Extracting inertial features from stochastic barrier re-crossing trajectories: Effects of temporal resolution limits

The folding of biomolecules is typically described as a stochastic search for structure over the conformational energy landscape. While diffusive dynamics have been very successful at describing folding reactions, the estimation of inertial contributions to these dynamics has received much less attention. Recent theoretical work has shown that the analysis of "loops" in a trajectory originating from the barrier top can be used to calculate the transition state theory reaction rate. As the latter relies on inertial effects, it implicitly offers a method for extracting the system's effective mass from the loop dynamics. Here, we apply this theory to experimental data to quantify the effects of inertia. Looking first at the dynamics of a micron-scale bead in a bistable potential as a model system, we find that the mass implied by the theory is much greater than the true mass of the bead. Inertial Langevin simulations reveal that the theory only yields correct mass values when the sampling rate is high compared to the characteristic timescale of the system. Applying the theory to the folding of a DNA hairpin held under tension reinforces this lesson, finding an unphysically high mass. These results establish the temporal resolution limits needed to quantify inertial effects accurately from folding trajectories.