Abstract
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.
Highlights
Nonconcatenated and unknotted ring polymer melts have been fascinating physicists for years, and still a complete understanding of their properties is lacking
We have shown that a small number of spherically confined, unknotted, and non-concatenated rings in melt maintain the universal features of the main static and dynamic characteristics known from the bulk systems
Further work is necessary to unambiguously determine the structure factor and contact probability scaling properties for these “hybrid” space-filling conformations. We hypothesize that this could be relevant when interpreting the scaling of the contact probabilities within different chromatin domains
Summary
Nonconcatenated and unknotted ring polymer melts have been fascinating physicists for years, and still a complete understanding of their properties is lacking. The majority of chromosomes is affected by the confinement geometry, and their conformations result from the competition between the confinement and the compression due to topological constraints In this direction, the work studied a single long ring in cubic confinement and found that the conformations of the ring’s subchains are consistent with the crumpled globule picture in terms of ν = 1/3 but found γ ≃ 0.9. We investigate the impact of confinement, ring topology, and a small number of polymer chains on static and dynamic properties of the system. We report mean inter-ring threading properties, which are important for the dynamics of systems with long rings.44,47–53 We find that they are similar to the bulk systems but vary with the rings’ radial position within the confining sphere. Performing this procedure every step is computationally more costly, and as we checked, this has no effect on the dynamics, as seen in Fig. S10 of the supplementary material
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