The PMF profiles of proteins GB1 and gpW along the coordinate of extension obtained from umbrella sampling. Typical histograms of conformations along the reaction coordinate of GB1 and gpW are shown in panels (a) and (b). Just a few umbrella sampling windows are selected to show a sufficient sampling along the coordinate. Totally 95 umbrella sampling simulations were performed for GB1 and 60 for gpW. (c) PMF of GB1 protein at zero force (red curve) shows a kink at extension of ∼ 3.18 nm, where the slope changes from ∼ 292 pN to ∼ 74 pN. At stretching forces of 30 pN, 60 pN, and 90 pN, PMF calculated from Eq. (4) is shown as blue, yellow, and gray curves, respectively. (d) PMF of gpW at zero force (red curve) shows a smooth curve which increases approximately linearly with extension. The slope of the curve is ∼ 29 pN. Blue, yellow, and gray curves show PMF at stretching forces of 10 pN, 20 pN, and 30 pN, respectively. Insets of both figures show typical conformations of GB1 and gpW with certain extension from the simulation.