Decay of topology in open polymers.(*)

Attilio Stella, Department of Physics and Astronomy, INFN,
University of Padova, Italy.

Topological disentanglement occurs in several situations involving knotted fluctuating filaments, like DNA ejection from viral capsids or rheological experiments with polymers subject to elongational flows. We propose a model for the dynamics of unknotting of open polymers under tension. Disentanglement occurs when the knot reaches the ends of the chain and includes decays into simpler knots and eventual full unknotting. The model contains the minimal number of crossings and the minimal length of the knots as parameters, and is amenable to analytical treatment. The crossings behave as particles diffusing along the chain and suitable rules allow to reconstruct from their number and positions the type and location of the knot along the chain. Such picture is also consistent with results for globular polymers in equilibrium and subject to slip-links. These results are naturally interpreted by regarding the essential crossings of the delocalized knots as particles competing for a share of the backbone on which they are diffusing. Predictions for torus and twist knots are in
remarkable agreement with extensive simulation results for realistic models of the systems we have in mind, at both high and low tension.

* Based on collaborative work with M. Caraglio, B. Marcone, F. Baldovin, and E. Orlandini.