Biomedical Engineering Reference
In-Depth Information
practice is not new and has several analogous counterparts in a wide variety of sys-
tems. What one often finds when considering the fundamental description of physical
systems is that the same general dynamic model holds across a wide variety of pro-
cesses. This is the case in forced bond rupture, where the description simplifies to a
system in contact with its surroundings while an external forcing shifts the equilib-
rium from an initial state to some final state. The aim here is to formulate models
that allow us to learn something useful about the system under study, preferably
extrapolated to the equilibrium, unperturbed case.
The seminal works of Evan Evans (Evans & Ritchie, 1997; Evans, 2001; Evans
and Williams, 2001) brought the theory and technique of DFS to an audience of
modern scientists in the biophysical and materials sciences who were eager to make
use of the burgeoning advancement in nanoscale technologies to study fundamental
processes in physical chemistry, ultimately with single-molecule resolution. But the
history of the theory of this stochastic process reaches much further back into the
works of Tobolsky and Eyring (1943), Zhurkov (1965), Bell (1978) and many others
who investigated the effects of force on the lifetime of materials under stress. Since
then, a number of modifications have been proposed that aim to improve upon the
basic theory of forced escape over a barrier. While it is not possible to consider
every approach here, an attempt is made to present a general analysis of the typical
scenarios encountered in the laboratory.
3.1.1 U
NIMOLECULAR VERSUS
B
IMOLECULAR
S
YSTEM
The molecular systems that are commonly studied by single-molecule manipula-
tion techniques fall under two main categories: (1) Unimolecular systems, character-
ized by force-induced conformational changes, which disrupt intramolecular bonds;
(2) Bimolecular systems, which describe the intermolecular binding between two
separate molecules (Figure 3.1). In bulk, these two systems are governed by the fol-
lowing equilibrium constants.
=
[
A
]
A
B
,
K
eq
unimolecular
[
B
]
=
[
AB
]
+
,
AB
A
B
K
eq
bimolecular
[
A
][
B
]
where [
i
] is the concentration of species
i
. In the case of the unimolecular system,
A
and
B
define
different conformations of the same molecule
. The probability of finding
unimolecular systems in one conformation or another is governed by the equilibrium
free energy between states within the energy landscape of the individual molecule.
Therefore, equilibria between the states of unimolecular systems are independent of
the concentration of molecules in the system. Examples include the folded/unfolded
conformations of proteins and ribonucleic acid (RNA) or the isomers of a moiety.
On the contrary, bimolecular equilibria are controlled by the concentration of both
molecules involved in the reaction. This can be inferred from the units in the equilib-
rium constant of inverse concentration (nominally M
−
1
). For example, if molecule
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