Power law exponents characterizing human DNA

Abstract

The size distributions of all known coding and noncoding DNA sequences are studied in all human chromosomes. In a unified approach, both introns and intergenic regions are treated as noncoding regions. The distributions of noncoding segments Pnc S of size S present long tails Pnc S S−1− nc, with exponents nc ranging between 0.71 for chromosome 13 and 1.2 for chromosome 19 . On the contrary, the exponential, short-range decay terms dominate in the distributions of coding exon segments Pc S in all chromosomes. Aiming to address the emergence of these statistical features, minimal, stochastic, mean-field models are proposed, based on randomly aggregating DNA strings with duplication, influx and outflux of genomic segments. These minimal models produce both the short-range statistics in the coding and the observed power law and fractal statistics in the noncoding DNA.