Biomedical Engineering Reference
In-Depth Information
TABLE 5.1
Various Methods for Determining Bin Sizes of a Distribution and Their Effect
on
Determination
a
F*
Choice
Sturges
Scott
Square Root
Freedman
Diaconis
Operator
Reference
(Sturges, 1926)
(Scott, 1979)
(Freedman &
Diaconis, 1981)
3
5σ
n
1
/
3
.
=
√
n
2
IQR
(
x
)
Formula
b
k
=[
log
2
n
+
1
]
h
=
k
h
=
visual
n
1
/
3
h
16.9
15.1
12.9
9.6
5
k
7.6
8.6
10
13.4
16
F
∗
1
(in pN)
21
±
18
18
±
16
17
±
9
12
±
9
16
±
7
F
∗
2
(in pN)
ND
ND
35
±
8
33
±
11
38
±
9
a
Data set:
n
=
100, ave
=
26, stdev
=
20, min
=
2, max
=
131, Q1
=
12.75, Q3
=
35
b
k
is the number of bins,
h
is the size of each bin,
n
is the total number of values, and
IQR
(
x
)isthe
interquartile range defined as Q3-Q1.
The spreadsheet is used to calculate numerical points that can be used to draw the fit
line over the distribution.
Since most relevant biological interactions involve multiple parallel bonds, we
decide to combine all rupture events into a single analysis. Thus, all the rupture
events collected at various retraction speeds were pooled together. However, it is
thus necessary to build a distribution of effective loading rate (LR*). Determining
bin sizes is again a key element. In the end, we obtained a complex 2D plot that
shows the distribution of rupture forces in function of effective loading rates.
Finally, with a data set (
F*
, ln(LR*)), it is possible to build the Bell-Evans plot
(Fig. 5.8) to obtain the energy barrier width from the slope of the fitting line and the
dissociation constant
k
off
by extrapolating the fitting line until
F*
= 0 (Figure 5.8).
It is noteworthy that other approaches do not rely on the identification of most prob-
able rupture forces to compute the kinetic dissociation constant
k
off
(F)
(Serpe et al.
2008).
The interpretation of the energy landscape using energy barriers as described by
Bell-Evans (Bell, 1978; Evans & Ritchie, 1997) provides useful information related
to the chemistry of binding. For instance, the width of an energy barrier measured at
1 A or less likely involves the rupture of hydrogen bonds or salt bridges from a rigid
ligand (Teulon et al. 2008; Teulon et al. 2011). However, a putative energy barrier
width of 10 A likely implies a stretching or deformation of one or both partners
before the rupture.
5.8 SINGLE AND MULTIPLE SLOPES IN BELL-EVANS PLOTS
Bell-Evans plots are obtained by measuring the dependence of rupture forces on
the loading rate. The energy landscape, as defined in the framework of the one-
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