Trapping a Knot into Tight Conformations by Intra-Chain Repulsions.

Liang Dai,Patrick Doyle

doi:10.3390/polym9020057

Abstract

Knots can occur in biopolymers such as DNA and peptides. In our previous study, we systematically investigated the effects of intra-chain interactions on knots and found that long-range repulsions can surprisingly tighten knots. Here, we use this knowledge to trap a knot into tight conformations in Langevin dynamics simulations. By trapping, we mean that the free energy landscape with respect to the knot size exhibits a potential well around a small knot size in the presence of long-range repulsions, and this potential can well lead to long-lived tight knots when its depth is comparable to or larger than thermal energy. We tune the strength of intra-chain repulsion such that a knot is weakly trapped. Driven by thermal fluctuations, the knot can escape from the trap and is then re-trapped. We find that the knot switches between tight and loose conformations—referred to as “knot breathing”. We use a Yukawa potential to model screened electrostatic interactions to explore the relevance of knot trapping and breathing in charged biopolymers. We determine the minimal screened length and the minimal strength of repulsion for knot trapping. We find that Coulomb-induced knot trapping is possible to occur in single-stranded DNA and peptides for normal ionic strengths.

Highlights

IntroductionKnotting occurs in biopolymers, such as DNA [1,2,3,4,5] and proteins [6,7,8,9,10], and other polymers.Simulations have been performed to investigate knot behaviors under various conditions, such as in free space [1,11], in spatial confinement [12,13,14,15], under pulling forces [16,17], in good/bad solvents [18], in a crowding environment [19], with different bending stiffness [20,21], and during translocation through a nanopore [22,23]
2 shows typical simulation where a knot switches between tight conformations and a flexible chain awith a triangle repulsion, the critical interaction range for repulsion-induced knot
We tune the strength of repulsion so that a knot is moderately trapped in tight conformations, and we can observe knot breathing, the escaping and re-trapping of the knot

Summary

Introduction

Knotting occurs in biopolymers, such as DNA [1,2,3,4,5] and proteins [6,7,8,9,10], and other polymers.Simulations have been performed to investigate knot behaviors under various conditions, such as in free space [1,11], in spatial confinement [12,13,14,15], under pulling forces [16,17], in good/bad solvents [18], in a crowding environment [19], with different bending stiffness [20,21], and during translocation through a nanopore [22,23]. Knots in DNA or filaments can be tied manually [28,29], formed spontaneously [30]. The spontaneously-formed knot in fluorescently labeled DNA under tension [29] or in nanochannels [30] can be identified as a bright spot diffusing along DNA and disappearing only at one end. The knots in DNA can be identified by atomic-force microscopy (AFM) imaging [33]. DNA knots were identified by nanopore translocation experiments [34]

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Discussion

Conclusion