The architecture of the genome integrates scale independence with inverse symmetry

The simplest building blocks of the genome, the k-mers, show two properties that are widely observed. Their frequency distribution is scale-free (a variant Zipfian distribution), and the inverse symmetry of k-mers is observable on the same strand. These phenomena are linked; Watson–Crick base pairing generates inverse symmetry (IS) under the condition that the same frequency distribution of k-mers is present on both strands of the genome. A stable scale-free equilibrium distribution of k-mer frequency in all genomes is predicted by a purely probabilistic theory, the Conservation of Hartley–Shannon Information (CoHSI). This does not replace the diverse mechanism-based explanations of IS that have been advanced, but in principle, it aggregates all operative mechanisms. CoHSI predicts that both the scale-free distribution of k-mers and the IS that follows from it should decay gradually and stochastically as the genome size decreases and the length of the k-mers increases. These predictions were tested in 178 genomes from all domains of life and viruses. The precision of both the Zipfian distribution of k-mer frequency and of IS decayed progressively as the genome size decreased and k-mer length increased, regardless of the structure of the genome; DNA or RNA, nuclear or plastid, double- or single-stranded. No clear partition into IS-compliant and non-compliant genomes could be inferred. These results suggest that both IS and scale-free distributions of k-mer frequency in genomes are linked properties that emerge probabilistically and in a mechanism-agnostic manner across the three domains of life and viruses.