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

<p>Abstract</p> <p>Background</p> <p>Identification of approximate tandem repeats is an important task of broad significance and still remains a challenging problem of computational genomics. Often there is no single best approach to periodicity detection and a combination of different methods may improve the prediction accuracy. Discrete Fourier transform (DFT) has been extensively used to study primary periodicities in DNA sequences. Here we investigate the application of DFT method to identify and study alphoid higher order repeats.</p> <p>Results</p> <p>We used method based on DFT with mapping of symbolic into numerical sequence to identify and study alphoid higher order repeats (HOR). For HORs the power spectrum shows equidistant frequency pattern, with characteristic two-level hierarchical organization as signature of HOR. Our case study was the 16 mer HOR tandem in AC017075.8 from human chromosome 7. Very long array of equidistant peaks at multiple frequencies (more than a thousand higher harmonics) is based on fundamental frequency of 16 mer HOR. Pronounced subset of equidistant peaks is based on multiples of the fundamental HOR frequency (multiplication factor <it>n </it>for <it>n</it>mer) and higher harmonics. In general, <it>n</it>mer HOR-pattern contains equidistant secondary periodicity peaks, having a pronounced subset of equidistant primary periodicity peaks. This hierarchical pattern as signature for HOR detection is robust with respect to monomer insertions and deletions, random sequence insertions etc. For a monomeric alphoid sequence only primary periodicity peaks are present. The 1/<it>f</it>^{<it>β </it>}– noise and periodicity three pattern are missing from power spectra in alphoid regions, in accordance with expectations.</p> <p>Conclusion</p> <p>DFT provides a robust detection method for higher order periodicity. Easily recognizable HOR power spectrum is characterized by hierarchical two-level equidistant pattern: higher harmonics of the fundamental HOR-frequency (secondary periodicity) and a subset of pronounced peaks corresponding to constituent monomers (primary periodicity). The number of lower frequency peaks (secondary periodicity) below the frequency of the first primary periodicity peak reveals the size of <it>n</it>mer HOR, i.e., the number <it>n </it>of monomers contained in consensus HOR.</p

Computational methods of identification of pseudogenes based on functionality: entropy and GC content.

Spectral entropy and GC content analyses reveal comprehensive structural features of DNA sequences. To illustrate the significance of these features, we analyze the β-esterase gene cluster, including the Est-6 gene and the ψEst-6 putative pseudogene, in seven species of the Drosophila melanogaster subgroup. The spectral entropies show distinctly lower structural ordering for ψEst-6 than for Est-6 in all species studied. However, entropy accumulation is not a completely random process for either gene and it shows to be nucleotide dependent. Furthermore, GC content in synonymous positions is uniformly higher in Est-6 than in ψEst-6, in agreement with the reduced GC content generally observed in pseudogenes and nonfunctional sequences. The observed differences in entropy and GC content reflect an evolutionary shift associated with the process of pseudogenization and subsequent functional divergence of ψEst-6 and Est-6 after the duplication event. The data obtained show the relevance and significance of entropy and GC content analyses for pseudogene identification and for the comparative study of gene-pseudogene evolution