In Chapter 17, the generation of NADH and FADH₂ by the oxidation of acetyl CoA was identified as an important function of the citric acid cycle. In oxidative phosphorylation, electrons from NADH and FADH₂ are used to reduce molecular oxygen to water. The highly exergonic reduction is accomplished by a number of electron-transfer reactions, which take place in a set of membrane proteins known as the electron-transport chain.

In oxidative phosphorylation, the electron-transfer potential of NADH or FADH₂ is converted into the phosphoryl-transfer potential of ATP. To better understand this conversion, we need quantitative expressions for these forms of free energy. The measure of phosphoryl-transfer potential is already familiar to us: it is given by ΔG°′ for the hydrolysis of the activated phosphoryl compound. The corresponding expression for the electron-transfer potential is , the reduction potential (also called the redox potential or oxidation–reduction potential).

Consider a substance that can exist in an oxidized form X and a reduced form X⁻. Such a pair is called a redox couple and is designated X : X⁻. The reduction potential of this couple can be determined by measuring the electromotive force generated by an apparatus called a sample half-cell connected to a standard reference half-cell (Figure 18.5). The sample half-cell consists of an electrode immersed in a solution of 1 M oxidant (X) and 1 M reductant (X⁻). The standard reference half-cell consists of an electrode immersed in a 1 M H⁺ solution that is in equilibrium with H₂ gas at 1 atmosphere (1 atm) of pressure. The electrodes are connected to a voltmeter, and an agar bridge allows ions to move from one half-cell to the other, establishing electrical continuity between the half-cells. Electrons then flow from one half-cell to the other through the wire connecting the two half-cells to the voltmeter. If the reaction proceeds in the direction

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X⁻ + H⁺ → X + ½ H₂

the reactions in the half-cells (referred to as half-reactions or couples) must be

Thus, electrons flow from the sample half-cell to the standard reference half-cell, and the sample-cell electrode is taken to be negative with respect to the standard-cell electrode. The reduction potential of the X : X⁻ couple is the observed voltage at the start of the experiment (when X, X⁻, and H⁺ are 1 M with 1 atm of H₂). The reduction potential of the H⁺: H₂ couple is defined to be 0 volts. In oxidation–reduction reactions, the donor of electrons, in this case X⁻, is called the reductant or reducing agent, whereas the acceptor of electrons, H⁺ here, is called the oxidant or oxidizing agent.

The meaning of the reduction potential is now evident. A negative reduction potential means that the oxidized form of a substance has lower affinity for electrons than does H₂, as in the preceding example. A positive reduction potential means that the oxidized form of a substance has higher affinity for electrons than does H₂. These comparisons refer to standard conditions—namely, 1 M oxidant, 1 M reductant, 1 M H⁺, and 1 atm H₂. Thus, a strong reducing agent (such as NADH) is poised to donate electrons and has a negative reduction potential, whereas a strong oxidizing agent (such as O₂) is ready to accept electrons and has a positive reduction potential.

The reduction potentials of many biologically important redox couples are known (Table 18.1). Table 18.1 is like those presented in chemistry textbooks, except that a hydrogen ion concentration of 10⁻⁷ M (pH 7) instead of 1 M (pH 0) is the standard state adopted by biochemists. This difference is denoted by the prime in . Recall that the prime in ΔG°′ denotes a standard free-energy change at pH 7.

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The standard free-energy change ΔG°′ is related to the change in reduction potential by

in which n is the number of electrons transferred, F is a proportionality constant called the Faraday constant [96.48 kJ mol⁻¹V⁻¹ (23.06 kcal mol⁻¹ V⁻¹)], is in volts, and ΔG°′ is in kilojoules or kilocalories per mole.

The free-energy change of an oxidation–reduction reaction can be readily calculated from the reduction potentials of the reactants. For example, consider the reduction of pyruvate by NADH, catalyzed by lactate dehydrogenase. Recall that this reaction maintains redox balance in lactic acid fermentation (Figure 16.11).

The reduction potential of the NAD⁺ : NADH couple, or half-reaction, is −0.32 V, whereas that of the pyruvate:lactate couple is −0.19V. By convention, reduction potentials (as in Table 18.1) refer to partial reactions written as reductions: oxidant + e⁻ → reductant. Hence,

To obtain reaction A from reactions B and C, we need to reverse the direction of reaction C so that NADH appears on the left side of the arrow. In doing so, the sign of must be changed.

For reaction B, the free energy can be calculated with n = 2.

Likewise, for reaction D,

Thus, the free energy for reaction A is given by

The driving force of oxidative phosphorylation is the electron-transfer potential of NADH or FADH₂ relative to that of O₂. How much energy is released by the reduction of O₂ with NADH? Let us calculate ΔG°′ for this reaction. The pertinent half-reactions are

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The combination of the two half-reactions, as it proceeds in the electron-transport chain, yields

The standard free energy for this reaction is then given by

This release of free energy is substantial. Recall that ΔG°′ for the synthesis of ATP is 30.5 kJ mol⁻¹ (7.3 kcal mol⁻¹). The released energy is initially used to generate a proton gradient that is then used for the synthesis of ATP and the transport of metabolites across the mitochondrial membrane.

How can the energy associated with a proton gradient be quantified? Recall that the free-energy change for a species moving from one side of a membrane where it is at concentration c₁ to the other side where it is at a concentration c₂ is given by

ΔG = RT ln (c₂/c₁) + ZF Δ V

in which Z is the electrical charge of the transported species and ΔV is the potential in volts across the membrane (Section 13.1). Under typical conditions for the inner mitochondrial membrane, the pH outside is 1.4 units lower than inside [corresponding to ln (c₂/c₁) of 3.2] and the membrane potential is 0.14 V, the outside being positive. Because Z = +1 for protons, the free-energy change is (8.32 × 10⁻³ kJ mol⁻¹ K⁻¹ × 310 K × 3.2) + (+1 × 96.48 kJ mol⁻¹ V⁻¹ × 0.14 V) = 21.8 kJ mol⁻¹ (5.2 kcal mol⁻¹). Thus, each proton that is transported out of the matrix to the cytoplasmic side corresponds to 21.8 kJ mol⁻¹ of free energy.