Figure 4:

Impact of topological linking and entanglement on mixing at compartment domains or chromosomal interfaces. (Top) Simulations were performed on three types of interfaces: (A) Topologically unlinked domains, (B) Topologically linked domains via strand-passage, and (C) Topologically open domains via free-end movements. Chains are shown in yellow and cyan with ends highlighted by the red and black balls. The interface remains smooth and unmixed for the topologically insulated domains in panel A, while the two topologically open domains in panels B and C exhibit considerable mingling. The interface mixing of the simulated chains is quantified by computationally generating percolation paths (simul-walks) similar to the C-walks obtained by MC-3C. (Middle) The number of inter-chomosomal (or inter-domain) steps that occur within each inter-chain simul-walk is presented. . (Bottom) The fraction of intra-domain steps in simul-walks with at least one inter-domain interaction is shown in solid black lines (compare to Figure 2D and Figure 3E, F for C-walks). The unmixed interfaces in simulation A demonstrate a higher fraction of intra-domain steps in simul-walks with at least one inter-domian crossing. Randomly permutating those same simul-walks results in a lower fraction of intra-domain steps shown by gray dots. In contrast, for the mixed and catenated interfaces in simulations in panels B and C, the fraction of intra-domain steps in simul-walks is indistinguishable from permutated simul-walks indicating extensive mixing. Sum of p-values for the unmixed interfaces in simulation A is <10⁻⁸ while in B and C it is 1.15 and 0.45 respectively. Source data are available online.