(a) CTCF (light blue ellipse) diffuses inside the nucleus (large yellow circle). It interacts with one of three zone types: (1) small, Cognate DNA Binding Sites (CBSs) (red arrow). (2) Transiently trapping zones (TTZs) of size 200 nm (purple). (3) Trapping zones of different dimensions, whose size is derived from a power-law distribution (Power-law distributed Trapping Zones – PTZs – green; for details about PTZs, please see Fig. 3 and below).
(b) The protein (light blue) is observed at 3 time points (x1, x2, x3) along its stochastic trajectory (red curve). Left: Outside of the zones, CTCF performs free diffusion. The angle of two consecutive steps is uniformly distributed for this mode of motion. Middle: If CTCF leaves a TTZ (x1), diffuses freely (x2), and then reattaches back to the TTZ (x3), the angle distribution is anisotropic. Right: While inside a zone, CTCF can be reflected from its boundary. The angle distribution, in this case, will be anisotropic
(c) The angle distribution for a protein performing diffusion in a nucleus containing only CBSs and TTZs. See Supplementary Table 2 for the simulation parameters.
(d) Angle distribution of the trajectory computed from the simulation when the nucleus contains only zones of type 1 and 2 (CBSs and TTZs). CTCF is trapped with high probability (Ptrap = 0.99) when touching the zones (red curve). (black curve). The protein is trapped with low probability (Ptrap = 0.1) when touching the zone (black curve).
(e) Plot of f180/0 vs. lag time averaging over all displacement lengths of the simulation data shown in d.
(f) Plot of f180/0 vs. mean displacement length averaging over all lag times. The data shown in (e-f) is the result of n=30 independent simulations. In each simulation, the trajectory of CTCF was recoded until its 10000’s capture event. Error bars in (e-f) show standard deviation from 50 subsamplings with replacement using 50% of the data and centre values show value using 100% of the data.
(g-h) Anisotropy heatmaps showing f180/0 vs. length of the first and second displacement for high binding probability (Ptrap = 0.99) (g) and for smaller binding probability (Ptrap = 0.1) (h). See Supplementary Table 2 for the full parameters used.