Inspired by bacterial chromosome organization, we study the compaction and clustering of a heterogeneous ring polymer in a crowded medium using molecular dynamics simulations. The polymer consists of several large monomers interspersed along the backbone and small intervening monomers. In a crowded medium, the entropy of crowding particles or crowders favors the collapse of chain molecules, such as chromosomes. Our study shows that the compaction transition of heterogeneous polymers by crowders is well-correlated with the clustering of large monomers: when the large monomers are sufficiently large, both occur concomitantly in the same narrow (biologically relevant) range of the volume fraction of crowders. It also indicates that cylindrical confinement makes crowding effects more effective. The results presented here suggest that phase separation and clustering are essential features of bacterial chromosome organization.
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Each rRNA operon is associated with as many as RNAPs.7–9,26 Each RNAP is about 10 nm in size.7 If 70 RNAPs were assumed to be close-packed into an imaginary sphere, the sphere would be as large as 40 nm.15,29 Since ac ≈ 5 nm,7 the maximum value of aM used in this work corresponds to aM = 6ac ≈ 30 nm. This is close to the size of the aforementioned imaginary sphere. However, these numbers should not be taken too literally. Indeed, our hard-sphere model of an operon is coarse-grained. Furthermore, clustering of a heterogeneous polymer depends not only on depletion forces but also the entropic cost for looping the intervening polymer, which is larger for a larger loop. In other worlds, the choice of aM is not completely independent of that of loop size. The simulation results obtained with our parameter choices capture some of the essential features of what was observed with the E. coli chromosome8,9 (see Sec. III).