A Study of Fractality and Long-Range Order in the Distribution of Transposable Elements in Eukaryotic Genomes Using the Scaling Properties of Block Entropy and Box-Counting

Abstract

Repeats or Transposable Elements (TEs) are highly repeated sequence stretches, present in virtually all eukaryotic genomes. We explore the distribution of representative TEs from all major classes in entire chromosomes across various organisms. We employ two complementary approaches, the scaling of block entropy and box-counting. Both converge to the conclusion that well-developed fractality is typical of small genomes while in large genomes it appears sporadically and in some cases is rudimentary. The human genome is particularly prone to develop this pattern, as TE chromosomal distributions therein are often highly clustered and inhomogeneous. Comparing with previous works, where occurrence of power-law-like size distributions in inter-repeat distances is studied, we conclude that fractality in entire chromosomes is a more stringent (thus less often encountered) condition. We have formulated a simple evolutionary scenario for the genomic dynamics of TEs, which may account for their fractal distribution in real genomes. The observed fractality and long-range properties of TE genomic distributions have probably contributed to the formation of the “fractal globule”, a model for the confined chromatin organization of the eukaryotic nucleus proposed on the basis of experimental evidence.

Keywords

• fractality
• block-entropy
• Shannon entropy
• entropic scaling
• box-counting
• power-law distribution
• genome evolution
• transposable elements
• eukaryotic genome