Stochastic Modeling of Reversible Bond Breakage

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) = where k denotes the force constant of the pulling device. The other protocol, called force-clamp mode, crmsists in the application of a constant external force, F(t) = Fext- 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 simation, 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]. 

If the reversible dynamics of bond rupture is considered in the force clamp mode, one can exploit an analogy to the treatment of single molecule fluorescence to treat the statistical properties of the transition events [108, 109]. If one considers two states, A (closed) and B (open) with rates k, = k(A — B) and = (B A), the equilibrium constant is given by = A b/ a- Due to the strong exponential dependence of the kinetic rates on the external force, in the Bell model given by a( ) = and k F) = one can vary Kover a broad range. This 

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