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222 crystal
was quantiied by measuring the mean-square displacements (MSDs) at
various intervals (see Fig. 8.3 ) . From the linear increase in MSDs with time, the
diffusion rate constants of migrating monovacancy defects were determined
to be
The mobility of monovacancy defects along each axis of the
C
D a = 20.5 nm 2 /s along the
a
-axis, which includes rows of contiguous
biotin-bound subunits, and
D b = 48.8 nm 2 /s along the
b
-axis, which includes
rows of contiguous biotin-unbound subunits.
The linear relationship between MSDs and time of this migration indicates
that the migration of monovacancy defects occurs by a random walk. The
one-dimensional diffusion constant
D
is expressed as
D
=
δ 2 /2
τ
, where
δ
is
the step length and
τ
is the time for each step (stepping time). 21 In the
C
222
crystal of streptavidin, the step length
is 5.9 nm in both axes because the
minimum step length corresponds to the lattice constant. Therefore, the
stepping time
δ
for the movements along each axis can be estimated to be
τ a = 0.85 seconds and
τ
τ b = 0.36 seconds for the
a
- and
b
-axis, respectively.
Figure 8.3. Plot of mean-square displacements (MSDs) of monovacancy defects
against time. The MSDs as a function of time was measured from 94 trajectories. Error
bars indicate standard error. The MSDs of defects along the a - and b -axes in the C 222
crystal are compared. Data itted to a linear function yielded diffusion constants
D a =
20.5 nm 2 /s and D b = 48.8 nm 2 /s for the directions along the a - and b -axes, respectively.
Closed circle, MSDs with the a -axis that includes rows of contiguous biotin-bound
subunits; open circle, MSDs with the b -axis that includes rows of contiguous biotin-
unbound subunits.
D a ) arises from a free energy
difference between the biotin-bound subunit-subunit interaction and
biotin-unbound subunit-subunit interaction. When a streptavidin molecule
adjacent to a monovacancy defect moves to the defect site along the
This anisotropy in lateral mobility (i.e.,
D b >
-axis,
two intermolecular bonds between biotin-unbound subunits (“u-u bond”)
and one intermolecular bond between biotin-bound subunits (“b-b bond”)
a
 
 
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