Genome-level parameters describe the pan-nuclear fractal nature of eukaryotic interphase chromosomal arrangement

Long-range inter-chromosomal interactions in the interphase nucleus subsume critical genome-level regulatory functions such as transcription and gene expression. To decipher a physical basis of diverse pan-nuclear inter-chromosomal arrangement that facilitates these processes, we investigate the scaling effects as obtained from disparate eukaryotic genomes and compare their total number of genes with chromosome size. First, we derived the pan-nuclear average fractal dimension of inter-chromosomal arrangement in interphase nuclei of different species and corroborated our predictions with independently reported results. Then, we described the different patterns across disparate unicellular and multicellular eukaryotes. We report that, unicellular lower eukaryotes have inter-chromosomal fractal dimension ≈ 1 at pan-nuclear dimensions, which is analogous to the multi-polymer crumpled globule model. Multi-fractal dimensions, corresponding to different inter-chromosomal arrangements emerged from multicellular eukaryotes, such that closely related species have relatively similar patterns. Using this theoretical approach, we computed that the average fractal dimension from human acrocentric versus metacentric chromosomes was distinct, implying that a multi-fractal nature of inter-chromosomal geometry may facilitate viable large-scale chromosomal aberrations, such as Robertsonian translocation. Next, based on inter-chromosomal geometry, we also report that this average multi-fractal dimension in nocturnal mammals is distinct from diurnal ones, and our result seems to corroborate the plasticity of the inter-chromosomal arrangement reported among nocturnal species. (For example, the arrangement of heterochromatin versus euchromatin in rod photoreceptor and fibroblast cells of Mus musculus is inverted.) Altogether, our results substantiate that genome-level constraints have also co-evolved with the average pan-nuclear fractal dimension of inter-chromosomal folding during eukaryotic evolution.