Biomedical Engineering Reference
In-Depth Information
multiple bonds is that all bond ruptures are detected. However, if detection is limited
by noise, then significant fraction of single bond ruptures might miss the detection,
particularly at low and high probe velocities. This might result in considerable con-
tribution of multiple bond ruptures that is not described by Equation 4.3 (Guo et al.
2008). Therefore, additional experiments are usually necessary for verification of the
single bond nature of measured interactions. Several recommendations are given in
the section below.
4.5.2 E
FFECTS OF
M
ULTIPLE
I
NTERACTIONS ON
M
EASURED
D
ATA
In the data analysis, only the last rupture event is usually included in statistics of bond
ruptures, thus, facilitating removal of multiple bond ruptures from analysis. However,
it is possible that the apparently single rupture transition (like shown in Figure 4.7)
corresponds to simultaneous rupture of more than one bond (Guo et al. 2008; Guo
et al. 2010a; Mayyas et al. 2010). Such events might occur if significant fraction of
force that was holding two bonds gets transferred onto the remaining bond that will
in turn rupture quickly. If rupture of the last bond occurs on the time scale shorter
than the rupture detection time, then the last bond rupture remains undetected.
According to Equation 4.3, if
P
tot
0.25, then among multiple bond ruptures,
the most prevalent will be ruptures, of two bonds (more than 90% of all multiple
bond ruptures). Therefore, in this subsection, the focus will be on two-bond rup-
tures. It might be expected that if two bonds are loaded simultaneously by external
force, then measured force of bond rupture will be higher than the force of a single
bond rupture. It has been shown that if a large number of bonds are loaded simulta-
neously and the force is distributed evenly between these bonds, then total rupture
force is proportional to the number of bonds (Seifert, 2000). However, if only two
bonds are loaded simultaneously, then the most probable rupture force will be less
than two times the rupture force of a single bond (Tees et al. 2001; Williams, 2003).
Nonetheless, if forces are distributed evenly between bonds, then in the histogram
of rupture forces, well-separated peaks are expected. However, if the load is not dis-
tributed evenly between the tethers the total rupture force decreases further and peaks
in the histogram of rupture forces might significantly overlap (Gu et al. 2008; Guo
et al. 2008). The unequal distribution of forces is expected in experiments that utilize
polymeric linkers to immobilize molecules because tethers are often polydisperse,
also tethers might attach at different heights along the tip and at different positions
on the sample surface. Even small difference in contour lengths of linkers might
result in substantial shift in the distribution of rupture forces toward lower values as
illustrated in Figure 4.9 (Gu et al. 2008; Guo et al. 2010a).
If distributions of rupture forces show a shoulder at the high force side of the
distribution, then multiple bond ruptures might be suspected. Therefore, to avoid
ambiguity in the data analysis, measurements should be repeated with lower grafting
density of molecules on the substrate. However, this approach might not significantly
change distribution of rupture forces if interactions are multivalent or if molecules
cluster on the surface during immobilization. In this case, probability to form multi-
ple bonds might be affected by changing grafting density of biomolecules on the
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