Melts of nonconcatenated rings in spherical confinement

Motivated by the chromosomes enclosed in a cell nucleus, we study a spherically confined system of a small number of long unknotted and nonconcatenated polymer rings in a melt and systematically compare it with the bulk results. We find that universal scaling exponents of the bulk system also apply in the confined case; however, certain important differences arise. First, due to confinement effects, the static and threading properties of the rings depend on their radial position within the confining sphere. Second, the rings' dynamics is overall subdiffusive, but anisotropic along the directions parallel and perpendicular to the sphere's radius. The radial center of mass displacements of the rings are in general much smaller than the angular ones, which is caused by the confinement-induced inhomogeneous radial distribution of the whole rings within the sphere. Finally, we find enhanced contact times between rings as compared to the bulk, which indicates slow and predominantly coordinated pathways of the relaxation of the system.