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

776 Chapter 14: Energy Conversion: Mitochondria and Chloroplasts
1 3
hydrolysis
ATP ADP + P i
AT EQUILIBRIUM:
synthesis rate = hydrolysis rate
hydrolysis rate =
hydrolysis
rate constant ×
concentration
of ATP
synthesis
rate constant ×
conc. of × conc. of
phosphate ADP
= hydrolysis
rate constant ×
conc. of
ATP
2
+
synthesis
ATP
thus,
conc. of
ADP
× conc. of
phosphate
concentration
of ATP
hydrolysis
rate constant
= = equilibrium constant K
synthesis
rate constant
ADP P i
Figure 14–29 The basic relationship
synthesis rate =
synthesis
rate constant ×
conc. of
phosphate
× conc. of
ADP
or abbreviated,
[ADP] [ P i ]
[ATP]
= K
4
For the reaction
ATP ADP + P i
the following equation applies:
ΔG = ΔG o + RT In
[ADP] [ P i ]
[ATP]
where ΔG and ΔG o are in Joules per mole, R is the gas
constant (8.3 J/mole K), T is the absolute temperature
(K), and all the concentrations are in moles per liter.
When the concentrations of all reactants are at 1 M, ΔG = ΔG o
(since RT ln 1 = 0). ΔG o is thus a constant defined as the
standard free-energy change for the reaction.
At equilibrium the reaction has no net effect on the disorder of
the universe, so ΔG = 0. Therefore, at equilibrium,
_ RT In
[ADP] [ P i ]
[ATP]
= ΔG
o
But the concentrations of reactants at equilibrium must satisfy
the equilibrium equation:
[ADP] [ P i ]
[ATP]
Therefore, at equilibrium,
ΔG o = _ RT In K
= K
We thus see that whereas ΔG o indicates the equilibrium point for a
reaction, ΔG reveals how far the reaction is from equilibrium. ΔG is
a measure of the “driving force” for any chemical reaction, just as the
proton-motive force is the driving force for the translocation of protons.
which ADP and P i will join to form ATP will be equal to the rate at which ATP
hydrolyzes to form ADP and P i . In other words, when ∆G = 0, the reaction is at
equilibrium (see Figure 14–29).
It is ∆G, not ∆G°, that indicates how far a reaction is from equilibrium and
determines whether it can drive other reactions. Because the efficient conversion
of ADP to ATP in mitochondria maintains such a high concentration of ATP
relative to ADP and P i , the ATP hydrolysis reaction in cells is kept very far from
equilibrium and ∆G is correspondingly very negative. MBoC6 Without m14.18/14.29 this large disequilibrium,
ATP hydrolysis could not be used to drive the reactions of the cell. At low
ATP concentrations, many biosynthetic reactions would run backward and the
cell would die.
between free-energy changes and
equilibrium in the ATP hydrolysis
reaction. The rate constants in boxes 1
and 2 are determined from experiments in
which product accumulation is measured
as a function of time (conc., concentration).
The equilibrium constant shown here, K,
is in units of moles per liter. (See Panel
2–7, pp. 102–103, for a discussion of
free energy and see Figure 3–44 for a
discussion of the equilibrium constant.)
The ATP Synthase Is a Nanomachine that Produces ATP by
Rotary Catalysis
The ATP synthase is a finely tuned nanomachine composed of 23 or more separate
protein subunits, with a total mass of about 600,000 daltons. The ATP synthase
can work both in the forward direction, producing ATP from ADP and phosphate
in response to an electrochemical gradient, or in reverse, generating an electrochemical
gradient by ATP hydrolysis. To distinguish it from other enzymes that
hydrolyze ATP, it is also called an F 1 F o ATP synthase or F-type ATPase.
Resembling a turbine, ATP synthase is composed of both a rotor and a stator
(Figure 14–30). To prevent the catalytic head from rotating, a stalk at the periphery
of the complex (the stator stalk) connects the head to stator subunits embedded
in the membrane. A second stalk in the center of the assembly (the rotor stalk) is
connected to the rotor ring in the membrane that turns as protons flow through it,
driven by the electrochemical gradient across the membrane. As a result, proton