  During the life cycle of bacterial cells the non-mixing of the two
ring-shaped daughter genomes is an important prerequisite for the cell division
process. Mimicking the environments inside highly crowded biological cells, we
study the dynamics and statistical behaviour of two flexible ring polymers in
the presence of cylindrical confinement and crowding molecules. From extensive
computer simulations we determine the degree of ring-ring overlap and the
number of inter-monomer contacts for varying volume fractions $\phi$ of
crowders. We also examine the entropic de-mixing of polymer rings in the
presence of mobile crowders and determine the characteristic times of the
internal polymer dynamics. Effects of the ring length on ring-ring overlap are
also analysed. In particular, on systematic variation of the fraction of
crowding molecules a $(1-\phi)$-scaling is found for the ring-ring overlap
length along the cylinder axis, and a non-monotonic dependence of the 3D
ring-ring contact number is predicted. Our results help to rationalise the
implications of macromolecular crowding for circular DNA molecules in confined
spaces inside bacteria as well as in localised cellular compartments inside
eukaryotic cells.
