3.3 Theoretical Analyses on Packing Structure …
39
the packing in the α E −β E and α TP −γ interfaces is somewhat loose. These results are
in good accord with the results from the molecular dynamics (MD) simulation with
all-atom potentials by Ito and Ikeguchi [10, 13].
Values of S/k B of subcomplexes I, II, and III are given in Table 3.2(a). The intrasubunit and inter-subunit contributions to S/k B of each subcomplex are also given.
The intra-subunit contribution is the sum of values of S/k B for the subunits forming
each subcomplex (e.g., β E , α E , α TP , and the γ subunit forming subcomplex I). “S/k B
of each subcomplex” minus “intra-subunit contribution” is the inter-subunit contribution which represents the contribution from the interface packing between subunits
in the subcomplex. A larger inter-subunit contribution implies higher packing efficiency in the interfaces. In Table 3.2(a), value for a subcomplex relative to that for
subcomplex III is given in parentheses. It is observed that the values of S for the
three subcomplexes follow the order, “|S| of subcomplex III” << “|S| of subcomplex
II” < “|S| of subcomplex I”. “|S| of subcomplex III” including the α DP −β DP , α E −γ,
and β DP −γ interfaces is the smallest, indicating that the atoms in this complex is the
most closely packed. Looking at the values in parentheses, we can conclude that the
difference between subcomplexes in terms of |S| comes primarily from that in terms
of the inter-subunit contribution. Hereafter, we state that subcomplexes I, II, and III
are loosely, moderately, and closely packed, respectively.
Table 3.2(b) gives values of S/k B of subcomplexes I−γ, II−γ, and III−γ. Value
for a subcomplex relative to that for subcomplex III is given in parentheses. We find
that “|S| of subcomplex III−γ” < “|S| of subcomplex II−γ” < “|S| of subcomplex
I−γ”. We can state that subcomplexes I−γ, II−γ, and III−γ are loosely, moderately,
and closely packed, respectively. The basic characteristics of the packing structure
of the α 3 β 3 γ complex are determined by those of the α 3 β 3 complex. However, values
of |S| and the differences in terms of |S| among subcomplexes I, II, and III are much
larger than those among subcomplexes I−γ, II−γ, and III−γ. This result suggests
that incorporation of the γ subunit in the α 3 β 3 complex enlarges the water-entropy
Table 3.2 Values of S/k B (k B
is the Boltzmann constant) for
subcomplexes I, II, and III (a)
and for subcomplexes I−γ,
II−γ, and III−γ (b) defined in
Fig. 3.10
(a)
Subcomplex
S/k B
Intra-subunit
contribution
Inter-subunit
contribution
I
−61244.9
(−625.8)
−61826.8
(−234.6)
581.9
(−391.2)
II
−61027.9
(−408.8)
−61760.7
(−168.5)
732.8
(−240.3)
III
−60619.1
(0)
−61592.2 (0) 973.1 (0)
(b)
Subcomplex
S/k B
I−γ
−50908.5 (−602.8)
II−γ
−50598.2 (−292.5)
III−γ
−50305.7 (0)
39
the packing in the α E −β E and α TP −γ interfaces is somewhat loose. These results are
in good accord with the results from the molecular dynamics (MD) simulation with
all-atom potentials by Ito and Ikeguchi [10, 13].
Values of S/k B of subcomplexes I, II, and III are given in Table 3.2(a). The intrasubunit and inter-subunit contributions to S/k B of each subcomplex are also given.
The intra-subunit contribution is the sum of values of S/k B for the subunits forming
each subcomplex (e.g., β E , α E , α TP , and the γ subunit forming subcomplex I). “S/k B
of each subcomplex” minus “intra-subunit contribution” is the inter-subunit contribution which represents the contribution from the interface packing between subunits
in the subcomplex. A larger inter-subunit contribution implies higher packing efficiency in the interfaces. In Table 3.2(a), value for a subcomplex relative to that for
subcomplex III is given in parentheses. It is observed that the values of S for the
three subcomplexes follow the order, “|S| of subcomplex III” << “|S| of subcomplex
II” < “|S| of subcomplex I”. “|S| of subcomplex III” including the α DP −β DP , α E −γ,
and β DP −γ interfaces is the smallest, indicating that the atoms in this complex is the
most closely packed. Looking at the values in parentheses, we can conclude that the
difference between subcomplexes in terms of |S| comes primarily from that in terms
of the inter-subunit contribution. Hereafter, we state that subcomplexes I, II, and III
are loosely, moderately, and closely packed, respectively.
Table 3.2(b) gives values of S/k B of subcomplexes I−γ, II−γ, and III−γ. Value
for a subcomplex relative to that for subcomplex III is given in parentheses. We find
that “|S| of subcomplex III−γ” < “|S| of subcomplex II−γ” < “|S| of subcomplex
I−γ”. We can state that subcomplexes I−γ, II−γ, and III−γ are loosely, moderately,
and closely packed, respectively. The basic characteristics of the packing structure
of the α 3 β 3 γ complex are determined by those of the α 3 β 3 complex. However, values
of |S| and the differences in terms of |S| among subcomplexes I, II, and III are much
larger than those among subcomplexes I−γ, II−γ, and III−γ. This result suggests
that incorporation of the γ subunit in the α 3 β 3 complex enlarges the water-entropy
Table 3.2 Values of S/k B (k B
is the Boltzmann constant) for
subcomplexes I, II, and III (a)
and for subcomplexes I−γ,
II−γ, and III−γ (b) defined in
Fig. 3.10
(a)
Subcomplex
S/k B
Intra-subunit
contribution
Inter-subunit
contribution
I
−61244.9
(−625.8)
−61826.8
(−234.6)
581.9
(−391.2)
II
−61027.9
(−408.8)
−61760.7
(−168.5)
732.8
(−240.3)
III
−60619.1
(0)
−61592.2 (0) 973.1 (0)
(b)
Subcomplex
S/k B
I−γ
−50908.5 (−602.8)
II−γ
−50598.2 (−292.5)
III−γ
−50305.7 (0)