Chromatin looping is a major epigenetic regulatory mechanism in highereukaryotes. Besides its role in transcriptional regulation, chromatin loopshave been proposed to play a pivotal role in the segregation of entirechromosomes. The detailed topological and entropic forces between loops stillremain elusive. Here, we quantitatively determine the potential of mean forcebetween the centers of mass of two ring polymers, i.e. loops. We find that thetransition from a linear to a ring polymer induces a strong increase in theentropic repulsion between these two polymers. On top, topological interactionssuch as the non-catenation constraint further reduce the number of accessibleconformations of close-by ring polymers by about 50%, resulting in anadditional effective repulsion. Furthermore, the transition from linear to ringpolymers displays changes in the conformational and structural properties ofthe system. In fact, ring polymers adopt a markedly more ordered and alignedstate than linear ones. The forces and accompanying changes in shape andalignment between ring polymers suggest an important regulatory function ofsuch a topology in biopolymers. We conjecture that dynamic loop formation inchromatin might act as a versatile control mechanism regulating and maintainingdifferent local states of compaction and order.
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