2 refined analysis performed in ref. [19] revealed that this dependence is more complicated but still monotonically decreasing. The unfolding times for 1e2i measured in our simula- tions are shown as the red curve in Fig. 1. In contrast to the above expectations, increasing the force in the range 3-3 . 5 ϵ/ ˚ A surprisingly results in a larger stability of the protein. ϵ is the typical effective energy of tertiary na- tive contacts that is consistent with the value ϵ/ ˚ A ≃ 71 pN derived in [15]. A solution for this paradox is accom- plished by realizing that unfolding is dominated by two distinct, alternative routes that are dominant at different force regimes. A routing switch occurs when threshold is crossed between weak and intermediate forces. At higher forces, mechanical unfolding is dominated by a route that involves a jammed slipknot. This jamming gives rise to the unexpected dependence of unfolding time on applied force. Characterizing this mechanism is the central goal of this Letter. FIG. 2: A slipknot (left) consists of a threaded loop ( k 1 − k 2 , in red) which is partialy threaded through a knotting loop ( k 2 $_{−}$k 3 , in blue). An example of a protein configuration with a tightened slipknot is shown in the right panel. To describe the evolution of a slipknot quantitatively requires a refined description. A slipknot is character- ized by the three points shown in Fig. 2. The first point k$_{1}$ is determined by eliminating amino acids con- secutively from one terminus until the knot configura- tion is reached (which can be detected e.g. by applying the KMT algorithm [20]). The two additional points, k$_{2}$ and k$_{3}$ , correspond to the ends of this knot. In the native state the protein 1e2i contains a slipknot with k$_{1}$ = 10 , k$_{2}$ = 128 , k$_{3}$ = 298. These three points divide the slipknot into two loops, which are called the knotting loop and the threaded loop . The former one is the loop of the trefoil knot and the latter one is threaded through the knotting loop. Unfolding of the slipknot upon stretch- ing depends on the relative shrinking velocity of these two loops (see Fig. 3). When the threaded loop shrinks faster than the knotting loop, the slipknot unties. In the opposite case the slipknot gets (temporarily) tightened or jammed, resulting in a metastable state associated to a local minimum in the protein’s FEL. Upon further stretching, this configuration eventually also unties. The evolution of both loops of the slipknot is encoded in the time dependence of the points k$_{1}$, k$_{2}$, k$_{3}$ , see Fig. 3. pathway I pathway II catch−bonds slip−bonds FIG. 3: The behavior of the slipk not during stretching (top) is determined by the relative beh avior of its two loops, en- coded in the time dependence of k 1 , k 2 and k 3 (bottom). If the threaded loop shrinks faster than t he knotting loop, k 1 merges with k 2 (bottom left) and the slip knot untightens (pathway I, top left). If the knotting loop shrin ks faster, k 2 approaches k 3 (bottom right, ≃ 14000 τ ) and t he slipknot gets temporarily tightened (pathway II, top right). This is a metastable state which can eventually untie further stretching , with k 1 finally merging with k 2 (bottom right, ≃ 19000 τ ). Kinetic stud- ies were performed slightly above folding temperature using overdamped Langevin dynamics w ith typical folding times of 10000 τ . Before discussing the stretch ing of 1e2i, we explain why a slipknot formed by a uniform ly elastic polymer should smoothly unfold under stretchin g. To simplify the discus- sion we approximate the thread ed and knotting loops by circles of size R$_{t}$ and R$_{k}$ . The se two loops shrink during stretching and, when the threa ded one eventually van- ishes, the slipknot gets untied. I f both loops have similar sizes, the slipknot is very unst able and unties immedi- ately. When the threaded loop is much larger than the knotting one, R$_{t}$ >> R$_{k}$ , unt ightening can be explained as follows. The elastic energy associated to local bend- ing is proportional to the squar e of the curvature. If the loop is approximated by a circle of radius R , then its local curvature is constant and equa ls R − $^{1}$. The total elastic energy is ∮ dsR − 2 ∼ R − 1 [2 1 ]. From the assumption R$_{t}$ >> R$_{k}$ we conclude that u pon stretching it is ener- getically favorable to decrease R$_{t}$ rather than R$_{k}$ . This happens until both radii becom e equal and then, just as above, the slipknot gets very un stable and untightens. In this discussion we have not yet taken into account that when a slipknot is stretched so me parts of a chain slide along each other. This effect co uld be incorporated by in- cluding the friction generated b y the sliding [22]. But in the slipknot the sliding region associated with the knot- ting loop is much longer than the region associated to