Mesoscale mixing of chromosomes

It is not well studied why chromosome mixing is a very slow process. In a previous study, the chromosome was assumed to be an infinitely long polymer and modeled as a ring polymer. This study suggests that topological constraints can slow down chromosome mixing dynamics. In this talk, we present our simulations of how the extent of chromosome mixing dynamics changes over time, as a function of the chromosome volume fraction, self-interactions, and binding to the lamina. We simulate a multi-chromosome nucleus using a bead-spring model with 4 polymer chains. We calculate the contact map and chromosome mixing index from our simulations and compare it with its maximal theoretical value for different chromosomal volume fractions and interactions. We consider two initial conditions: (i) when all chromosomes are separated and (ii) all chromosomes are mixed. Initial condition (i) predicts that the chromatin mixing index increases as a power law of the time, while initial condition (ii) predicts a steady-state or metastable, average value of the chromosome mixing index for which chromosomes are partially mixed. Using this, we estimate the time scale and the extent of chromosome mixing which can vary depending on the volume fraction, interactions, and chromosome size.