Entropic alignment of topologically modified ring polymers in cylindrical confinement

When subjected to cylindrical confinement, parts of topologically modified ring polymers can be localized along the long axis of the cylinder by introducing loops within the ring polymer. This was achieved by introducing cross-links between specific monomers of the polymer. The loops formed as a result of this cross-linking has been termed as "internal loops" in this work. The emergent organization of the polymer segments occurs because of the entropic repulsion between these internal loops [Phys. Rev. E 106, 054502 (2022)2470-004510.1103/PhysRevE.106.054502]. These principles were used to identify the underlying mechanism of bacterial chromosome organization [Soft Matter 18, 5615 (2022)10.1039/D2SM00734G]. Here, we outline functional principles associated with entropic interactions, leading to specific orientations of the ring polymers relative to their neighbors in the cylindrical confinement. We achieve this by modifying the ring polymer topology by creating internal loops of two different sizes within the polymer, and thus create an asymmetry. This allows us to strategically manipulate polymer topology such that segments of a polymer face certain other segments of a neighboring polymer. The polymers therefore behave as if they are subjected to an "effective" entropic interaction reminiscent of interactions between Ising spins. But this emergent spatial and orientational organization is not enthalpy-driven. We consider a bead spring model of flexible polymers with only repulsive excluded volume interactions between the monomers. The polymers entropically repel each other and occupy different portions of the cylinder, and moreover, the adjacent polymers preferentially reorient themselves along the axis of the cylinder. We further substantiate our observations by free-energy calculations. To the best of our knowledge, this is the first study of the emergence of effective orientational interactions by harnessing entropic interactions in flexible polymers. The principles elucidated here could be relevant to understand the interactions between different sized loops within a large chromosome.