Three-Quasiperiodicity, Mutual Correlations, Ordering and Long-Range Modulations in Genomic Nucleotide Sequences for Viruses

Abstract

Using Fourier transform, we investigate the structural characteristics of genomes for several viruses. The mutual correlations and ordering of the different nucleotides in genomes are compared versus their counterparts from the random sequences with the same nucleotide composition. In order to assess the stastical significance of correlations and ordering we introduce the expression for structural entropy of a sequence and derive the corresponding analytical criteria. The method specially aimed at the investigation of the long-range correlations is described as well and the relationship between the long-range correlations and the modulations of three-quasiperiodicity is discussed.

Hierarchical structure of cascade of primary and secondary periodicities in Fourier power spectrum of alphoid higher order repeats

“…Spectral analysis employing Discrete Fourier transform is used to reveal periodicity in symbolic sequences, like genomic and protein sequences [ 7 , 9 , 14 , 16 , 17 , 20 , 36 - 53 ], to investigate long-range correlations [ 4 , 5 , 54 , 55 ] and to study the problem of sequence similarity [ 14 , 56 - 62 ].…”

“…A sharp peak of period three was found in a search for periodic regularities on a sample set of human exons [ 5 , 9 , 10 , 22 , 54 , 60 , 64 ]. The three-base periodicity in exons is caused by unbalanced nucleotide distributions in the three coding positions, while in intron sequences the nucleotides distribute uniformly.…”

Detection of Periodicities in Gene Sequences: A Maximum Likelihood Approach

“…Homologous periodicity occurs when short fragments of DNA are repeated in tandem to give periodic sequences [4]. Most current approaches for finding periodicities transform the symbolic DNA sequence to a numerical sequence [5], [6], [7]; these techniques are primarily aimed at the detection of homological periodicities. Some researchers have also explored the detection of imperfect or eroded periodicities which model a sequence of similar units repeated but with some changes.…”

Latent Periodicities in Genome Sequences

“…Most current approaches to detecting periodicities transform the symbolic sequences into numerical sequences and compute Fourier transform [11], [9], [12], [13] or perform exact periodic subspace decomposition (EPSD) [14]. Though this is computationally convenient, it imposes a mathematical structure that is not present in the data.…”