Spectral sum rules and search for periodicities in DNA sequences

TL;DR

This paper explores the detection of periodic patterns in DNA sequences using Fourier transform and spectral sum rules, providing a statistical framework to distinguish true periodicities from random noise.

Contribution

It introduces a novel application of spectral sum rules and De Finetti distribution to assess the significance of periodicities in genomic DNA sequences.

Findings

Spectral sum rules effectively identify significant periodicities.

De Finetti distribution offers a practical approximation for significance testing.

Fourier analysis reveals latent periodicities despite mutations.

Abstract

Periodic patterns play the important regulatory and structural roles in genomic DNA sequences. Commonly, the underlying periodicities should be understood in a broad statistical sense, since the corresponding periodic patterns have been strongly distorted by the random point mutations and insertions/deletions during molecular evolution. The latent periodicities in DNA sequences can be efficiently displayed by Fourier transform. The criteria of significance for observed periodicities are obtained via the comparison versus the counterpart characteristics of the reference random sequences. We show that the restrictions imposed on the significance criteria by the rigorous spectral sum rules can be rationally described with De Finetti distribution. This distribution provides the convenient intermediate asymptotic form between Rayleigh distribution and exact combinatoric theory.