36
3 Mechanism of Unidirectional Rotation of γ Subunit in F 1 -ATPase
α TP
β DP
β E
α E
α DP
β TP
ATP H 2 O
(ATP just before
hydrolysis reaction)
is bound.
γ
No nucleotides are bound;
Only Pi remains.
ATP is bound.
Closed
Structure
Closed
Structure
Open
Structure
Fig. 3.9 Catalytic dwell state of α 3 β 3 γ complex. This is the initial state for one ATP hydrolysis
cycle in scenario (A)
shown in Fig. 3.9 [3, 6–8] (see Fig. 3.6 also). It is quite stable in terms of the water
entropy as discussed in Sect. 3.2. According to the experimental studies by Noji
and coworkers [9], after the ATP hydrolysis to ADP and Pi in a β subunit, ADP first
dissociates from the β subunit. In the catalytic dwell state, the remaining Pi, ATP, and
ATP• • •H 2 O are bound to the β subunits denoted by β E , β TP , and β DP , respectively.
The three α subunits are named α E , α TP , and α DP , respectively, as shown in Fig. 3.9.
The α 3 β 3 γ complexes shown in Figs. 3.2a, b, and 3.6 or 3.9 share qualitatively the
same characteristics of the packing structure.
3.3.2 Methods of Theoretical Analyses
We analyze the packing structure of the α 3 β 3 γ complex using the crystal structure of
F 1 -ATPase from bovine heart mitochondria (PDB ID: 2JDI) [3, 10] corresponding to
the catalytic dwell state shown in Fig. 3.2a where Pi is not bound to β E . The purpose
of this analysis is to unveil the basic characteristics of the packing structure common
in the α 3 β 3 γ complexes shown in Figs. 3.2a, b, and 3.6 or Fig. 3.9. The missing
residues (402–409 in α TP , 388–395 in β E , 48–66, 87–104, 117–126, 149–158, and
174–205 in γ) are added using MODELLER [11] on the basis of the crystal structure
whose PDB ID is 1E79 [12]. AMP-PNP and Mg
2+ are bound to β TP and β DP , and no
nucleotides are bound to β E . For the theoretical analyses, AMP-PNP is replaced by
ATP. Since there is no ATP-Mg
2+ bound to β E , β E has significantly fewer atoms than
the other two β subunits. To compare the packing efficiencies of proteins or protein
interfaces impartially, we calculate the hydration entropy S < 0 of ATP-Mg
2+ and
add it to S of any protein, protein pair, or protein complex including β E . Refer to our
earlier publication [13] for more details.
3 Mechanism of Unidirectional Rotation of γ Subunit in F 1 -ATPase
α TP
β DP
β E
α E
α DP
β TP
ATP H 2 O
(ATP just before
hydrolysis reaction)
is bound.
γ
No nucleotides are bound;
Only Pi remains.
ATP is bound.
Closed
Structure
Closed
Structure
Open
Structure
Fig. 3.9 Catalytic dwell state of α 3 β 3 γ complex. This is the initial state for one ATP hydrolysis
cycle in scenario (A)
shown in Fig. 3.9 [3, 6–8] (see Fig. 3.6 also). It is quite stable in terms of the water
entropy as discussed in Sect. 3.2. According to the experimental studies by Noji
and coworkers [9], after the ATP hydrolysis to ADP and Pi in a β subunit, ADP first
dissociates from the β subunit. In the catalytic dwell state, the remaining Pi, ATP, and
ATP• • •H 2 O are bound to the β subunits denoted by β E , β TP , and β DP , respectively.
The three α subunits are named α E , α TP , and α DP , respectively, as shown in Fig. 3.9.
The α 3 β 3 γ complexes shown in Figs. 3.2a, b, and 3.6 or 3.9 share qualitatively the
same characteristics of the packing structure.
3.3.2 Methods of Theoretical Analyses
We analyze the packing structure of the α 3 β 3 γ complex using the crystal structure of
F 1 -ATPase from bovine heart mitochondria (PDB ID: 2JDI) [3, 10] corresponding to
the catalytic dwell state shown in Fig. 3.2a where Pi is not bound to β E . The purpose
of this analysis is to unveil the basic characteristics of the packing structure common
in the α 3 β 3 γ complexes shown in Figs. 3.2a, b, and 3.6 or Fig. 3.9. The missing
residues (402–409 in α TP , 388–395 in β E , 48–66, 87–104, 117–126, 149–158, and
174–205 in γ) are added using MODELLER [11] on the basis of the crystal structure
whose PDB ID is 1E79 [12]. AMP-PNP and Mg
2+ are bound to β TP and β DP , and no
nucleotides are bound to β E . For the theoretical analyses, AMP-PNP is replaced by
ATP. Since there is no ATP-Mg
2+ bound to β E , β E has significantly fewer atoms than
the other two β subunits. To compare the packing efficiencies of proteins or protein
interfaces impartially, we calculate the hydration entropy S < 0 of ATP-Mg
2+ and
add it to S of any protein, protein pair, or protein complex including β E . Refer to our
earlier publication [13] for more details.