Eur. Phys. J. B 64, 519-523 (2008)
https://doi.org/10.1140/epjb/e2007-00347-4

The elusiveness of polymer knots

Physics Department, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Corresponding author: ^a kardar@mit.edu

Received: 10 September 2007
Revised: 8 November 2007
Published online: 19 December 2007

Abstract

Knots are a topological property of closed curves, and while not rigorously defined, are also expected to occur in sufficiently long open polymers. We argue, however, that energetic and entropic factors favor tight knots, with the entanglements localized on relatively small segments. Knots are statistically rare in swollen (coil) polymers, but abundant in compact (globular) configurations. Yet, our investigation of the Protein Data Bank reveals very few knotted structures in globular proteins. We shall discuss some particularly intriguing examples of this set, including the most complicated protein knot appearing in Human ubiquitin hydrolase.