54
3 Mechanism of Unidirectional Rotation of γ Subunit in F 1 -ATPase
(3) Thus, changes of β DP →β’ DP →β TP , β E →β’ E →β DP , and β TP →β’ TP →β E occur
in subcomplexes I−γ, II−γ, and III−γ, respectively. The γ subunit rotates by
120° in the clockwise direction in response to the change in the packing structure
of the α 3 β 3 complex, primarily to recover the closely packed interfaces with
β DP and α E . Though the overall structures before and after the 120° rotation are
the same, one ATP molecule is synthesized in aqueous solution: The system
free energy becomes lower by the free-energy change upon the APT synthesis
reaction in aqueous solution under the physiological condition, −G ~ −20k B T
(T = 298 K). We note that in the solution condition that the ATP synthesis
reaction occurs, G defined by Eq. (2.1) is positive (see Sect. 2.1.1).
3.7 Normal and Inverse Rotations with the Same
Frequency (Rotations in Random Directions) Under
Solution Condition that ATP Hydrolysis and Synthesis
Reactions Are Equilibrated
In scenario (C) defined in Sect. 3.3, the ATP hydrolysis and synthesis reactions
are in equilibrium. Even in this chemical equilibrium state, the reactions are not
stopped: The hydrolysis and synthesis reactions occur with the same frequency
(see Sect. 2.1.1). Hence, the ATP hydrolysis accompanied by the normal rotation expounded in Fig. 3.16 and the ATP synthesis leading to the inverse rotation
expounded in Fig. 3.21 take place with the same frequency. States (a) in these two
figures are the same, and the chemical compounds bound to β DP , β TP , and β E are,
respectively, ATP• • •H 2 O, ATP, and Pi. In essence, the rotation does not occur.
Even under the solution condition that the ATP hydrolysis reaction occurs, the
frequency of the ATP synthesis reaction does not vanish (see Sect. 2.1.1): It is just
that the frequency of the ATP hydrolysis reaction is much higher than that of the ATP
synthesis reaction. Hence, in scenario (A) the ATP synthesis reaction rarely occurs
with the inverse rotation, which was actually observed in experiments [22].
3.8 Inverse Rotation Compelled by External Torque
Imposed on Central Shaft and Occurrence of ATP
Synthesis Under Solution Condition that ATP
Hydrolysis Reaction Should Occur
3.8.1 What Will Happen When Inverse Rotation is Forcibly
Executed?
We then discuss scenario (D) defined in Sect. 3.3. It was experimentally revealed by
Muneyuki and coworkers [32–35] using F 1 -ATPase from thermophilic Bacillus strain
3 Mechanism of Unidirectional Rotation of γ Subunit in F 1 -ATPase
(3) Thus, changes of β DP →β’ DP →β TP , β E →β’ E →β DP , and β TP →β’ TP →β E occur
in subcomplexes I−γ, II−γ, and III−γ, respectively. The γ subunit rotates by
120° in the clockwise direction in response to the change in the packing structure
of the α 3 β 3 complex, primarily to recover the closely packed interfaces with
β DP and α E . Though the overall structures before and after the 120° rotation are
the same, one ATP molecule is synthesized in aqueous solution: The system
free energy becomes lower by the free-energy change upon the APT synthesis
reaction in aqueous solution under the physiological condition, −G ~ −20k B T
(T = 298 K). We note that in the solution condition that the ATP synthesis
reaction occurs, G defined by Eq. (2.1) is positive (see Sect. 2.1.1).
3.7 Normal and Inverse Rotations with the Same
Frequency (Rotations in Random Directions) Under
Solution Condition that ATP Hydrolysis and Synthesis
Reactions Are Equilibrated
In scenario (C) defined in Sect. 3.3, the ATP hydrolysis and synthesis reactions
are in equilibrium. Even in this chemical equilibrium state, the reactions are not
stopped: The hydrolysis and synthesis reactions occur with the same frequency
(see Sect. 2.1.1). Hence, the ATP hydrolysis accompanied by the normal rotation expounded in Fig. 3.16 and the ATP synthesis leading to the inverse rotation
expounded in Fig. 3.21 take place with the same frequency. States (a) in these two
figures are the same, and the chemical compounds bound to β DP , β TP , and β E are,
respectively, ATP• • •H 2 O, ATP, and Pi. In essence, the rotation does not occur.
Even under the solution condition that the ATP hydrolysis reaction occurs, the
frequency of the ATP synthesis reaction does not vanish (see Sect. 2.1.1): It is just
that the frequency of the ATP hydrolysis reaction is much higher than that of the ATP
synthesis reaction. Hence, in scenario (A) the ATP synthesis reaction rarely occurs
with the inverse rotation, which was actually observed in experiments [22].
3.8 Inverse Rotation Compelled by External Torque
Imposed on Central Shaft and Occurrence of ATP
Synthesis Under Solution Condition that ATP
Hydrolysis Reaction Should Occur
3.8.1 What Will Happen When Inverse Rotation is Forcibly
Executed?
We then discuss scenario (D) defined in Sect. 3.3. It was experimentally revealed by
Muneyuki and coworkers [32–35] using F 1 -ATPase from thermophilic Bacillus strain