Chapter 4: Biochemical redox reactions

4.1 Introduction

4.2 Biochemical redox half-reactions, the Faraday conststant and the reduction potential

4.2.1 Defining the reduction potential:

4.2.2 The standard reduction potential is also the midpoint potential of a redox

couple

4.3 Determining the value of the midpoint potential

4.4 Solution (ambient) potentials and electrochemical cells

4.5 Example: the potentiometric titration of NAD

4.6 How midpoint potentials are used to depict biochemical electron transfer systems

4.7 Ambient potential in a living cell and oxidative stress

4.7.1 Oxidative stress.

4.8 The pH-dependence of the midpoint potential

4.9 Example: The pH-dependence of the midpoint potential of the NADox/NADred redox

couple

4.10 Thermodynamic reciprocity of interactions between proton binding and reduction

potential

4.11 Application: Determining the midpoint potential of E.coli thioredoxin

4.12 Application: A mutation that raises the midpoint potential of the regulatory

disulfide the the γ-subunit of the chloroplast ATP synthase from Arabidopsis

4.13 Application: Impact of mutations on the midpoint potential of an [4Fe-4S] cluster

in the electron transfer protein:ubiquinone oxidoreductase

4.14 Application: Determining the mitochondrial ambient potential

4.15 Summary

1

Chapter 4: Biochemical redox reactions

4.1 Introduction

In Chapter 3 we developed the use of the chemical potential in dealing with

biochemical reactions. This formalism applies to all reactions whether or not they involve

hydrolysis of ATP, DNA cleavage or oxidation/reduction changes. However, for the many

reactions in chemistry which involve electrons being transferred from one species to another,

i.e., reduction and oxidation (hence, redox), there is a specific language and set of parameters

that have been developed, namely the concepts of the reduction potential and the “half-

reaction” or "half-cell reaction". Chemical and biochemical redox reactions can all, in

principle, be carried out by transferring the electrons from the molecule being oxidized to an

electrode located in one solution, and then delivering electrons to the molecule being reduced

via another electrode located in a separate solution. In many cases, chemical and biochemical

reactions can in reality be performed in this manner. The electrical charges need to be able to

travel from one electrode to another, and this can be done using a wire, in conjunction with a

salt bridge in which ions (e.g., K+ and Cl-) move between the solutions in order to maintain

charge neutrality in each solution as electrons are added to one side and removed from the

other. A schematic diagram is shown in Figure 4.1. The thermodynamics of such reactions

are, of course, the same as we discussed in the last chapter. The parameter of interest remains

the transformed reaction Gibbs free energy, , but the terminology used is often that of

electrochemistry when dealing with redox reactions. The focus on electron transfer, and the

proton transfer reactions which are frequently linked to electron transfer, are particularly

helpful in understanding many biochemical reactions.

'rGΔ

In addition to biochemical redox reactions, we will also discuss in this chapter the

characterization of electron carriers in electron transfer pathways or in other redox processes

2

and the characterization of the prosthetic groups within redox-active enzymes. The first group

includes c-type cytochromes, quinols, NADH, etc., and the second group includes protein-

bound hemes, flavins, Fe/S clusters, disulfides, and many more.

Figure 4.1: Schematic of a redox reaction being carried out in an electrochemical device where electrons from the reductant are delivered to the oxidant through a wire. The maximal electrical work that can be accomplished is equal to the Gibbs reaction free energy of the reaction.

4.2 Biochemical redox half-reactions, the Faraday conststant and the reduction potential

Let’s take a look at the oxidation of NADH by O , a reaction catalyzed by the

mitochondrial respiratory chain. The equation indicates a reaction with oxygen, and it is

indicated that we will determine the thermodynamics with respect to dissolved oxygen in the

aqueous phase (aq).

2

(4.1)

(4.1) 22 NADH + 2 H + O (aq) 2 NAD + 2 H O+2

+

Chemical reaction vs biochemical reaction notation: The reaction of NADH and O , as it

appears in equation is the way one typically would write out a chemical reaction. At

constant pH, we need to recall that the proton concentration does not change, so formally in

the biochemical reaction, hydrogens and charge need not be conserved. Protons can appear

2

(4.1)

3

from or vanish into an infinite proton reservoir. Formally, the proper way to describe this

biochemical reaction at constant pH is

(4.2) 22 NAD + O (aq) 2 NAD + 2 H Ored ox 2

This can be disorienting, especially if one is not used to it, so it can be excused to balance the

reaction so as to keep track of what is going on. However, in using the transformed Gibbs

free energy, the protons are not included in the equilibrium expression.

In this reaction, NADH (or NAD ) is the reductant. That is, electrons are taken from

NAD and delivered to O , which is the oxidant. The oxidant has the stronger tendency than

the reductant to take electrons. We can separate the biochemical reaction in equation

into two half-reactions,

red

red 2

(4.2)

(4.3)

12 2

1

half-reaction 1: O (aq) + 4 e 2 H O

half-reaction 2: 2 NAD + 4 e 2 NAD ox red

−

−

in which we have, again, removed the protons since pH is held constant. The half reactions

are written following a convention of placing the oxidant on the left. The net reaction in (4.2)

is reaction 1 minus reaction 2 as they are written in (4.3). We can think of these half-reactions

as reactions that might take place at the surfaces of the two electrodes in Figure 4.1. In this

electrochemical set-up (Figure 4.1) electrons are donated by the oxidation of NAD at one

electrode and delivered through a wire to the second electrode, where O is reduced to water.

This is a current, and we could get electrical work from the system if we had an electrical

device such as a motor inserted into our circuit. The maximal work we could obtain is given

by the transformed Gibbs free energy of the reaction, . Remember that this is the

maximal work per mole of reaction progress (

red

2

'rGΔ

ξ , introduced in the previous chapter) at the

particular concentrations present. This is not the amount of work that we could get if we let

the reaction run down to equilibrium. The realization that the electrical work is equivalent to

4

'rGΔ is helpful because is stresses the fact that the chemical driving force for this redox

reaction is related to the spontaneous movement of electrons from the reductant (electron

donor) to the oxidant (electron acceptor, which oxidizes the reductant). The work capacity of

this reaction ( ) is usually expressed in terms of joules, but can also be expressed in terms

of electrical work, or volts. One joule is defined as the amount of energy gained when 1

coulomb of charge is moved against a potential of 1 volt, where a coulomb is the amount of

charge transported by a current of 1 ampere in 1 second. Recall that the electrical work

required to move an amount of charge (Q) from a position where the potential is ψ to a

position where the electrical potential is ψ is

'rGΔ

1

2

2 1(elw )Q= Ψ −Ψ (4.4)

The amount of absolute charge in 1 mole of electrons is 96,485 coulombs, so the energy of

moving 1 mole of electrons, Q = -96,485 coulombs, to a more negative potential, =

-1 volt, is (-96,485)(-1) = 96,485 joules. Doing work on the system is positive. This gives us

a conversion factor between joules and volts, two different units of energy.

2 1( )Ψ −Ψ

(4.5) 1 volt = 96,485 joules

The conversion factor is called the Faraday constant, F.

(4.6) = 96,485 coulombs/molF

In the system pictured in Figure 4.1, electrical current will move from left (NAD ) to

right (O ), which means that the electric potential of the electrode on the left is more negative

than that on the right. Since electrical work is nonPV work, this means that it is equivalent to

reversible work ( ). The maximal electrical work per mole of reaction

progress (the extent of reaction parameter, ξ) must be equal to the transformed Gibbs free

energy of the reaction under the defined conditions, as it would proceed if both reactants were

red

2

el revdw dw dG= =

5

present in the same solution. As the reaction is written in equations and , we can see

that

(4.2) (4.3)

(4.7) '( ) 4(96, 485)right left rQ Ψ −Ψ = − ΔΨ = Δ G

The negative sign comes from the charge (Q) being negative, and the 4 is the absolute value

of the stoichiometry number of the electrons as the reaction has been written in (4.2) and

(4.3), four electrons per mole of O2. We will use the notation “ eν ” to indicate the absolute

value of the stoichiometry number, so in this case, 4eν = . The spontaneous direction of

reaction is from left to right, and the value of is negative. The direction of the

current flow (NAD

(4.2) 'rGΔ

red to O2) is also from left to right as we have drawn our device in Figure

4.1, towards the more positive electrode. The potential to do work is given by the voltage

difference between the two electrodes and this work potential must be equivalent to .

From equation , since . Clearly, if we know

the value of the transformed Gibbs free energy of reaction, we can readily calculate the

potential difference between the two electrodes in the setup in Figure 4.1.

'rGΔ

(4.7) ' 0 it follows that ( ) 0r right leftGΔ < Ψ −Ψ >

The reason for going through all of this is to emphasize the reality that redox reactions

can and often are examined using an electrode as either an electron source (reductant) or an

electron acceptor (oxidant). Let us now convert the expression for the reaction free energy to

units of volts. If we generalize equation (4.7) we see that

'

'

e r

r

e

F G

or

GF

ν

ν

− ΔΨ = Δ

ΔΔΨ = −

(4.8)

6

Figure 4.2: Transformed Gibbs reaction free energy converted to an electric potential difference for a redox reaction for a 1-electron and 2-electron reaction. This is a plot of equation (4.8).

Each of the four electrons drops down the potential ΔΨ , so the total reaction free

energy is equal to the votage drop, converted to units of joules, multiplied by the number of

moles of electrons, 4 in this case. Figure 4.2 shows a plot of the relationship in (4.8). For a

1-electron reaction, the slope of the line shows that 1 kJ is equivalent to about 10 mV. For a

2-electron reaction, the slope if half.

By dividing the expression for by '

rGΔ e Fν we get the following.

' '

2

' '

2

' '

2

[ ]ln[ ][ ( )]

[ ]ln where 4[ ][ ( )]

[ ]ln4 [ ][ ( )]

o oxr r

red

ooxr r

ee e e red

o ox

red

NADG G RTNAD O aq

NADG G RTF F F NAD O aq

NADRTE EF NAD O aq

νν ν ν

Δ = Δ −

Δ Δ= −

= −

=

)

(4.9)

where E' is the electric potential difference between the two electrodes '(E = ΔΨ and E'o is

the electric potential difference under standard state conditions (1 M of each reactant,

298.15K, pH 7, specified ionic strength). We can calculate the value of E'o from the values of

the transformed Gibbs free energies of formation for reaction (4.2).

7

' ' '

2 2

'

'

'

''

2 2 2

2(1059.11) 2( 155.6) 2(1120.09) (16.4)

449.56 /

( 449.56) 1.164 volts 4(96485)

o o o

ox red

or f NAD f H O f NAD f

or

or

oo r

e

G G G G G

G

G kJ mol

GEFν

Δ = Δ + Δ − Δ −Δ

Δ = + − − −

Δ = −

Δ −= − − =

'o

O

(4.10)

If, for example, the concentrations of reduced and oxidized NAD are the same and the

concentration of O2(aq) is 250 μM (2.5 x 104 M), then the potential between the electrodes

would be

' '4

2

'

'

[ ] (8.31)(298) 1ln 1.165 ln( )[ ][ ( )] 4(96485) 2.5 10

1.165 0.053

1.112 volts

o ox

e red

NADRTE EF NAD O aq x

E

E

ν −= − = −

= −

=

(4.11)

Note that a negative value of converts to a positive value of , and both indicate a

spontaneous reaction direction from left to right as the reaction is written (electrons flowing

towards the more positive side). In this example, there is a strong driving force for the

reaction as written in

'rGΔ 'E

(4.2) to proceed from left to right. The numbers confirm what is

obvious, which is that NADH is a strong reductant for oxygen.

4.2.1 Defining the reduction potential:

The half-reactions defined in (4.3) each contain the oxidized and reduced form of a

reactant, such as NADox and NADred. These constitute a “redox couple”. Every redox

reaction, such as (4.2), involves two redox couples. Depending on the conditions of the

reaction, the spontaneous direction of the redox reaction will be from the reduced form of one

of the redox couples to the oxidized form of the second redox couple. The convention is to

8

compare the thermodynamics of "redox couples" on the basis of their reduction potentials,

which we will now define. Let's generalize by splitting the following reaction

(4.12) ox red red oxA + B A + B

into two half-reactions.

(4.13)

1ox red

1ox red

A + A

B + B

e

e

e

e

ν

ν

−

−

The convention in dealing with biochemical half-reactions is to always write them with the

electrons on the left, i.e., the reaction direction from left to right is a reduction. The

transformed Gibbs free energy of reaction for (4.12) is given by

' ' [ ][ln[ ][

o red oxr r

ox red

A BG G RTA B

Δ = Δ −]]

(4.14)

which we can also write as

' ' [ ][ln[ ][

o red ox

e ox

]]red

A BRTE EF A Bν

= − (4.15)

Equation (4.15) is called the Nernst equaton. We will split equation (4.14) into two parts,

corresponding to the half-reactions in (4.13).

'' ' [ ] [ ]ln ln

[ ] [ ]oo red red

r r A r Box ox

AG G RT G RTA B

B⎡ ⎤ ⎡ ⎤Δ = Δ − − Δ −⎢ ⎥ ⎢ ⎥

⎣ ⎦ ⎣ ⎦ (4.16)

The two expressions on the right in (4.16) can be related to the half-reactions in (4.13). We

can now define a transformed reaction Gibbs free energy for each half-reaction.

'

' '

'

[ ]ln[ ]

[ ]ln[ ]

o

o redr A r A

ox

redr B r B

ox

AG G RTA

BG G RTB

⎡ ⎤Δ = Δ −⎢ ⎥

⎣ ⎦

⎡ ⎤Δ = Δ −⎢ ⎥

⎣ ⎦

(4.17)

9

The expressions in (4.17) can also be obtained by starting with the half-reactions in (4.13) and

using the procedures described in the Chapter 3, considering the electron to be formally one

of the reactants, and assigning the electron a chemical potential of zero.

The standard state transformed Gibbs reaction free energy of the half-reactions can be

obtained from the corresponding Gibbs free energies of formation.

(4.18)

' ' ' ' '

' ' ' ' '

( )

( )

red ox red ox

red ox red ox

o o o o or A A A f A f A

o o o o or B B B f B f B

G G

G G

μ μ

μ μ

Δ = − = Δ −Δ

Δ = − = Δ −Δ

G

G

'oBG

For the full reaction (4.12) the standard state Gibbs free energy of reaction can be written as

(4.19) ' 'o or r A rG GΔ = Δ − Δ

Divide (4.17) through by e Fν to convert to units of volts to obtain the following.

'

' '

'

[ ]ln[ ]

[ ]ln[ ]

o

o redA A

e o

redB B

e o

ARTE EF A

BRTE EF B

ν

ν

⎡ ⎤= −⎢ ⎥⎢ ⎥⎣ ⎦

⎡ ⎤= −⎢ ⎥⎢ ⎥⎣ ⎦

x

x

'oB

(4.20)

In (4.20), ' and oAE E are defined as the standard reduction potentials of the redox couples

Aox/Ared and Box/Bred, respectively.

''

''

oo r A

Ae

oo r B

Be

GEF

GEF

ν

ν

Δ= −

Δ= −

(4.21)

We also note that since , ' 'o or r A rG GΔ = Δ − Δ 'o

BG

'oB

(4.19), then for the full reaction (4.12)

' 'o oAE E E= − (4.22)

10

The minus sign in front of 'oBE in (4.22) results from the convention of writing the half–

reactions with the oxidized form on the left, as in (4.13). The full reaction is equal to reaction

A minus reaction B in(4.13). The quantitative relationship between and 'or AGΔ 'o

AE in (4.21)is

exactly the same as shown in Figure 4.2. To get a better feeling for equation (4.20), we will

convert to a log10 instead of natural log, and assume T = 298.15K, to get

' ' ' '[ ]59 log (mV units for and )[ ]

o oredA A

e ox

AA AE E

Aν= − E E (4.23)

Assuming a standard reduction potential of +100 mV, the data in Figure 4.3 for a 1-electron

and 2-electron reaction. For a 1-electron reaction the slope is -59mV per log unit, or per order

of magnitude change in the ratio of [[ ]

red

ox

AA

] . The slope is half this value for a 2-electron

reaction, about -30 mV/log unit.

Figure 4.3: Plot of equation (4.23) assuming the temperature is 298K and ' 100o

AE mV= . For a 1-electron reaction, the slope is 59 mV/log unit, and for a 2-electron reaction, the slope is about 30 mV/log unit. This is the change in the reduction potential for every 10-

fold change in the ratio [[ ]

red

ox

AA

] . The larger this ratio, the better the reducing power, or

the more negative the value of the solution potential.

11

4.2.2 The standard reduction potential is also the midpoint potential of a redox couple

In equation (4.20), when 50% of A has been reduced, then [Ared] = [Aox] and the logarithmic

term is equal to zero. At this point,

(4.24) ' ' when 50% of A is reduced.oA AE E=

For this reason, the standard reduction potential is also referred to as the midpoint potential

of the redox couple, and is designated as , the potential at which half of the redox

couple is reduced and half oxidized. If we had an electrode maintained at a potential of

, submerged in a solution of “A” , at equilibrium half of “A” would be reduced. Often

the pH is indicated, and the superscript prime indicates constant pH. If no pH is designated, it

should be assumed the

',m pHE

',m pHE

'mE refers to pH 7. It is important to recognize that for biochemical

redox reactions, it is conventional to define the standard state as pH 7, whereas for chemical

reactions, the usual definition of the standard state concentration (activity) of 1 M is used.

4.3 Determining the value of the midpoint potential

Values of many standard reduction potentials (or midpoint potentials) are tabulated ,

and some are shown in Table 4.1(1-3). Most of the redox couples shown in Table 4.1 are

involved in enzyme catalyzed reactions in E. coli (4)as well as in many other organisms.

Note that these all apply to standard conditions at pH 7 ([H+] = 10-7 M).

Redox couple

eν Standard reduction potential( '

,7or om'oE E ),mV

O2/H2O 4 815

3 2NO / NO− −

2 420

2 4NO / NH− + 6 360

O2/H2O2 2 295 DMSO/DMS1 2 160 TMAO/TMA 2 130 ubiquinone/dihydro-ubiquinol 2 110 fumarate/succinate 2 30 menaquinone/dihydro-menaquinol 2 -80 glucose/gluconate 2 -140 oxaloacetate/malate 2 -165 pyruvate/L-lactate 2 -185

12

dihydroxyacetone phosphate/ glycerol-3-phosphate

2 -190

acetaldehyde/ethanol 2 -195 NADox/NADred 2 -320 H+/H2 2 -420 CO2/formate 2 -430 acetate/acetaldehyde 2 -580 acetate/pyruvate 2 -700 1dimethylsulfide (DMS) 2trimethylamine N-oxide (TMAO); trimethylamine (TMA)

If not, they can be determined either from existing data or experimentally. Three approaches

are given below.

Method 1: One way is to calculate values from the Gibbs free energies of formation of

the reduced and oxidized forms of the redox couple. Many of these are tabulated. For

example,

'oE

1

' ''

/

3 3'

/

'/

NAD + 2 e NAD

(1120.09 10 ) (1059.11 10 )2(96485)

0.316 volts or -316 mV

red ox

ox red

ox red

ox red

ox red

o of NAD f NADo

NAD NADe

oNAD NAD

oNAD NAD

G GE

F

x xE

E

ν

−

⎡ ⎤Δ −Δ⎣ ⎦= −

−= −

= −

(4.25)

Note that we must convert kilojoules to joules by multiplying the transformed Gibbs free

energies of formation by 1000. The same exercise can be done for the standard reduction

potential of the O2/H2O redox couple, yielding

13

2 2

2 2

2 2

2 2

12 2

' ''

/

3 3'

/

'/

O + 4 e 2 H O

2

2( 155.6 10 ) (16.4 10 )4(96485)

0.848 volts or 848 mV

o of H O f Oo

O H Oe

oO H O

oO H O

G GE

F

x xE

E

ν

−

⎡ ⎤Δ −Δ⎣ ⎦= −

− −= −

=

(4.26)

Method 2: The equilibrium constants of many biochemical redox reactions are also

tablulated, many determined experimentally. If one can determine the equilibrium constant

for a reaction involving two redox couples, and if one knows the midpoint potential of one of

the redox couples, then the second is easily calculated. For the generalized reaction in (4.12),

the equilibrium constant can be expressed in terms of the standard reduction potentials or

midpoint potentials.

''

' '/ /

'

( )'

ooer

o oe A A B Box red ox red

FEGRT RT

F E ERT

K e e

K e

ν

ν

Δ−

−

= =

=

(4.27)

Method 3: A third way is to experimentally determine the potential developed between the

redox couple of interest and a reference redox couple. The convention is to report standard

reduction potentials versus the standard hydrogen electrode (SHE). The standard hydrogen

electrode is a platinum electrode that is in contact with hydrogen gas at a pressure of 1 bar

and an aqueous solution of 1 M protons. Either hydrogen gas can be oxidized to yield protons

or protons can be reduced to form hydrogen gas at this electrode. The convenience of this

esoteric choice of the standard hydrogen electrode is that the reduction potential of the H+/H2

redox couple, . This is because +2

oH /H

E = 02

0oHμ = for hydrogen gas, the most stable form of

the element under standard conditions and, by definition, the standard state chemical potential

14

of a solution of 1 M protons . Hence, the measured potential for any redox couple in

the standard state (pH 7, 1 M concentrations) in relation to the standard hydrogen electrode is

simply its standard reduction potential.

0oH

μ + =

2

' '/ /

' '/

ox red

ox red

o o omeasured A A H HvsSHE

o omeasured A AvsSHE

E E E

E E

+= −

=

(4.28)

It is useful to keep in mind that the sign of the standard reduction potential refers to whether

the redox couple will be more reducing (negative value of ) or more oxidizing

(positive value of ) than the proton/hydrogen couple in the standard hydrogen

electrode. Also, a negative means that current will flow from the electrode measuring

the redox couple of interest to the standard hydrogen electrode, and a positive means

current will flow from the standard hydrogen electrode to the reactants in the setup in Figure

4.1. Note that in Table 4.1, the biochemical definition of the standard potential for the H

'/ox red

oA AE

'/ox red

oA AE

'/ox red

oA AE

'/ox red

oA AE

+/H2

couple is -420 mV vs SHE. This is because the biochemical definition of the standard state is

at pH 7, or [H+] = 10-7 M. At 298K, going from 1 M to 10-7 M is a change of 7 log units, or -

7(∼60 mV/log unit) = -420 mV (see Figure 4.3).

The standard hydrogen electrode is convenient from a computational viewpoint since

the midpoint potential of the H+/H2 redox couple is zero. However, from a practical

viewpoint, the standard hydrogen electrode is not convenient at all. Instead, it is common to

use either a saturated calomel reference electrode or a silver chloride reference electrode.

These are readily purchased and are packaged with a salt bridge and porous glass frit, ready

to be inserted into the electrochemical solution.

The calomel electrode uses the redox couple of mercury metal (liquid) and Hg2Cl2.

12 2Hg Cl 2 e 2 Hg(l) + 2 Cl− −+

15

The name derives from the fact the Hg2Cl2 is also called “calomel”. The reduction potential

depends on the concentration of chloride, and these reference electrodes are most often used

with a saturating solution of KCl. At room temperature, .

Hence, if a calomel reference electrode is used, one can simply add +241 mV to the potential

obtained to the value versus the standard hydrogen electrode.

241 versus SHEcalomelE mV= +

Another choice as reference electrode is the silver chloride electode. This uses the

redox couple of silver metal and silver chloride.

1 0AgCl + e Ag (s) + Cl− −

As with the calomel electrode, the silver chloride electrode reduction potential depends on the

concentration (activity) of chloride, and is routinely used with saturated KCl solution. The

solution potential of the silver chloride electrode at room temperature is +205 mV vs SHE.

For any biochemical reaction, the data obtained are always converted to values versus the

standard hydrogen electrode by adding 205 mV to the value obtained with the Ag/AgCl

reference electrode. To experimentally determine the midpoint potential of a redox-active

biochemical substance, it is necessary to use an electrochemical cell and to manipulate the

solution potential, as described in the following section.

4.4 Solution (ambient) potentials and electrochemical cells

Let’s consider a simple electrochemical cell containing a biochemical redox couple of

interest. In this example we have two electrodes and the device is conceptually identical to

that shown in Figure 4.1. One electrode is in direct contact with the solution containing the

material being studied. The second electrode is the reference electrode which is in contact

with the electrochemical solution through a salt bridge. The most commonly used reference

electrodes are the saturated calomel electrode and the silver chloride electode, discussed in

the previous section. The voltage measured between the two electrodes (Figure 4.4) will be

16

dependent on the reduction potential of the redox couple in solution and the reduction

potential of the reference electrode.

Figure 4.4: Schematic of a simple electrochemical cell. This version has two electrodes. The solution must be made anaerobic because O2, being a strong oxidant, will interfere with the system. Argon gas is frequently used to flush the system. The working electode is often platinum gauze, increasing the surface area that can react with redox-active solution components. The reference electrode is usually a saturated calomel electrode or a silver chloride electrode. Mediators are required to convey electrons between most biochemical reagents and the working electrode.

What happens if we have more than one redox couple present in the same solution at

equilibrium? At equilibrium, the reduction potentials of all the redox couples must be the

same, and this reduction potential will be monitored by the electrode that is in

electrochemical contact with the solution. This is called the solution potential or ambient

potential and is designated as Eh. If the solution potentials are not the same for the redox

couples, this indicates that the solution is not in equilibrium.

Mediators help attain equilibrium: It is almost aways necessary to include mediators in the

electrochemical solution since most biochemical compounds will not readily react at the

surface of the electrode. The mediators are selected based on their ability to undergo redox

chemistry at the electrode surface and also by their ability to equilibrate with the biochemical

redox couples in solution. The mediators are themselves redox couples, existing in reduced

and oxidized forms, and they are each characterized by a midpoint potential, 'omE . If the

17

solution potential is far from the 'omE value of a particular mediator, the concentration of either

the value of [[ ]

red

ox

AA

]mfor the mediator will be either very small ( 'o

hE E>> ) or very large

( 'oh mE E<< ). In the first instance, this means the [Ared] is very small and in the second case,

[Aox] is very small. Under these conditions, the rate by which the mediators can transfer

electrons and help reach equilibrium will be very slow. For this reason, a number of

mediators with a range of 'omE values is often present in the electrochemical solution in

addition to the biochemical redox couple(s) being studied. A list of several mediators is

shown in Table 4.2.

Mediator/Reductant/Oxidant 'omE

potassium ferricyanide +430 p-benzoquinone +280 2,6-dichlorophenol indophenol +217 mV 2,5-dimethyl benzoquinone +180 phenozine methosulfate +80 mV ascorbate +30 duroquinone +5 methylene blue +11 mV menadione 0 pyocyanine 34 mV 2,5-dihydroxy-p-benzoquinone -60 anthroquinone -100 indigo carmine -125 mV anthroquinone 1,5-disulfonate -170 9,10-anthraquinone 2,6-disufonic acid -185 mV anthroquinone 2-sulfonate -225 benzyl viologen -350 dithionite -3861

1The midpoint value of dithionite is very dependent on pH and also concentration. See (5)

Potentiometric titrations: One can perform a potentiometric titration by changing the

solution potential while, simultaneously, monitoring the red

ox

AA

ratio of the redox couple of

interest using some chemical or spectroscopic methods. The electrochemical cells are

constructed to facilitate removing samples at different Eh values or to determine the

absorbance spectrum, for example, as a function of the solution potential. Obviously, one

18

must be able to change the solution potential systematically to do this. Most commonly, an

electrochemical cell such as that schematically shown in Figure 4.4 is used, along with a

calomel or silver chloride reference electrode. There are several ways to manipulate the

solution potential. Regardless of which method is used, one is changing the ratio red

ox

AA

for all

of the redox couples in solution and, thus, changing the solution potential.

1. One can add reductant (e.g., a buffered solution of dithionite) or oxidant (e.g., a buffered

solution of ferricyanide) to change the solution potential.

2. One can use a potentiostat, which is a device that uses a third electrode to add or remove

electrons from solution using an external source of electrons, and in this way alter the

solution potential.

3. One can use a dominant redox couple which will equilibrate with the system to be studied,

and whose total concentration is substantially greater than that of other redox-active

components in the solution. One adds a known amount of [Ared] and a known amount of

[Aox]. In this way, during the equilibration, the [[ ]

red

ox

AA

] ratio for the dominant redox couple

remains essentially fixed (since it is present at much higher concentration than any other

redox couple), and determines the solution potential. The solution potential can be readily

calculated by using equation (4.20) if the values of ' and oAE eν are known for the dominant

redox couple. The concentrations of all the other redox couples will equilibrate to be

consistent with the solution potential.

If one has, for example, two redox couples present at equilibrium, the solution

potential, hE , must be the same as the reduction potentials of each redox couple.

19

'

' '

' [ ] [ ]ln ln[ ] [ ]

o

h A B

o red redh A B

e ox e o

E E E

or

A BRT RTE E EF A F Bν ν

= =

x

⎡ ⎤ ⎡ ⎤= − = −⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

(4.29)

Note that in equation (4.29) the electron stoichiometry numbers eν are those that apply for

each redox couple separately. From equation (4.23) we can see that for a 1-electron reaction,

a change of the solution potential by about 60 mV will change the ratio of [[ ]

red

ox

AA

] by 10-fold,

increasing the ratio for -60 mV, and decreasing it for a change of +60 mV.

4.5 Example: the potentiometric titration of NAD

Now let’s look at an example of how the equations we have derived can be used to

determine the value of a midpoint potential as well as the number of electrons transferred in a

half-reaction. Figure 4.5 illustrates simulated data of a potentiometric titration of NAD,

which shows the fraction of NAD that is reduced as a function of the solution potential, Eh.

We expect the data to fit to the following equation.

' ' [ln[ ]

o redh NAD m

e o

NADRTE E EF NADν

= = −]

x

(4.30)

In practice it is common to switch to from the natural logarithm to log10.

' [2.303 log[ ]

o redh m

e o

NADRTE EF NADν

= −]

x

(4.31)

At 298K,

2.303 (2.303)(8.31)(298) 0.059 volts or 59 mV96485

RTF

= = (4.32)

Therefore, with this value inserted, assuming 298K we get (using mV units)

' [59 log[ ]

o redh m

e o

NADE ENADν

= −]

x

(4.33)

20

By determining the fraction of NAD that is reduced as a function of Eh, we can determine the

values of both ' and oe Eν NAD experimentally.

The data are plotted in two ways in Figures 4.5 and 4.6. In Figure 4.5, the percentage

of the total NAD that is reduced is plotted as a function of Eh. The reduction of NAD can be

determined by monitoring its optical absorbance, making this a “spectro-electrochemical

titration”. The value of presenting data in this way is that one can readily see that the over the

range of Eh values the NAD has gone from fully oxidized to fully reduced.

Figure 4.5: Potentiometric titration of NAD showing the fraction of NAD that is reduced (NADred/NADtotal) as a function of the solution potential (Eh). The midpoint is about -320 mV (vs SHE).

Since this is an equilibrium measurement, it should make no difference in which

direction one does the titration, reducing or oxidizing. In practice, it is important to

demonstrate reversibility to be sure that equilibrium has been attained at each point. The

potential at which 50% of the NAD has been reduced, readily seen by inspecting the plot in

panel A, is equal to the midpoint potential of NAD under the conditions being examined. At

pH 7, this is about –320 mV.

21

In Figure 4.6, [log[ ]

red

ox

NADNAD

] is plotted versus the solution potential, Eh. We expect from

equation (4.33) to get a straight line where the intercept will be 'omE and the slope will be

59

eν− . The data do fit a straight line with a slope of –30 mV, indicating, as we expect, the

eν = 2 and this is a 2-electron redox reaction. The solution potential where

[ ]log 0[ ]

red

ox

NADNAD

= is the midpoint potential

Figure 4.6: The same data as in Figure 4.5 plotted as the logarithm of the ratio red

ox

NADNAD

. The data fit a straight line with a slope of -30 mV/log unit, consistent with

2eν = .

4.6 How midpoint potentials are used to depict biochemical electron transfer systems

Any redox couple that has a more negative standard reduction potential will be a

stronger reductant than any redox couple whose standard reduction potential is more positive

(see Table 4.1). This applies, of course, to standard state conditions (pH 7, 1 M

concentrations). So, for example, NADred is the reductant for O2. The standard potential for

the reaction between NADred and O2, as written in (4.2) is

22

'

2 2

' '/ /

'

'

848 ( 316)

1164 mV

o

ox red

o oO H O NAD NAD

o

o

E E E

E

E

= −

= − −

=

(4.34)

Notice that we do not multiply in '/ox red

oNAD NADE (4.34) by a factor of two because of the

difference in the stoichiomety numbers for the electrons ( 2eν = for the NAD couple and 4

for the O2 half-reaction. This is because the reduction potentials essentially are already

normalized per electron.

Figure 4.7 is an example of the use of reduction potentials in the biochemical literature.

This shows the "Z scheme" describing the energetics of the light-driven reactions in plant

photosynthesis. The various redox components that make up the photosynthetic electron

transfer chain are all located according to their standard reduction potentials. More negative

values are interpreted as "higher energy", meaning that they are better reductants. The Z

scheme shows the role of the two photosynthetic reaction centers, photosystem I (PSI and

photosystem II (PSII). The absoption of a photon of light results in creating an excited state

of chlorophyll P680, which becomes a very strong reductant. The reduction potential is

decreased about 1.5 volts, and the electron is transferred through a chain of redox active

groups whose reduction potentials get progressively more positive. The ChlP680+/ChlP680

redox couple has a more positive reduction potential than O2/H2O, and oxidizes water to O2,

with intermediates being a Mn cluster and a tyrosine. After a second light reaction in in

photosystem I, followed by another linear chain of redox reactions, the end product is

NADPred. We will not go into any further details, but just point out that this kind or scale is

frequently used to represent electron transport chains in biochemistry. The tendency is that

electrons are transferred from redox couples with more negative reduction potentials to those

with more positive potentials. Since these are standard state potentials, one must beware that

23

the true reduction potentials will be altered by concentrations of the reduced and oxidized

forms. However, in many instances, the redox centers are fixed within proteins or protein

complexes, so there is no change in concentration possible as electrons are transferred within

a complex with fixed geometry. However, in the functioning electron transport chain, the

ratios of each redox component, red

ox

AA

, will be determined by the steady state concentrations.

If redA is oxidized very rapidly by the next redox component along the chain then

red oxA A<< and the reduction potential will be considerably more positive (i.e., better oxidant)

than indicated by the midpoint potential. Although there are a number of exceptions (6),

generally, electron transfer is in the direction towards components with the more positive

midpoint potential. The thermodynamics of electron transfer reactions are no different than

other biochemical reactions and must always progress towards the minimum Gibbs free

energy. We will consider the kinetics of electron transfer reactions in a separate chapter.

Figure 4.7: The Z scheme diagram, illustrating the use of reduction potentials of a series of redox couples involved in electron transfer chains. Each redox active participant is placed at a height in the diagram corresponding to its reduction potential with H2O/O2 at about +0.8 volts. Light generates strong reductants and the electron ends up reducing NADPox to NADPred. The electron-

24

deficient P680 Chlorophyll is a stronger oxidant than O2, and water is oxidized to form O2 as the electrons from water re-reduce chlorophyll P680. Govindjee website

Figure 4.8 shows another example, illustrating the photosynthetic scheme for green sulfur

bacteria (Chlorobiaceae). In this case, light activates a bacteriochlorophyll (P840) which

becomes a strong reductant, reducing the primary acceptor (A0), which is a modified

bacteriochlorophyll. Electrons then flow to a quinine-like molecule, A1, and then, via several

Fe/S centers to a ferredoxin. There are two options at this point. There is a cyclic electron

transfer pathway in which the electrons are passed to a menaquinone within the membrane

and, eventually, reduces the oxidized P840. This pathway includes the bc1 complex which

couples the electron transfer reaction to the generation of a transmembrane proton

electrochemical gradient, Δp in this diagram. This will be discussed in the next chapter.

Alternatively, the ferredoxin can reduce NADPox to NADPred. In this non-cyclic pathway,

electrons from the oxidation of H2S are used to reduce P840, yielding elemental sulfur, which

can be further oxidized by these organisms to sulfate.

Figure 4.8: Schematic of the photosynthetic electron transfer pathways of the green sulphur bacteria. The redox components are placed according to their midpoint potentials. Light (hν) excites the P840 active-site chlorophyll, which becomes a strong reductant, initiating electron transfer which can be either cyclic or non-cyclic. (Figure is Fig. 5.5 in (7))

25

4.7 Ambient potential in a living cell and oxidative stress

In addition to the many metabolic redox reactions, there are many other redox-

dependent processes in both eukaryotic and prokaryotic cells, including protein folding,

transcriptional regulation, enzyme regulation and signal transduction. Whereas in the

laboratory one is usually striving to reach equilibrium to make a measurement, in living cells,

as we have already discussed the reactant concentrations are maintained in a steady state that

is distinctly not at equilibrium. The concentrations of the reduced and oxidized forms of

redox couples within cells is determined by the rates by which they are produced and utilized

in a myriad of biochemical reactions. We saw, for example, in Section 3.13, the results of

one mathematical model of glycolysis showing that many, but not all of the reactions were

close to equilibrium conditions. In general, in some sets of biochemical redox reactions will

be near equilibrium because the rates of the reactions are fast compared to the reactions

coupling the reactions to others taking place within the cell.

One natural set of barriers to rapid redox equilibration within cells are the boundaries

between intracellular compartments and organelles(8, 9). Hence, the ambient potential of the

cytoplasm of a mammalian cell is distinct from that of the nucleus or that of the endoplasmic

reticulum or the mitochondrion. However, even within these organelles, not all the redox

reactions are necessarily maintained at or even near a single solution potential. In the

cytoplasm, for example, there are sets of reactions that are equilibrated with the

NADred/NADox redox couple, and another set of reactions equilibrated with the

NADPred/NADPox couple. These are not necessarily in equilibrium with each other because of

the kinetics of the reactions linking these reaction networks(9).

Many cellular processes that are redox-regulated depend on the redox status of disulfide

bonds between cysteines is key enzymes or transcription factors, for example. The formation

of disulfide bonds may also be simply part of the protein folding process required for forming

26

a stable, native protein. One has an equilibrium between the reduced and oxidized cysteine

pair within a protein

(4.35) 12protein(CySSCy) + 2 e protein(CySH)−

We can also refer to this as the cysteine/cystine or sulfhydryl/disulfide redox couple. As this

reaction has been written, the reduced cyteines are assumed to be protonated, but this depends

entirely on the pH. Protons have not been included to balance the reaction to emphasize that

this reaction occurs at constant pH.

Figure 4.9: The structure of glutathione. Oxidation forms a disulfide-linked dimmer.

In eukaryotic cells, there are two major systems which determine the redox status of

Prot(CySH)2 /ProtCySSCy in proteins: 1) glutathione, a tripeptide with one cysteine (Figure

4.9), which can exist in either a reduced (GSH) or oxidized form (GSSG); and 2)

thioredoxins (Trx) or proteins within the thioredoxin family(10). Thioredoxins are small

proteins which contain a pair of cysteines in an exposed loop (see Figure 4.10) which can

also be either reduced or oxidized, Trx(SH)2/TrxSS. There are a number of different

thioredoxins with specific roles, as well as proteins with thioredoxin folds or domains that are

redox-active. In mammalian systems, free cysteine circulates in the plasma and the redox

status of this cyteine pool is the major determinant of the equilibrated redox couples that are

extracellular.

27

Figure 4.10: Structure of the reduced form of yeast thioredoxin 1 from yeast

(Saccharomyces cerevisiae). (Figure is from (11). ) The reported “redox status” of a cell or cellular compartment is usually determined

experimentally by the redox status of one of the key redox couples listed above(9, 10). Of

course, the effective solution potential will be different for various compartments within a

eukaryotic cell, such as the cytoplasm, mitochondrion, endoplasmic reticulum, etc.

Depending on the process, the ambient potential of interest may be one reported by

glutathione, but one of the other key dominant redox couples (such as thioredoxin or NAD)

may be more significant. Figure 4.11 shows some representative ambient potentials for

different eukaryotic cellular compartments. Generally, the mitochondrion and cell cytoplasm

are considered to be “reducing environments”, and this is supported by the quantitative

measurement of the steady state redox potentials indicated in Figure 4.11.

28

Figure 4.11: Estimates of the ambient potentials of cellular compartments in a

eukaryotic cell, including the circulating blood plasma. Different dominant redox couples are indicated. These values will be dependent on the physiological state of the cell (Figure is from (9)).

The glutathione-linked solution potential within the mitochondrion is about -300 mV,

which is significantly more reducing than the GSH/GSSG potential in the cytoplasm (-260

mV for proliferating cells). These values will depend on the physiological state. The

endoplasmic reticulum, which is where protein disulfides are made, is much more oxidizing,

with a GSH/GSSG potential of about -150 mV. In general, protein disulfides are rarely found

within the cytoplasm but are much more common in secreted proteins. However, the

formation of disulfides as part of protein folding, is not a spontaneous reaction with O2 in

most cases, but is catalyzed by specific enzymes(10, 12, 13), both in eukaryotic cells (in the

endoplasmic reticulum) and in prokaryotes (in the periplasm of Gram negative bacteria).

4.7.1 Oxidative stress.

Oxidative stress (14)describes pathological situations usually resulting from the

production of reactive oxygen species (ROS), which includes hydrogen peroxide (H2O2),

superoxide (O2-), peroxynitrites (OONO-), organic hydroperoxides (ROOH) and hydroxyl

radicals (HO•). These are “pro-oxidants” and can promote the oxidation of cellular

components, resulting in disease states. Reactive oxygen species can be generated by

elements of the respiratory chain in mitochondria. Reaction of reactive oxygen species with

the glutathione pool will result in reducing the concentration of reduced glutathione and may

29

result in lowering the total concentration of glutathione. A cascade of redox consequences

results, leading to various pathological conditions, depending on the context.

4.8 The pH-dependence of the midpoint potential

The majority of redox or electron transfer reactions in biochemistry are accompanied by

proton transfer reactions, such as the reduction of a disulfides in (4.35). For example, if there

is a proton binding site on reactant A, the reduction of Aox to Ared will increase the negative

charge on the molecule and, if there is a proton binding site available, the positively charged

proton might bind. In principle, each reactant in (4.12) could be comprised of multiple

protonated species, as discussed in the previous chapter. Hence, reactant Aox will consist of a

mixture of Aox , Aox(H+)1, Aox(H+)2, Aox(H+)3 etc. up to some maximum number of bound

protons, depending on the number of available sites. Upon reduction, Ared will, similarly, be

comprised of a distribution of protonated species. This is important because the reduction

potential of each different protonated species may be unique. It is likely to be easier to reduce

a more protonated species since it carries more postive charge, i.e., the protonated species will

have a more positive reduction potential. However, by using the transformed thermodynamic

functions, assuming a constant pH, we need not be concerned about the specifics of the

distributions of the protonated species in order to define the basic thermodynamics. This

assumes, as we did in defining the transformed Gibbs free energy function, that the

protonation reactions are rapid and the protonated species are always equilibrated. However,

it is clear that upon reduction, the distribution of the protonated species may change and,

more important for us at this time, the average number of bound protons may also change.

In Chapter 3 we derived the expression in equation (3.47) describing the pH-

dependence of the transformed Gibbs reaction free energy, , and the same relationship is 'rGΔ

30

also valid for the pH-dependence of the standard state transformed Gibbs reaction free

energy, . 'orGΔ

'

'

, ,

( ) 2.303( )

or

r HT P

G RT NpH ξ

⎡ ⎤∂ Δ= Δ⎢ ⎥∂⎣ ⎦

(4.36)

In this expression, recall that is the change in the number of bound protons (per mole of

reaction progress) for the reaction under the specified conditions. Let’s go back to reaction

r HNΔ

(4.12), but assume that there are coupled protonation reactions. Substituting from equation

(4.22), we get

' '

' ', , , ,

( ) ( ) 2.303( ) ( )

o o

r A r Br H

T P T P

G G RT NpH pH

ξ ξ

⎡ ⎤ ⎡ ⎤∂ Δ ∂ Δ− =⎢ ⎥ ⎢ ⎥

∂ ∂⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦Δ (4.37)

or for each half reaction

'

'

'

'

, ,

, ,

( ( )) 2.303 ( )( )

( ( )) 2.303 ( )( )

o

o

mr H

eT P

mr H

eT P

E A RT N ApH F

E B RT N BpH F

ξ

ξ

ν

ν

⎡ ⎤∂= − Δ⎢ ⎥

∂⎢ ⎥⎣ ⎦

⎡ ⎤∂= − Δ⎢ ⎥

∂⎢ ⎥⎣ ⎦

(4.38)

where and are the changes in number of bound protons (per mole) for

each half reaction, and

( )r HN AΔ ( )r HN BΔ

(4.39) ( ) ( )r H r H r HN N A NΔ = Δ −Δ B

For each half-reaction, we can substitute numerical values at 298K in equation (4.38) to get

the following.

'

', ,

( ( )) change in protons bound 59 59( ) number of electrons transferred

o

m r H

eT P

E A NpH

ξν

⎡ ⎤∂ Δ= − = − •⎢ ⎥

∂⎢ ⎥⎣ ⎦ (4.40)

If is constant over the pH range of interest, this is simply integrated to yield r HNΔ

31

' '

2 1, , 259 ( )o o r H

m pH m pHe

N1E E pH

νpHΔ

= − − (4.41)

This says that the pH-dependence of the midpoint potential can be used to determine the

change in the number of bound protons for a redox half-reaction, provided that we know the

number of electrons ( eν ) involved in the reaction.

4.9 Example: The pH-dependence of the midpoint potentials of the NADox/NADred and

oxaloacetate/malate redox couples.

We will consider as an example the redox equation

(4.42)

L-malate + NAD oxaloacetate + NAD

half-reaction 1: NAD + 2 e NAD

half-reaction 2: oxaloacetate + 2 e malate

ox red

ox red−

−

This reaction is catalyzed by malate dehydrogenase and is part of the TCA cycle. We saw in

Section 4.5 that both the ' and oe mEν values for a NAD half-reaction could be experimentally

determined by potentiometric titration, as in Figure 4.5. We can now determine the value of

for the reduction of NAD by plotting the value of the midpoint potential r HNΔ'

(o

m )E NAD as a

function of pH by using equation (4.40). The result is a straight line, shown in Figure 4.12,

with a slope of -30 mV per pH unit. The fact that this is a straight line means that is not

changing over the pH range being examined (pH 5 to 9). The fact that the slope of the line in

Figure 4.12 is not zero means that there is a change of protonation of NAD upon reduction,

as we already know. The slope of –30 mM/pH unit tells us that

r HNΔ

r H

e

Nν

Δ is 1/2, so

over the full range of pH (since

1r HNΔ =

2eν = ). The midpoint potential of NAD gets more negative

as the pH is increased. NADred is a better reductant at higher pH.

32

(4.43) -1 + + -1 +ox redNAD +2e +H NAD or NAD +2e +H NADH

Also shown in Figure 4.12 is the pH-dependence of the midpoint potential of the

oxaloacetate (OAA)/malate redox couple. From Table 4.1, we see that ',7 165o

mE mV= − for

this redox couple, which is also indicated in Figure 4.12. The pH-dependence of the

midpoint potential is a straight line with a slope of -59 mV/log unit. Since this is a 2-electron

reaction ( 2eν = ), we conclude from equation (4.40) that 2r HNΔ = throughout the pH

range.

At any pH, the difference between the two lines is

' ' ', , ,

''

,

( / ) ( /o o om pH m pH ox red m pH

oo r

m pHe

E E NAD NAD E OAA malate

GEFν

Δ = −

ΔΔ = −

)

(4.44)

Under standard state conditions (1 M concentrations) the reaction would go in the

opposite direction than indicated in (4.42). Under metabolic steady state conditions, however,

the direction of the reaction is as written, as required by the TCA cycle to produce NADred.

Figure 4.12: The pH-dependence of the NADred/NADox and the OAA/L-malate redox couples.

33

4.10 Thermodynamic reciprocity of interactions between proton binding and

reduction potential

In the example of NAD, described above, the oxidized form remained deprotonated

and the reduced form remained fully protonated throughout the pH range. Now let’s look at

a situation where we have a redox couple, Aox/Ared, in which both the oxidized and the

reduced forms can bind 1 proton, but that the proton affinity, or pK, is shifted upon

reduction. We will assign the pK of the oxidized form, pKox a value of pH 6. Upon

reduction from Aox to Ared, the proton affinity is greater so it will become protonated at a

higher pH value (lower [H+]). Furthermore, we will specify that we are able to measure the

extent to which A is reduced, but cannot distinguish whether it is protonated or

unprotonated. The experiment will be to change the solution potential, and measure the

apparent midpoint potential, , at a series of different pH values, as in Figure 4.12. The

question is how does the apparent midpoint potential vary with pH from pH 4 to 10, a span

that encompasses both the pK of the reduced and oxidized forms of the redox couple. This

is a useful problem to examine because we will introduce some of the procedures that will

be used throughout the text when approaching problems dealing with thermodynamics in a

number of different contexts.

',

om pHE

To begin, let's identify the number of different molecular species we have in our

solution. These are

Aox : oxidized, not protonated

AoxH+: oxidized, protonated

Ared : reduced, not protonated

Aox H+ : reduced, protonated

These four species are related by several equations. The protonation reactions are written in

the direction of deprotonation, and the equilibrium constant is a proton dissociation

34

equilibrium constant, used to define the pK. Note that the pH at which half of the species

(e.g., Aox) is protonated, (e.g., [Aox] = [ oxA H + ]), then [H+] = Kox, or pH = pKox. Also, since

we are dealing with chemical species and not biochemical components, we have dropped the

“primes” over the thermodynamic parameters.

+ +ox ox red red

'

1) A A + A H + A + A H

2) protonation of the oxidized species: A

[A ][ ] ; ( ) log[ ]

3) protonation of the reduced species: A

total

ox ox

ooxox r ox ox ox

ox

red re

A H H

HK G H pK KA H

A H

+ +

++

+

+

=

+

= Δ = −

'

1 1

[A ][ ] ; ( ) log[ ]

4) reduction of the oxidized species: A

[ ] [ ]59log ; ( ) 2.303 log[ ] [ ]

5) reduc

d

oredred r red red red

red

ox red

o ored redh m r m

ox ox

H

HK G H pK KA H

e A

A AE E G e RT FEA A

+

++

+

−

−

+

= Δ = −

+

= − Δ = − = − 1o

2 2

tion of the protonated oxidized species: A

[ ] [ ]59log ; ( ) 2.303 log[ ] [ ]

ox red

o ored redh m r m

ox ox

H e A H

A H A HE E G e RT FEA H A H

+ − +

+ +−

+ +

+

= − Δ = − = − 2o

(4.45)

In equations 4 and 5, above, it is assumed that the temperature is 298K, in order to get the

value of 59 mV. In these equations, Eh is the solultion potential, experimentally determined.

It is usual to use units of mV in place of volts, but remember to use volts when changing

units to joules.

The protonation and redox reactions above can be put into a simple thermodynamic

cycle, shown in Figure 4.13. We can see from Figure 4.10 that there are two different

pathways to go from the oxidized species Aox to the protonated, reduced species, AredH+.

35

Since, the transformed Gibbs reaction free energy is a state function, the free energy change

must be identical no matter which way we go. Aox can be either protonated first and then

reduced, or reduced first and then protonated. The the free energy change will be the same.

Hence, we can conclude that

(4.46) 2 1( ) ( ) - ( ) (r ox r r r redG H G e G e G H+ − −−Δ + Δ = Δ + Δ )+

The negative sign in front of the reaction free energy terms for the protonation reactions

come from the fact that we defined these in the direction of deprotonation in (4.45). From

(4.46) it follows that

2 1

ln 2.303 log

59( ) ( )

red red

ox ox

o oox red m m

K KRT RTF K F

pK pK E E

=

− = −

K (4.47)

Figure 4.13: Thermodynamic cycle showing two equivalent pathways of going from Aox to AredH+(indicated by the red arrows). Equation (4.47) tells us that if the difference in the midpoint potentials between the

protonated and deprotonated forms is specified, this also defines the difference between the

pK values of the reduced and oxidized forms. This is more readily seen in a free energy

diagram, Figure 4.14, which shows the drop in the standard state molar free energy as

36

reactants are converted to products. We will encounter these diagrams at many points in the

text, particularly when we discuss the thermodynamics of ligand binding.

Figure 4.14: Free energy diagram showing the relative values of the standard state molar Gibbs free energy values of the system in different chemical states. Each level is labelled by the species present. For example, the top line (Aox + H+ + e- ) stands for the sum of the standard state chemical potentials for each of the species, (

ox

o oA

oH e

μ μ μ+ −+ + ), etc. The bottom line is the level of the standard state chemical potential of AredH+. The two sets of vertical lines on the left show the situation in which reduction increases the proton affinity of molecule A. By necessity, protonation of molecule A must also increase the affinity for the electron, indicated by the larger magnitude of the drop in free energy associated with reduction of AoxH+ compared to Aox. The two sets of vertical lines on the right depict the situation where reduction of molecule A has no effect on the proton affinity, and vice versa. The coupling free energy quantifies the mutual influence between the protonation and electron transfer reactions. One important concept that is easily understood in terms of a free energy diagram is the idea

of thermodynamic coupling or cooperativity. In the current problem, we have stipulated that

reduction of the molecule A results in increasing the affinity for proton binding. Let’s

rearrange equation (4.46)

(4.48) 2 1( ) ( ) ( ) ( )o o o or r r red r oxG e G e G H G H− − +Δ − Δ = Δ − Δ +

The difference in the reaction free energy of reducing the protonated and deprotonated

forms is exactly matched by the difference of the reaction free energy of protonating the

37

reduced and oxidized forms. These differences are called the coupling free energy,

. or couplingGΔ

(4.49) 2 1( ) ( ) ( ) (o o o o or coupling r r r red r oxG G e G e G H G− − +Δ = Δ −Δ = Δ −Δ )H +

If the reaction free energy of binding a proton is favored by, say -20 kJ/mol by reduction,

then the binding of a proton will, by necessity, make the reduction more favorable by the

same -20kJ/mol. If reduction has no influence on the protonation, then protonation will

have no influence on the reduction potential, i.e., 0or couplingGΔ = and there is no

cooperativity. This is called reciprocity, and is a form of cooperativity. This concept is

encountered very frequently in biochemical reactions and in ligand binding. The coupling

free energy is shown on the free energy diagram in Figure 4.14 by showing the case where

it is assumed that there is no coupling ( 0or couplingGΔ = ) on the right side. The standard state

free energy of the system is lower due to the addition of the favorable (negative) coupling

free energy, which stabilizes redA H + relative to oxA , shown by the lower standard state free

energy in the diagram.

The equations in (4.45) represent a specific model that we can use to simulate data or, if

we were really doing an experiment, to fit to data. Although we have equations defining

1omE and 2

omE , these cannot be directly measured. Instead, we measure the "apparent" or

transformed midpoint potential, . We are now back to the “prime” in because

we are keeping the pH constant during the reaction and grouping species in pseudo-isomer

groups that differ only by the state of protonation. This is simply the transformed

thermodynamic parameter, as we discussed in the previous chapter. The value of is

what we can actually measure by a potentiometric titration since we have no way to know

whether the molecule is protonated or not. It is useful to see how is related to the non-

',

om appE '

,o

m appE

',

om appE

',

om appE

38

transformed reduction potentials of the unprotonated and protonated chemical species

( 1 and om 2

omE E , respectively).

',

[59log[ ]

o red redh m app

ox ox

]A A HE EA A H

+

+

+= −

+ (4.50)

We can substitute from the proton equilibrium constants in (4.45)

' ', ,

',

[ ][1 ][ ]59log 59log

[ ][ ] [1 ]

[ ][1 ][ ]59log 59log

[ ][ ] [1 ]

o ored red red redh m app m app

ox ox ox

ox

o red redh m app

ox

ox

HA A H A KE E E

HA A H AK

HA KE E

HAK

+

+

++

+

+

++

= − = −+ +

+= − −

+

(4.51)

From the definition of 1omE in equations (4.45) we can now substitute into (4.51)

1[ ]59 log[ ]

oredh m

ox

A E EA

− = − (4.52)

From which we get

', 1

[ ][1 ]59log

[ ][1 ]

o o redm app m

ox

HKE EHK

+

+

+= +

+ (4.53)

This tells us the dependence of , which is what can be measured, on pH. As the proton

concentration gets very low (

',

om appE

([ ] ;[ ] )red oxH K H K+ +<< << , equation (4.53) predicts that both

[ ][1 ]red

HK

+

+ and [ ][1 ]ox

HK

+

+ will approach 1, so the expression within the logarithm in equation

(4.53) will also approach a value of 1. Since log(1) is zero, at high pH (low proton

concentration) ',

om app m1

oE E≈ , which is the midpoint potential of the unprotonated species. At

very acidic pH, the values of both [

red

HK

+ ] and [

ox

HK

]+ become much larger than 1, so

39

', 1 1

', 1

[ ] [ ][1 ] [ ]59log 59log

[ ] [ ][1 ] [ ]

[ ]59log[ ]

o o ored redm app m m

ox ox

o o oxm app m

red

H HK KE E EH HK K

KE EK

+ +

+ +

+= + ≈ +

+

≈ +

(4.54)

Finally, we substitute from equation (4.47) to see that at low pH, we get

', 1 1 2

', 2 ox red

[ ]59 log ( )[ ]

when pH<<pK ,pK

o o o ooxm app m m m m

red

o om app m

K1

oE E E EK

E E

≈ + = + −

≈

E

(4.55)

The apparent midpoint potential has limiting values which correspond the the midpoint of

the protonated form of the substrate at low pH, and the midpoint of the unprotonated form at

high pH. When the pH is below the pK's of both the reduced and oxidized forms of A, then

essentially A remains protonated whether it is oxidized or reduced, and there is no further

dependence of the apparent midpoint potential on pH. There is also no dependence of the

apparent midpoint potential on pH above the pK's of both the reduced and oxidized forms

(pH > 8 in this problem), and both the reduced and oxidized forms remain unprotonated.

Figure 4.15 is a plot of equation (4.54), assuming a value of , and that K1 100 mVomE = ox =

10-6 (pKox = 6) and Kred = 10-8 (pKred = 8).

40

Figure 4.15: The apparent midpoint potential of a biochemical in which the reduced form has a pK of 8 and the oxidized form has a pK of 6. The o

mE of the unprotonated form is assigned a value of 100 mV, which is the limiting value of the measured .

The

',

om appE

omE value of the protonated species is the limiting value of at acidic pH ,

which is 220 mV (better oxidant).

',

om appE

The pattern observed is that the 'o

mE changes in between the pK values of the reduced

and oxidized forms and is more-or-less flat outside this range. The behavior shown in

Figure 4.15 is very different from the pH-dependence of the midpoint potential of the NAD

(or the OAA/malate) redox couple (Figure 4.12), which does not reach limiting values at

either low or high pH. This is because at all pH values examined, NADred is always

protonated whereas NADox is always deprotonated. The value of r HNΔ remains 1

throughout the entire pH range. This is not the case for the current example. Figure 4.16

shows the pH titration of the oxidized and reduced forms of species A, with respective pK

values of 6 and 8 for the oxidized and reduced forms. The value of r HNΔ is also shown.

Clearly, above pH 8 and below pH 6, the value of r HNΔ drops to zero, and this means there

will be no dependence of the midpoint potential on pH at values much below pH 6 or above

pH 8. This is what is observed.

41

Figure 4.16: pH-titration of the reduced and oxidized biochemical compound which has a pK of 6 in the oxidized state and a pK of 8 in the reduced state. The difference in the number of bound protons, , upon reduction is shown as a function of pH. r HNΔ This example is useful to learn how to visualize what the equations mean in terms of the

behavior of the system. Using graphical representations and free energy diagrams, and the

ability to check the limiting behaviour of equations (e.g., very high or very low pH, etc.) are

all generally useful in approaching problems in quantitative biology and physical

biochemistry.

4.11 Application: Determining the midpoint potential of E.coli thioredoxin(15)

Thioredoxins are small (about 11 kDa) proteins that is found in many cells and has a

multiplicity of functions(16). The protein contains two cysteine residues at its active site

(see Figure 4.10) which can undergo a two-electron oxidation to form a disulfide bond. The

range of midpoint potentials among thioredoxins is substantial (10), from ' 270omE mV= − for

the cytosolic Trx of E. coli (but see below) to the E. coli periplasmic DsbA with

' 122omE mV= − − . Thioredoxins are typically engaged in disulfide exchange with target

proteins, resulting in the oxidation of cysteine pairs

in or the reduction of disulfide bonds in these

proteins (see Figure 4.17). These redox

conversions of the target proteins can be part of a

signal transduction pathway or result in the direct

regulation of enzymes.

Figure 4.17: Reversible disulfide exchange between a thioredoxin (human Trx1) and a target protein. Thioredoxins can catalyze both the reduction of disulfides and the oxidiation of cysteines to form a disulfide via the formation of a covalent mixed disulfide intermediate. (from Figure 2 in (10))

42

As an example, we will look at a redox titration of the thioredoxin (Trx) from E. coli,

with the question being how many protons are taken up by the protein upon reduction of the

active-site disulfide to two sulfhydryls(15). The redox titration was performed using 0.1

mg/ml pure protein at selected pH values. The solution potential (Eh) was experimentally set

by using different defined ratios of dithiothreitol (DTT), for which vs

SHE, or glutathione, which has a more positive midpoint potential, vs SHE.

These are the dominant redox couples (Section 4.4). The reaction being monitored is

' 327 mV oE = −

' 240 mVoE = −

,7m

,7m

red ox ox redDTT Trx DTT Trx+ + (4.56)

The DTT and Trx can react directly with each other so no mediators are necessary to

facilitate the oxidation-reduction reactions. The total amount of DTT (reduced + oxidized)

is about 2 mM, much higher than the concentration of thioredoxin. Hence, it is considered

that the ratio of [[ ]

red

ox

DTTDTT

] that is initially put into the solution is not going to change very

much after reaction with the relatively small amount of thioredoxin (0.1 mg/ml is about 10

µM Trx). This is “poising” the redox potential. The solution potential is equal to

' ',7

' ',7

[ ]( ) ( ) ln2 [

[ ]( ) ( ) ln[ ]

o redh m m

ox

o redh m m

e ox

DTTRTE E DTT E DTTF DTT

andTrxRTE E Trx E Trx

F Trxν

= = −

= = −

] (4.57)

We have left the number of electons required to reduce thioredoxin, eν ,as an unknown to

be determined. The experiment is done by measuring at each value of [[ ]

red

ox

DTTDTT

] , the extent

of reduction of thioredoxin by reacting the free sulhdryls on the protein with a fluorescent

label and quantifying the concentration of reduced thioredoxin. A titration of the wild type

E. coli thioredoxin is shown in Figure 4.18. The value of Eh is determined from the amount

43

of reduced and oxidized DTT added to the solution, and the experimentally determined

amounts of reduced and oxidized thioredoxin nicely fit a Nernst equation (4.57) with

2eν = , as we expect for a two-electron redox reaction, with the .

The data are plotted as the fraction of thioredoxin that is reduced as a function of E

',7 ( ) 285 10 mVo

mE Trx = − ±

h. The

same data give a straight line if [log[ ]

red

ox

TrxTrx

] is plotted vs Eh with a slope of 2.303( )2

RTF

which is about 30 mV per log unit, or -30 mV for every 10-fold change in the value of

[ ][ ]

red

ox

TrxTrx

.

Figure 4.18: Potentiometric titration of E. coli thioredoxin. The ' 285omE mV= − . (from

Figure 1 in (15)) The reduction of thioredoxin is expected to be accompanied by proton uptake for

form –SH groups, but the net number of protons taken up will depend on the pK values of

the two cysteines, which may, in turn, depend on their local environments within the

protein. The pH-dependence of the measured value of the midpoint potential ', (o

m pH )E Trx is

shown in Figure 4.19. The data fall on a straight line from pH 6 to about pH 10, with a

slope of -59 mV/pH unit. Using equation (4.40) and knowing that this is a 2-electron

44

reduction ( ( eν = 2)

2)

, we conclude that the number of bound protons increases by 2

upon reduction of E. coli thioredoxin over this range of pH. The slight

curvature above pH 10 was fit to a model that postulates that the pK values for each

protonatable site (presumably, the two cysteines) is about 10.

( r HNΔ =

Figure 4.19: pH-dependence of the midpoint potential of E. coli thioredoxin. The slope is -59 mV/log unit, indicating 2 protons are taken up along with the 2 electrons. 4.12 Application: A mutation that raises the midpoint potential of the regulatory

disulfide the the γ-subunit of the chloroplast ATP synthase from Arabidopsis (17).

The ATP synthase in the chloroplast couples the proton electrochemical gradient

across the thylakoid membrane to the synthesis of ATP from ADP and Pi. We will discuss

how to deal with the thermodynmamics of membrane electrical and chemical gradients in

the next chapter, but for this example we are interested in the fact that the activity of the

ATP synthase is regulated by the redox status of a disulfide bridge in the γ-subunit of the

enzyme complex. This is a level of regulation that is only found in the ATP synthase from

chloroplasts and not in the mitochondrial or prokaryotic ATP synthases. The γ-subunit of

the chloroplast enzyme has an extra domain of about 40 amino acids with two cysteines

45

which are in redox equilibrium in vivo with a specific thioredoxin f. The chloroplast ATP

synthase can exist in either an active or inactive conformation. In the light, the

photosynthetic reaction centers generate an electrochemical gradient across the membrane,

and the magnitude of this gradient determines whether the ATP synthase is active or

inactive. In the light, the activity is maximal as ATP is synthesized, but in the dark, the

ATP synthase is inactivated so as not to catalyze the hydrolysis of ATP. The thioredoxin-

mediated redox regulation lowers the threshold of the transmembrane potential at which this

transition occurs, resulting in facilitating the synthesis of ATP at low light conditions.

Reduction of the γ-subunit disulfide bridge by thioredoxin f is necessary for efficient

photosynthesis (ATP synthesis) under conditions of low light.

Mutants in Arabidopsis were isolated which were defective in the activation of the

ATP synthase. These mutants were mapped to positions near the γ-subunit cysteines. The

midpoint potential of the γ-subunit cysteines at pH 7.9 was measured by using 20 mM DTT

with different ratios of [[ ]

red

ox

DTTDTT

]

)

to poise the solution potential, as described in the last

Section, using equation (4.57). However, in this experiment, we need the value of

',7.9 (o

mE DTT at pH 7.9 and not at pH 7. We know from equation (4.40) that

'

', ,

( ) 59( )

o

m r H

eT P

E NpH

ξν

⎡ ⎤∂ Δ= −⎢ ⎥

∂⎢ ⎥⎣ ⎦ (4.58)

For DTT at in this pH range, we can assume 2r HNΔ = and that 2eν = , which allows us to

integrate equation (4.58) to yield the following.

(4.59)

' ',7.9 ,7

',7.9

59(pH 7.9 - pH 7)

327 59(0.9) 380 mV

o om m

om

E E

E

= −

= − − = −

46

This value of for DTT was used to determine the solution potential, and at each

solution potential the redox status of the regulatory disulfide bridge is deduced by using a

biochemical assay to measure the activation of the ATP synthase. The results are shown in

Figure 4.20.

',7.9

omE

Figure 4.20: Potentiometric titration of the activation of the ATP synthase from Arabidopsis used to monitor the redox status of the cysteine pair in the γ-subunit. Mutations lower the , making it more difficult for the thioredoxin to reduce the γ-subunit disulfide, resulting in the phenotype of the mutations. (Figure from (17))

',7.9

omE

The mutants shift the midpoint potential of the γ-subunit disulfide from about -337 mV to -

376 mV, making it more difficult to reduce. The midpoint potential at pH 7.9 of thioredoxin f

from Arabidopsis is -325 mV. The more negative midpoint potential of the ATPase subunit

results in the inability of thioredoxin to reduce the γ-subunit disulfide, and results in less

efficient photosynthesis at low light. Note that since the concentrations of the reduced and

oxidized forms are not known, the discussion is in terms of midpoint potentials, which

correspond to what would be the actual potentials if there were equal concentrations of

reduced and oxidized forms. The actual reduction potentials of the thioredoxin and the

ATPase disulfide will depend on the ratios of the reduced and oxidized species in the cell.

47

4.13 Application: Impact of mutations on the midpoint potential of an [4Fe-4S] cluster

in the electron transfer protein:ubiquinone oxidoreductase (18).

In the following example, a potentiometric titration is performed using mediators to

facilitate the redox equilibrium of the solution containing the electron transfer

protein:ubiquinone oxidoreductase (ETF-QO). This enzyme is located in the inner

mitochondrial membrane and transfers electrons from the electron transfer protein (ETF) to

the ubiquinone pool in the membrane and, hence, into the repiratory chain. The electron

transfer protein is the electron acceptor for at least 10 different dehydrogenases, including

acyl-CoA dehydrogenases necessary for the oxidation of fatty acids. As a result, inherited

defects in the ETF-QO result in a metabolic disease known as multiple acyl-CoA

dehydrogenase deficiency. The ETF-QO contains a single [4Fe-4S] which is about 12 Å

from a second redox prosthetic group, FAD. The quinone binding site is located near the

FAD. Figure 4.21 shows a portion of the structure, indicating that two amino acids, Tyr533

and Thr558 in the porcine ETF-QO, are hydrogen bonded to cysteine Sγ sulphur atoms that

are bound to the [4Fe-4S] cluster.

Figure 4.21: The structure of the [4Fe-4S] cluster and the nearby FAD redox centers in the porcine electron transfer protein:ubiquinone oxidoreductase (ETF-QO). The hydrogen bonds from the hydrogen bonds from Y533 and T558 are important to the midpoint potential of the [4Fe-4S] cluster, which is shown as the box-like structure in the Figure. (Figure is taken from (18)) The effects of mutations eliminating these hydrogen bonds on the midpoint potential of the

[4Fe-4S] cluster and on enzyme activity was investigated (18). The [4Fe-4S] cluster in this

48

enzyme undergoes one-electron redox chemistry, being either in the reduced [4Fe-4S]1+ or

oxidized [4Fe-4S]2+ state. The reduced state is paramagnetic and can be detected and

quantified using electron spin resonance (EPR) spectroscopy.

2 1[4 4 ] [4 4 ]Fe S e Fe S 1+ − +− + −

Mutations in the equivalent residues in a bacterial (Rhodobacter sphaeroides) homologue of

the porcine ETF-QO, Y501F and T525A, were prepared, as well as the double mutant

Y501F/T525A.

The potentiometric titration was performed in an anaerobic vessel at 4oC in a 20 mM

Hepes buffer, pH 7.4, containing about 50 µM enzyme plus a set of mediators, each 25 µM

concentration.

Figure 4.22: Potentiometric titration of the [4Fe-4S] center in the R. sphaeroides ETF-QO protein. The redox status of the protein was monitored by removing samples poised at the indicated values of the solution potential (Eh) and recording the electron spin resonance spectrum. Mutations alterning the equivalent of Y533 and T558 (Figure 4.21) to non-hydrogen bonding amino acids were examined. The mutants shift the to lower values, with the double mutant having the lowest midpoint potential. (Figure is taken from (18))

',7.4

omE

The mediators and (their midpoint potentials) used were the following: 2,6-dichlorophenol

indophenol (+217 mV), phenozine methosulfate (+80 mV), methylene blue (+11 mV),

pyocyanine (-34 mV), indigo carmine (-125 mV) and 9,10-anthraquinone 2,6-disufonic acid

49

(-185 mV). It is typical to use a large set of mediators, as in this example, so that at any

solution potential, at least one mediator has a significant concentration of reduced and

oxidized form present. Indigo carmine might be able to facilitate direct reduction of the

enzyme and also equilibrate with the electrode, but if the solution potential (Eh) is, for

example, -250 mV, far from its midpoint potential ( 'omE = -125 mV), then most of the indigo

carmine (about 99%) will be reduced.

' ' [ ]ln[ ]

o redh A A

e o

ARTE E EF Aν x

⎡ ⎤= = −⎢ ⎥

⎢ ⎥⎣ ⎦ (4.60)

Since the concentration of the oxidized form of the mediator will be very small, any

redox reactions in which it participates will be very slow. This is one reason why it is usual

to use a set of mediators that cover the range of the solution potential to be examined. In

this example, the solution potential was adjusted by adding aliquots of a strong reductant,

dithionite. After the addition of a small amount of dithionite, the solution potential is

measured against a reference silver chloride electrode. After equilibration is reached, the

measured voltage stops changing, and this is the solution potential vs the Ag/AgCl

reference electrode. This was converted to the solution potential versus the standard

hydrogen electrode by adding 200 mV.

(4.61) , , / 200 mVh SHE h Ag AgClE E= +

After the solution potential was determined, aliquots of the solution were

removed and the fraction of reduced [4Fe-4S]1+ cluster was determined spectroscopically.

Another aliquot of dithionite was added to reduce the solution potential further and the

procedure was repeated. Data in Figure 4.22 show that the mutations lower the midpoint

potential of the [4Fe-4S] cluster: wild type, ',7.4

omE = +37 mV; Y501F, -64 mV;

T525A, -58 mV; and Y501F/T525A,

',7.4

omE =

',7.4

omE = '

,7.4o

mE = -128 mV. The data for each fit a

50

Nernst equation with 1eν = , as expected. Enzyme activity is also diminished in the

mutants, indicating that the electrochemical properties of the [4Fe-4S] cluster are important

for the function of the enzyme.

We can express the change in midpoint potential as a change in the difference in

the standard state chemical potentials between the reduced and oxidized forms of the

enzyme-bound [4Fe-4S] cluster. From equation (4.21)

' '

'o o

o r FeS red oxFeS

e e

GE'o

F Fμ μ

ν νΔ

= − =− (4.62)

The shift in the midpoint potential is equivalent to a change in the difference between the

standard state molar transformed Gibbs free energies. A more negative value of 'omE means

that the value of ' 'o ored oxμ μ− ( ) is more positive. The sign of changes from

negative in the wild type to positive in several of the mutants. This is shown graphically in

the free energy diagram in Figure 4.23.

'or FeSG= Δ 'o

r FeSGΔ

Figure 4.23: A free energy diagram illustrating that the mutations near the [4Fe-4S] cluster probably lower the standard state chemical potentials of both the oxidized and reduced forms, but that the effect of the mutations is greater on the more positively

51

charged oxidized from of the cluster. For mutant 3, representing the Y501F/T525A double mutant, the oxidized form becomes more stable than the reduced form under and the sign of changes. 'o

r FeSGΔ The absolute values of ' and o

red ox'oμ μ are not known and the measurement tells us only the

difference. Presumably, the hydrogen bonds in the wild type protein place a partial positive

charge near the [4Fe-4S] cluster which will be more destabilizing for the more positively

charged, oxidized form of the cluster (charge = +2) than for the reduce form of the cluster

(charge = +1). Removing these hydrogen bonds by mutagenesis will have a larger influence

on the oxidized form of the enzyme, decreasing 'ooxμ to a greater extent than 'o

redμ . The net

result is that values of change. 'or FeSGΔ

4.14 Application: Determining the mitochondrial ambient potential (19).

Determining the ambient or solution potential in a living cell is an experimental

challenge. In eukaryotic cells this most frequently is done by determining the

concentrations of reduced and oxidized glutathione (see Section 4.3.2) in a particular

cellular compartment. One way to do this is to express a reporter protein that is sensitive of

the redox potential and direct this protein to the cellular compartment of interest. One

approach has been to engineer the Green Fluorescent Protein (GFP) to respond to the

ambient potential. The GFP is a protein with a naturally occurring fluorescent

chromophore, which will be described in more detail in a later Chapter. Cysteine pairs have

been introduced on the protein surface in locations where they can form a disulfide bridge.

One of these “reduction-oxidation sensitive” GFPs (roGFP) is shown in Figure 4.24.

52

Figure 4.24: Structure of a “reduction-oxidation sensitive” GFP (roGFP) with a pair of cysteiines located on the surface which can form a disulfide bridge. The fluorescence from the chromophore, shown within the protein, is altered by the redox status of the nearby cysteine pair. (Figure is modified from (19)) The flurorescence from the protein changes depending on the redox state of the cysteine

pair. The fluorescence of the roGFP can be monitored in living cells using fluorescence

microscopy, which leads to a determination of the value of [[ ]

red

ox

roGFProGFP

] within the

compartment where the roGFP is located. The ',7

omE for the roGFP redox couple was

determined using DTT in the same way as described in Section 4.11 for thioredoxin.

Adjusting the ratio of [[ ]

red

ox

DTTDTT

] and using (30',7 323 mVo

mE = − oC) for the DTT redox

couple, equation (4.57) was used to determine the value of the solution potential, Eh. Figure

4.25 shows the fraction of roGFP which is reduced as a function of solution potential. The

value of ',7

omE for the roGFP2 shown is -272 mV. The variant roGFP1, which has one

additional mutation, was determined to be -287 mV.

53

The expression roGFP1 was done in HeLa cells and the targeting of this protein to the

mitochondria was successfully demonstrated by fluorescence microscopy. Adding H2O2 to

the cells resulted in complete oxidation of the roGFP1 reporter molecule, and adding DTT to

the cell culture resulted in full reduction of the disulfide in roGFP1.

Figure 4.25: Potentiometric titration of a roGFP2. The ',7

omE was measured to be -272

mV. (Figure is from (19)) In the absence of these externally added redox reagents, the fluoresecence microscopy

showed that roGFP1 was 67% reduced in the HeLa cell mitochondria under the growth

conditions used in these experiments. Hence, [ 1 ] (0.67) 2.0[ 1 ] (0.33)

red

ox

roGFProGFP

= = .

The pH inside mitochondria has been estimated to be 7.98, so it was necessary to

determine the value of the midpoint potential or roGFP1 at this pH ( ). This was

calculated using equation

',7.98

omE

(4.58), assuming that the 2-electron reduction of roGFP1 is

accompanied by the uptake of 2 protons, so both =2 and 2r HN ν+ eΔ = for the half-reaction

below.

(4.63) 11 2 2 1ox redroGFP H e roGFP+ −+ +

The two basic equations that are used are

54

' ', ,7

',7.98

',7.98 ,7.98

,7.98

59(pH - 7) where pH = 7.98

= 287 59(0.98)

345

[ 1 ]ln where 2[ 1 ]

[ 1 ] = 345 (30) log [ 1 ]

34

o om pH m

om

o redh m e

e ox

red

ox

h

E E

E mV

androGFPRTE E

F roGFP

roGFProGFP

E

νν

= −

− −

= −

= − =

− −

= −

,7.98

5 (30) log 2

354 mVhE

−

= −

(4.64)

Note that the solution potential reported by this probe is entirely dependent on which, if

any, internal redox pool is equilibrated with roGFP1. Whether the experimentally

determined value represents the redox state of the glutathione or the thioredoxin redox

status depends on the way in which roGFP1 is being reduced within the organelle. From

our perspective, it is most important to understand the principles of how the

measurement is made and the assumptions that are necessary to interpret the data.

4.15 Summary

In this chapter we have introduced the language of electrochemistry to the

thermodynamics of chemical reactions. In dealing with biochemical redox reactions,

the same concepts discussed in Chapter 3 are applied, but we use units of volts (or

millivolts) in place of joules. Instead of referring to a transformed Gibbs reaction free

energy, we convert this into an electric potential. Reactions are divided into half-cell

reactions in which electrons are treated as reaction components. The standard state

55

reaction free energy of a half-reaction is converted to a standard reduction potential or a

midpoint potential. The reason for changing nomenclature and units is that for many

biochemical redox reactions, the methods of electrochemistry can be directly applied,

allowing these parameters to be directly measured, as in potentiometric titrations. Since

there are so many redox reactions in living cells that are coupled to each other by

sharing reaction components (e.g., NAD, NADP, glutathione) the ambient potential of a

cell or cellular compartment is a meaningful term, and the pathology of oxidative stress

can be quantified and characterized. Finally, it is important to note that most

biochemical redox reactions also involve coupled protonation reaction, making the

reactions pH-dependent. Methods have been described to measure these effects

quantitatively.

56

(1) Alberty, R. A. (2004) Standard apparent reduction potentials of biochemical half reactions and thermodynamic data on the species involved. Biophys Chem 111, 115-22.

(2) Alberty, R. A. (2001) Standard apparent reduction potentials for biochemical half reactions as a function of pH and ionic strength. Arch Biochem Biophys 389, 94-109.

(3) Goldberg, R. N., Tewari, Y. B., and Bhat, T. N. (2004) Thermodynamics of enzyme-catalyzed reactions--a database for quantitative biochemistry. Bioinformatics 20, 2874-7.

(4) Unden, G., and Bongaerts, J. (1997) Alternative respiratory pathways of Escherichia coli: energetics and transcriptional regulation in response to electron acceptors. Biochim Biophys Acta 1320, 217-34.

(5) Mayhew, S. G. (1978) The redox potential of dithionite and SO-2 from equilibrium reactions with flavodoxins, methyl viologen and hydrogen plus hydrogenase. Eur J Biochem 85, 535-47.

(6) Moser, C. C., Farid, T. A., Chobot, S. E., and Dutton, P. L. (2006) Electron tunneling chains of mitochondria. Biochim Biophys Acta 1757, 1096-109.

(7) White, D. (2000) The Physiology and Biochemistry of Prokaryotes, Second ed., Oxford Universitiy Press, New York.

(8) Go, Y. M., and Jones, D. P. (2008) Redox compartmentalization in eukaryotic cells. Biochim Biophys Acta.

(9) Kemp, M., Go, Y. M., and Jones, D. P. (2008) Nonequilibrium thermodynamics of thiol/disulfide redox systems: A perspective on redox systems biology. Free Radic Biol Med 44, 921-37.

(10) Berndt, C., Lillig, C. H., and Holmgren, A. (2008) Thioredoxins and glutaredoxins as facilitators of protein folding. Biochim Biophys Acta.

(11) Pinheiro, A. S., Amorim, G. C., Netto, L. E., Almeida, F. C., and Valente, A. P. (2008) NMR solution structure of the reduced form of thioredoxin 1 from Sacharomyces cerevisiae. Proteins 70, 584-7.

(12) Gross, E., Sevier, C. S., Heldman, N., Vitu, E., Bentzur, M., Kaiser, C. A., Thorpe, C., and Fass, D. (2006) Generating disulfides enzymatically: reaction products and electron acceptors of the endoplasmic reticulum thiol oxidase Ero1p. Proc Natl Acad Sci U S A 103, 299-304.

(13) Wang, W., Winther, J. R., and Thorpe, C. (2007) Erv2p: characterization of the redox behavior of a yeast sulfhydryl oxidase. Biochemistry 46, 3246-54.

(14) Mates, J. M., Segura, J. A., Alonso, F. J., and Marquez, J. (2008) Intracellular redox status and oxidative stress: implications for cell proliferation, apoptosis, and carcinogenesis. Arch Toxicol.

(15) Setterdahl, A. T., Chivers, P. T., Hirasawa, M., Lemaire, S. D., Keryer, E., Miginiac-Maslow, M., Kim, S. K., Mason, J., Jacquot, J. P., Longbine, C. C., de Lamotte-Guery, F., and Knaff, D. B. (2003) Effect of pH on the oxidation-reduction properties of thioredoxins. Biochemistry 42, 14877-84.

(16) Hoshino, Y., Shioji, K., Nakamura, H., Masutani, H., and Yodoi, J. (2007) From oxygen sensing to heart failure: role of thioredoxin. Antioxid Redox Signal 9, 689-99.

(17) Wu, G., Ortiz-Flores, G., Ortiz-Lopez, A., and Ort, D. R. (2007) A point mutation in atpC1 raises the redox potential of the Arabidopsis chloroplast ATP synthase gamma-subunit regulatory disulfide above the range of thioredoxin modulation. J Biol Chem 282, 36782-9.

57

(18) Usselman, R. J., Fielding, A. J., Frerman, F. E., Watmough, N. J., Eaton, G. R., and Eaton, S. S. (2008) Impact of mutations on the midpoint potential of the [4Fe-4S]+1,+2 cluster and on catalytic activity in electron transfer flavoprotein-ubiquinone oxidoreductase (ETF-QO). Biochemistry 47, 92-100.

(19) Hanson, G. T., Aggeler, R., Oglesbee, D., Cannon, M., Capaldi, R. A., Tsien, R. Y., and Remington, S. J. (2004) Investigating mitochondrial redox potential with redox-sensitive green fluorescent protein indicators. J Biol Chem 279, 13044-53.

58