Biomedical Engineering Reference
In-Depth Information
plot near the low rupture forces. To tackle the identification of elementary events,
a mathematical treatment has been developed by Williams (Williams, 2003). It was
shown that the kinetic equations for the uncorrelated parallel bond rupture cannot
be solved analytically. However, a simplified numerical solution can be successfully
used as the one developed by Sulchek et al. (Sulchek et al. 2005) that presents a direct
experimental verification of the Markovian model described by Williams. This model
uses normalized forces (
F
) and normalized loading rates (
R
)suchas
r
f
β
k
off
where
f
β
is the thermal force scale defined as
k
B
T/
x
β
and the equivalent single-bond
approximation is defined as
f
f
β
=
F
and
R
=
1
k
off
f
β
−
1
n
2
exp
N
n
=
1
1
F
n
R
=
−
where
N
is the number of bonds and
F*
is the normalized most probable rupture
force. To operate a Williams plot, first it is necessary to normalize most probable
rupture forces and loading rates and to plot these values according to
F*
versus ln[
R
].
Then, it is necessary to model the N-attachments by computing theoretical values of
R
in function of given
F*
and
n
. Adjusting
k
off
and
parameters allow the theoretical
curve to match the normalized experimental data points (Figure 5.10c). In the end,
one obtains a normalized plot with fitting lines that correspond to the description of
N-attachment. At each curve, a set of
k
off
and
x
β
values are also obtained.
γ
5.10 EXISTING SOFTWARE AND METHODS FOR DFS DATA
ANALYSIS
In this last section, we would like to provide a nonexhaustive selection of exist-
ing software or website that performs DFS analysis. First, we should recommend a
very didactical website on data processing and analysis in force spectroscopy (tech-
nical aspects of single molecule force spectroscopy) from Boris Akhremitchev lab:
(http://www.chem.duke.edu/
boris/research/force spectroscopy/force spectroscopy
.htm). Readers will find a very interesting and educative presentation, where most
of the different aspects of DFS are pictured in detail with many classical and very
useful references. Boris A is now here: http://www.chem.duke.edu/
∼
boris
It is clear now that using a program for automatic detection of rupture events is
a major improvement for two reasons. This detection is a time saver and automated
analysis eliminates measurement bias related to subjective choices of the person per-
forming the analysis. Even if, as previously explain, choosing the number of bin and
their width remains operator's skill dependant!
Several home-made softwares have been developed in AFM groups during the
past years and can be found in the following papers or websites.
∼
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