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binding and dissociation events in which bR trimers bound to different sites
at the border between the crystal and non-crystal areas. These events can be
classiied into types “I”, “II” and “III” depending on the number of interaction
sites involved. Type II binding events are predominant (~74%), whereas type
I (~6%) and type III (~20%) events are less frequent. The lifetime of the
type I bonds was too short to obtain clear images of the corresponding event,
preventing reliable statistics.
Figure 8.6b
shows a histogram of the lifetime of type II bonds which was
measured using AFM images taken at 0.1 s/frame (tip velocity, 75 μm/s). This
histogram could be well itted by a single exponential (correlation coeficient,
r
= 0.9), from which the average lifetime
τ
2
was estimated to be 0.19 ± 0.01
seconds. To ensure that the observed dissociation events are not signiicantly
affected by the AFM tip during scanning, we examined the dependence of
the average lifetime on the tip velocity while a constant vertical force was
maintained. The inset in
Fig. 8.6b
shows the average lifetime as a function of
tip velocity and indicates that the average lifetime is about 0.17 ± 0.06 seconds,
irrespective of tip velocity. Thus, we conclude that the tip-sample interaction
does not signiicantly affect the natural association and dissociation kinetics
of the bR trimer.
Figure 8.6c
shows a histogram of the type III bond lifetime,
from which the average lifetime
τ
3
was estimated to be 0.85 ± 0.08 seconds.
The longer lifetime of type III bonds compared with type II obviously arises
from a relationship of
E
3
are the association energies
responsible for type II and type III interactions, respectively. The average
lifetime ratio,
τ
2
/
τ
3
, is given by
E
3
<
E
2
< 0, where
E
2
and
τ
2
/
τ
3
= exp[(
E
3
E
2
)/
k
B
T
]
(8.3)
Because the type II interaction contains two elementary bonds, whereas the
type III interaction contains three, the energy difference
E
3
E
2
corresponds
to the association energy of the single elementary bond. From the ratio
τ
2
/
be about
0.9 kcal/mol at 300 K. This value
is approximately consistent with that estimated by differential scanning
calorimetry.
26,27
1.5
k
B
T
, which corresponds to
8.3.3 Crystal Dynamics of Annexin V
Annexin V is a soluble protein, belonging to a protein family that binds to
negatively charged phospholipids, in particular DOPS, in the presence of
calcium ions. It undergoes 2D crystallization on lipid monolayers.
28
The
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