A Hybrid Technique for the Periodicity Characterization of Genomic Sequence Data

The detection of structure within the DNA sequence has long captivated the interest of the research community. Among the various statistical characterizations of sequence data, one measure of structure within sequences is the degree of correlation or periodicity at various displacements along the sequence. Periodicity characterization of sequence data provides a compact and informative representation that has been used in many studies of structure within genomic sequences, including DNA sequence analysis [1], gene and exon detection [2], tandem repeat detection [3], and DNA sequence search and retrieval [4].To measure such periodicity, autocorrelation has been widely employed [1, 5–11]. Similarly, Fourier analysis and its variants have been used for periodicity characterization of sequences [4, 9, 12–24]. In some cases [25, 26], the Fourier transform of the autocorrelation sequence has also been computed, however using existing symbolic-numeric mappings such as binary indicator sequences [27], this transform can also be calculated without first determining the autocorrelation. Other recent promising approaches to periodicity characterization for biological sequences include the periodicity transform [28], the exactly periodic subspace decomposition [3], and maximum-likelihood statistical periodicity [29], however these techniques have yet to be adopted by biologists for the purposes of sequence structure characterization.Studies of structure within sequences, such as those referenced above, have tended to use either the autocorrelation or the Fourier transform, and to the author's knowledge, the limitations of each have not been compared in this context. In this paper, the limitations of both approaches are investigated using synthetic symbolic sequences, and caveats to their characterization of sequence data are discussed. A hybrid approach to periodicity characterization of symbolic sequence data is introduced, and its use is illustrated in a comparative manner on