APS/Gerhard Hummer and William Eaton

Figure 1: Transition path projected on schematic two-dimensional free-energy surface. The surface is indicated by contour lines and coloring, with the red and yellow areas bounded by blue contours corresponding to low (favorable) free energies. The molecular extension $x$ in the horizontal direction and a coordinate $y$, not observed directly in experiment, together separate the folded (left) and unfolded basins (right), shown with representative structures (orange) of a DNA hairpin (folded: left; folding transition state: middle; coil: right). The molecule spends the vast majority of time in one or the other basin, with very rare but very rapid transitions between them. The transition path is the (yellow thick) segment of the unfolding trajectory (continuous white), directly connecting the folded ($x) and unfolded states ($x>xU$), whose boundaries are indicated by dashed vertical lines. Thin white dashed lines indicate trajectories failing to cross the barrier. The bottom panel shows the corresponding one-dimensional free-energy surface, obtained by integrating out also $y$, to define the relevant quantities entering the approximate expression Eq. ($2$) used by Neupane et al.[1] for the mean transition path time [4, 8].