Biomedical Engineering Reference
In-Depth Information
Bound state
AB
Unbound state
A + B
k
off
Catch
Fx
β
Δ
G
*(
F
)
Δ
G
*
x
β
Reaction coordinate
FIGURE 6.3
Diagram of the energy profile for an equilibrium biomolecular complex disso-
ciation (continuous line) and under the application of an external force
F
(dashed line); Δ
G
∗
and Δ
G
∗
(
being the corresponding activation free energies. The possibility of an increase
of the energy barrier upon applying the external force is also represented (dotted line) (see
the text).
F
)
from the maximum of the unbinding force distribution:
x
β
ln
r
F
x
β
k
B
T
F
∗
=
(6.2)
k
off
k
B
T
Equation 6.2 predicts a linear relationship between the most probable force
F
∗
with
the natural logarithm of the loading rate. Then, by plotting
F
∗
as a function of
ln
, the equilibrium parameters
k
off
and
x
β
can be extracted from the slope and
the intercept of a linear fit.
The Bell-Evans model has provided a successful description of the most proba-
ble unbinding force trend with the loading rate for several biomolecular complexes.
Indeed, it represents a landmark for describing unbinding processes as studied by
DFS or by other single-molecule techniques (Lee et al., 2007; Bizzarri and Cannis-
traro, 2009). When two or even three distinct linear regimes for the most probable
unbinding force as a function of the natural logarithm of the loading rate have been
observed, the existence of two or three energy barriers, respectively, between the
bound and the unbound states have been hypothesized. On the other hand, models
predicting a dependence for the unbinding force with the loading rate as
F
∗
∼
(
r
F
)
ν
,
whereνcan assume the value 1, 1/2 or 2/3 depending on the shape of the energy bar-
rier, have been developed (Dudko et al., 2003; Hummer and Szabo, 2003; Friddle,
2008).
ln
(
r
)
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