Diffusion mechanisms of localised knots along a polymer

¹ NORDITA - Blegdamsvej 17, DK-2100 Copenhagen, Denmark
² Biophysics Department, Risø National Laboratory - Frederiksborgvej 399 DK-4000 Roskilde, Denmark
³ Department of Physics, Princeton University - Princeton, NJ 08544, USA
⁴ Division of Solid State Physics, Lund University - Sölvegatan 14 S-223 62 Lund, Sweden
⁵ Institut für Physik, Humboldt Universität zu Berlin - Newtonstraße 15 D-12489 Berlin, Germany

Corresponding author: metz@nordita.dk

Received: 4 August 2006
Accepted: 20 September 2006

Abstract

We consider the diffusive motion of a localised knot along a linear polymer chain. In particular, we derive the mean diffusion time of the knot before it escapes from the chain once it gets close to one of the chain ends. Self-reptation of the entire chain between either end and the knot position, during which the knot is provided with free volume, leads to an L³ scaling of diffusion time; for sufficiently long chains, subdiffusion will enhance this time even more. Conversely, we propose local “breathing”, i.e., local conformational rearrangement inside the knot region (KR) and its immediate neighbourhood, as additional mechanism. The contribution of KR-breathing to the diffusion time scales only quadratically, , speeding up the knot escape considerably and guaranteeing finite knot mobility even for very long chains.