Biomedical Engineering Reference
In-Depth Information
(a)
(b)
F* (pN)
260
240
220
200
180
160
140
120
100
80
60
40
20
0
Bell-Evans plot
Bell-Evans Plot
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
50 100 150 200 250 300
Force (pN)
Force (pN)
Force (pN)
F = 0
In (loading rate (pN/s)
2
3
4
5
6
7
8
9
10
11
In(r
e
)
35
(c)
Williams plot
= 0.4 nm and
k
off
= 0.12 s
-1
with x
β
30
Williams n = 1
Williams n = 2
25
20
Bell Pop 2
Bell Pop 1
nsb
15
10
5
0
0.0
2.5
5.0
7.5
10.0
In[r
f
x
β
/(
k
B
Tk
off
)]
FIGURE 5.10
Bell-Evans and Williams plots for multiple parallel bonds. (a) Theoretical
Bell-Evans plot of the most probable rupture forces (
F*
) versus the logarithm of the load-
ing rate. Two fitted line are obtained when multiple Gaussian distributions are observed
(lower inset) at a given loading rate. (b) Experimental Bell-Evans plot showing multiple fits
(lines) and their standard deviations (dotted lines); these fits are well separated from one fitto
another. The standard deviation of most probable loading rates is shown by horizontal bars. (c)
Williams plot representing the correlation between normalized most probable rupture forces
versus normalized logarithm of the loading rate. Data points from (b) are normalized. To
obtain the fit line, a simulation is performed by manually adjusting the energy barrier width
(
x
β
) and the natural kinetic dissociation rate (
k
off
). From the fit, it can be seen that single-bond
rupture corresponds to filled circle symbols whereas that of double bond ruptures corresponds
to open symbols. Note that the light gray square symbols at the bottom of the plot could not
be fitted and thus are attributed to nonspecific rupture events.
Evans plot becomes more complicated (Figure 5.10b) due to the presence of multiple
fits. These fits should not be confused with the observed nonlinearity in Bell-Evans
plots (see above) that is commonly attributed to the presence of multiple energy
barriers in the dissociation pathway.
The main difficulty in the interpretation of multiple fitting lines in a Bell-Evans
plot is the correct attribution of the elementary interaction (n = 1). The presence
of rupture forces corresponding to nonspecific events often pollutes the Bell-Evans
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