Analyzing the Variability of the 3D Structure of Chromatin Fiber Using Statistical Shape Theory

The relationship between geometric folding of the chromatin fiber and genome function is a key issue in cell biology. We propose different approaches based on statistical shape theory to investigate the geometric variability of chromatin folding in nuclei of interphase human fibroblasts. Our main purpose is to assess the degree of variability of folding of the chromatin fiber, measured by fluorescent in situ hybridization, using BAC probes in combination with 3D confocal microscopy. We employ point-based registration, the complex Bingham distribution, generalized Procrustes analysis, and the Kendall spherical coordinate system. The approaches have been applied using 337 3D multi-channel microscopy images. We have analyzed the geometric structure formed by gene-rich highly expressed genomic regions and areas that are gene-poor and have a low transcriptional activity. It turned out that the structure formed by these genomic regions exhibit high shape variation, however, most of them can be characterized by a non-uniform shape distribution.