Fig. 1.

(A–C) Schematic illustration of three multidimensional free energy landscapes $U_0\left(x,\mathbf{r}\right)$ at zero force, plotted in terms of end-to-end extension x versus the other conformational degrees of freedom $\mathbf{r}$. N and U could represent the native and unfolded basins. The white dotted lines are local minima of $U_0\left(x,\mathbf{r}\right)$ with respect to $\mathbf{r}$ at a given x. The landscape in A is weakly multidimensional with respect to x, according to the conditions described in the main text, whereas B and C are strongly multidimensional. (D–F) The $\left[\log k_{\text{u}}\left(f\right),f\right]$ plots for the energy landscapes given in A–C obtained from Brownian dynamics simulations. The WMD landscape (left) produces downward curvature. The landscape suggesting parallel pathways (B) produces upward curvature (E), where the solid line is the least squares fit to a double exponential model. The SMD in C produces even stronger upward curvature, giving rise to catch bond behavior with $k_{\text{u}}\left(f\right)$ decreasing at low forces and subsequently increasing at larger f values.