The relationship between the hidden periodicities in DNA sequences and the nucleosome units is investigated. It is shown that in the vicinity of lengths of about 200 bases there are statistically significant periodicities which remain approximately universal for exon-intron sequences both in the different genes and the different eukaryotic species. The additional analysis displays, nevertheless, that these approximately coincident universal periodicities can be generated by a variety of mechanisms. The relevance of the features observed to the structure of chromatin is discussed.

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.

A method of Transitional Automorphic Mapping of the Genome on Itself (TAMGI) is aimed at combining detection and reconstruction of correlational and quasi-periodic motifs in the viral genomic RNA/DNA sequences. The motifs reconstructed by TAMGI are robust with respect to indels and point mutations and can be tried as putative therapeutic targets. We developed and tested the relevant theory and statistical criteria for TAMGI applications. The applications of TAMGI are illustrated by the study of motifs in the genomes of the severe acute respiratory syndrome coronaviruses SARS-CoV and SARS-CoV-2 (the latter coronavirus SARS-CoV-2 being responsible for the COVID-19 pandemic) packaged within filament-like helical capsid. Such ribonucleocapsid is transported into spherical membrane envelope with incorporated spike glycoproteins. Two other examples concern the genomes of viruses with icosahedral capsids, satellite tobacco mosaic virus (STMV) and bacteriophage PHIX174. A part of the quasi-periodic motifs in these viral genomes was evolved due to weakly specific cooperative interaction between genomic ssRNA/ssDNA and nucleocapsid proteins. The symmetry of the capsids leads to the natural selection of specific quasi-periodic motifs in the related genomic sequences. Generally, TAMGI provides a convenient tool for the study of numerous molecular mechanisms with participation of both quasi-periodic motifs and complete repeats, the genome organization, contextual analysis of cis/trans regulatory elements, data mining, and correlations in the genomic sequences.

Fourier analysis of the short-range periodicities for the complete set of sequences coding for tRNA genes in genome of Bacillus subtilis proves that periodicities with periods p = 2, 3, 4, and 6 sites are the inherent properties of tRNAs. The related periodicities should be understood in a broad statistical sense and their identifying needs the elaborate statistical methods. To improve the statistics, the analysis of significant periodicities was performed for the binary R-Y, S-W, and K-M sequences. Generally, such short-range periodicities are produced via biased positioning of particular nucleotides rather than via the tandem multiplication and subsequent modifications of repeats, though the latter mechanism may also be realized. Quasi-coherently piercing long segments of tRNA, the short-range periodicities create the effective long-range structural coupling between the acceptor stem and the anticodon loop and may participate in the mechanisms of molecular recognition. The periodicities with p = 2 and 4 provide the natural ground for the translation with spontaneous or programmed frameshifting and are present in tRNAs decoding the most frameshift-prone codons. The observation of short-range periodicities suggests that the mechanisms of amino-acylation of tRNAs and codon-anticodon pairing are not independent. Their study may also provide the important information related to the origin and evolution of the genetic code.