Page 164 - Thermodynamics of Biochemical Reactions

9.4 Half-Reactions with Reactants Involving Multiple Species at Specified pH 163

which could, in principle, be catalyzed separately:

Methane + (i)O, = methanol El0 = 0.773 V (9.3-1)
(+)O, + NADP,,, = NADP,, + H,O E'" = 1.166 V

If these reactions were carried out in two galvanic cells in series, the electromotive
force would be 0.773 + 1.166 = 1.939 V for a two electron change, and the
standard transformed Gibbs energy of the overall monooxygenase reaction would
be -2F(1.939) = - 374.13 kJ mol-'. as expected.
The methane monooxygenase reaction can, in principle, be carried out in two
other ways by the enzyme complex that catalyzes it: It can be carried out in three
half-reactions at three catalytic sites as follows:

0, + 4e- = 2H,O (9.3-2)

Methanol + 2e- = methane + H,O
NADP,, + 2e- =NADP,,,

Or it can be carried out in two half-reactions at two catalytic sites as follows:

0, + 4e- = 2H,O (9.3-3)

Methanol + NADP,, + 4e- = methane + NADP,,, + H,O

Table 9. 3 shows the reduction potentials for these half-reactions that would have
to be somehow matched to the reduction potentials of sites in the enzyme. A good
deal is known about the mechanism of this enzyme-catalyzed reaction (Gassner
and Lippard, 1999).

9.4 HALF-REACTIONS WITH REACTANTS INVOLVING
MULTIPLE SPECIES AT SPECIFIED pH

The reason for a separate section on half reactions with reactants involving
multiple species is that they cannot be represented by a single chemical equation.
Acid dissociation reactions are also involved, and as a consequence the pH and
ionic strength dependencies of standard apparent reduction potentials are more
complicated than for the reactions in Tables 9.2 and 9.3. These biochemical half
reactions and biochemical reactions considered involve reactants with pKs in the
range pH 5 to 9. They include carbon dioxide (pK 6.2), malate (pK = 5.25),
citrate(pK, = 6.39, pK, = 4.75), cysteine (pK = 8.37), ammonia (pK = 9.25), and
reduced glutathione (pK = 8.37), where the pKs are for 298.15 K and zero ionic
strength. When carbon dioxide is a reactant in a biochemical reaction, the
expression for the apparent equilibrium constant can be written in terms of
P(C0,) or [CO,tot], where [CO,tot] is the sum of the concentrations in aqueous
solution of CO,, H,CO,, HCO,, and COi-. The standard transformed Gibbs
energies and enthalpies of C0,tot have been calculated three different ways
(Alberty, 1995b, 1997e, 1998b), which give the same results (see Section 8.7). When
the apparent equilibrium constant of a biochemical reaction involving carbon
dioxide is written in terms of P(CO,), the pK = 6.2 does not show up in the pH
dependencies of E'O and K', but when the apparent equilibrium constant is written
in terms of [CO,tot] it does. The advantage of using [CO,tot] is that it is more
immediately relevant to the reactions inside of the living cell. Note that when
CO,(g) in a biochemical reaction is replaced by CO,tot, H,O has to be added to
the other side of the biochemical reaction. The pH dependencies of some of the
half reactions in Table 9.4 are shown in Fig. 9.2.