3 the threaded loop. Thus this effect results in a faster tightening of the threaded rather than the knotting loop, facilitating even more the untightening of the slipknot. The above argument should apply to slipknots in biomolecules because they are characterized by a per- sistence length that in principle is simply related to their elasticity [23]. For DNA this effect is described by worm- like-chain models (WLC) [24] and it has been confirmed experimentally. Although WLC models are too simple to describe the protein general behavior, they are use- ful in some limited applications. Thus at first sight one might expect that slipknots in proteins should smoothly untie upon stretching. Proteins, however, are much more complicated than DNA or uniformly elastic polymers. The presence of stabilizing native tertiary contacts leads to a jumping character during stretching [12]. In addi- tion their bending energy is not uniform along the chain due to the heterogeneity of the amino-acid sequence. As a consequence it turns out that the intuition obtained through the above analysis of polymers or WLC models is misleading. 2 3 4 5 F GLYPH<LBracket1> Ε GLYPH<Slash1> GLYPH<Angstrom> GLYPH<RBracket1> 0.5 1 Prob GLYPH<LParen1> pathway I GLYPH<RParen1> FIG. 4: Dependence on the applied stretching force of the probability of choosing pathway I rather than II (see Fig. 3). This varying probability leads to the complicated dependence of the total unfolding time on the stretching force observed in Fig. 1. Our analysis of the evolution of the endpoints k$_{1}$, k$_{2}$, k$_{3}$ (Fig. 3, bottom) reveals that for various stretching forces unfolding proceeds along two distinct pathways (Fig. 3, top). In pathway I the slipknot smoothly unties, which is observed for relatively weak forces. At intermediate forces pathway II starts to dominate and the knotting loop can shrink tightly before the threaded one vanishes. In this regime the protein gets temporarily jammed (Fig. 3, right), leading to much longer unfolding times (catch pathway). The probability of choosing pathway I at dif- ferent forces is shown in Fig. 4. This pathway competi- tion explains the nontrivial total unfolding time depen- dence observed in Fig. 1. The two different pathways I and II arise from com- pletely different unfolding mechanisms. Pathway I starts and continues mostly from the C-terminal side, along 16 α , 15 β , 14 α , 13 β , 12(helices bundle), 11 α (here the number denotes a consecutive secondary structure as counted from N-terminal, and α or β specifies whether this is a helix or a β -sheet; for more details about the structure of 1e2i see the PDB). This is followed by unfold- ing of helices 11 α , 10 α that allows breaking of the con- tacts inside the β -sheet created by the N-terminal, with unfolding proceeding also from the N-terminal. Pathway II also starts from the C-terminal but rapidly (as soon as helix 15 is unfolded) switches to the N-terminal. In this case, differently from pathway I, the β -sheet from the N-terminal unfolds even before 13 β . These scenarios indicate that the pathway I should be dominant at weak forces since they are not sufficient to break the β -sheet during first steps of unfolding. The jammed pathway is typical only if stretching forces are sufficiently strong for unfolding to proceed from the two terminals of the pro- tein. A similar phenomenon was firstly proposed in ref. [25] and referred to as catch-bonds. Experimental evidence suggesting this mechanism was first observed for adhe- sion complexes [26, 27]. Using AFM, at large forces the ligand-receptor pair becomes entangled and therefore ex- pands the unfolding time. A theoretical description of this mechanism was given in ref. [28, 29, 30]. The kinetic data can also be used to determine the as- sociated free energy landscape (FEL) [7]. In an initial simplification we associate the barriers along the stretch- ing coordinate as the the kinetic bottlenecks during the mechanical unfolding event. Generalizing Bell’s model, a recent description of two-state mechanical unfolding in the presence of a single transition barrier has been devel- oped in [19], with the rate equation τ ( F ) = τ$_{0}$ ( 1 − νF x † Δ G ) 1 − 1 $^{/ν}$e − Δ G k B T ( 1 − (1 − νF x $^{†}$/ Δ G ) 1 /ν ) , (1) where ν encodes the shape of the barrier. Here x † denotes the distance between the barrier and the unfolded basin (in a first approximation it can be regarded as F indepen- dent) and lies on the reaction coordinate along the AFM pulling direction. It can be experimentally determined by measuring how the stretching force modulates the un- folding times τ . The height of the barrier is denoted by Δ G . Fig. 1 (unfolding times are given by solid red line) shows that this single barrier theory is not sufficient for the full range of forces. As described before, in the higher force regime, additional basins have to be included in the energy landscape. Models with several metastable basins have been called multi-state FEL models [31]. Evidence supporting the need of multi-states FEL was confirmed by AFM experiments in different systems [32, 33]. To construct a multi-state FEL that incorporates two unfolding pathways I and II we use a linear combina- tion of eq. (1)-like expressions with different shapes and barrier heights. Each one of them essentially accounts for the distinct barrier along a relevant unfolding route. Fitting the stretching data to eq. (1) with a cusp-like