In confinement, overlapping polymers experience entropic segregating forces that tend to demix them. This plays a role during cell replication, where it facilitates the segregation of daughter chromosomes. It has been argued that these forces are strong enough to explain chromosome segregation in elongated bacteria such as E. coli without the need for additional active mechanisms [S. Jun and B. Mulder, Proc. Natl. Acad. Sci. U. S. A., 2006, 103, 12388]. However, entropic segregation can only set in after the initial symmetry has been broken. We demonstrate that the timescale for this induction phase is exponentially growing in the chain length, while the actual segregation time scales only quadratically in the chain length. Thus the induction quickly becomes the dominating, slow process, and makes entropic segregation much less efficient than previously thought. The slow induction might also explain the long delay in chromosome segregation observed in experiments on E. coli.
Entropic forces tend to demix polymers in confinement, which has been argued to at least facilitate DNA segregation in cylindrical bacteria. Ring polymers as found in modern bacteria such as Escherichia coli experience even stronger segregating forces than linear ones due to the fact that rings additionally constrain themselves. Using a territorial "renormalized" Flory approach we obtain a scaling prediction for the segregation force and speed of ring polymers and confirm this prediction by molecular dynamics simulations. The ring topology also affects the induction phase, when the initial symmetry is broken before segregation sets in. We show that the induction time still scales exponentially with the chain length and thus dominates the overall time scale of entropic segregation, although it is significantly shorter than the one for linear chains.
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