3.4 Normal Rotation Under Solution Condition …
47
β β DP
(a)
(b)
(c)
β DP
HO
β E
βsubunit in
subcomplex III−γ
βsubunit in
subcomplex II−γ
βsubunit in
subcomplex I−γ
β DP
β’ TP
β TP
(c)
(b)
(a)
β TP
β’ E
β E
(c)
(b)
(a)
>
>
>
>
ATP
ATP H 2 O
ADP, Pi
Pi
Category (1)
Category (2)
Fig. 3.17 Changes in chemical compounds bound to three β subunits in subcomplexes I−γ, II−γ,
and III−γ, respectively, during one ATP hydrolysis cycle in scenario (A). In state (a), for example,
ATP• • •H 2 O (see the caption for Fig. 3.6), ATP, and Pi are bound to β DP , β TP , and β E , respectively.
ATP(ATP• • •H 2 O), an intermediate between ATP and ATP• • •H 2 O, is bound to β’ TP in state
(b). ATP(ATP• • •H 2 O) represents an intermediate between ATP and ATP• • •H 2 O. The packing
efficiency (PE) of β’ TP in state (b) is lower than the PE of β DP in state (a) or (c) but higher than the
PE of β TP in state (a) or (c). In states (a), (b), and (c), two of the three β subunits are in category
(2) and the other β subunit is in category (1) (see Fig. 3.14), thus retaining the high stability of the
α 3 β 3 γ complex
In state (a) shown in Fig. 3.16, the ATP dissociation from β TP , for example, is
not likely to occur for the following two reasons: First, under the solution condition
assumed, the ATP dissociation causes an increase in system free energy; second, in
the resultant state, two of the three β subunits are in category (2) and the other β
subunit is in category (1), vitiating the high structural stability of the α 3 β 3 γ complex.
The nonuniform packing structure of state (a), which is most favored by the
water-entropy effect, is thus retained during one ATP hydrolysis cycle for preventing
a water-entropy loss. Currently, it is difficult to explain why the γ subunit rotates
by 40° in state change (a)→(b) and by 80° in state change (a)→(b). If the crystal
structure of state (b) was experimentally available, the explanation would be made
possible by performing additional theoretical analyses.
3.4.3 Crucial Importance of Water-Entropy Effect
in Unidirectional Rotation
A protein complex is driven to take a structure which mitigates the water crowding and
increases the translational, configurational entropy of water as much as possible: This
47
β β DP
(a)
(b)
(c)
β DP
HO
β E
βsubunit in
subcomplex III−γ
βsubunit in
subcomplex II−γ
βsubunit in
subcomplex I−γ
β DP
β’ TP
β TP
(c)
(b)
(a)
β TP
β’ E
β E
(c)
(b)
(a)
>
>
>
>
ATP
ATP H 2 O
ADP, Pi
Pi
Category (1)
Category (2)
Fig. 3.17 Changes in chemical compounds bound to three β subunits in subcomplexes I−γ, II−γ,
and III−γ, respectively, during one ATP hydrolysis cycle in scenario (A). In state (a), for example,
ATP• • •H 2 O (see the caption for Fig. 3.6), ATP, and Pi are bound to β DP , β TP , and β E , respectively.
ATP(ATP• • •H 2 O), an intermediate between ATP and ATP• • •H 2 O, is bound to β’ TP in state
(b). ATP(ATP• • •H 2 O) represents an intermediate between ATP and ATP• • •H 2 O. The packing
efficiency (PE) of β’ TP in state (b) is lower than the PE of β DP in state (a) or (c) but higher than the
PE of β TP in state (a) or (c). In states (a), (b), and (c), two of the three β subunits are in category
(2) and the other β subunit is in category (1) (see Fig. 3.14), thus retaining the high stability of the
α 3 β 3 γ complex
In state (a) shown in Fig. 3.16, the ATP dissociation from β TP , for example, is
not likely to occur for the following two reasons: First, under the solution condition
assumed, the ATP dissociation causes an increase in system free energy; second, in
the resultant state, two of the three β subunits are in category (2) and the other β
subunit is in category (1), vitiating the high structural stability of the α 3 β 3 γ complex.
The nonuniform packing structure of state (a), which is most favored by the
water-entropy effect, is thus retained during one ATP hydrolysis cycle for preventing
a water-entropy loss. Currently, it is difficult to explain why the γ subunit rotates
by 40° in state change (a)→(b) and by 80° in state change (a)→(b). If the crystal
structure of state (b) was experimentally available, the explanation would be made
possible by performing additional theoretical analyses.
3.4.3 Crucial Importance of Water-Entropy Effect
in Unidirectional Rotation
A protein complex is driven to take a structure which mitigates the water crowding and
increases the translational, configurational entropy of water as much as possible: This