Entropic organization of topologically modified ring polymers in spherical confinement

Under high cylindrical confinement, two athermal ring polymers segregate to two halves of the cylinder to maximize their entropy. This has been identified as the primary mechanism of chromosome segregation in cylindrical E. coli cells. In contrast, chromosomes in eukaryotic cells are confined in a spherical nucleus. As ring polymers will remain mixed within spherical confinement, in this work, we provide a simple mechanism to tune entropic interactions and drive organization within the sphere by creating asymmetric topological modifications in the ring-polymer architecture. We introduced cross-links between specific monomers on the ring polymer contour to create a cluster of internal loops connected to a bigger loop. Consequently, we observed an emergent radial organization of the polymer segments in the sphere. For a single topologically modified ring polymer within a sphere, the monomers of the bigger loop were probabilistically found closer to the periphery. However, for multiple such polymers in the sphere, the small loops were localized near the periphery. We considered the bead-spring model of polymers, where there are only repulsive excluded volume interactions between the monomers, ensuring that the observed organization is purely entropy-driven. We also observe a similar organization when we allow topological constraint release by allowing chains to cross each other, as is relevant for chromosome physics. This leads us to a separate investigation where we infer that excluded volume interactions between beads are enough to give a Flory exponent of 0.6, even if we allow linear polymeric chains to cross each other. Finally, we discuss the plausible relevance of our studies to the organization of euchromatin and the more condensed heterochromatin in eukaryotic chromosomes.