Optimizing chromosome disentanglement via chromatin loop organization

Chromosome structure is actively regulated by a concerted action of various proteins to avail vital cellular functions, like the mitotic segregation of chromosomes. We seek to understand the microscopic scheme underlying the structure manipulation that leads to a compact disentangled mitotic state from a less compact and more entangled state in interphase, and vice-versa. We model cellular chromosomes as polymer brushes in a confined volume, and calculate the level of inter-chromosome entanglement in a fluctuating-topology ensemble for various steady-state configurations defined by structural parameters like the grafting density and side chain or loop length. We find that entanglements are minimized for certain brush configurations that depend on net chromosome length. Comparing with existing experimental observations we suggest that chromosomal loops are important for maintaining a low level of entanglement during the cell cycle. Our model provides a steady-state description of chromosomes that is consistent with experimental observations for both the interphase and mitotic stages, where the cell-cycle-specific reorganizations in the structure are accounted for by evolution of the steady state, likely driven by loop extrusion.