Spherical Harmonics for 3D Modeling of Chromosomes Territories in Normal and Aneuploid Nuclei

DNA is packaged into chromosomes, which occupy a specific region in the three-dimensional (3D) nuclear space known as the chromosome territories (CTs). The spatial organization (SO) of CTs within the nucleus is non-random and any disruption of this organization leads to undesired changes, such as disease states. Determining how CTs organize in the nucleus can allow us to unravel any changes occurring during aneuploidy (loss or gain of chromosomes), a hallmark of cancer. Here, we describe a 3D modeling approach to allow precise shape estimation and localization of CTs in the nucleus of human embryonic stem cells (hES) undergoing progressive but defined aneuploidy. The hES cell line WA09 acquires an extra copy of chromosome 12 in culture with increasing passages. Both diploid and aneuploid nuclei were analyzed to quantitate the differences in the localization of CTs for chromosome 12 as it transitions from euploidy to aneuploidy. The CTs were detected with chromosome specific DNA probes via multi-color fluorescence in situ hybridization (FISH) in conjunction with confocal microscopy. We employed spherical harmonic (SPHARM) surface modeling to generate a well-defined 3D surface for both the nuclei and enclosed CTs, thereby allowing precise quantification of their size and shape. The estimated models were compared across multiple cells by aligning the nuclei to a well-defined template followed by determining CT position with respect to a local landmark. Our results present evidence of statistically significant changes in the spatial organization of CTs in trisomy-12 cells when compared to diploid cells from the same population. Additionally we observed, that changes in CT proximity relationships may affect gene expression of co-regulated genes.