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The large-scale organization of the genome inside the cell nucleus is critical for the cell’s function. Chromatin—the functional form of DNA in cells—serves as a template for active nuclear processes such as transcription, replication, and DNA repair. Chromatin’s spatial organization directly affects its accessibility by ATP-powered enzymes, e.g., RNA polymerase II in the case of transcription. In differentiated cells, chromatin is spatially segregated into compartments—euchromatin and heterochromatin—the former being largely transcriptionally active and loosely packed, the latter containing mostly silent genes and densely compacted. The euchromatin-heterochromatin segregation is crucial for proper genomic function, yet the physical principles behind it are far from understood. Here, we model the nucleus as filled with hydrodynamically interacting active Zimm chains—chromosomes—and investigate how large …