizing system balance
each other out energetically. If something is done to re-
move all restraints on one, the other should be expected
run down also. As we see, this is what in fact happens.

Experimentally. this means that some electron car-
rier must not be reacting with the mediator. There are
several ways to accomplish this. The most direct is to use
a mediator which reacts so slowly with one of the cyto-
chromes that the reaction never reaches equilibrium. An-
other possibility is to allow the mediator-cytochrome
reaction to reach equilibrium. but arrange it so that the
cytochrome does not equilibrate with other cytochromes.
This last suggestion will make more sense after we have
examined some of the more complicated reaction mechanisms.

We can now return to discussing the reversed-elec-
tron transport theory. The overriding experimental fact
in the discussion is that ATP hydrolysis does not occur.
Consequently, it is an experimental fact that some step
in the set of all possible reactions does not occur. If
it could be demonstrated that the missing step is eq.
III.B.3 the problem would be solved and Slater would be
correct.

Unfortunately. negative statements are difficult to
prove. Lambowits and Wikstrom (32) and Dutton and Storey
(19) have demonstrated that short-circuiting occurs in

mung-bean mitochondria. Wikstrom has also shown that

3#
massive quantities of mediator can short-circuit animal
mitochondria (69). This has been taken as proof that the
reverse electron transport theory is correct. However.
all this proves is the uncontested statement that short-
circuited mitochondria catalyze ATP hydrolysis.

Chance's group has collected much evidence that the
mediators are reacting with electron carriers in equili-
brium with the cytochromes, if not with the desired cyto-
chromes themselves (18, 20, 80). This would mean that
the desired cytochrome is indeed measured electrically.
and would contradict the reverse electron transport theory.

The most telling argument against the theory is the
observation that only cytochromelbt shows the shift in
complex III, and only cytochromes'g and $3 in complex IV.
If, as the reverse electron transport theory requires,
the shift is the result of the mediator only reacting with
cytochrome 2, then everything between‘bt andlg, and be-
tweeng,and‘g should show a similar shift. This is not
the case. Moreover, the size of the shift of cytochrome
§_is less than half that of 33, and in the Opposite direc-
tion. This is also difficult to reconcile with reversed
electron transport (35).

0. Introduction to Class 1 and 2 Theories

The members of the other two classes of explanation

have in common the feature that there is some change in

35

the cytochrome being measured, resulting in a real mid-
point potential change. To understand this. suppose that
there exists two forms of cytochrome b, which are spectro-
scopically indistinguishable:

111.0.1 21(e) a 21() + e‘ 3 22(e) - §2( ) + e'

Por simplicity, let

IH'C'Z [91”1/[21‘efl 3 B1 ' [Bin/[22(9)] ‘ B2
If the ratios can be measured, they can be adjusted exper-
imentally. and we can take 31 = 32 = B. Then. given that
a redox system contains some form of‘b, the measured poten-
tial will be either .

111.0.3 v1 = v‘1’+ (RT/F) 1n B
or

111.0.4 v2 = vg + (RT/F) in B

D. Clgss g_Theories: Lgx]‘/|red] Changes

Suppose that in the system under discussion the media-
tor only reacts with 21' while the spectroscOpe measures
both b1 and be. This presumption is made in all class 2
theories. Then the true potential is

III.D.1 v0 = V‘1’+RT/Fln bl()]/£‘g1(e)]

but one calculates

III.D.2 v = v° RTF %7_D()T+.._2b()l:
c 1+ /ln_1¢+22(o)

Suppose
111.D.3 .1220 = K00!) 121‘)

36
and
111.D.u 22(e) = Ke(x) 192(e)
Then

. a b (1 + K x )
III.D 5 Vc V? + (RT/F) 1“ WM

av°+(RTF)1ni_1_1_§a.§£)_L
1 / <1+x4h>

+ (am) 1n L131<>]/fio_1(e>]
Depending on what the parameter. x. is. the midpoint
potential will appear to vary. X is usually taken to be
the phosphate potential. ‘

Before proceeding we must discuss the assumption of
spectral indistinguishability. The situation can be best
illustrated with the g cytochromes. If we monitor 605 nm,
a wavelength characteristic of the‘g cytochromes. and per-
form a redox titration. we observe the sigmoidal curve
characteristic of two redox components. From this, we can
calculate the midpoint potentials of these components. If
we repeat the experiment in the presence of a high phos-
phate potential we obtain two different values. However,
only about one-half of the 605 absorbance is involved in
these changes (71. 75).

There are three possible interpretations of these
observations:

1) Cytochromes‘a and'g3_both contribute to the 605

nm band. but have different midpoint potentials.

2) Either cytochrome a or £3, but not both, contri-

37
bute to the 605 band, and they have the same midpoint
potential.

3) Some combination of the above.

Explanation number 2 is somewhat unusual, and requires
some additional explanation. It was originally put forth
by Nicholle. (an) and has recently been adOpted by Wik-
strom and by Chance (71). Its advantage is that it allows
cytochromes §,and 23 to have separate, well defined ab-
sorbance peaks, and thus keeps them spectrally distin-
guishable. Its problem is that as thus far stated there
is no way to produce the sigmoidal curve. since §,and £3
are given the same midpoint potential. The problem is
solved by assuming that bothIg and;3 can exist in either
of two different forms, with each form having a different
midpoint potential. Moreover, the value of these mid-
point potentials depends upon the phosphate potential.
Purthermore, it is postulated that which state'a is in
depends upon the state of 53, and vice versa.

Since this seems gg,hgg, one may wonder why explana-
tion 1) does not win by default. The answer is that 1) is
not completely free of problems. The chief problem is
that the extinction coefficients of cytochrome‘a appear
to depend upon what, if anything. is bound to £3. These
extinction shifts largely disappear if the data are inter-
preted according to explanation 2).,

Since both explanations lead to undesirable consequences,

38
the choice becomes one of a choice of evils. To us, explan-
ation 1) is the lesser evil, since its basic premises seem
more reasonable. The only advantage of explanation 2) is
that smaller shifts in extinction coefficients are re-

quired, but some shifts are needed even in this case.

i. Marbach and Viggais

We may now return to our discussion of Class 2 models.
The model of Marbach and Vignais (39) is poorly develOped,
but appears to belong in Class 2. The novel feature of
this model is the postulated existence of a long "arm” on
the F1 complex which can rest in either of two stable posi-
tions. One position has the end of the armeffectively
complexed to cytochrome b, while the other has the end of
the arm in the middle of the ATP synthetase. Denoting the
position of this arm-end as I, and the ATP synthetase as
P, we can describe the steps as follows:

III.D.7 F + 032 + ZED-I = 2p(e) + Q + F-(m)2

233(e) + ADP + Pi + F-(IH)2 a 22(e)-I + ATP
+ H20 +.P
22(e)-I + 230 = 2330-1 + 29,“)

In the scheme of III.D.1 - III.D.5. 21 corresponds to b,
and‘bz to 2:1. While one could go on and develop the
quantitative details, Marbach and Vignais are content to
stop here, and relate their model to experimental evidence
purely on a qualitative basis.

The primary proponents of Class 2 theories are Wilson

1“ Rf‘mm

FIGURE 6
Fundamental scheme of the Class 2 theories.

38a

C u)

 

 

 

 

 

 

b“) 9 K-:
a
‘0 k»:
v x ‘ fl
b4 {— k3
/ buk)
bku

bu

 

bo-I

 

K:

s “11 W‘Eqm

39
and co-workers, such as DeVault. The simplest way to see
their interrelationships is to consider Figure 6. If in
Figure 6 the mediator reacts only with‘b() and.b(e) we
can use the same analysis as before and find:

III._D.8 vb = vg + (RT/F)ln 112/111, + (RT/F)ln ()

The trouble with Figure 6 is that the scheme is too cyclic:
the net reaction is 0 = 0, and there is nothing produced
which can transfer energy. Wilson and DeVault have pro-

posed ways to overcome these problems.

2. Devault

While the exact diagram has varied somewhat from paper
to paper (16, 20), DeVault's latest scheme is much like
Figure 6 except that he has it transforming I.into 1 (20)
(Figure 7).

As DeVault notes, there are other places one can in-
sert the 1's into the square: consideration of these addi-
tional models. however, reveals no new features. The gist
of all of them is to produce 1 , which can react to form
ATP:

111.D.9 ADP + Pi + 1" 2 ATP + 1

This model is. then, part of the chemical theory.
Thus. the considerations discussed earlier apply. The
only new feature introduced is the matter of short-cir-
cuiting, or, whether the b()/b(e) couple operate at the

same redox potential as the b()-I/b(e)-I couple.

FIGURE 7
DeVault's mechanism of energy coupling.
A) Basic scheme converting 1 into I
B) Scheme with a reaction ”cut” to prevent energy
dissipation.

39a

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C 0 cu)
H but) A \ K' 4 be 1
I ‘) k... I} /
A) ‘1. K4 k4 Kt
J
c ._ K" a 50-1
“-1 ‘ / K5 \
5‘0 bx“)
CU etc)
I" b“) \ “' '/—: to 1
4r .-
JP I
B) ./
K‘- k ‘i K4 k:
Jr R s L
.1” e j M
I») k, ,\
b 0 he“)
K

Figure 7

#0
First of all. if the four reactions of Figure 7 are
all in equilibrium, then y’and 2:1 will in fact be at the
same redox potential. The proof of this is somewhat

laborious, but straightforward:

K1
111.D.10a me) + 93) = 20 + 2(a)
K-l
K2
111.D.10b y) + 1 =- 20-1
K-z
K E,
IIIeDeIOC E()-I + 2146) =3 £(e)-I~+ Ek() E
K_3 3E.
K4 I.
111.D.10d pun-1” a 1~+ p_(e)
M:
K
III.D.10e net: 1~ = I
K

We wish to measure

111.D.11 vb_I a vg_1 + (RT/F)1n£b()-I]/[:b(e)-IJ
but

|p()-1 I = K2[_1;()J[1] andfp(e)-1J = [ya] [1"]11'1

vb-I -.- v§_ I + (RT/Fun (K2[1][b()])/(K'1[I'Jb(e))
III.B.12 = vg_ 1 +(RT/F)(an2 + 1 /[I"'J

nK
+ m(§(>]/fb_(e>]l)

From III.B.10e:
III.D.13 [114”] = K111211311“

Substituting III.B.13 into III.B.12:
Vb-I a V111 + (RT/F) (anz + ann .. 1nK1K2K3Ku +ln £897)
111.D.1u Vb..1 a vg_1 - (RT/F) (ink1 + 111113 - 1n[32()]/b(e))

41

But
(me/run K1 = mg and (RT/F)ln K3: vg_I :
thus:

111.D.15 Vb—I = vg_I + vg gig/gmI + (Rm/F)1n[_t_>_()J/[p(e)]

= vb

Since DeVault explicitly says he wishes to keep the
two potentials distinct, he only allows the mediator to
react with one species. In addition, although he does not
seem to realize it, the preceeding analysis shows that one
of the reactions must be ”cut" so that equilibrium is not
attained. The most natural choice is reaction 111.D.10a,
resulting in Figure 78. Then the observed redox potential
will be given by either:
vg+ (RT/F) 1n 0 + 33”“1

2(e) + b(e)-I

V°+(RTF)1 ‘30 +K 1b”
b g. / n b(e) +KI; I” y.)

111.D.16 v =v°+ 11111 1+K I
m b ‘/’“.m§d=1

+ (RI/F)1n[p,()]/fig(e)]

or: .
- + “W“ m “l *+""z~i)1.11

-1
v§_I +(RT/F)ln 1 + K2 LI]

1 + 1(qu [1"]

+ (Rs/rt) 1n Egg-£5.

V

obs

 

III.D.17

 

lgf‘ '~"~€-e-.-me"

#2
depending upon which species the mediator reacts with. Be-
cause of 111.D.9, I and I depend upon P, and hence redox
potentials will depend upon P. As before, if we try to
frees the reaction into a simple Nernst equation, the ob-
served midpoint potentials will appear to depend on P.
If we also assume that the mediator only reacts with,bk or

2, we can make the shift positive or negative.

3e "ilBOn .h

Wilson, on the other hand, modifies this scheme so
that it becomes possible to bring both species to the g
same redox potential. (79) His scheme is Figure 8. In
this scheme L is some hypothetical electrically active
ligand. It is seen that in the part of the scheme corres-
ponding to Figures 6 and 7, one step has been explicitly
cut. It thus becomes possible to have all of these steps
at the same redox potential without short-circuiting the
system. However, these steps are on a side chain of the
electron transfer chain, which consists of reactions 1. 2,

5, and 6. The mediator cannot react with all of the latter
steps without short-circuiting the system. Wilson makes
the same assumption we did in eq.-III.B.1, that only one
species is measured electrically. His redox expression,

then, is a special case of III.B.S:

111.D.18 v a v0 + (awn-(1n _EpKz[IJP'-+ 1
pru [IJP + 1

b()-L()-IL
+ 1n fithO-I] )

 

FIGURE 8

Wilson's scheme of energy coupling. The portion in
dotted lines corresponds to the basic scheme of
Pig. 5.

hZa

 

 

50-- La)
I
V
bIcI-Lm

81
“-5
“4
K:

 

 

 

 

”\I
If

I
I
I
I
I
I
I
l
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I

f

I

 

1"]
+
I’D-LL)
,II

Im—Lo-I

\

K-3
“3

 

. - n - ~

 

TI

 

IN + ber-LI)
VII.
Im-In-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

Figul’e 8

IV. THE PAIR MODEL

Before discussing the details of the pair model, we
must first say a word about methodology. The usual method
of calculating redox potentials involves writing down the
chemical reactions of the system and applying the Nernst
equation. This method has limited usefulness for our pro-
blem, as the system is not readily specified by ordinary
chemical reactions. Instead, we shall first write out the
grand partition function of the system. From this, the
chemical potential of an electron in the system can be
calculated, and the redox potential then calculated from
the chemical potential.

Besides the electron e’ our system contains an alter-
native negative charge a', and besides the positive charge
p..’ we have an alternative positive charge u+. This gives
us four possible pairs in the system, e‘-p+,.e'-u+. a'-p+,

a'-u+: with energies Esp: EeusE Eau' We assume that the

ap'
system is in thermodynamic equilibrium and that the pairs
do not interact with one another. Denoting the number of
cytochromes by C, and the number of e’-p+, e‘-u+, a'-p+.
a‘-u+ pairs by Nap, Neu: Nap: Nau' we can write the

grand partition function 25 as (27):

Rd 28 = [1 + zezpexp(-BEep) + ZezuexP('fiEeu)

+ zazpexp(-£Eap) + zazuexp(-fiEau) ] C.

43

' "11—TIIT'T'T'KTIT'

5‘. TT

II
where the z's are the fugacities of the charges, with ”i a
epr/Ui) and /U-1 the electrochemical potential. Since

the expectation value for the number as electrons is (27)

(e) : Ze 5&2: 9112,

it follows that

w - ~I. )]
IV.2 cab w(?£.,)+ZuWP(Q '6
(e) = ‘ +242, .2“. IL'Ii’Zu‘I‘P (“'50) +24 2, upHFqJ-Iza «KM-95:1?

This can be easily solved for z :

-1-"'.‘r'.—'—IF"F’

 

 

e
IV . 3 Ze : I f 2"}, qu-QE...) +me (4511)] . (e) _
2' “P“QEQ') +Zuuf ('25...) c "' (G) *

Since 28:: exp(QPo¢) and flu: -FV, where V is the half-cell
redox potential, we can immediately write for the redox po-

tential

 

.. _ 31 1+ z.[2.wI>I~IE-.I+ In» Mind]
V " F 2m. ZrWI’Q‘y) *zawe- IE...)
0- 0
+3? “MT"

and for the midpoint potential:

In“ V2-81 9,, I +z..[2.up ME») + 2.. MI:- HEM]

F 29 9499015,) +ZILOVPG‘PEN.)

There are three special cases to consider.

Case ;: Only the e"-p+ pair i§_present.

Then za = z“): 0 and the midpoint potential for this
special case reduces to

IV.5‘ V? = (l/F)(;ap - Eep)

In the original formulation of the pair theory, the

‘positive charge p+ is an ionOphore containing Mg++ and

“5
either Pi‘ or ADP‘. Therefore ”Ab is the chemical potential
of the ionOphoric complex. We can obtain a more useful
expression for the midpoint potential if we assume the
ionophoric complex dissociation reaction is in equilibrium:

p01 a p + I
where 1 stands for ionophore and care should be taken not
to confuse p, the general positive charge, with the phos-
phate potential P.
We then have the relationship:
(p) < I>/<p-I>= K
(p-I>= K-1<p> 1 a K'1(1, <p> - (p-I) <p> )
where It a total number of ionophores present.
(13-1): K'1It<p>
if It (p-Ionophore) . This is true whenever the system
is not saturated with p. Then.we can write the desired
result:
(p-I> = K'<p‘>
where Ki‘a K'llt.
Now
,up =7“; 4- RT 1n<pI>'
The midpoint potential may then be expressed as
v3 r'1(a§+ RT 1n <p-1> -E

ep)
= r1914; - Eep + RTan' (p>)
1v.6 a F'1(Const. + RT 1n<p> )
We see that the midpoint potential is pr0portional to

Ithe concentration of the electron’s partner, implying that

#6

variations in the concentration of the partner cause the
midpoint potential to vary. This is a real shift in the
midpoint potential, and not an apparent shift due to mea-
surement of the wrong cytochrome, or the creation of a
new species not measureable spectrosc0pically.

Page 2.: 2n_11 22:12: ans. 2:24: pairs are 2__resent-

In this case 2a a 0 and the midpoint potential reduces
to

V3 2 + (RT/F) 1n (zpexp(-9Eep) + zuexp(-,8Eeu))

or

1v.7 v3 = v‘1’+ (RT/F) 1n 1 + (zu/zp)exp(-,B(Eeu-Eep))

This means that adding a second type of positive charge
causes the midpoint potential to shift positive relative
to V3. Since this also means that there are two types of
reduced cytochromes present, those with e“-p+ pairs and
those with e"-u‘+ pairs, we can express this by saying that
alternative pairing at the reduced cytochrome increases the
midpoint potential. Discussion of the physical significance
of this will be deferred until a later section.

Page 1. 21111 211" and 25:21 pairs present-

This is similar to Case 2, except that we now have

two types of oxidized cytochrome and z a 0. The mid-

u
point potential is
o o
IV.8 v3 a v1 -_(RT/F) ln(i + zaexp(-fl E31,”
and it can be seen to have shifted negatively relative to

IVY. Thus alternative pairing at the oxidized cytochrome

1&7
decrease the midpoint potential. Again, the discussion
of this case will be deferred.

A. 2.11.9. _.2i__Com ete ..__.Inode and 93mm.

To turn these simple systems into a system capable of
producing ATP we need a way to insert the ATP precursors
into the pairs, and a mechanism for forming ATP from these
precursors. Let us ignore the latter complication for the
moment, and concentrate on the former, for it was this con-
sideration which led to the first formulation of the pair
model.

We start with two of our simple systems, one containing
e'-pI pairs. and the other e'-p§ pairs. We arrange these
systems so that each transfers its pair between two cyto-
chromes, denoted by X and Y, and then transfers the positive
charge in its pair to a common site. If we interpret pi.
the positive charge in the first system. as being a,Pi con-
taining positively charged ionophore: p5 as an ADP contain-
ing positively charged ionOphore: and the common site as
the F1 complex, we have a master system capable of trans-
ducing electronic energy into ATP.

These considerations readily explain the fact that
two electrons are required to make-one ATP molecule at a
phosphorylation site. There are two possible ways to arrange
a two-electron transfer in the electron transfer chain.

One way is to use a single element, and have this element

Ca

#8
transfer two electrons. one at a time:
2t ., pk —. 5; (Scheme A)
The other way is to use two elements in parallel. and have
each transfer one electron:
In;-*In;'*sz
EH;‘*Ih;"£E

(Scheme B)

Experimentally, it has not been possible to distinguish be-
tween the two, although the first scheme is commonly assumed
(33). For our purposes, however, the second is more useful.
for two reasons. First, scheme (A) can be regarded as a
special case of scheme (B), so that only one calculation
is needed. Second, in the original pair model. where p1
and p2 are different charges, it is easier to imagine two
cytochromes. each specialized for one charge, than one
cytochrome which can transport either.

Figure 9 diagrams the main features of the model. p;
and p5 are the ordinary, deprotonated, p1 and p2, while
PI and p; are p; and p; complexed with an mg*+ containing
ionophore. We treat the ionophore as a site in the system
for p; and p5: thus we ignore its chemistry except as an
influence on the energy of p; and p5. Again, we assume
we have C of each cytochrome. We can then write for the
grand partition fwnctionm

1v.1.1 zg - [zx(1)-zx(2)-zy(1)-zy(2)]°
Where

Eu... IE. E1 1.7.3 La

FIGURE 9
Steps in the original pair model process for coupling

oxidative phosphorylation to the electron transfer chain.
The initial state of the system, (A), contains no pairs.
The first step is the entry of a PI'H+ and a PE-fi+ pair,
(B), each of which associate with a.x cytochrome. The
next step is the entry of two e'--H+ pairs (D), which also
associate with a X cytochrome. This step may proceed

step (B) as in (C). After both pairs are in place, PI and
PE enter a.lgf+ containing ionOphore, to form complexes
we denote by P: and PE. These change pairs with the elec-
trons to form e'-PI and e'-P§ pairs, with the protons re-
turning to the solution (B). Next, the pairs are trans-
ferred to the Y cytochromes (F). Next, the P's are trans-
ported to the F1 complex. where they are combined. The
electron then pairs to a proton as in (G). If the P1-P2
complex remains after the electrons have left the I cyto-
chromes. we have the situation in.(H). whereas. if the

electrons remain after P1-P2 is removed, we have (1).

#8a

 

 

 

FI

 

Figure q

 

‘IBII

 

 

 

PI

 

 

PI

 

 

 

 

 

PI

 

 

 

 

“9

with the expression 'pi' to be replaced by either p1 or p2.
depending upon the argument of 2x or 21' The various terms
can be understood by studying Figure 9.

We have assumed that I is independent of I. This is
only an approximation for cytochrome p 4. g3 (71. 35). but
this assumption leads to interesting results in its own
right.

Once again, we can compute the expectation value for

electrons on each cytochrome:

 

 

IY.A , 2 1
(42,40) : C242" (“Pm") * 1" ZJHWI'IEXW) 1' ZHWPI’IEMIIJI
Zx (I)
IV .A , 3
<9 3) : C Zita “PI‘QEYenI‘I ZIrI “PI‘QE‘IJJ +Zuz nine/KP ('QEYumI)
‘1‘ 2y“)

From these, we can express the redox potential in

terms of either <ex(i)> or (er(i)> :

 

IV.A.4a
V3.3 I14 1+ Zulu W (4510.14) «ng 5 V Ii)
F ZN WI’QEXN) +2711; ('IEXem-I) "' Zn“? ("951:”) C“ (“1““) X
IV.A.‘Ib
'3. .. 3.1 I + thh W ('VEYPIh) (61(3)) _-: Vv“)

 

F Z" W VISION) +zflz'zz" ”(..'EY'I") I‘lfiw 6'5““) C "(370.9

50
where the Vx(i) and VY(i) are all equal to the actual redox
potential Y, but are expressed in terms of different (e) .

At this point, let us insert the observation that the
redox potential will depend upon an, and hence upon the pH.
We do so because the next step in the argument is to hold
the pH constant, and consequently pH dependence will not
be apparent in the final expression. Before taking this
step, however, we wish to describe in greater detail why
explicit pH dependence expressions are not useful.

As mentioned, the redox potential can be expressed in
terms of the fugacity of a proton paired to an electron.
This proton is attached by weak forces, rather than covalent
bonds. However, covalently bound protons also can affect
the redox potential if the pH is shifted (20). Consequently.
there are two effects present, and either will mask the
other. For this reason explicit expressions will not be
derived.

To appreciate the implications of these results. let
us interpret p1 as Pi, p2 as ADP, and plpz as ATP: and let
us express the fugacities in terms of solution concentra-
tions as we did in equation IY.5. We shall simplify the
expressions by holding the pH, and hence s3, constant, and
by expressing the coefficients as 111, 112, etc.. instead
of writing out the constants explicitly. We may now write
the midpoint potentials as:

11.11.51. v§(1) . -(RT/F) ln((1+111<Pi>)/(X12+113<Pi>))

on

51

1v.A.5b VfiIz) - 4111/11) 1nI 1+121 (ADP)

IV.A.5c v§(1) 3 -(nr/r) 11,“ 1 " 3441*”)
112+!” (Pi) +1“, (111»

11.1.54 v§(2) =- -(ns/r) ln( 1 * Y21 “1”

1221-123 (ADP) +121, (ATP)

Since (P101 (ADP) . the midpoint potentials of 11 and
X2. and of 11 and Y2, will not, in general. be equal. This
implies the apparent existence of four cytochromes instead
of two. In addition, the midpoint potentials are depen-
dent on‘Pi) , (ADP) , and.(ATP) and not on the phosphate
potential, contrary to experimental observations. Conse-
quently, this analysis is incomplete.

The reason that v§(1)¢v§(2) and v§III¢V§I21 is that
we have tacitly assumed the 1 and 2 cytochromes to be dis-
tinguishable. Physically, this is an unrealistic assumption.
A better assumption is that cytochromes x1 and 12 on the
one hand, and 11 and 12 on the other, are physically indis-
tinguishable. In that case we can only discuss (ex) and
(03) :

(ex)?.(ex(1)) + (ex(2))
(cop-2mm» + «112»

If we attempt to solve for so we find

52
IV.A.6

 

(ex) = 3 C Z. [21: WHEXuI) tial-III “#(‘I'Ennfl I z.;up£vcx.,;)]
‘“ Zxcn
By setting
ZquPb'QEu“) 3 G;
W(“‘X¢'.) "' 2%.; I‘PL‘VEIQII) 3 G7.
4- + 2 some II) =0.
IV.‘.7 2': H "

WWI...) meet-111....) "‘ R‘
2'; 'IZH WC‘IEWJ) 7' R3

we can simplify to

CltIGIthZIJ CL. [0. ‘I R. z 't]
(fix): ‘ 'I’
m1“ *1! [Ovatlfl] z'.‘, 4 ZC[G.+R; 2"]
leading to

IV .A. 8 0 3 1: (JC‘ (Cg’XQII’ RahXQfiazzP.) 'I' Z.(0-<cx>)[n‘.zh(e.~a.z.,) +Q31fJQI'RJfJ-J

" <1s)Q3 R) Z hzh

If the measurements are made near the midpoint,

O 2 (ex) and the middle term on the right is approximately
zero. Then

Ive‘e9 2‘ = Q3 R3 thh _—<es)
(031mg) ( 0.. +0: 1'.) 2c . (e0

 

Again expressing the fugacities as concentrations , and
simplifying the coefficients. we find:

IV.A.10 R1 x. (9' Pa.)
v: , ‘ F II; that) *Xe‘h? "' X‘<'IP3>

Dividing numerator and denominator by (pl) (p2) , and set-

time Pf'Pi. PzaADP. and (mpg) /<p1> <p2> :- P results in

 

53

1v.1.11
1: RF 352155341 $5+7£f+ur

A similar argument for the Y cytochromes produces:

 

IVeA;12 RT (m) ‘I’ Y.P +Ya <P3’<9W>P
W 2 - .7 Y’ I 2% RE...) I?" *r‘ixm' ”#99 ‘Y‘wmfifim

The various undefined coefficients are easy to obtain and

are omitted for brevity.

We now have midpoint potential expressions which de-
pend upon the phosphate potential. Unfortunately. they
depend upon other parameters as well. This is not necessarily
fatal to the original pair theory. as one may assume that
the contribution of these terms is small. However. this
lends to unrealistic physical assumptions. As an example,
to eliminate most of the single concentration terms one
has to assume that the cytochromes work in perfect syn-
chrony. that is, that Pi and ADP enter the system.simul-
taneously, and then progress through the subsequent steps
simultaneously.

Besides the difficulties with the phosphate potential
measurements, the original pair theory has some other weak-
nesses: we will briefly discuss two of them. The first
weakness concerns the reaction mechanism. The second
weakness concerns the stoichiometry of the nucleotide car-
riers.

A complete energy coupling theory must contain a mole-

54
cular reaction mechanism for the phosphorylation reaction.

At the current state of the art, it only seems possible to
postulate general schemes: the molecular mechanisms can
only be speculated. This is particularly evident in the
two principal energy coupling theories, the chemical and
the chemiosmotic.

In the chemical theory. energy is coupled through
chemical reactions with a high energy intermediate. The
specific mechanism cannot be stated without knowledge of
this intermediate, and the weakness of the theory is that
the intermediate has not been isolated. In the chemiosmo-
tic theory electronic energy is first converted into con-
centration and potential gradients, and then these gra-
dients power phosphorylation. At present, one can only
speculate as to how gradients energize the phosphorylation
reaction..

The original pair theory fits into this pattern. The
model explains very well how energy may be transferred to
ADP and Pi: it does not explain how the energised ADP and
P1 are combined into ATP. Blondin and Green (3) have
suggested that there is a specific ionophore which cata-
lyses the reaction: this must be considered speculation
until some evidence for the existence of this ionOphore
is obtained. Until a detailed reaction mechanism is ex-
hibited, the pair model cannot be said to have been demon-

strated.

v

55
While the mechanism.problem is not unique to the pair

model, the phosphate carrier problem is. A quick examina-
tion of the mechanism of Figure 2 reveals that both Pi

and ADP transport should be stoichiometrically coupled to
eleotron transport. Unfortunately, there are data which
are not easily reconciled with this requirement. For
example, there is evidence that the ADP/ATP exchange is
only partially electrogenic (6#). Also, the drug atrac-
tyloside blocks ADP transport without uncoupling the phos-
phorylation of internal ADP (33. 64).

To these two difficulties we may now add the problem
of the phosphate potential dependence of the midpoint
potentials. These problems hav in common their origin in
the coupling of the phosphate carriers to the electron
transport chain. Therefore. we shall now investigate a
modification of the pair model. which removes these ob-

Jections, while retaining the pair model characteristics.

B. Egg,Ppip Model gpg Cplculations

Our starting point is the suggestion by Williams (73)
that the driving force in oxidative phosphorylation is a
high local concentration of protons in the immediate vi-
cinity of the phosphorylation site, with the electron trans-
fer chain supplying the energy needed to maintain these
Tprotons in the membrane“. Since the acid catalyzed dehy-

dration of Pi and ADP into ATP is a well-established che-

56

mical reaction (72), the problem of the reaction mechanism
is taken care of nicely. The pair theory can provide a
method to supply the energy necessary to deliver these
protons to the F1 complex by modifying our model and taking
pi and p3 of Figure 9 to be “high energy protons” Hi.

These protons are formally distinguished by the subscript

h to indicate that they cannot be exchanged with a “low
energy” solution proton 3* without the energy being dissi-
pated.

Since Pi and ADP no longer pair with the electron we
have eliminated the problem of the phosphate carriers
being stoichiometrically coupled to the electron transfer
chain. Technically, we have a new problem, that of ener-
gizing these carriers. We know of no evidence that the
carriers by themselves directly affect the redox poten-
tials: therefore we shall ignore this complication in this
paper.

We shall now explore the problem of the phosphate po-
tential dependence by deriving the new expressions for the
midpoint potentials. Since the positive charges are now
exclusively protons. we have to consider a third cyto-
chrome, 2, as in Figure 10. The problem of whether these
cytochromes are arranged in scheme (A) or (B) of Section
# no longer exists, as we no longer have two different
positive charges p; and p;. This means that if scheme (B)

is in fact correct, and there are, for example, two "Y's”

 

III I I'll.

ESE...» L...

FIGURE 10

Diagram of the modified pair theory. The diagram
is constructed to emphasize the flow of the state, rather
than the states themselves. A high energy proton. Hi,
paired to an electron at X, is transferred to Y. There,
the high energy proton is replaced with a low energy pro-
ton H+. The high energy proton. now at the F1 complex.
pairs with an anion a' and is used to catalyze the forma-
tion of ATP. The H+-e’ pair is transferred to Z, where
H+ is free to exchange with solution protons.

56a

 

 

5'65

 

 

 

 

 

 

 

 

 

 

Figure. IO

57
present in an electron transfer chain, that the same possi-
ble states exist for both ”Y's”, and in computing the
grand partition function the only difference between a par-
tition function based on scheme (A) and one based on scheme
(B) would be in the interpretation of the cytochrome con-
centration factor. Since this interpretation is simpler
in scheme (A). that scheme will be assumed.

The grand partition function now becomes:
III. B. 1 23: (1+z.zI.:Ith-eEx..1)° ("2.2. eoI-Ismv2.1.wI-Itmhza.apt-11w)
0c(l*zezAWI"EleaI)

neglecting the possibility of two pairs being associated
with Y for sake of simplicity. The previous arguments
lead to the following expressions for the midpoint poten-

tials:
IV.B.2a V; : -5; “(I/35W FORM)

0 _ I +2.25%I'IENII
1v.13.2b V «5;!» 2hWI..¢m)+z,wbfivu)

 

IV.B.2c
° = -- I,» (Imam-Is...»

At the F1 complex the following reaction occurs:

1v.B.3 kHi+Pi+ADP=ATP+kH+
with the exact value of k depending upon the exact stoichio-
metry of the reaction. While many believe k to be 2 (33).
Williams (72) believes 1 to be the correct value. For either

case we may write

(‘A'rP/‘ADP‘PII (”r/‘11)]: Kp

58

or

k _ k
IV.B.# 2h - 2x lp/Kp

with

IV'B'S 5p '- zATp/zwpzpi
2p is preportional to the phosphate potential P.
Substituting:

IV.B.6a V3: -51 bum.
IV.B. 61) V: 3.3.: M{(I*BII?)/(’1I8l¢)}
IV.B.6c v; t-E} Inc?

with
IY.B.7a 11.22.01.» (-?EX“I/K?

IVeBe7c ‘8‘: Z‘WI'VE'kq)
1v.13.7d 8,: Z‘WPIE'QQIK?‘

1V.B.7e C. =2,w(-?Ez,.)

C. New Pgip gods; - Discusgiog

1. Pho h tam

In this model we can be more specific concerning the
direction of the shifts. V2, not being associated with
any Hh containing pair, does not depend upon the phosphate

potential. V2 varies from -00 to +00 as mp varies from 0

59

tooo . .1111. v? varies from 4111/1?) ln (1/132) to 4111/11)
ln (Bl/B3). In the last case, the negative algebraic com-
ponent of the shift is B1,.which arises from an alternative
pairing for the oxidized cytochrome, as in case 3 of the
simple model. There is a positive component to the shift,
B2, due to an alternative pairing of the reduced cyto-
chrome, as in case 2 of the simple model. These same
effects are present in the original pair model, but are
more difficult to see.

To calculate the direction in which V? varies with
the phosphate potential. let us first assume that 131/33 >
i/Bz. From eq. IV.B.7 this inequality may be written:

2.12:. up (“9511...) > I
IVeCe 1 .1 2‘! up. ('VEYOII) ll WG'VEY“)

Thus far, all of the quantities involved in the inequality
may be preperly taken as constant. We now multiply both

sides by s;1:

Z‘Zh Wk VEVeHIZs 21 We Peal) > I
z. 2. up ('95 u.)
IV.C.2

ze of course, depends upon a number of parameters, in-
cluding the phosphate potential.
The left side of eq. IV.C.2 may be rewritten as

ZAZIIWI'KM) Z. Z). ##(‘QE'IIIQ .- <YAII7 < You.)

2. 2., ”(451(0) .. < Yu)<Yo)

 

 

60

as may be seen by calculating the expectation values from
the partition function and forming their product. This
product is analogous to the equilibrium constant for a
chemical reaction. and may be interpreted the same way.

The denominator contains the states of the system prior

to energy transfer to the P1 complex. and the numerator
those states present after energy transfer. Thus, the num-
erator must be larger than the denominator if forward elec-
tron transfer is tc be the favored direction for the reac-
tion. It is logical to assume the system to be so con-
structed that forward electron transfer is, in fact. the
favored reaction. consequently, the numerator is larger
than the denominator, eq. IV.C.2 is correct as written. and

our initial assumption about the inequality was correct:

131/33 > 1/32

(RT/F) 1n 131/33 > (RT/P) 1n 1/32
D
.. RT 33 T

IV.C.3 V“; -"'E' ‘5', ( ”fight-5' =V;(P:c)
Consequently. v; increases with ‘p' while V? decreases.

'X' represents a schematic cytochrome lying before
a ”phosphorylation site“, ”I“ the cytochrome associated
with the site. and 'Z' the-cytochrome after the site.
The modified pair theory predicts that the midpoint poten-
tials should shift in opposite directions depending upon
whether the cytochrome lies directly before the site, or

61
is associated with it. This shift results in X becoming
a more effective electron acceptor and Y becoming a less
effective electron acceptor upon increasing the phosphate
potential. which will express itself by inhibiting for-
ward electron transport at high phosphate potentials.
This can explain respiratory control. Moreover. the cyto-
chromes known to have phosphate potential dependent mid-
point potentials.‘gt,lg. and‘33.,appear to be located where
the direction of the their shifts would require: ‘pt before

an 1 e »s_-—-.c

the site in complex III,'3 before the site in complex IV,
and1§3 at the site in complex IV (80).

A new problem. however. has arisen. The model pre-
dicts that for each phosphorylation site there should be
two cytochromes with varying midpoint potentials. one in-
creasing with the phosphate potential and the other de-
creasing. In complex III only'pt has been shown to have
a phosphate potential dependent midpoint potential. Cyto-
chrome‘pk appears to be the electron acceptor from‘pt, and
would thus correspond to the ”Y” of our model. Its mid-
point potential is unaffected by changes in the phosphate
potential. There are two possible explanations for this
discrepancy in the model. The first one is that there
may be an interaction between the two cytochromes Just as
there is between‘g andl53. If this interaction was not
accounted for. a shift in‘pk could be ascribed to 2t° The
second possibility is that there is an as yet unidentified

62
electron carrier between‘bt and‘pk which accepts the elec-
trons instead ofIQk.

We mentioned that the slepe of the Qt midpoint poten-
tial versus log P plot was 60 mY/unit. The pair model pre-
dicts that the slope should be RT/kF. This implies that
the value of k in eq. IV.B.# should be 1. Since two pro-
tons are transferred per pair of electrons, this means one
of the protons is dissipated, probably by“equilibrating
with the solution before it can be used to dehydrate Pi
and ADP.

In complex IV..§3 corresponds to Y, while‘g corres-
ponds to I. lost researchers agree that the midpoint poten-
tial of‘g depends upon the phosphate potential: what is de-
batable is the sign of the shift. Some investigators
measure a positive shift, as the pair model predicts (75):
others interpret the spectroscopy differently (71) and
conclude that there is negative shift. The problem lies
in the nature of the interaction between'g and'g3. and must
at present be regarded as undecided (contrast 71 with #5
and #9).

The slope for cytochrome‘g3 requires a more involved

analysis. The slepe is predicted to be

a v; RT (8.8. -B.)z:' W” ML") ( 3: * 3’23”]

—-——‘--—.
a

3152,
< 3,? Weren’t/(w. 8.231")

Table 1

Midpoint potential changes in cytochromes with increasing
phosphate potential

Cytochrome 32;; Pgedicted Observed ‘5
bt x + + 1
bk Y - o
a X + t?
a3 Y - - 1

62a

A‘l I Ll

63
. RT 3
IVeCe4 : i? (I ~ 5:153)

However. eq. IV.C.3 showed that B3/BIB2 is less than one.
Consequently, the right side of eq. IV.C.h will be less than
RT/kP. making a value of uOmY/unit reasonable for this ex-
pression. which corresponds to the ”Y” cytochrome. This
cytochrome corresponds to cytochrome'33, which is the one
with a slope of no mV/unit. These results are summarized

in Table Ie

2. Uncouple; Effects
We have mentioned that uncouplers affect the midpoint

potential. To explain this. we must first describe how
uncoupling occurs in the pair model. Since the energy is
stored in a pair. the only way to dissipate that energy is
to modify the pair. Thus. in the pair model. uncouplers
are postulated to act by inducing the formation of a new
pairing of the electron. a pair containing less energy than
the normal pair. This new pair, while functionally part

of the electron transfer chain, is unable to provide energy
for oxidative phosphorylation. Thus uncoupling is really
the substitution of one coupled process for another (h).

We will not specify anything about the nature of this
new pair. except to list some possibilities. The electron
could be paired with the uncoupler itself. most likely
with the uncoupler functioning as an ionOphore complexed

to a cation (5). Or the uncoupler could modify the ener-

b“
getics so that the electron now pairs to a “low energy”
proton. Finally, the electron could pair to some other
positive charge injected by the uncoupler (5).

The net result of these new pairs being formed is that
we are left with a situation much like case 2 of the simple
model. with uncoupler pairs and regular pairs competing.

If in addition the anionic form of the uncoupler is also
involved in a binding of the cytochrome, we have case 3
of the simple model. Since case 2 produces a positive
shift, and case 3 a negative shift, an uncoupler can con-
ceivably shift the midpoint potential in either direction.

Because this effect has not been studied in detail ex-
perimentally, we can only speak qualitatively about it,
and hence we will not develop any formalism beyond that
provided by the simple model. However. an examination of
this model shows that the magnitude of the shift should
depend upon the uncoupler fugacity. and therefore. upon
the uncoupler concentration. This has. in fact. been ob-

served experimentally (#5).

D. Cogpgrisog with Other Models

iithout going into great detail, we shall now dis-
cuss how the pair model relates to other explanations of
the redox potential shifts. The most convenient way to
organise these theories is to first consider the Nernst

equations

”a".

65

IV.D.1 v - v° + (RT/P) 1n (<ox>/<red>)

If V shifts, there are clearly four possible explanations:

1) Yo has shifted

2) <ox)/<red> has shifted

3) There is a missing term on the right which has

shifted

h) Some combination of the above
v. shall ignore possibility (h), as it adds nothing new,
and look at (1) - (3).

The reversed-electron transfer theory belongs to class
(3). As mentioned in the introduction. a redox system con-
taining a redox couple in equilibrium with ATP synthesis
and a mediator reacts with, but for the other cytochromes
between the phosphorylation site and the mediator the cor-
rect relationship is:

Iv.n.2 v . v0 + (RT/P) ln(<ox>/<red>)

* (V; 4- (RT/1') In P)
'where the + or - sign depends upon which side of the phos-
phorylation site the mediator is located.

This explanation is in contrast to.that offered by
the pair model..where it is assumed that a, is known or.
in experimental terms. that the electrode measures the
“correct” potential. Therefore, the calculated shifts oc-
cur regardless which cytochromes the mediator react with.
The effects produced by driving electron transport back-
'wards are incorporated in the pair model. Changing the

m ‘H".".'."'3-rr1'mcr

 

1"]! {III

 

66
phosphate potential will tend to drive the reaction for-
wards or backwards. This driving is the source for the
shifts in the midpoint potentials through the pairings.
The pairs do come to equilibrium but not the electrons by
themselves.

This position disposes of the vexing question regarding
the site of action of the mediator. Thus far there is
no answer which is satisfactory to all experimentalistss
the only point on which there is agreement being that the
mediator cannot react with every cytochrome in the electron
transfer chain without short-circuiting the entire system.
he have to be careful by what we mean by ”reaction“ here.
If the mediator is capable of transferring electrons be-
tween different cytochromes short-circuiting indeed will
”take place. The transfer, however. will be effective only
if it goes from pair states to pair states and moving only
electrons will not accomplish this. Unless the possibility
of pairing for the transferred electron and its abandoned
partner are simultaneously offered, there will be no short-
circuit even though the mediator "reacts" with every cyto-
chrome..

One objection against the reverse electron theory is
that if the mediators react with a specific cytochrome. then
all cytochromes on the same side of that cytochrome should
show identical P dependent shifts in midpoint potential.
This objection does not apply to the pair model. because

I“. ‘Im rig-1m"

67
if the electron is paired to a low energy proton. i.e.
one which can equilibrate with the solution without dissi-
pating free energy. its midpoint potential is independent
of the phosphate potential. We have chosen the corres-
ponding cytochrome z to be after the transducing cytochromes.
but it could have been placed in front as well.

The other common explanations fall under class (2) in
the above scheme. With them there exists a second form of
the cytochrome. which greatly increases in concentration
upon energization of the mitochondrion. Since the two
forms are spectroscopically indistinguishable. this means
that the logarithmetic term in eq. IV.D.1 should actually
be written

Iv.n.3 (RT/P) ln (<ox>1 +<ox>2/<red)1 +(red>2)
However. the two forms are in equilibrium.with one another.
and IV.D.3 can be solved in terms of the phosphate poten-
tial and whichever cytochrome reacts with the mediator.
giving an expression similar to eq. IV.B.6b.

Formally. this explanation is close to the pair model.
as the pair model assumes alternative pairings. However.
there is a physical distinction. in that these alternative
pairs do not result in a second chemically distinct form
of cytochrome. This is because the pairs involve weak
bonds. and chemical distinctions require chemical bonds.
Thus one should expect that the absorption spectra should

not reveal these alternative pairs. while one must wonder

 

68

why the alternative cytochromes have not been seen.

Indeed. the pair model falls under class (1) of our
scheme. This seems paradoxical. since V° is a constant
for simple systems. Actually. V° is constant for a given
specification of a cytochrome. but we have shown that the
pair theory requires that the number and energy states of
all pairs be known to fully specify a cytochrome. lodifying
the cytochrome by introducing new pairs changes its mid-
point potential. ‘le may consider the pair model to unite

 

the features of both the two cytochrome and reverse elec-

r7
Ia
r.‘
..‘. ..

tron transport theories into a unified. more general model.

 

 

V. FURTHER SPECULATIONS AND SUGGESTIONS
' FOR EXPERIMENTALISTS

By this time it should be apparent that the data are
capable of a variety of interpretations. Some of the am-
biguities can only be resolved by further experimentation;
others could not be discussed earlier because a complete
analysis needed the formalism of the pair model. We shall

now take a look at some of these ambiguities.

As . 921 Be ”Appgpnt' Redo; 8’11!!!

Not surprisingly. the most important experimental
question has not yet been resolved. This is the question
of whether the shifts occur through reversed electron trans-
port. with the mediator reacting only with cytochromeIQ
instead of'g or‘ps or whether the shifts are real. with
the mediator reacting with the desired cytochrome. We have
previously discussed how the known experimental data can '
be interpreted in terms of either theory. This leaves
the decision between the two interpretations to be made
on the basis of probability and consistency with other
theories.

To understand why we are so pessimistic. let us con-

sider the two most direct approaches to the problem. First.

69

70
let us try to demonstrate experimentally that cytochrome
.2 reacts with a mediator. To do this, we must experimen-
tally extract cytochrome'p from the mitochondria. Thus
far. it has not been possible to extract‘b in an active
form. so this experiment is impossible at the present
atate of the art. However. even if this were possible. it
would not be conclusive. since the extracted.b,would be in-
dependent of the membrane. and the membrane undoubtably
contributes to the necessity of using mediators. Conse-
quently. no experiments done on membrane free cytochromes
can be conclusive.

These considerations lead to the second approach: to
remove all cytochromes butIQ from the mitochondrion. Again.
however. only cytochrome g.is readily extractable from mito-
chondria. Consequently. if the same shifts occur in the
extracted mitochondrion.nothing is proved. since one can
argue that the mediator is still not reacting with‘p but
with some component other than‘g. Conversely. if the
chifts now disappear. it does not necessarily mean that the
mediator only reacts with‘g. since one can argue that the
salt solution used for extraction denatured the membrane
so that the'bemediator reaction can no longer occur.

Therefore. as we have suggested earlier. the decision
between real and apparent redox shifts must be made on the
basis of probabilities. On this basis. we feel that the

arguments put forth for real redox shifts are stronger

N" e';‘.

71
than those for apparent shifts. In particular. the ob-
servation that not all electron carriers show a shift.
while the reversed electron transfer theory suggests that
they should (35). is a particularly strong argument. stronger
than the arguments of Slater and likstrom.

However. on the basis of consistency with energy
coupling theories the reversed electron transport theory
becomes strong indeed. The reason is that this theory is
independent of the mechanism of energy coupling. meaning
in particular that it is consistent with the chemiosmotic
theory. The alternative theories we have divided into
class 2 and class 1 theories. The class 2 theories all
involve the cytochrome in the energy transduction process.
meaning that they are variations of the chemical theory.

The class 1 theory is the pair model. This means that the
chemiosmotic theory is consistent only with the reversed
electron transport explanation for the redox shifts. There-
fore. if one believes the discussion of the redox shifts.

one is led to doubt.the chemiosmotic hypothesis.

B. Semi-reversed Elegtrop Trgggport Theogy

Vikstrom's latest theory is that a real shift is
occuring with the 3 cytochromes. but that the b cyto-
chromes display reversed electron transport.* The reason
_for this is that Wikstrom now believes that phosphoryla-
tion in complex IV takes place between cytechromelga and

‘1'?"3'.

 

llllu'llllll Jill-II It'll
‘11

72

molecular oxygen. rather than betweenlg and‘ga. This means
that the redox reaction between cytochrome‘g andlg3is no
longer considered to be in equilibrium.with the phosphoryla-
tion reaction. and there is nothing left to reverse. Wik-
strom now explains the redox shifts as being due to con-
formational changes in the cytochromes. the changes' func-
tion being respiratory control (70).

We have earlier discussed how‘Wikstrom and Chance
have reinterpreted the spectroscOpic data. What needs to
be added here is an acknowledgment that the pair model
worked out in Section IV is inadequate insofaras the cyto-
chrome oxidase data are concerned, since it does not incor-
porate interaction effects. The next step in the develop-
ment of the pair theory is to remove this restriction and
see if the behavior of cytochrome oxidase can be satisfac—
torily modeled. Iithout actually performing the calculation.
we will sketch out how this model may be constructed.

We have written the partition function for a two cyto-

chrome system containing but one class of pair as
c , . . .
Z. si 2- 53%;? ”345125953? #845
, po ..o

with EisiEx where Ex is the energy of one pair on cyto—
chrome X. and similarly for Y. Since the terms containing
1 are separate from those containing 3. we may sum the
partition function using the binomial theorem. However.

(this separability is the result of our assumption regarding

 

73
the lack of interactions. A more general expression is to
write

E aEx-i-E

X XV

where Ex’a as before. and Exy is the energy change due to
having a pair on Y. One can replace these in the partition
function. and calculate a new function . which includes
interaction effects.

The difficult part is to write the correct form for
Exy' It will have to depend upon the spin state of Y. as
well as on any ligands which may be present. Once con-
structed. however. the free energy of X follows immediately.
from which one may predict the spectra of X. And by re-
peating our calculations one may compute the redox poten-

tial of X.

C. Phogphate Potential Dependencg

We have presented two pair models. differing obser-
vationally in the redox potential dependence of the phos-
phate potential. We argued that the modified pair theory
was the more plausible partly because its redox potentials
depended strictly upon the phosphate potential and not on
Pi. ADP. or ATP by themselves. and that this was what the
data are. However. our suspicious minds keep thinking
that the reason no data have appeared showing dependence
_on individual nucleotides is because no experimentalist

believed that such could be the case. and thus all such

 

7h
data have been surpressed. This is a point which can easily

be proven by experimentation.

D. Ungguplg; Effects

Equally untouched experimentally are the effects of
uncouplers upon the redox potential. Thus far uncouplers
have been used in experiments srtictly as a control: to
demonstrate that a particular effect is due to redox energy.
While uncoupler effects have been reported. there has not
been any place for them in the energy coupling theories.
The pair model does have a place for uncoupler effects
however. and they no longer can be ignored.

We explained that the pair model views uncouplers as
providing an alternative partner for the electron. This
new pair should show all of the effects the usual pair does.
in particular. its redox energy should depend upon the un-
coupler concentration. lore experiments along these lines
are in order.

Pianlly. our new model removes one of the objections
which uncoupler experiments have raised against the pair
theory. that of maximum uncoupler to phosphorylation site
ratios of less than one. In the original formulation (3).
where the uncoupler molecule itself had to pair with the
electron. these ratios were difficult to reconcile. In
the new model. where either high or low energy protons

pair with the electron. all the uncoupler need do is amplify

 

75

the natural source of low energy protons. There are many

ways in which this can be accomplished.

E. Conclusions

The new pair model. related to the proton in the mem-
brane hypothesis of Williams. has been shown to be generally
consistent with the experimental data concerning the phos-

‘3'

phate potential and uncoupler effects upon the midpoint
potentials of cytochromes. The model's strongest point

('6 I! a

is that it makes midpoint potential shifts a natural fea-
ture of energy transduction. As with all theories proposed
to date. some ad hoc postulates are necessary. suggesting
that more information is needed before a completely defini-
tive theory can be proposed. Such a theory would have to
consider the interaction of several electrons with each

other.

APPENDIX

76

APPENDIX I
ON ACTIVITY COEFFICIENTS

Is PrOb‘
Given a reaction system A() + B(e)? A(e) + B()
We can calculate the half-cell redox potential by

RT
VA'V: ‘ ultimo. an”:
where a a the activity of the species in question.

 

Now upon the addition of in! of Uncoupler U. or ATP.

“5:"..me
‘. \v

we observe that for the same concentrations of A() and A(e)
we new measure V; . Writing the activities as the product
of an activity coefficient Y and a concentration. this effect

can be described as

R T be [h a]
\k’: vzq'3F‘bnlhmIfiUO +4X

II. Ems-mama!
Now this can be explained in two ways:

A) The added chemical causes You to shift to Y...“ . re-
sulting in

. u a
v.=v:+£.1!~ ‘éJ—g—M +x

SEND
uh"! X: 11..., 7“,“)

B) V2 shifts. This implies a change of some sort in at
least one of the species. say A(). Thus A() becomes A'().

77

78
However. ,auxxe'.) and [A()] =- [A'()] so the sole obser-
vable effect is in V2.

I a I f 3.1 ”h in“ (“(3.3
V3 V7: ”F Yemtfl‘”)

III. Reasons for Preferring g) eve; A):
In the absence of independent information about .

there is no way of confirming one explanation and denying

the other. Any decision to use one scheme over the other

is to an extent arbitrary. However. there are some rea-

sons for preferring B) to A).

1) Perfect solutions (Solutions obeying the same assump-
tions as ideal gasses. eg.. no interactions) can be
described by the equation

‘ f“ = '. .. aunts]

This is an exact equation for these assumptions. Ac-
tivity coefficients do not occur. In this kind of redox
reaction any change in VA has to involve V2 because un-
der these assumptions there is nothing to change in the
logarithmic term.

Now. the point is that the pair model we have devel-
oped contains the assumption of no interactions. Yet. this
model does predict a shift in V1. with the shift appearing
in the V2 term. It seems unnatural to try to force this
shift into a change in activity coefficients.

2) The change will have to be in the wrong direction.

 

FIGURE 1 1
Iethod of computation of midpoint potentials.
a) Extrapolation to equal concentrations.
b) Extrapolation to equal concentrations and
zero concentrations for A'() and A().

78a

 

 

 

a)

VT

 

73b

 

 

r [so] _,
a u

0' W]

 

RI h [flu]

—

111‘ m]

79

To see this. we need to understand how midpoint potentials
are actually computed. A collection of V2 vs. 1n AA:
values are measured. and VA plotted againstggag§$ .
as in Figure 11a. The value of V where 12% I 1 is
approximately V2. and would be exactly V2 if Ina/y... a 1.

Now the exact way to calculate V2 is to repeat the
calculation for different concentrations of [A()] :- [A(e)] .
and extrapolate to zero concentration where the activity
coefficient is defined to be unity. This has not been
done for our system. However. one can easily imagine how
the results would have to look in order for the actual mid-
point potentials to be identical under the two conditions.
This has been done in Figure 11b. where it is seen that
adding ATP or Uncoupler causes the extrapolated curve to
shift markedly. This implies that the magnitude should
be dependent upon the value of [A( )] :- [A(e)] . which has

not been observed.

 

ELL-fa? Km.-.

 

 

 

 

 

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80

 

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decadevcd

81

 

 

 

 

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APPENDIX III

LIST OF SYMBOLS

m1 - 522.1235 M m d «I
A().A(e) Oxidized or reduced electron 11
carrier
ADP Adenosine Diphosphate 1
ATP Adenosine Triphosphate 1
e’ unpaired electron 10
E1 Free energy of particle 'i' #3
P Faraday's Constant 21
P1 ATP-ass Complex 2
G1 Free energy change in species 'i' 8
I Intermediate in chemical theory 11
K1 Equilibrium constant of reaction 20
number 'i'
Ligand in Wilson's theory 42
W Hediator 29
N1 Number of particles of type 'i' 43
present in ensemble
P Phosphate Potential 8
Pi Inorganic Phosphate 1
R Gas Constant '8
T Absolute Temperature 8
V. V° Redox. or midpoint. potential 21
21 Grand partition function of system i #3

33

8h
Transmembrane potential
Chemical potential of species '1'
Stoichiometric coefficient
Chemiosmotic correction factor

High energy bond symbol

28

2h
28
11

- "r

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35

an hl’
L I
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1.

2.

3.

h.

5.

6.

7.

9.

10.

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