48
3 Mechanism of Unidirectional Rotation of γ Subunit in F 1 -ATPase
is the water-entropy effect (see Sect. 2.8). The β subunits in F 1 -ATPase are coupled
with the ATP hydrolysis reaction, an irreversible process, through their catalytic
actions. They are involved in the ATP hydrolysis cycle. Due to the water-entropy
effect, the packing efficiencies of the three β subunits and those of subcomplexes
I−γ, II−γ, and III−γ become significantly different. The orientation of the γ subunit
is determined in response to the nonuniform packing structure of the α 3 β 3 complex
through the water-entropy effect. The retainment of the closely packed β DP −γ and
α E −γ interfaces is particularly important. The packing efficiency of a β subunit is
intimately related to the chemical compound bound to it. As the ATP hydrolysis reaction proceeds, the chemical compounds bound to the three β subunits successively
change, and the packing efficiencies of the three β subunits and those of subcomplexes I−γ, II−γ, and III−γ also successively change. This structural change of the
α 3 β 3 complex induces the orientational change of the γ subunit.
The hydration entropy of each β subunit to which one of ATP, ADP + Pi, Pi, and
nothing is bound, that of the α 3 β 3 complex, and the large dependence of hydration
entropy of the α 3 β 3 γ complex on the orientation of the γ subunit are important
thermodynamic quantities for elucidating the unidirectional rotation. The force for
rotating the γ subunit is generated by not ATP but water. If the rotation was driven
by the free energy by ATP hydrolysis reaction as claimed by the prevailing view, the
γ subunit would rotate by 120° during the hydrolysis in β DP .
After the 120° rotation of the γ subunit, the absolute value of hydration entropy
|S| of a subcomplex (the magnitude of water-entropy loss caused by the presence a
subcomplex) increases by ~626k B for subcomplex III, decreases by ~−409k B for
subcomplex II, and decreases by ~−217k B for subcomplex I (see Table 3.2(a)).
Therefore, the hydration entropy of the α 3 β 3 γ complex is kept almost unchanged
during one ATP hydrolysis cycle, i.e., a single rotation (the 120° rotation). During
the rotation, a very large increase in |S| for one of the three subcomplexes is cancelled
out by large decreases in |S| for the other two subcomplexes, causing no free-energy
barrier for the rotation of the γ subunit.
It was shown with surprise by an experimental study [1] that the three β subunits
in the α 3 β 3 complex (i.e., without the γ subunit) exhibit cyclic structural changes in
the same rotary direction as in the α 3 β 3 γ complex (see Fig. 3.5). Only one of the
three β subunits takes open structure, and when an open-to-closed transition occurs
for this β subunit, the opposite closed-to-open transition simultaneously occurs for
its counterclockwise neighboring β subunit. This experimental result is in accord
with our physical picture discussed in Sect. 3.4.2.
Geometrically, the axle of the γ subunit penetrates the central cavity with cylindrical shape of the α 3 β 3 complex (see Fig. 3.12). In an interesting experimental work
[26], the γ subunit was truncated so that the remaining head of the γ subunit outside
the cavity could sit on the concave entrance of the α 3 β 3 complex. Strikingly, the
truncated γ subunit rotated in the normal direction, though the average rotary speed
was lower and moments of irregular motion were exhibited. This experimental result
is suggestive of the following: Wide, closely packed α−γ and β−γ interfaces are
not necessarily required for entropically correlating the γ subunit with the packing
structure of the α 3 β 3 complex; even narrow, closely packed interfaces enable the γ
3 Mechanism of Unidirectional Rotation of γ Subunit in F 1 -ATPase
is the water-entropy effect (see Sect. 2.8). The β subunits in F 1 -ATPase are coupled
with the ATP hydrolysis reaction, an irreversible process, through their catalytic
actions. They are involved in the ATP hydrolysis cycle. Due to the water-entropy
effect, the packing efficiencies of the three β subunits and those of subcomplexes
I−γ, II−γ, and III−γ become significantly different. The orientation of the γ subunit
is determined in response to the nonuniform packing structure of the α 3 β 3 complex
through the water-entropy effect. The retainment of the closely packed β DP −γ and
α E −γ interfaces is particularly important. The packing efficiency of a β subunit is
intimately related to the chemical compound bound to it. As the ATP hydrolysis reaction proceeds, the chemical compounds bound to the three β subunits successively
change, and the packing efficiencies of the three β subunits and those of subcomplexes I−γ, II−γ, and III−γ also successively change. This structural change of the
α 3 β 3 complex induces the orientational change of the γ subunit.
The hydration entropy of each β subunit to which one of ATP, ADP + Pi, Pi, and
nothing is bound, that of the α 3 β 3 complex, and the large dependence of hydration
entropy of the α 3 β 3 γ complex on the orientation of the γ subunit are important
thermodynamic quantities for elucidating the unidirectional rotation. The force for
rotating the γ subunit is generated by not ATP but water. If the rotation was driven
by the free energy by ATP hydrolysis reaction as claimed by the prevailing view, the
γ subunit would rotate by 120° during the hydrolysis in β DP .
After the 120° rotation of the γ subunit, the absolute value of hydration entropy
|S| of a subcomplex (the magnitude of water-entropy loss caused by the presence a
subcomplex) increases by ~626k B for subcomplex III, decreases by ~−409k B for
subcomplex II, and decreases by ~−217k B for subcomplex I (see Table 3.2(a)).
Therefore, the hydration entropy of the α 3 β 3 γ complex is kept almost unchanged
during one ATP hydrolysis cycle, i.e., a single rotation (the 120° rotation). During
the rotation, a very large increase in |S| for one of the three subcomplexes is cancelled
out by large decreases in |S| for the other two subcomplexes, causing no free-energy
barrier for the rotation of the γ subunit.
It was shown with surprise by an experimental study [1] that the three β subunits
in the α 3 β 3 complex (i.e., without the γ subunit) exhibit cyclic structural changes in
the same rotary direction as in the α 3 β 3 γ complex (see Fig. 3.5). Only one of the
three β subunits takes open structure, and when an open-to-closed transition occurs
for this β subunit, the opposite closed-to-open transition simultaneously occurs for
its counterclockwise neighboring β subunit. This experimental result is in accord
with our physical picture discussed in Sect. 3.4.2.
Geometrically, the axle of the γ subunit penetrates the central cavity with cylindrical shape of the α 3 β 3 complex (see Fig. 3.12). In an interesting experimental work
[26], the γ subunit was truncated so that the remaining head of the γ subunit outside
the cavity could sit on the concave entrance of the α 3 β 3 complex. Strikingly, the
truncated γ subunit rotated in the normal direction, though the average rotary speed
was lower and moments of irregular motion were exhibited. This experimental result
is suggestive of the following: Wide, closely packed α−γ and β−γ interfaces are
not necessarily required for entropically correlating the γ subunit with the packing
structure of the α 3 β 3 complex; even narrow, closely packed interfaces enable the γ