Biomedical Engineering Reference
In-Depth Information
binding sites, the occurrence of multiple unbinding processes, and so on. When the
histogram displays a single-mode distribution, the unbinding force has been evalu-
ated from the maximum of the distribution or through a fit with a Gaussian function.
When multiple peaks are observed, the first peak has been commonly assumed as
due to a single unbinding event. More specifically, if the peaks in the distribution
are equally spaced, the distance between two subsequent peaks has been assumed
as the quantum for the unbinding force. Alternatively, a Poisson statistical method
has been developed to determine the unbinding force when a finite number of inter-
acting biomolecular pairs are expected to be found within the tip-substrate contact
area (see Chapters 3 and 4 and Lo et al., 2001). However, more accurate and refined
procedures are generally required to analyze the force distributions in the presence
of multiple unbinding events (see Chapters 3 through 5).
Notably, the first DFS studies on biomolecular systems have been focused on the
unbinding force intensity at a fixed value of the loading rate. Successive investi-
gations have put into evidence that the unbinding force alone does not necessarily
reflect the effective strength of the interaction since this force strongly depends on
the loading rate and then the equilibrium energy profile is altered (see Figure 6.3).
As widely treated in Chapter 3, the determination of equilibrium properties of a
biomolecular complex from DFS data obtained in nonequilibrium conditions can be
achieved by applying suitable models. A phenomenological description of the effects
of an applied force on the chemical reaction energy profile has been first provided
by Bell and Evans-Ritchie (see Figure 6.3; Bell, 1978; Evans and Ritchie, 1997).
According to the proposed model, the application of a weak external force
F
yields
a lowering of the activation energy barrier Δ
G
∗
given by Δ
G
∗
(
Δ
G
∗
−
Fx
β
,
where
x
β
is the width of the energy barrier (see dashed line in Figure 6.3). It should
be noted that the possibility of an increase of this energy barrier upon the applica-
tion of a force, with a concomitant prolonged lifetime of the complex, has also been
predicted (see dotted line in Figure 6.3; Prezhdo and Pereverzev, 2009). Such an
increase which gives rise to the so-called “catch bonds,” has been later on confirmed
experimentally (see Subsection 6.3.5).
Starting from the Bell model, and in the framework of the reaction rate theory for
thermally activated processes, Evans and Ritchie described the unbinding process of
a biomolecular complex in terms of crossing over a single energy barrier under the
application of the force with a constant loading rate (Evans and Ritchie, 1997). They
cast the probability distribution
P
(
F
) of the unbinding force
F
into the equation:
F
)=
⎡
⎣
⎛
⎝
k
B
T
⎞
⎤
⎦
Fx
β
Fx
β
k
B
T
+
k
off
k
B
T
x
β
r
F
⎠
−
1
e
k
off
r
F
P
(
F
)=
e
(6.1)
where
k
off
is the dissociation rate at equilibrium,
k
B
is the Boltzmann constant, and
T
is the absolute temperature (see Chapter 3). This distribution was found to be
asymmetric and skewed toward low force values. Under the assumption of single
unbinding events, the most probable unbinding force
F
∗
can be generally derived
Search WWH ::
Custom Search