Biomedical Engineering Reference
In-Depth Information
rupture event is a particular sample from the complex distributions of hundred forces
needed to describe the process at each loading rate. Besides, if one calculates the
effective bond loading rate for each rupture event, all the data collected at various
retraction speeds can be combined into a single analysis.
5.5 LOADING RATE
DFS experiments on single molecules is meaningless when the loading rate depen-
dence of measured forces is not taken into account (Evans & Ritchie, 1997; Merkel
et al. 1999; Evans & Ludwig, 2000; Gergely et al. 2000; Fantner et al. 2006;
Prakasam et al. 2006). The nominal loading rate is the product of the spring con-
stant of the cantilever (N/m) and the retract velocity (m/s) and it is often assumed
that it remains constant from one measure to the other. However, in the presence of
multiple bonds, it is more appropriate to use the effective loading rate, which is the
loading rate measured before bond rupture (Friedsam et al. 2003) using the following
relationship:
k
samp
·
v
k
eq
·
k
cant
r
e
=
k
cant
,
where
k
samp
=
k
samp
k
cant
−
k
eq
1
+
and
k
eq
is the slope of the retract curve before the unbinding event. The identifica-
tion of rupture events (Odorico et al. 2007a), as computed in YieldFinder (Odorico
et al. 2007b), requires the estimation of the stiffness constant (
k
samp
) of the study
system based on the series-parallel spring model and the effective loading rates
(Erdmann, 2005), which is the loading rate really experienced by the molecular
bonds (Figure 5.4).
In a multiparallel systems
k
samp
=
nk
bond
,where
k
bond
remains unknown. The
number of parallel bonds can be extracted from Bell-Evans or Williams' plots of all
combined experimental rupture force events. In case of multiple parallel bonds, a
distribution of loading rates can be obtained. It is then possible to obtain the most
frequent loading rate as peaks in that distribution. For each most frequent loading
rate, it is then possible to determine the distribution of rupture forces necessary to
build the Bell-Evans plot.
To study the ligand-receptor rupture force dependence with the loading rate, the
probe approach and retract velocity can be varied typically within the range of 100
nm/s to 1
m/s (adjusted by changing the scan rate, the retract velocity, or the ramp
size). For biological samples, useful spring constants (
k
cant
) of commercial cantilever
are in the range of 6-200 pN/nm, leading to nominal loading rates between 600
pN s
−
μ
1
and 200,000 pN s
−
1
12.2 in log scale). With advanced instruments,
it is also possible to adjust the contact time when recording FD curves. The effect
of the piezo velocity (i.e., loading rate) is easily seen on FD curves by observing a
shift toward higher rupture forces at high velocity. Usually recording nondistorted
FD curves require reducing piezo speed and in all cases not to exceed 1-2
(6.4
−
m/s.
Otherwise, shorter or stiffer cantilever should be used (Kim et al. 2010). While the
μ
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