Fig. 4: Emergent BAF scaling behaviors in heterogeneous binding environments.

Source data are provided as a Source Data file. a Simulation of binding dynamics in a two-dimensional fractal environment constructed using a Hilbert space-filling curve, with specific binding sites highlighted in green. b Representative molecular trajectory showing trapping behavior due to interactions with specific binding sites in the fractal environment. c MSD characterization of molecular motion. d BAF analysis for molecules in this newly modified fractal environment. e Non-Gaussian probability density of molecular displacements. f Simulation snapshots of the binding dynamics between protein polymer and binding site distributed along a chromatin fiber. g A representative trajectory of the protein polymer showing significant heterogeneity, including hopping behavior, which is zoomed in the inset. h MSD of the protein polymers. i BAF analysis, revealing a scaling exponent of approximately -2.5 (indicated by a red dashed line), deviating from the theoretical prediction of -1.5. j PDFs of molecular displacements at two time intervals. k Simulation of polymer-polymer interactions in a heterogeneous binding environment, induced by two coexisting phases. l Trajectory of a polymer molecule transitioning between condensed (red) and dilute (green) regions. m MSD of polymer molecules exhibiting normal diffusion. n BAF analysis of polymer–polymer associations in the phase-separated system. o Displacement probability density showing non-Gaussian characteristics. Data points in BAF and MSD characterizations represent averages over 200, 150 and 500 independent simulation runs, respectively, for three different heterogeneous adsorption systems. Error bars indicate the standard deviation across independent trajectories. Power-law fitting were performed for each BAF curve over the following time ranges: (d) 2500000 to 100000000 steps; (i) 3500000-17000000 steps; (n) 30000–4300000 steps. Scaling exponents and errors are shown in the respective panels.