Influence of Rigidity and Knot Complexity on the Knotting of Confined Polymers

Abstract

We employ computer simulations and thermodynamic integration to analyse the effects of bending rigidity and slit confinement on the free energy cost of tying knots, $\Delta F_{\mathrm{knotting}}$, on polymer chains under tension. A tension-dependent, non-zero optimal stiffness ${\kappa }_{\min }$ exists, for which $\Delta F_{\mathrm{knotting}}$ is minimal. For a polymer chain with several stiffness domains, each containing a large amount of monomers, the domain with stiffness ${\kappa }_{\min }$ will be preferred by the knot. A {\it local} analysis of the bending in the interior of the knot reveals that local stretching of chains at the braid region is responsible for the fact that the tension-dependent optimal stiffness has a non-zero value. The reduction in $\Delta F_{\mathrm{knotting}}$ for a chain with optimal stiffness relative to the flexible chain can be enhanced by tuning the slit width of the 2D confinement and increasing the knot complexity. The optimal stiffness itself is independent of the knot types we considered, while confinement shifts it towards lower values.

arXiv comment18 pages, 6 figures

References in corpus (11)

• Forces During Bacteriophage DNA Packaging and Ejection
• Probing the entanglement and locating knots in ring polymers: a comparative study of different arc closure schemes
• What is the length of a knot in a polymer?
• Fractal Dimension and Localization of DNA Knots
• Numerical study of linear and circular model DNA chains confined in a slit: metric and topological properties
• On the size of knots in ring polymers
• Persistence length of semiflexible polymers and bending rigidity renormalization
• Poly(dA:dT)-rich DNAs are highly flexible in the context of DNA looping
• Confinement of knotted polymers in a slit
• Effect of bending rigidity on the knotting of a polymer under tension
• Stiff knots

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