Polymer dynamics relates chromosome mixing to temporal changes in biological contact maps

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. Genomewide, biological contact maps in humans and Drosophila show only a low degree of contact between different chromosomes; however, the mixing in yeast is considerably higher. Recent theoretical estimates considered topological mixing of chromosomes by polymer reptation, and suggested that the time scale for chromosome mixing is years. This implies that a cell will typically divide before its chromosomes mix by reptation. Here, we use a generic polymer simulation to quantify the dynamics of chromosome mixing over time. We introduce the chromosome mixing index that quantifies the mixing of distinct chromosomes in the nucleus. We find that the chromosome mixing index increases as a power-law with time, and the scaling exponent varies non-monotonically with self-interaction and volume fraction. By comparing the chromosome mixing index with both subdiffusion due to (nontopological) intermingling of chromosomes as well as longer-time reptation, we show that the scaling exponent of the chromosome mixing index is related to intermingling for relatively small chromosome attractions and to reptation for large attractions. The model is extended to realistic biological conditions.