Fractality and Entropic Scaling in the Chromosomal Distribution of Conserved Noncoding Elements in the Human Genome

Conserved, ultraconserved and other classes of constrained non-coding elements (referred as CNEs) represent one of the mysteries of current comparative genomics. These elements are defined using various degrees of sequence similarity between organisms and several thresholds of minimal length and are often marked by extreme conservation that frequently exceeds the one observed for protein-coding sequences. We here explore the distribution of different classes of CNEs in entire chromosomes, in the human genome. We employ two complementary methodologies, the scaling of block entropy and box-counting, with the aim to assess fractal characteristics of different CNE datasets. Both approaches converge to the conclusion that well-developed fractality is characteristic of elements that are either marked by extreme conservation between two or more organisms or are of ancient origin, i.e. conserved between distant organisms across evolution. Given that CNEs are often clustered around genes, especially those that regulate developmental processes, we verify by appropriate gene masking that fractal-like patterns emerge irrespectively of whether elements found in proximity or inside genes are excluded or not. An evolutionary scenario is proposed, involving genomic events, that might account for fractal distribution of CNEs in the human genome as indicated through numerical simulations.