constant of the cantilever dominates the force ramp in the experiment. Polymer
linkers display a nonlinear compliance that requires more sophisticated treatment
to correctly describe the elastic properties of the molecular chain. Figure 39 shows
that no correlation between contour length and average forces was found experimentally. This is attributed to the considerably small length of the decylene
(C 10 H 20 ) spacers. Regardless of this finding, only molecules in a contour length
interval of 10–30 nm were selected for further analysis to avoid unnecessary
histogram broadening.
Comparison with Theory
The profound understanding of breakage and rebinding of hydrogen bridges under
external load is a major goal in understanding the function of complex biological
structures. Calix[4]arene catenanes are an ideally suited model system for studying
reversible binding, experimentally with dynamic force spectroscopy (DFS) and
theoretically by means of MD simulations (described in detail in Sect. 3.1).
Theories based on diffusive barrier crossing with a fluctuating cantilever assume
either a one-well potential, when no rebinding is taken into account, or a two-well
potential when rebinding is included [107–109, 148, 149]. Here, a similar approach
was used to evaluate the rates of barrier crossing and location of barriers using
stochastic models to capture the force spectra obtained experimentally. In order
to extract relevant parameters from the energy landscape of the calixarene dimer,
it is mandatory to first estimate the number of dominant states and barriers. The
following scrutiny is based on data analysis recently published by Janke et al. [95].
First, it is instructive to analyze the increase in length ΔL of the molecule
upon rupture, extracted from fitting a WLC function to the data as done before
(vide supra) and compare this result, at least qualitatively, with MD simulations
(Fig. 40a–c). Figure 40c shows a single pulling trajectory obtained from MD
simulations displaying two distinct length jumps. The first sudden length increase
can be attributed to H-bond breakage because it exceeds the typical reach of
H-bonds (0.3 nm), and the second smaller sudden jump is assigned to the opening
of an intermediate conformation. A more comprehensive study has been published
by Schlesier et al. [98].
Both the experimentally obtained histogram (Fig. 40a) and the histogram
compiling data from MD simulations (Fig. 40b) display the same bimodal distribution in ΔL centered at 1 and 2 nm, indicative of a intermediate state. The
breakage of the H-bonds does not follow a specific sequence nor does it display
the signature of cooperativity. It was found that the intermediate state was
reasonably stable (>10 ns) in prolonged simulations at elevated temperature
(460 K) under constant force. Possible conformations of the strained dimers
captured by MD simulations at various times with the intermediate state at 1 ns
are shown in Fig. 40d. Assignment of an intermediate state is often difficult
and usually interfered indirectly from nonlinear force spectra [150]. A nonlinear
relationship between hF rup i and ln(dF/dt) does not necessarily imply the presence
Mechanical Properties of Single Molecules and Polymer Aggregates
49
linkers display a nonlinear compliance that requires more sophisticated treatment
to correctly describe the elastic properties of the molecular chain. Figure 39 shows
that no correlation between contour length and average forces was found experimentally. This is attributed to the considerably small length of the decylene
(C 10 H 20 ) spacers. Regardless of this finding, only molecules in a contour length
interval of 10–30 nm were selected for further analysis to avoid unnecessary
histogram broadening.
Comparison with Theory
The profound understanding of breakage and rebinding of hydrogen bridges under
external load is a major goal in understanding the function of complex biological
structures. Calix[4]arene catenanes are an ideally suited model system for studying
reversible binding, experimentally with dynamic force spectroscopy (DFS) and
theoretically by means of MD simulations (described in detail in Sect. 3.1).
Theories based on diffusive barrier crossing with a fluctuating cantilever assume
either a one-well potential, when no rebinding is taken into account, or a two-well
potential when rebinding is included [107–109, 148, 149]. Here, a similar approach
was used to evaluate the rates of barrier crossing and location of barriers using
stochastic models to capture the force spectra obtained experimentally. In order
to extract relevant parameters from the energy landscape of the calixarene dimer,
it is mandatory to first estimate the number of dominant states and barriers. The
following scrutiny is based on data analysis recently published by Janke et al. [95].
First, it is instructive to analyze the increase in length ΔL of the molecule
upon rupture, extracted from fitting a WLC function to the data as done before
(vide supra) and compare this result, at least qualitatively, with MD simulations
(Fig. 40a–c). Figure 40c shows a single pulling trajectory obtained from MD
simulations displaying two distinct length jumps. The first sudden length increase
can be attributed to H-bond breakage because it exceeds the typical reach of
H-bonds (0.3 nm), and the second smaller sudden jump is assigned to the opening
of an intermediate conformation. A more comprehensive study has been published
by Schlesier et al. [98].
Both the experimentally obtained histogram (Fig. 40a) and the histogram
compiling data from MD simulations (Fig. 40b) display the same bimodal distribution in ΔL centered at 1 and 2 nm, indicative of a intermediate state. The
breakage of the H-bonds does not follow a specific sequence nor does it display
the signature of cooperativity. It was found that the intermediate state was
reasonably stable (>10 ns) in prolonged simulations at elevated temperature
(460 K) under constant force. Possible conformations of the strained dimers
captured by MD simulations at various times with the intermediate state at 1 ns
are shown in Fig. 40d. Assignment of an intermediate state is often difficult
and usually interfered indirectly from nonlinear force spectra [150]. A nonlinear
relationship between hF rup i and ln(dF/dt) does not necessarily imply the presence
Mechanical Properties of Single Molecules and Polymer Aggregates
49