Topological interactions between ring polymers: Implications for chromatin loops

TL;DR

This study investigates the topological and entropic forces between chromatin loops modeled as ring polymers, revealing increased repulsion and structural ordering due to topology, which may regulate chromatin organization.

Contribution

It provides a quantitative analysis of how topological constraints influence the interactions and conformations of chromatin loops modeled as ring polymers.

Findings

Entropic repulsion increases with ring topology.

Topological constraints reduce accessible conformations by about 50%.

Ring polymers are more ordered and aligned than linear polymers.

Abstract

Chromatin looping is a major epigenetic regulatory mechanism in higher eukaryotes. Besides its role in transcriptional regulation, chromatin loops have been proposed to play a pivotal role in the segregation of entire chromosomes. The detailed topological and entropic forces between loops still remain elusive. Here, we quantitatively determine the potential of mean force between the centers of mass of two ring polymers, i.e. loops. We find that the transition from a linear to a ring polymer induces a strong increase in the entropic repulsion between these two polymers. On top, topological interactions such as the non-catenation constraint further reduce the number of accessible conformations of close-by ring polymers by about 50%, resulting in an additional effective repulsion. Furthermore, the transition from linear to ring polymers displays changes in the conformational and structural properties of the system. In fact, ring polymers adopt a markedly more ordered and aligned state than linear ones. The forces and accompanying changes in shape and alignment between ring polymers suggest an important regulatory function of such a topology in biopolymers. We conjecture that dynamic loop formation in chromatin might act as a versatile control mechanism regulating and maintaining different local states of compaction and order.