Topology plays a critical role in regulating the three-dimensional organization of DNA across a wide range of length scales. At the kilobase-pair scale, various biological processes generate over- and underwinding of the DNA double helix, a phenomenon known as DNA supercoiling. To accommodate excess torsional stress, DNA undergoes large-scale configurational rearrangements, resulting in the formation of plectonemes. We recently studied the emergence and coexistence of multiple plectonemic domains using a statistical-mechanical model that builds on the classical two-phase description of stretched, supercoiled DNA. Despite its simplicity, the resulting theory shows excellent agreement with Monte Carlo simulations of the twistable wormlike chain model. 
At the megabase scale, we investigated microscopy data of interphase chromosomes obtained using multiplexed fluorescence in situ hybridization (FISH). By analyzing distance distributions and associated scaling laws, we found that, for a given genomic locus, chromatin can adopt two distinct conformational states, indicating the coexistence of different topological organizations, which we denote as phase α and phase β. These phases exhibit distinct scaling behavior: the α phase is consistent with a crumpled-globule–like organization, whereas the β phase corresponds to a more extended yet confined conformation, such as a looped domain architecture.