Polarity-Registered Nuclear Mapping Reveals Discrete Topological Classes of Chromosome Organization

Chromosome organization within the nucleus is tightly linked to gene regulation and cell identity, yet its quantitative comparison across cells remains challenging due to variability in nuclear geometry and orientation. Current approaches largely rely on radial metrics and lack a shared coordinate framework integrating polarity and three-dimensional spatial information. Here, we introduce a polarity-registered and geometrically normalized nuclear coordinate system enabling homolog-resolved mapping of chromosome territories (CTs) across cell populations. By combining affine normalization of nuclear shape with alignment to intrinsic polarity cues, we transform heterogeneous nuclei into a shared spatial reference frame where radial and angular chromosome positions can be directly compared. Applying this framework to human mesenchymal stem cells (hMSCs), we identify discrete and recurrent nuclear topological classes defined by polarity state, cytoskeletal organization, and homolog-specific chromosome positioning. Homolog-resolved analysis reveals asymmetric spatial behaviors: one homolog maintains stable positioning, whereas the other undergoes polarity-dependent reorganization. Single-cell micropatterning further shows thatgeometric confinement reproducibly stabilizes these topological classes, indicating that defined mechanical and polarity constraints control nuclear organization. This framework enables quantitative classification of nuclear architecture and shows that chromosome organization in adherent cells adopts discrete, reproducible spatial states. This approach provides a foundation for integrating imaging-based spatial genomics with population-level analyses of nuclear organization and cellular heterogeneity.