content_image/398411.jpg content_image/398414.jpg
<img src='content_image/398411.jpg'>

ν = 1 / 2 approximation (another possibility ν = 2 / 3 for the cubic potential in general leads to similar results [19]) determines accurately the location and the height of the potential barriers. Pathway II involves two barriers: first until the moment of creation of the intermediate which is followed the untieing event. They are characterized by ( x$_{1}$, Δ G$_{1}$ ) and ( x$_{2}$, Δ G$_{2}$ ) arising respectively from the lower and upper fits in Fig. 5 (left). The superposition of these two fits gives the overall mean unfolding time for pathway II (dotted-dashed curve in green in Fig. 1). For the ordinary slipknot unfolding (pathway I), the results x$_{I}$ and G$_{I}$ arise from the dashed blue curve in Fig. 1. This analysis leads to the results 

<img src='content_image/398414.jpg'>

We conclude that the free energy landscape consists of two “valleys”. The force-dependent probability of choos- ing one of the valleys during stretching depends on the details of the protein structure. It is determined from our simulations as shown in Fig. 4. Using these probability values and the parameters above for x and Δ G , we can accurately represent the simulation data using a linear combination of equations of the form (1). This agreement supports our analytical analysis and generalizes eq. (1) for the full of range forces. In addition it demonstrates that structure-based models sufficiently capture the ma- jor geometrical properties of a slipknotted protein. A schematic representation of the free energy landscape for pathway II is shown in Fig. 5 (right). 

Summarizing, we have analyzed the process of tighten- ing of the slipknot in protein 1e2i and determined the cor- responding free energy landscape. Its main feature is the presence of a metastable configuration with a tightened slipknot, which is observed for sufficiently large pulling forces. This phenomenon does not exist for uniformly elastic polymers. In this Letter we concentrated on pro- tein 1e2i but similar behavior has also been observed for 

other proteins with slipknots, e.g. 1p6x. Our results provide testable predictions that can now be verified by AFM stretching experiments. 

We appreciate useful comments of O. Dudko. The work of J.S. was supported by the Center for Theo- retical Biological Physics sponsored by the NSF (Grant PHY-0822283) with additional support from NSF-MCB- 0543906. P.S. acknowledges the support of Hum- boldt Fellowship, DOE grant DE-FG03-92ER40701FG- 02, Marie-Curie IOF Fellowship, and Foundation for Pol- ish Science. 

[1] M. L. Mansfield, Nature Struct. Biol. 1 213 (1994). 

[2] P. Virnau, L. A. Mirny and M. Kardar, PLOS Comp. Biol. 2 1074 (2006). 

[3] T. O. Yeates, Todd S. Norcross and N. P. King, Curr. Opinion in Chem. Biol 11 596 (2007). 

[4] W. R. Taylor, Comp. Biol. and Chem. 31 151 (2007). 

[5] J. I. SuGLYPH<suppress>lkowska, P. SuGLYPH<suppress>lkowski and J. N. Onuchic, PNAS 106 3119 (2009). 

[6] D. Bolinger, J. I. SuGLYPH<suppress>lkowska, Hsiao-Ping Hsu, L. A. Mirny, M. Kardar, J. N. Onuchic and P. Virnau, sub- mitted . 

[7] P.E. Leopold, M. Montal and J.N. Onuchic, PNAS 89 8721 (1992). 

[8] J. N. Onuchic and P. G. Wolynes, Curr. Opin. Struct. Biol. 14 70-75 (2004). 

[9] M. Rief, M. Gautel, F. Oesterhelt, J. M. Fernandez and H. E. Gaub, Science 276 1109 (1997). 

[10] M. T. Alam, T. Yamada, U. Carlsson and A. Ikai, FEBS Lett. 519 35 (2002). 

[11] T. Bornschloegl, D. M. Anstrom, E. Mey, J. Dzubiella, M. T. Rief and K. Forest, Biophys. J. 96 1508 (2009). 

[12] J. I. SuGLYPH<suppress>lkowska, P. SuGLYPH<suppress>lkowski, P. Szymczak and M. Cieplak, Phys. Rev. Lett. 100 058106 (2008). 

[13] J. I. SuGLYPH<suppress>lkowska, P. SuGLYPH<suppress>lkowski, P. Szymczak and M. Cieplak, PNAS 105 19714 (2008). 

[14] J. Dzubiella, Biophys. J. 96 831 (2009). 

[15] J. I. SuGLYPH<suppress>lkowska and M. Cieplak, J. Phys. Cond. Mat. 19 283201 (2007). 

[16] N. D. Socci, J. N. Onuchic and P. G. Wolynes Proc. Natl. Acad. Sci. USA 96 2031-2035 (1999). 

[17] J. Vogt, R. Perozzo, A. Pautsch, A. Prota, P. Schelling, B. Pilger, G. Folkers, L. Scapozza and G. E. Schulz, Pro- teins: Struct.,Funct., Genet. 41 545 (2000). 

[18] G. I. Bell, Science 200 618 (1978). 

[19] O. K. Dudko, G. Hummer and A. Szabo, Phys. Rev. Lett. 96 108101 (2006). 

[20] K. Koniaris and M. Muthukumar, Phys. Rev. Lett. 66 2211 (1991). 

[21] L. D. Landau and E. M. Lifshitz Theory of Elasticiy 3rd edition 

[22] B. Audoly, N. Clauvelin and S. Neukirch, Phys. Rev. Lett. 99 , 164301 (2007), R. Gallotti and O. Pierre-Louis, Phys. Rev. E 75 031801. 

[23] C. Bustamante, J. F. Marko, E. D. Siggia and S. Smith, Science 265 1599 (1994). 

[24] C. Bouchiat, M.D. Wang, J.-F. Allemand, T. Strick, S.M. 

