Poincaré recurrences of DNA sequences

Area of Science:

• Genomics
• Statistical Physics
• Bioinformatics

Background:

• Understanding DNA sequence statistical properties is crucial for deciphering genomic organization and evolutionary relationships.
• Poincaré recurrences offer a novel lens for analyzing complex, long-range patterns within biological sequences.

Purpose of the Study:

• To investigate the statistical properties of Poincaré recurrences in Homo sapiens, mammalian, and other DNA sequences.
• To explore the implications of these properties for understanding inter-species proximity and evolutionary history.

Main Methods:

• Analysis of large-scale DNA sequence data (up to 15 billion base pairs) from the Ensembl Genome database.
• Statistical examination of Poincaré recurrence probabilities and correlations using established mathematical frameworks.

Main Results:

• Poincaré recurrence probability decays algebraically with an exponent β≈4, despite pronounced oscillatory dependence.
• Recurrence correlations decay with an exponent ν≈0.6, indicating an anomalous superdiffusive walk.
• For Homo sapiens, the diffusion coefficient stabilizes at larger distances (>1 million base pairs), suggesting distinct statistical behavior.

Conclusions:

• The Poincaré recurrence approach reveals novel proximity features among different species.
• This method provides new insights into the evolutionary history and organization of genomes.
• The observed superdiffusive behavior and its convergence in human DNA warrant further investigation.