30
3 Mechanism of Unidirectional Rotation of γ Subunit in F 1 -ATPase
change in hydration entropy (or equivalently, the change in water entropy) is a principal component of the free-energy change. In Chap. 3, we elucidate the mechanism of unidirectional rotation of the γ subunit in F 1 -ATPase with emphasis on the
water-entropy effect. It is worthwhile to recall that unlike in vacuum the electrostatic
interaction is much less important than one might expect (see Sects. 2.6 and 3.4.5).
Hereafter, we often use the term “packing structure” for a protein or protein
complex. As the packing of protein atoms (i.e., atoms in the backbone and side
chains) becomes closer, the EV generated by the protein reduces, which is more
favorable in terms of the water entropy. We also use the term “packing efficiency”
signifying the degree of close packing. Closer packing can be referred to as “higher
packing efficiency” (when the atoms are more closely packed, we state that they
are packed with higher efficiency). For a protein complex, not only the atoms in
each protein in the complex but also those in the interface between each protein
pair needs to be more closely packed. In general, however, it is not possible to meet
both of these requirements by uniform packing, i.e., by impartial packing of all
the atoms constituting the complex. As discussed for a protein in Sect. 2.7, it is
often that nonuniform packing is more favorable than the uniform packing. Here,
the nonuniform packing implies that only the atoms amenable to close packing are
preferentially packed with higher efficiency and the packing of the other atoms is left
looser. For a protein complex, we refer to the differences in the packing efficiency
among the proteins forming the complex and among the protein interfaces as the
“packing structure”.
3.2 Nonuniform Binding of Nucleotides to α 3 β 3 or α 3 β 3 γ
Complex
We first review the experimentally determined structures of the α 3 β 3 complex. In the
absence of nucleotides in aqueous solution, the α 3 β 3 complex takes a structure with
three-fold symmetry as shown in Fig. 3.1a [1]. The structures of the three β subunits
are the same: All of them take open structure [1, 2]. In aqueous solution of AMP-PNP,
an analogue of ATP whose hydrolysis reaction does not occur, AMP-PNP is bound
to two of the three β subunits and nothing is bound to the other β subunit as shown
in Fig. 3.1b [1]. Each of the β subunits to which AMP-PNP is bound takes closed
structure whereas the β subunit to which nothing is bound takes open structure. The
packing of atoms constituting the β subunit in the closed structure should be closer
than that in the open structure.
We then review the experimentally determined structures of the α 3 β 3 γ complex.
According to the crystal structures of F 1 -ATPase from bovine heart mitochondria
in aqueous solution where AMP-PNP and ADP are dissolved as nucleotides, AMPPNP is bound to two of the three β subunits and nothing is bound to the other β
subunit in the absence of azide (see Fig. 3.2a), and AMP-PNP, ADP, and nothing
are bound to the three β subunits, respectively, in the presence of azide [3] (see
3 Mechanism of Unidirectional Rotation of γ Subunit in F 1 -ATPase
change in hydration entropy (or equivalently, the change in water entropy) is a principal component of the free-energy change. In Chap. 3, we elucidate the mechanism of unidirectional rotation of the γ subunit in F 1 -ATPase with emphasis on the
water-entropy effect. It is worthwhile to recall that unlike in vacuum the electrostatic
interaction is much less important than one might expect (see Sects. 2.6 and 3.4.5).
Hereafter, we often use the term “packing structure” for a protein or protein
complex. As the packing of protein atoms (i.e., atoms in the backbone and side
chains) becomes closer, the EV generated by the protein reduces, which is more
favorable in terms of the water entropy. We also use the term “packing efficiency”
signifying the degree of close packing. Closer packing can be referred to as “higher
packing efficiency” (when the atoms are more closely packed, we state that they
are packed with higher efficiency). For a protein complex, not only the atoms in
each protein in the complex but also those in the interface between each protein
pair needs to be more closely packed. In general, however, it is not possible to meet
both of these requirements by uniform packing, i.e., by impartial packing of all
the atoms constituting the complex. As discussed for a protein in Sect. 2.7, it is
often that nonuniform packing is more favorable than the uniform packing. Here,
the nonuniform packing implies that only the atoms amenable to close packing are
preferentially packed with higher efficiency and the packing of the other atoms is left
looser. For a protein complex, we refer to the differences in the packing efficiency
among the proteins forming the complex and among the protein interfaces as the
“packing structure”.
3.2 Nonuniform Binding of Nucleotides to α 3 β 3 or α 3 β 3 γ
Complex
We first review the experimentally determined structures of the α 3 β 3 complex. In the
absence of nucleotides in aqueous solution, the α 3 β 3 complex takes a structure with
three-fold symmetry as shown in Fig. 3.1a [1]. The structures of the three β subunits
are the same: All of them take open structure [1, 2]. In aqueous solution of AMP-PNP,
an analogue of ATP whose hydrolysis reaction does not occur, AMP-PNP is bound
to two of the three β subunits and nothing is bound to the other β subunit as shown
in Fig. 3.1b [1]. Each of the β subunits to which AMP-PNP is bound takes closed
structure whereas the β subunit to which nothing is bound takes open structure. The
packing of atoms constituting the β subunit in the closed structure should be closer
than that in the open structure.
We then review the experimentally determined structures of the α 3 β 3 γ complex.
According to the crystal structures of F 1 -ATPase from bovine heart mitochondria
in aqueous solution where AMP-PNP and ADP are dissolved as nucleotides, AMPPNP is bound to two of the three β subunits and nothing is bound to the other β
subunit in the absence of azide (see Fig. 3.2a), and AMP-PNP, ADP, and nothing
are bound to the three β subunits, respectively, in the presence of azide [3] (see