Topological and geometrical entanglement in a model of circular DNA undergoing denaturation

TL;DR

This study uses Monte Carlo simulations to analyze topological and geometrical entanglement in circular DNA during denaturation, revealing a first-order transition in linking probability and distinct behaviors of linking number and writhe.

Contribution

It provides new insights into the topological and geometrical changes in circular DNA during denaturation, highlighting the abrupt transition in linking probability and the scaling of entanglement measures.

Findings

Linking probability exhibits a first-order transition at denaturation.

Average linking number is near zero in denatured phase and scales with √N in native phase.

Writhe scales with √N in both phases.

Abstract

The linking number (topological entanglement) and the writhe (geometrical entanglement) of a model of circular double stranded DNA undergoing a thermal denaturation transition are investigated by Monte Carlo simulations. By allowing the linking number to fluctuate freely in equilibrium we see that the linking probability undergoes an abrupt variation (first-order) at the denaturation transition, and stays close to 1 in the whole native phase. The average linking number is almost zero in the denatured phase and grows as the square root of the chain length, N, in the native phase. The writhe of the two strands grows as the square root of N in both phases.