Diffusion mechanisms of localised knots along a polymer

Abstract

We consider the diffusive motion of a localized 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 L^3 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, L^2, speeding up the knot escape considerably and guaranteeing finite knot mobility even for very long chains.

7 pages, 2 figures. Accepted to Europhys. Lett

References in corpus (5)

• Anomalous Dynamics of Forced Translocation
• What is the length of a knot in a polymer?
• When translocation dynamics becomes anomalous
• Equilibrium shapes of flat knots
• Tight and loose shapes in flat entangled dense polymers

Cited by in corpus (11)

• How knots influence properties of proteins
• Tightening of knots in proteins
• Spontaneous knotting and unknotting of flexible linear polymers: equilibrium and kinetic aspects
• Sequence-specific size, structure, and stability of tight protein knots
• The Energy Landscape, Folding Pathways and the Kinetics of a Knotted Protein
• Effect of topology on dynamics of knots in polymers under tension
• Monomer distributions and intra-chain collisions of a polymer confined to a channel
• Stochastic unfolding of nanoconfined DNA: experiments, model and Bayesian analysis
• Distribution of label spacings for genome mapping in nanochannels
• Topological disentanglement of linear polymers under tension
• Free Energy of a Knotted Polymer Confined to Narrow Cylindrical and Conical Channels