40
3 Mechanism of Unidirectional Rotation of γ Subunit in F 1 -ATPase
effect: In other words, the water entropy is quite sensitive to the orientation of the γ
subunit in response to the packing structure of the α 3 β 3 complex.
An important result is that values of S/k B of β DP , β TP , and β E are
−16390.0, −16407.4, and −16427.6, respectively. Value relative to that for β DP
is −17.4 for β TP and −37.6 for β E . Hence, “|S| of β DP ” < “|S| of β TP ” < “|S| of β E ”.
This order is reflected on the order, “|S| of subcomplex III−γ” < “|S| of subcomplex
II−γ” < “|S| of subcomplex I−γ”. The order, “|S| of β DP ” < “|S| of β E ” and “|S| of
β TP ” < “|S| of β E ”, coincides with the experimentally known information that β DP and
β TP take closed structure but β E takes open structure. “|S| of β DP ” < “|S| of β TP ”, or
equivalently, the feature that β DP is more closely packed than β TP (i.e., the structure
of β DP is more closed), can be unveiled only by our theoretical analyses.
3.3.4 Packing Structure Stabilized by Water-Entropy Effect
Figure 3.11 shows the packing structure stabilized in terms of the water entropy,
which is revealed by our theoretical analyses. Subcomplexes I, II, and III are, respectively, loosely, moderately, and closely packed. The α DP −β DP , α E −γ, and β DP −γ
interfaces are the most closely packed among the α−β, α−γ and β−γ interfaces,
respectively. The sign of high inequality “” appears only in the order, “|S| of
subcomplex III” << “|S| of subcomplex II”. This is ascribed to the feature that the
β DP −γ interface is more closely packed than the β TP −γ interface.
We define the orientation of the γ subunit as follows (see Fig. 3.12). Residues
Arg8−Ile19 in the γ subunit come in contact with residues Asp386−Leu391 in
Loosely packed
Moderately packed
Closely packed
: Closely packed interface
“⎪S⎪of subcomplex III” <<“⎪S⎪of subcomplex II” <“⎪S⎪of subcomplex I” ,
“⎪S⎪of subcomplex III−γ ”<“⎪S⎪of subcomplex II−γ” <“⎪S⎪of subcomplex I −γ ”,
“⎪S⎪of β DP ” <“⎪S⎪of β TP ” <“⎪S⎪of β E ”.
Fig. 3.11 Packing structure of α 3 β 3 γ complex in catalytic dwell state. The definitions of subcomplexes I, II, III, I−γ, II−γ, and III−γ are shown in Fig. 3.10. The orientation of the γ subunit is
defined as indicated by the orange arrow. S < 0 is the hydration entropy. Smaller |S| implies a higher
packing efficiency of the atoms in a protein or protein complex
3 Mechanism of Unidirectional Rotation of γ Subunit in F 1 -ATPase
effect: In other words, the water entropy is quite sensitive to the orientation of the γ
subunit in response to the packing structure of the α 3 β 3 complex.
An important result is that values of S/k B of β DP , β TP , and β E are
−16390.0, −16407.4, and −16427.6, respectively. Value relative to that for β DP
is −17.4 for β TP and −37.6 for β E . Hence, “|S| of β DP ” < “|S| of β TP ” < “|S| of β E ”.
This order is reflected on the order, “|S| of subcomplex III−γ” < “|S| of subcomplex
II−γ” < “|S| of subcomplex I−γ”. The order, “|S| of β DP ” < “|S| of β E ” and “|S| of
β TP ” < “|S| of β E ”, coincides with the experimentally known information that β DP and
β TP take closed structure but β E takes open structure. “|S| of β DP ” < “|S| of β TP ”, or
equivalently, the feature that β DP is more closely packed than β TP (i.e., the structure
of β DP is more closed), can be unveiled only by our theoretical analyses.
3.3.4 Packing Structure Stabilized by Water-Entropy Effect
Figure 3.11 shows the packing structure stabilized in terms of the water entropy,
which is revealed by our theoretical analyses. Subcomplexes I, II, and III are, respectively, loosely, moderately, and closely packed. The α DP −β DP , α E −γ, and β DP −γ
interfaces are the most closely packed among the α−β, α−γ and β−γ interfaces,
respectively. The sign of high inequality “” appears only in the order, “|S| of
subcomplex III” << “|S| of subcomplex II”. This is ascribed to the feature that the
β DP −γ interface is more closely packed than the β TP −γ interface.
We define the orientation of the γ subunit as follows (see Fig. 3.12). Residues
Arg8−Ile19 in the γ subunit come in contact with residues Asp386−Leu391 in
Loosely packed
Moderately packed
Closely packed
: Closely packed interface
“⎪S⎪of subcomplex III” <<“⎪S⎪of subcomplex II” <“⎪S⎪of subcomplex I” ,
“⎪S⎪of subcomplex III−γ ”<“⎪S⎪of subcomplex II−γ” <“⎪S⎪of subcomplex I −γ ”,
“⎪S⎪of β DP ” <“⎪S⎪of β TP ” <“⎪S⎪of β E ”.
Fig. 3.11 Packing structure of α 3 β 3 γ complex in catalytic dwell state. The definitions of subcomplexes I, II, III, I−γ, II−γ, and III−γ are shown in Fig. 3.10. The orientation of the γ subunit is
defined as indicated by the orange arrow. S < 0 is the hydration entropy. Smaller |S| implies a higher
packing efficiency of the atoms in a protein or protein complex