Biomedical Engineering Reference
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the loading rate, the contact time, the contact energy between ligand and receptor
as well as the energy transferred to the system (Evans, 2001). Recent results show
that the application of the ergodic hypothesis is not enough to correlate results com-
ing from traditional bulk experiments. This is especially true with those obtained
on single molecules when the loading rate dependence of measured rupture forces
was not taken into account. It is believed that the understanding of dynamic strength
of molecular bonds starts with the control of the loading rate, and thus most his-
torical papers published before 1999 did not adequately portray an accurate kinetic
characterization of bond rupture.
*
We are aware that despite significant progress in ergodic and chaos theories, using
the ergodic hypothesis to justify the use of the microcanonical ensemble in statistical
mechanics remains controversial till date. However, we continue using
†
the expres-
sion
ergodic hypothesis
that could be understood by saying that for microscopic
quantities, average, and fluctuations over time are the same as average and fluctu-
ations over space or in other words after a sufficiently long time a system explores
all of its microscopic states. This very important condition explains the capacity to
reveal energy landscapes for single molecules that are different (in their details) than
those obtained from bulk experiments (Figure 5.1). The counterpart is that exploring
single molecule properties requires recording a huge number of experimental rupture
events.
The energy landscape of a bond rupture explored by DFS characterizes the
force-driven pathway along the pulling direction until bond rupture. A classical
representation of energy landscape is made in a one-dimension plot representing
the energy of the system versus the reaction coordinates (Kramers, 1940). The
shape of the energy landscape is thus constituted by the height of energy barri-
ers (mountains in Figure 5.1) and the energy barrier width (flat distance) between
the valley and the summit of the mountain. In this chapter, the height of the
energy barrier is characterized by a
k
off
value, whereas the energy barrier width is
called
x
β
.
5.3 SINGLE AND MULTIPLE BONDS
Most of the early works in force spectroscopy attempted to simplify their exper-
imental models for considering interactions limited to single bonds (Florin et al.
1994; Moy et al. 1994) using linkers in their biochemical setup (Hinterdorfer et al.
1996) or by filtering and selecting experimental results (Dammer et al. 1996; Baum-
gartner et al. 2000a). Actually from a biological point of view, it is very difficult to
design such simple setups in protein-protein, protein-membrane, protein-DNA, or
other biological interactions (Mammen et al. 1998). Besides, several important bio-
logical reactions involve multiple interactions as evidenced by antibody molecules
*
To our knowledge, the first mention that the rupture force vary with rupture speed was indicated in
1996 in a modeling paper by Grubm uller et al. (Grubm uller et al. 1996) citing a relevant experimental
observation done by Gil Lee et al. in 1993 (Lee et al. 1994).
†
As we do with physical principles, they cannot be demonstrated but experimentally verified anytime.
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