The Elusiveness of Knots in Polymers & Proteins

Summary

V.      Rarity of knotted proteins

• Knots are rare, but appear in some enzymatic proteins

IV.     Open polymers: pulling on knots; model polyethelene

• Knots are rare and tight in swollen polymers; abundant and loose in compact phases                                

III.     Entropic tightening of Slip-links and 'Flat' knots      

• Entropic considerations can also make (weakly) tight knots

II.      The tightness of Charged knots     

• Energetic considerations can lead to very (stongly) tight knots

I.       Introduction: Knots & Polymers

• A source of fascination of mystery in arts, nature, and science, and a playground for physicists

Fun observations!

 The 2008 IgNobel Prize in Physics to: Spontaneous knotting of an agitated string, by

Dorian Raymer & Douglas Smith, PNAS 104, 16432 (2007),

for proving that a heap of string will inevitably tangle.

 Ben-Naim et al, PRL 86, 1414 (2000); shows how a granular chain knot disentangles.

 Pieranski et al, New J Phys 3, 10 (2001); demonstrate the breaking of knots in sphaghetti (movie)

Taylor, Nature 421, 25 (2003);  employs Christmas decorations to simulte knots in proteins.

Acknowledgements

Paul Dommersnes, Ralf Metzler, Andreas Hanke

Yacov Kantor, Oded Farago, Roya Zandi

Peter Virnau, Grigory Kolesov, Leonid Mirny

Outline Introduction Charged Knots Slip-links Flat Knots Open Knots Protein Knots Summary