Fig. 5.

Structure of an actively extruded loop. All schematic plots are on log–log scales. (A) Schematic plot comparing the relaxation time (black) and time needed for a single cohesin domain to extrude a chromatin section with genomic length s (red). (B) Schematic plot of the mean square size of a loop with genomic length l. The red line segment indicates the regime consistent with $D=4$. The dotted line shows the mean square size of a chromatin section with genomic length $l/2$ without extrusion. (C) Relaxed sections (green circles) in a growing loop overlap in space forming a fractal with dimensionality $D=4$. The smallest relaxed section has the genomic length $g_{\mathit{min}}\approx z/\kappa$. The genomic length of each relaxed section (green circles) grows from $g_{\mathit{min}}$ next to the cohesin to $g\left(l\right)\approx {\left(g_{\mathit{min}}l/2\right)}^{1/2}\approx {\left[lz/\left(2\kappa \right)\right]}^{1/2}$ next to the cohesin binding site (red circle). (D) Mean square distance between two loci separated by a genomic distance $s$ within a loop of genomic length $l$ (Eq. 8). The average is taken over all loci pairs within the loop extruded by the same cohesin domain. The red line segment indicates the regime consistent with $D=4$. The dotted line shows the mean square distance without extrusion. (E) Average contact probability between loci separated by genomic length s within an extruded loop of length $l$. The red line segment indicates the regime consistent with $D=4$. (F) Volume fraction ${\varphi }_{\mathit{self}}$ of a chromatin section of length $s$ within its own pervaded volume where the section is part of a loop with length $l$. The red line segment indicates the regime consistent with $D=4$.