Force probe simulations of a reversibly rebinding system: Impact of pulling device stiffness

We present a detailed study of the parameter dependence of force probe molecular dynamics (FPMD) simulations. Using a well studied calix[4]arene catenane dimer as a model system, we systematically vary the pulling velocity and the stiffness of the applied external potential. This allows us to investigate how the results of pulling simulations operating in the constant velocity mode (force-ramp mode) depend on the details of the simulation setup. The system studied has the further advantage of showing reversible rebinding meaning that we can monitor the opening and the rebinding transition. Many models designed to extract kinetic information from rupture force distributions work in the limit of soft springs and all quantities are found to depend solely on the so-called loading rate, the product of spring stiffness and pulling velocity. This approximation is known to break down when stiff springs are used, a situation often encountered in molecular simulations. We find that while some quantities only depend on the loading rate, others show an explicit dependence on the spring constant used in the FPMD simulation. In particular, the force versus extension curves show an almost stiffness independent rupture force but the force jump after the rupture transition does depend roughly linearly on the value of the stiffness. The kinetic rates determined from the rupture force distributions show a dependence on the stiffness that can be understood in terms of the corresponding dependence of the characteristic forces alone. These dependencies can be understood qualitatively in terms of a harmonic model for the molecular free energy landscape. It appears that the pulling velocities employed are so large that the crossover from activated dynamics to diffusive dynamics takes place on the time scale of our simulations. We determine the effective distance of the free energy minima of the closed and the open configurations of the system from the barrier via an analysis of the hydrogen-bond network with results in accord with earlier simulations. We find that the system is quite brittle in the force regime monitored in the sense that the barrier is located near to the closed state.