Conserved Linking in Single- and Double-Stranded Polymers

TL;DR

This study introduces a lattice Monte Carlo model for ring polymers with conserved topological linking number, revealing its effects on polymer size and potential relevance to DNA topology.

Contribution

It presents a novel lattice model where linking number is conserved, showing its impact on polymer conformation and suggesting biological relevance.

Findings

Increased linking number mildly reduces polymer size.

Linking number conservation leads to anti-correlation between twist and writhe.

The effect on size grows with chain length.

Abstract

We demonstrate a variant of the Bond Fluctuation lattice Monte Carlo model in which moves through cis conformations are forbidden. Ring polymers in this model have a conserved quantity that amounts to a topological linking number. Increased linking number reduces the radius of gyration mildly. A linking number of order 0.2 per bond leads to an eight-percent reduction of the radius for 128-bond chains. This percentage appears to rise with increasing chain length, contrary to expectation. For ring chains evolving without the conservation of linking number, we demonstrate a substantial anti-correlation between the twist and writhe variables whose sum yields the linking number. We raise the possibility that our observed anti-correlations may have counterparts in the most important practical polymer that conserves linking number, DNA.