A model for segregation of chromatin after replication: segregation of identical flexible chains in solution

We study the segregation of two long chains from parallel but randomly twisted start conformations under good solvent conditions using Monte Carlo simulations to mimic chromatin segregation after replication in eukaryotic cells in the end of prophase. To measure the segregation process, we consider the center-of-mass separation between the two chains and the average square distance between the monomers which were connected before segregation starts. We argue that segregation is dominated by free diffusion of the chains, assuming that untwisting can be achieved by Rouse-like fluctuations on the length scale of a twisted loop. Using scaling analysis, we find that chain dynamics is in very good agreement with the free diffusion hypothesis, and segregation dynamics follows this scaling nearly. Long chains, however, show retardation effects that can be described by a new (to us) dynamical exponent, which is slightly larger than the dynamical exponent for Rouse-like diffusion. Our results indicate that nearly free diffusion of chains during a timescale of a few Rouse-times can lead to segregation of chains. A main obstacle during segregation by free diffusion is random twists between daughter strands. We have calculated the number of twists formed by the daughter strands in the start conformations, which turns out to be rather low and increases only with the square-root of the chain length.