Fig. 6.

Internal structure of actively extruded loops from hybrid MD—MC simulations with $v_{\mathit{ex}}\approx 0.6$ kbp per ${\tau }_0$ ($\kappa \approx 0.3$) starting from a relaxed polymer chain with unperturbed fractal dimension $D\approx 2$. (A) Mean square distance between two loci extruded by the same cohesin domain separated by genomic distance $s$ within a loop of genomic length $l$ (Eq. 8). Each blue curve corresponds to a different loop length l = 40, 80, 120, …, 600 kbp. The red lines show the predicted scaling behavior. The abscissa and ordinate are scaled by $1.1g\left(l\right)$ and $1.1{\xi }^2\left(l\right)$, respectively. $g\left(l\right)$ and ${\xi }^2\left(l\right)$ were obtained from a simulation of relaxed chromatin without extrusion (see Inset and SI Appendix for details). The factor of 1.1 shifts the crossover between scaling behaviors to $s/\left[1.1g\left(l\right)\right]=1$ and $<r_l^2\left(s\right)</\left[1.1{\xi }^2\left(l\right)\right]=1$ (dashed black lines). (B) Average contact probability between loci separated by genomic length s within an extruded loop, averaged over loop lengths $800\le l\le \mathrm{1,000}$ kbp. The dashed vertical line indicates the crossover to $P\left(s\right)\sim s^{-3/4}$, which is approximately $g\left(\mathrm{1,000} \text{kbp}\right)\approx 60 \text{kbp}$. The red lines show the predicted scaling behavior.