Poincar\'e recurrences of DNA sequence

TL;DR

This paper studies the statistical properties of Poincaré recurrences in DNA sequences, revealing algebraic decay and anomalous diffusion, which may provide insights into species evolution and genomic structure.

Contribution

It introduces a novel analysis of Poincaré recurrences in DNA, uncovering algebraic decay and super-diffusive behavior across species, especially in humans.

Findings

Recurrence probability decays algebraically with exponent ~4.

Correlations decay with exponent ~0.6, indicating super-diffusive walks.

In Homo sapiens, diffusion coefficient converges at large scales.

Abstract

We analyze the statistical properties of Poincar\'e recurrences of Homo sapiens, mammalian and other DNA sequences taken from Ensembl Genome data base with up to fifteen billions base pairs. We show that the probability of Poincar\'e recurrences decays in an algebraic way with the Poincar\'e exponent $\beta \approx 4$ even if oscillatory dependence is well pronounced. The correlations between recurrences decay with an exponent $\nu \approx 0.6$ that leads to an anomalous super-diffusive walk. However, for Homo sapiens sequences, with the largest available statistics, the diffusion coefficient converges to a finite value on distances larger than million base pairs. We argue that the approach based on Poncar\'e recurrences determines new proximity features between different species and shed a new light on their evolution history.