Molecular Biology of the Cell by Bruce Alberts, Alexander Johnson, Julian Lewis, David Morgan, Martin Raff, Keith Roberts, Peter Walter by by Bruce Alberts, Alexander Johnson, Julian Lewis, David Morg

CATALYSIS AND THE USE OF ENERGY BY CELLS
63
Converting this equation from the natural logarithm (ln) to the more commonly
used base 10 logarithm (log), we get
∆G° = –5.94 log K
The above equation reveals how the equilibrium ratio of X to Y (expressed as
the equilibrium constant, K) depends on the intrinsic character of the molecules,
(as expressed in the value of ∆G° in kilojoules per mole). Note that for every 5.94
kJ/mole difference in free energy at 37°C, the equilibrium constant changes by
a factor of 10 (Table 2–2). Thus, the more energetically favorable a reaction, the
more product will accumulate if the reaction proceeds to equilibrium.
More generally, for a reaction that has multiple reactants and products, such
as A + B → C + D,
K = [C][D]
[A][B]
The concentrations of the two reactants and the two products are multiplied
because the rate of the forward reaction depends on the collision of A and B and
the rate of the backward reaction depends on the collision of C and D. Thus, at
37°C,
∆G° = –5.94 log [C][D]
[A][B]
where ∆G° is in kilojoules per mole, and [A], [B], [C], and [D] denote the concentrations
of the reactants and products in moles/liter.
The Free-Energy Changes of Coupled Reactions Are Additive
We have pointed out that unfavorable reactions can be coupled to favorable ones
to drive the unfavorable ones forward (see Figure 2–29). In thermodynamic terms,
this is possible because the overall free-energy change for a set of coupled reactions
is the sum of the free-energy changes in each of its component steps. Consider,
as a simple example, two sequential reactions
X → Y and Y → Z
whose ∆G° values are +5 and –13 kJ/mole, respectively. If these two reactions
occur sequentially, the ∆G° for the coupled reaction will be –8 kJ/mole. This
means that, with appropriate conditions, the unfavorable reaction X → Y can be
driven by the favorable reaction Y → Z, provided that this second reaction follows
the first. For example, several of the reactions in the long pathway that converts
sugars into CO 2 and H 2 O have positive ∆G° values. But the pathway nevertheless
proceeds because the total ∆G° for the series of sequential reactions has a large
negative value.
Forming a sequential pathway is not adequate for many purposes. Often the
desired pathway is simply X → Y, without further conversion of Y to some other
product. Fortunately, there are other more general ways of using enzymes to couple
reactions together. These often involve the activated carrier molecules that we
discuss next.
Table 2–2 Relationship Between
the Standard Free-Energy
Change, ΔG°, and the Equilibrium
Constant
Equilibrium
constant
[X]
= K
[Y]
Free energy of X
minus free energy
of Y
[kJ/mole (kcal/mole)]
10 5 –29.7 (–7.1)
10 4 –23.8 (–5.7)
10 3 –17.8 (–4.3)
10 2 –11.9 (–2.8)
10 1 –5.9 (–1.4)
1 0 (0)
10 –1 5.9 (1.4)
10 –2 11.9 (2.8)
10 –3 17.8 (4.3)
10 –4 23.8 (5.7)
10 –5 29.7 (7.1)
Values of the equilibrium constant were
calculated for the simple chemical
reaction Y ↔ X using the equation
given in the text. The ΔG° given here
is in kilojoules per mole at 37°C, with
kilocalories per mole in parentheses.
One kilojoule (kJ) is equal to 0.239
kilocalories (kcal) (1 kcal = 4.18 kJ). As
explained in the text, ΔG° represents the
free-energy difference under standard
conditions (where all components are
present at a concentration of 1.0 mole/
liter). From this table, we see that if
there is a favorable standard free-energy
change (ΔG°) of –17.8 kJ/mole
(–4.3 kcal/mole) for the transition Y → X,
there will be 1000 times more molecules
in state X than in state Y at equilibrium
(K = 1000).
Activated Carrier Molecules Are Essential for Biosynthesis
The energy released by the oxidation of food molecules must be stored temporarily
before it can be channeled into the construction of the many other molecules
needed by the cell. In most cases, the energy is stored as chemical-bond energy
in a small set of activated “carrier molecules,” which contain one or more energyrich
covalent bonds. These molecules diffuse rapidly throughout the cell and
thereby carry their bond energy from sites of energy generation to the sites where
the energy will be used for biosynthesis and other cell activities (Figure 2–31).
The activated carriers store energy in an easily exchangeable form, either as
a readily transferable chemical group or as electrons held at a high energy level,
and they can serve a dual role as a source of both energy and chemical groups in
biosynthetic reactions. For historical reasons, these molecules are also sometimes
referred to as coenzymes. The most important of the activated carrier molecules