Topological interactions in systems of mutually interlinked polymer rings

TL;DR

This paper derives the free energy of two linked polymer rings with fixed segment distance, revealing that the topological interaction scales as the fourth power of the segment distance for large separations.

Contribution

It refines previous methods to calculate the free energy of linked rings, confirming the R^4 scaling of topological interaction at large distances.

Findings

Effective topological interaction scales as R^4 for large R.

Refinement of previous approaches to calculating linked ring free energy.

Confirms asymptotic behavior of topological interactions in linked rings.

Abstract

The topological interaction arising in interlinked polymeric rings such as DNA catenanes is considered. More specifically, the free energy for a pair of linked random walk rings is derived where the distance $R$ between two segments each of which is part of a different ring is kept constant. The topology conservation is imposed by the Gauss invariant. A previous approach (M.Otto, T.A. Vilgis, Phys.Rev.Lett. {\bf 80}, 881 (1998)) to the problem is refined in several ways. It is confirmed, that asymptotically, i.e. for large $R\gg R_G$ where $R_G$ is average size of single random walk ring, the effective topological interaction (free energy) scales $\propto R^4$.