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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 forother 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. 1213 (1994).
[2] P. Virnau, L. A. Mirny and M. Kardar, PLOS Comp.
Biol.21074 (2006).
[3] T. O. Yeates, Todd S. Norcross and N. P. King, Curr.
Opinion in Chem. Biol 11596 (2007).
[4] W. R. Taylor, Comp. Biol. and Chem. 31151 (2007).
[5] J. I. Su/suppress lkowska, P. Su/suppress lkowski and J. N. Onuchic, PNAS
1063119 (2009).
[6] D. Bolinger, J. I. Su/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, PNAS89
8721 (1992).
[8] J. N. Onuchic and P. G. Wolynes, Curr. Opin. Struct.
Biol.1470-75 (2004).
[9] M. Rief, M. Gautel, F. Oesterhelt, J. M. Fernandez and
H. E. Gaub, Science2761109 (1997).
[10] M. T. Alam, T. Yamada, U. Carlsson and A. Ikai, FEBS
Lett.51935 (2002).
[11] T. Bornschloegl, D. M. Anstrom, E. Mey, J. Dzubiella,
M. T. Rief and K. Forest, Biophys. J. 961508 (2009).
[12] J. I. Su/suppress lkowska, P. Su/suppress lkowski, P. Szymczak and M.
Cieplak, Phys. Rev. Lett. 100058106 (2008).
[13] J. I. Su/suppress lkowska, P. Su/suppress lkowski, P. Szymczak and M.
Cieplak, PNAS10519714 (2008).
[14] J. Dzubiella, Biophys. J. 96831 (2009).
[15] J. I. Su/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 962031-2035 (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. 41545 (2000).
[18] G. I. Bell, Science200618 (1978).
[19] O. K. Dudko, G. Hummer and A. Szabo, Phys. Rev. Lett.
96108101 (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. E75031801.
[23] C. Bustamante, J. F. Marko, E. D. Siggia and S. Smith,
Science2651599 (1994).
[24] C. Bouchiat, M.D. Wang, J.-F. Allemand, T. Strick, S.M.5
Blockand and V. Croquette, Biophys. J. 76409 (1999).
[25] M. Dembo, D.C. Torney, K. Saxman and D. Hammer.
Proc. R. Soc. Lond. B. Biol. Sci. 234 (1988).
[26] B. T. Marshall, M. Long, J. W. Piper, T. Yago, R. P.
McEver and Ch. Zhu, Science319630 (2003).
[27] W. Thomas, M. Forero, O. Yakovenko, L. Nilsson, P.
Vicini, E. Sokurenko and V. Vogel, Biophys. J. 90753
(2006).
[28] D. Bartolo, I. Derenyi and A. Ajdari, Phys. Rev. E. 65
051910 (2002).
[29] E. Evans, A. Leung, V. Heinrich and Ch. Zhu, PNAS10111281 (2004).
[30] V. Barsegov and D. Thirumalai, PNAS102, 1835 (2005).
[31] I. Schwaiger, M. Schleicher, A. A Noegel and M. Rief,
EMBO646 (2005)
[32] P. M. Williams, S. B. Fowler, R. B. Best, J. L. Toca-
Herrera, K. A. Scott, A. Stward and J. Clarke Nature
422446 (2003).
[33] C. Cecconi, E. A. Shank, C. Bustamante and S. Mar-
qusee,Science232057 (2005).
Minimal In
ation
Luis Alvarez-Gaum ea, C esar G omezb,a, Raul Jimenezc,a
aTheory Group, Physics Department, CERN, CH-1211, Geneva 23, Switzerland.
bInstituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, E-28049 Madrid, Spain.
cICREA & Institute of Sciences of the Cosmos (ICC), University of Barcelona, 08028 Barcelona, Spain.
Abstract
Using the universal Xsupereld that measures in the UV the violation of conformal invariance we build up a model
of multield in
ation. The underlying dynamics is the one controlling the natural
ow of this eld in the IR to the
Goldstino supereld once SUSY is broken. We show that
at directions satisfying the slow roll conditions exist only if
R-symmetry is broken. Naturalness of our model leads to scales of SUSY breaking of the order of 101113Gev, a nearly
scale-invariant spectrum of the initial perturbations and negligible gravitational waves. We obtain that the in
aton eld

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 forother 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. 1213 (1994).

[2] P. Virnau, L. A. Mirny and M. Kardar, PLOS Comp.

Biol.21074 (2006).

[3] T. O. Yeates, Todd S. Norcross and N. P. King, Curr.

Opinion in Chem. Biol 11596 (2007).

[4] W. R. Taylor, Comp. Biol. and Chem. 31151 (2007).

[5] J. I. Su/suppress lkowska, P. Su/suppress lkowski and J. N. Onuchic, PNAS

1063119 (2009).

[6] D. Bolinger, J. I. Su/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, PNAS89

8721 (1992).

[8] J. N. Onuchic and P. G. Wolynes, Curr. Opin. Struct.

Biol.1470-75 (2004).

[9] M. Rief, M. Gautel, F. Oesterhelt, J. M. Fernandez and

H. E. Gaub, Science2761109 (1997).

[10] M. T. Alam, T. Yamada, U. Carlsson and A. Ikai, FEBS

Lett.51935 (2002).

[11] T. Bornschloegl, D. M. Anstrom, E. Mey, J. Dzubiella,

M. T. Rief and K. Forest, Biophys. J. 961508 (2009).

[12] J. I. Su/suppress lkowska, P. Su/suppress lkowski, P. Szymczak and M.

Cieplak, Phys. Rev. Lett. 100058106 (2008).

[13] J. I. Su/suppress lkowska, P. Su/suppress lkowski, P. Szymczak and M.

Cieplak, PNAS10519714 (2008).

[14] J. Dzubiella, Biophys. J. 96831 (2009).

[15] J. I. Su/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 962031-2035 (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. 41545 (2000).

[18] G. I. Bell, Science200618 (1978).

[19] O. K. Dudko, G. Hummer and A. Szabo, Phys. Rev. Lett.

96108101 (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. E75031801.

[23] C. Bustamante, J. F. Marko, E. D. Siggia and S. Smith,

Science2651599 (1994).

[24] C. Bouchiat, M.D. Wang, J.-F. Allemand, T. Strick, S.M.5

Blockand and V. Croquette, Biophys. J. 76409 (1999).

[25] M. Dembo, D.C. Torney, K. Saxman and D. Hammer.

Proc. R. Soc. Lond. B. Biol. Sci. 234 (1988).

[26] B. T. Marshall, M. Long, J. W. Piper, T. Yago, R. P.

McEver and Ch. Zhu, Science319630 (2003).

[27] W. Thomas, M. Forero, O. Yakovenko, L. Nilsson, P.

Vicini, E. Sokurenko and V. Vogel, Biophys. J. 90753

(2006).

[28] D. Bartolo, I. Derenyi and A. Ajdari, Phys. Rev. E. 65

051910 (2002).

[29] E. Evans, A. Leung, V. Heinrich and Ch. Zhu, PNAS10111281 (2004).

[30] V. Barsegov and D. Thirumalai, PNAS102, 1835 (2005).

[31] I. Schwaiger, M. Schleicher, A. A Noegel and M. Rief,

EMBO646 (2005)

[32] P. M. Williams, S. B. Fowler, R. B. Best, J. L. Toca-

Herrera, K. A. Scott, A. Stward and J. Clarke Nature

422446 (2003).

[33] C. Cecconi, E. A. Shank, C. Bustamante and S. Mar-

qusee,Science232057 (2005).

Minimal In

ation

Luis Alvarez-Gaum ea, C esar G omezb,a, Raul Jimenezc,a

aTheory Group, Physics Department, CERN, CH-1211, Geneva 23, Switzerland.

bInstituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, E-28049 Madrid, Spain.

cICREA & Institute of Sciences of the Cosmos (ICC), University of Barcelona, 08028 Barcelona, Spain.

Abstract

Using the universal Xsupereld that measures in the UV the violation of conformal invariance we build up a model

of multield in

ation. The underlying dynamics is the one controlling the natural

ow of this eld in the IR to the

Goldstino supereld once SUSY is broken. We show that

at directions satisfying the slow roll conditions exist only if

R-symmetry is broken. Naturalness of our model leads to scales of SUSY breaking of the order of 101113Gev, a nearly

scale-invariant spectrum of the initial perturbations and negligible gravitational waves. We obtain that the in

aton eld