38
3 Mechanism of Unidirectional Rotation of γ Subunit in F 1 -ATPase
the packing efficiency of the atoms in the β subunit is higher). Our primary concern
is to verify that the order of packing efficiencies of subcomplexes I−γ, II−γ, and
III−γ is determined by that of β E , β TP , and β DP .
We calculate the water-entropy gain upon contact of subunits X and Y, ΔS XY ,
which is given by
S XY = “S of subunit pair X − Y ” − (“S of subunit X ” + S of “subunit Y ”).
(3.1)
ΔS XY is positive, and larger ΔS XY implies that the atoms in the interface between
subunits X and Y are more closely packed. The subunit pair X−Y is taken from the
complex, and subunits X and Y are obtained by simply separating the pair.
3.3.3 Results of Theoretical Analyses
Values of ΔS XY /k B (k B is the Boltzmann constant) calculated for all the α−β, α−γ and
β−γ pairs are collected in Table 3.1. In this table, ΔS XY /k B = 514.0 for X = α DP and
Y = β DP implies that the water entropy increases by 514.0k B upon the contact of α DP
and β DP . This increase arises primarily from the overlap of EVs generated by α DP and
β DP . The contact produces the close packing of atoms in the α DP −β DP interface (i.e.,
the contact of atoms in α DP and those in β DP with the shape complementarity at the
atomic level), leading to such a large water-entropy gain. The α DP −β DP , α E −γ, and
β DP −γ interfaces are the most closely packed and the α TP −β E , α DP −γ, and β TP −γ
interfaces are the most loosely packed among the α−β, α−γ and β−γ interfaces,
respectively. The packing in the α TP −β TP and β E −γ interfaces is rather close, and
Table 3.1 Values of
ΔS XY /k B (k B is the
Boltzmann constant)
calculated for α−β, α−γ and
β−γ pairs
Subunit Pair (X−Y )
S XY /k B
α DP −β DP
514.0
α TP −β TP
381.9
α DP −β TP
291.9
α E −β DP
283.8
α E −β E
230.0
α TP −β E
199.9
α E −γ
68.5
α TP −γ
17.5
α DP −γ
4.5
β DP −γ
88.5
β E −γ
65.4
β TP −γ
37.8
3 Mechanism of Unidirectional Rotation of γ Subunit in F 1 -ATPase
the packing efficiency of the atoms in the β subunit is higher). Our primary concern
is to verify that the order of packing efficiencies of subcomplexes I−γ, II−γ, and
III−γ is determined by that of β E , β TP , and β DP .
We calculate the water-entropy gain upon contact of subunits X and Y, ΔS XY ,
which is given by
S XY = “S of subunit pair X − Y ” − (“S of subunit X ” + S of “subunit Y ”).
(3.1)
ΔS XY is positive, and larger ΔS XY implies that the atoms in the interface between
subunits X and Y are more closely packed. The subunit pair X−Y is taken from the
complex, and subunits X and Y are obtained by simply separating the pair.
3.3.3 Results of Theoretical Analyses
Values of ΔS XY /k B (k B is the Boltzmann constant) calculated for all the α−β, α−γ and
β−γ pairs are collected in Table 3.1. In this table, ΔS XY /k B = 514.0 for X = α DP and
Y = β DP implies that the water entropy increases by 514.0k B upon the contact of α DP
and β DP . This increase arises primarily from the overlap of EVs generated by α DP and
β DP . The contact produces the close packing of atoms in the α DP −β DP interface (i.e.,
the contact of atoms in α DP and those in β DP with the shape complementarity at the
atomic level), leading to such a large water-entropy gain. The α DP −β DP , α E −γ, and
β DP −γ interfaces are the most closely packed and the α TP −β E , α DP −γ, and β TP −γ
interfaces are the most loosely packed among the α−β, α−γ and β−γ interfaces,
respectively. The packing in the α TP −β TP and β E −γ interfaces is rather close, and
Table 3.1 Values of
ΔS XY /k B (k B is the
Boltzmann constant)
calculated for α−β, α−γ and
β−γ pairs
Subunit Pair (X−Y )
S XY /k B
α DP −β DP
514.0
α TP −β TP
381.9
α DP −β TP
291.9
α E −β DP
283.8
α E −β E
230.0
α TP −β E
199.9
α E −γ
68.5
α TP −γ
17.5
α DP −γ
4.5
β DP −γ
88.5
β E −γ
65.4
β TP −γ
37.8