PROBING CELLULAR ADHESION AT THE SINGLE-MOLECULE LEVEL - Life at the Nanoscale: Atomic Force Microscopy of Live Cells - page 241

( γτ 0 r f )

k B T

_____ ______

γ ln

F * =

k B T

(11.6)

which describes how rupture forces depend on the applied loading rate ( Fig.
11.5c ) . Fitting Eq. (11.6) to the measured dynamic force spectrum allows us
to determine the parameters of the interaction and to calculate the force-
dependent lifetime ( Fig. 11.5d ) . In the case of multiple barriers, the most
probable rupture force will follow a series of linear regimes with the logarithm
of the loading rate, to which Eq. (11.6) can be itted separately. 5,48,68 The
resulting force dependence of lifetime would lead to a series of exponential
regimes described by

3

τ 0i being the intrinsic lifetime of
each barrier. Even if the observation of series of linear regimes in the dynamic
force spectrum has been mainly interpreted as successive barriers along the
dissociation coordinate, other interpretations such as intermediate states are
also plausible. 69
Recent developments have shown more direct approaches than DFS to
determine force-dependent lifetime 58,70 ( Fig. 11.5d open symbols). Dudko and
coworkers recently showed that Eq. (11.4) can be inverted to directly compute
the dissociation lifetime as a function of force,

τ ( F ) = τ 0i ( Fig. 11.6b ) ,

i

τ ( F ), from the distribution of

rupture forces at a constant loading rate

*

∫ F ∞

p ( f )

________
r f

τ (

F ) =

)

df (11.7)

p ( F

By doing so, Eqs. (11.2) or (11.3) can be itted to the resulting lifetime
versus force plots to determine the interaction parameters. We have

applied this method in the example given in Fig. 11.5 to directly estimate the
force-dependent lifetimes (open symbols in Fig. 11.5d ) . It can be seen that
the irst three points it very well with the lifetime calculated from the itted
parameters from DFS. However, the following points deviate considerably
from the expected trend. This can be due to the presence of an inner barrier
not detected in the spectrum that would appear at higher loading rates or
to the effect of possible multiple bonds rupture events in the probability
distribution of rupture forces. A more detailed analysis and validation of the
different methods should be carried out on receptor-ligand interactions. Even
if this approach appears to be quite convenient, we have described the most
established method of using the dynamic force spectrum and the Bell-Evans
model [ Eq. (11.6) ] to derive the interaction parameters.
Oberbarnscheidt and coworkers recently developed an alternative and
elegant approach, in which force curve data are directly used to extract force-

58

* See Eq. 10 in Ref. 56. See Eq. 10 in Ref. 56.