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are broken. On the other hand, when it moves to the defect site along the
-
the difference in the activation energies
b
E
a
and
E
b
for the step movement of a
monovacancy defect along the respective
a
- and
b
-axes simply corresponds
to the difference between the free energy changes
G
b-b
produced by
the formation of the respective u-u bond and b-b bond, namely,
G
u-u
and
E
b
E
a
=
G
u-u
G
b-b
;
namely, the u-u bond afinity is higher than the b-b bond. The ratio of the two
diffusion rate constants (
G
b-b
. Therefore, the observed relationship
D
b
>
D
a
indicates
G
u-u
<
D
b
/
D
a
) can be expressed by
D
b
/
D
a
= exp[-(
E
b
-
E
a
)/(
k
B
T
)]
(8.2)
where
k
B
is Boltzmann constant and
T
is the absolute temperature. Thus,
from the observed value of
D
b
/
D
a
~ 2.4, the free energy difference
G
u-u
G
b-b
is estimated to be approximately
0.88
k
B
T
(
T
~ 300 K), which corresponds
to
0.52 kcal/mol.
8.3.2 Crystal Dynamics of Purple Membrane
The purple membrane (PM) exists in the plasma membrane of
Halobacterium
halobium
, and its constituent protein, bacteriorhodopsin (bR), functions as
a light-driven proton pump. In the PM, bR monomers are associated to form
a trimeric structure, and the trimers are arranged in a hexagonal lattice.
However, several aspects in the crystal formation remain open; for example,
(i) trimer-trimer interaction sites and (ii) the existence of preformed trimers
in the luidic non-crystal region. In the 2D crystal of bR and any crystals in
general, they are in dynamic equilibrium with the constituents at the interface
between the crystal and the liquid. Here, we visualized dynamic events at
the interface in the PM to provide information on the crystal formation and
intermolecular interactions.
23
The PM adsorbed on a mica surface in a buffer solution (10 mM Tris-HCl
A 2D crystal lattice of bR is formed over the inner region surrounded by a
bR crystals.
Figure 8.4b
shows a magniied image of an edge region of the
PM captured at 1 s/frame. There is a distinct border between the crystal
and non-crystal areas. We found that the border shape luctuates with time,
indicating that the border region of the crystal is unstable and seems to be in
dynamic equilibrium with bR molecules in the non-crystal area. In fact, spike
noises were frequently observed in the non-crystal area and very likely to be
produced by moving bR molecules which are too fast to be clearly captured
at the imaging rate used (1 s/frame).
22
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