  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.
