# Confinement diameter smaller than the radius of gyration maximizes the chromosome mixing index.

(a) In the phantom chain case (*ϵ* = 0), the ratio of the diameter of confinement (2*R*_{c}) to the radius of gyration of a random-walk chain (*R*_{g}) is plotted as a function of the chain volume fraction in the nucleus. S5c Fig shows that the radius of gyration of a random-walk chain of *M* = 8810 beads is *R*_{g} = 90*σ* when the persistence length is 5 beads. The inset of the figure shows the time-average of the chromosome mixing index () as a function of the chain volume fraction (*ϕ*) in the nucleus. From both figures, it is clear that the chromosome mixing index reaches its maximum value when 2*R*_{c}/*R*_{g} < 1. Thus when *R*_{g} is large relative to 2*R*_{c} the confinement is effective; in the opposite case, the confinement is so large that the chains hardly mix with their diffusion in the large confinement volume greatly impeding mixing, even for phantom chains. (b) In the case of excluded volume chains (where *ϵ* ≠ 0), the confinement has an even larger effect. The radius of gyration for 4 chains of M beads each (4M beads in total, equivalent to the *Drosophila* genome) is taken to be *R*_{g} = 180*σ*. It is noteworthy that for *ϕ* = 0.01, in the phantom chain case (a) 2*Rc*/*Rg* > 1, but in the non-phantom chains case (b) 2*Rc*/*Rg* < 1.

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