44
2.4 Cell Processes
electrochemical “redox reactions.” Each full redox reaction is the sum of two separate half
reactions involving reduction and oxidation, each of which has an associated reduction
potential (E0), which is the measure of the equivalent electrode voltage potential if that spe
cific chemical half reaction was electrically coupled to a standard hydrogen electrode (the
term standard means that all components are at concentrations of 1 M, but confusingly the
biochemical standard state electrode potential is the same as the standard state electrode
potential apart from the pH being 7; the pH is defined as −log10[H+ concentration] and thus
indicates a concentration of H+ of 10−7 M for the biochemical standard state).
The reduction half reaction for the electron acceptor NAD+ is
(2.1)
NAD
H
e
NADH
V
+
+
−
+
+
= −
2
0 315
0
E
.
An example of a reduction half reaction at one point in the TCA cycle (see Figure 2.8) involves
an electron acceptor called of “oxaloacetate−,” which is reduced to malate−:
(2.2)
Oxaloacetate
H
e
Malate
V
−
+
−
+
+
= −
2
2
0 166
0
E
.
These two reversible half reactions can be combined by taking one away from the other, so
malate− then acts as an electron donor and in the process is oxidized back to oxaloacetate−,
which is exactly what occurs at one point in the TCA cycle (two other similar steps occur
coupled to the reduction of NAD+, and another coupled to FAD+ reduction, Figure 2.8). The
concentrations of oxaloacetate and malate are kept relatively low in the cell at 50 nM and
0.2 mM, respectively, and these low concentrations compared to the high concentration of
acetyl-CoA result in a large excess of NAD+.
A general reduction half reaction can be written as a chemical state O being reduced to a
chemical state R:
(2.3)
O + nH+ + ne- ⇌ R
where the free energy change per mole associated with this process can be calculated from
the electrical and chemical potential components:
(2.4)
∆
∆
G
G
RT
R
O H
nFE
n
=
+
[ ]
[ ][
]
= −
+
0
ln
where F is Faraday’s constant, 9.6 × 104 C mol−1, equivalent to the magnitude of the electron
charge q multiplied by Avogadro’s number NA, n electrons in total being transferred in the
process. This also allows the molar equilibrium constant K to be calculated:
(2.5)
K
nFE
RT
nqE
k T
=
=
exp
exp
B
0
0
where R is the molar gas constant, equal to kBNA, with absolute temperature T. Equation 2.4
can be rewritten by dividing through by −nF:
(2.6)
E
E
k T
nq
R
O H
B
n
=
−
[ ]
[ ][
]
+
0
ln
Equation 2.6 is called the “Nernst equation.”
The free energy of oxidation of NADH and FADH is coupled to molecular machines,
which pump protons across either the mitochondrial inner membrane (eukaryotes) or cyto
plasmic membrane (prokaryotes) from the inside to the outside, to generate a proton motive
force (pmf), Vpmf, of typical value −200 mV relative to the inside. The free energy required to
pump a single proton against this pmf can be calculated from Equation 2.4 equating Vpmf to