conclusion to be drawn from a comparison of the GROMOS G53A5, OPLSÀAA
[101], and AMBER GAFF [102] force fields is that there are only quantitative
differences in the results regarding rupture forces, rebinding ability, and structural
quantities. Thus, the fact that one imposes quite strong nonequilibrium conditions
on the system does not give rise to additional problems in MD simulations (at least
for the force fields studied).
2.2 Stochastic Modeling of Reversible Bond Breakage
As discussed above, the reversible opening of adhesion bonds or the reversible
unfolding of biomolecules has been investigated in the recent past with increasing
intensity. The fact that both the opening and the rejoining events can be observed
in favorable examples opens the way to more detailed information regarding the
energy landscape of the system under study. The analysis of experimental DFS data
showing irreversible rupture events is usually based on the phenomenological Bell
model [103]. In this model, it is assumed that the application of an external force
F to the system results in a decrease in the activation energy for bond rupture, E A ,
by an amount (FÁx). Here, x denotes the distance from the free energy minimum of
the closed structure to the transition state. Thus, the escape rate simply reads as
k(F) ¼ k 0 e
βFx (β¼1/T with the Boltzmann constant set to unity). Assuming firstorder kinetics for the escape from the closed state, one can calculate the rupture
force distribution if the time-dependence of the force, F(t), is known.
The time-dependence of the force is determined by the protocol applied in the
actual application of DFS. One common way to perform the experiments or
simulations is the force-ramp mode, in which the applied force increases with a
constant velocity, F(t) ¼ k c ÁvÁt, where k c denotes the force constant of the pulling
device. The other protocol, called force-clamp mode, consists in the application of a
constant external force, F(t) ¼ F ext . In the force-ramp case, one finds the logarithmic dependence of the mean rupture force and v quoted above. The simple model
appears to work quite well for small pulling velocities but fails if one pulls fast. In
this situation, more detailed calculations of the rupture force distributions via the
computation of the mean first passage time in model free-energy landscapes give
more reliable results [104].
The impact of reversible rebinding on the rupture force distributions has been
investigated only recently [105, 106] and showed that one reaches equilibrium
between the closed and open structure for vanishing pulling velocity and gave the
results of the Bell model for fast pulling. We have analyzed the behavior of both the
rupture force and rejoin force distributions for the stochastic dynamics in a doublewell potential and have considered the dependence of the shape of the distributions
and the mean forces on system parameters such as the pulling device stiffness k c for
the force-ramp protocol [107] (cf. Fig. 23). It was shown that it should be possible
to extract the equilibrium constant defined by the kinetic rates for bond rupture and
rejoining from the equilibrium forces, i.e., the mean forces obtained in the limit of
Mechanical Properties of Single Molecules and Polymer Aggregates
31
[101], and AMBER GAFF [102] force fields is that there are only quantitative
differences in the results regarding rupture forces, rebinding ability, and structural
quantities. Thus, the fact that one imposes quite strong nonequilibrium conditions
on the system does not give rise to additional problems in MD simulations (at least
for the force fields studied).
2.2 Stochastic Modeling of Reversible Bond Breakage
As discussed above, the reversible opening of adhesion bonds or the reversible
unfolding of biomolecules has been investigated in the recent past with increasing
intensity. The fact that both the opening and the rejoining events can be observed
in favorable examples opens the way to more detailed information regarding the
energy landscape of the system under study. The analysis of experimental DFS data
showing irreversible rupture events is usually based on the phenomenological Bell
model [103]. In this model, it is assumed that the application of an external force
F to the system results in a decrease in the activation energy for bond rupture, E A ,
by an amount (FÁx). Here, x denotes the distance from the free energy minimum of
the closed structure to the transition state. Thus, the escape rate simply reads as
k(F) ¼ k 0 e
βFx (β¼1/T with the Boltzmann constant set to unity). Assuming firstorder kinetics for the escape from the closed state, one can calculate the rupture
force distribution if the time-dependence of the force, F(t), is known.
The time-dependence of the force is determined by the protocol applied in the
actual application of DFS. One common way to perform the experiments or
simulations is the force-ramp mode, in which the applied force increases with a
constant velocity, F(t) ¼ k c ÁvÁt, where k c denotes the force constant of the pulling
device. The other protocol, called force-clamp mode, consists in the application of a
constant external force, F(t) ¼ F ext . In the force-ramp case, one finds the logarithmic dependence of the mean rupture force and v quoted above. The simple model
appears to work quite well for small pulling velocities but fails if one pulls fast. In
this situation, more detailed calculations of the rupture force distributions via the
computation of the mean first passage time in model free-energy landscapes give
more reliable results [104].
The impact of reversible rebinding on the rupture force distributions has been
investigated only recently [105, 106] and showed that one reaches equilibrium
between the closed and open structure for vanishing pulling velocity and gave the
results of the Bell model for fast pulling. We have analyzed the behavior of both the
rupture force and rejoin force distributions for the stochastic dynamics in a doublewell potential and have considered the dependence of the shape of the distributions
and the mean forces on system parameters such as the pulling device stiffness k c for
the force-ramp protocol [107] (cf. Fig. 23). It was shown that it should be possible
to extract the equilibrium constant defined by the kinetic rates for bond rupture and
rejoining from the equilibrium forces, i.e., the mean forces obtained in the limit of
Mechanical Properties of Single Molecules and Polymer Aggregates
31