The effect of loops on the mean-squared displacement of Rouse-model chromatin

Many researchers have been encouraged to describe the dynamics of chromosomal loci in chromatin using the classical Rouse model of polymer dynamics by the agreement between the measured mean-squared displacement (MSD) versus time of fluorescently-labelled loci and the Rouse-model predictions. However, the discovery of intermediate-scale chromatin organization, known as topologically associating domains (TADs), together with the proposed explanation of TADs in terms of chromatin loops and loop extrusion, is at odds with the classical Rouse model, which does not contain loops. Accordingly, we introduce an extended Rouse model that incorporates chromatin loop configurations from loop-extrusion-factor-model simulations. This extended Rouse model allowed us to investigate the impact of loops and loop extrusion on the dynamics of chromatin. We show that loops significantly suppress the averaged MSD of a chromosomal locus, consistent with recent experiments that track fluorescently-labelled chromatin loci in fission yeast [Bailey et al., bioRxiv (2021)]. We also find that loops slightly reduce the MSD's stretching exponent from the classical Rouse-model value of 0.5 to a loop-density-dependent value in the 0.4-0.44 range. Remarkably, stretching exponent values in this range have also been reported in recent experiments [Bailey et al., bioRxiv (2021) and Weber et al., Phys. Rev. Lett. 104, 238102 (2010)].