Induction of entropic segregation: the first step is the hardest

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.