Mesoscale, long-time mixing of chromosomes and its connection to polymer dynamics

Abstract

Chromosomes are arranged in distinct territories within the nucleus of animal cells. Recent experiments have shown that these territories overlap at their edges, suggesting partial mixing during interphase. Experiments that knock-down of condensin II proteins during interphase indicate increased chromosome mixing, which demonstrates control of the mixing. In this study, we use a generic polymer simulation to quantify the dynamics of chromosome mixing over time. We introduce the chromosome mixing index, which quantifies the mixing of distinct chromosomes in the nucleus. We find that the chromosome mixing index in a small confinement volume (as a model of the nucleus), increases as a power-law of the time, with the scaling exponent varying non-monotonically with self-interaction and volume fraction. By comparing the chromosome mixing index with both monomer subdiffusion due to (non-topological) intermingling of chromosomes as well as even slower reptation, we show that for relatively large volume fractions, the scaling exponent of the chromosome mixing index is related to Rouse dynamics for relatively weak chromosome attractions and to reptation for strong attractions. In addition, we extend our model to more realistically account for the situation of the Drosophila chromosome by including the heterogeneity of the polymers and their lengths to account for microphase separation of euchromatin and heterochromatin and their interactions with the nuclear lamina. We find that the interaction with the lamina further impedes chromosome mixing. Interphase chromosomes are polymer-like structures contained within the nucleus of a cell and are partially mixed. Chromosome mixing is key to understanding chromosome territories as well as the correlation in gene expression of different chromosomes. In this paper, we present a physical model that quantifies mesoscale mixing dynamics by introducing a single function, the chromosome mixing index, which is experimentally quantifiable from genomic contact maps. Based on simulations, we found that the dynamics of the mixing index are related to Rouse dynamics and reptation dynamics, depending on polymer concentrations and interactions. Our model bridges polymer dynamics and biological contact maps.