Fourier and Wavelet Transform Analysis, a Tool for Visualizing Regular Patterns in DNA Sequences

Dodin, Guy; Vandergheynst, Pierre; Levoir, P.; Cordier, C.; Marcourt, Laurence

doi:10.1006/jtbi.2000.2127

Cited by 105 publications

(64 citation statements)

References 13 publications

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“…Alternatively, the wavelet transform (WT) [110,111,112,113,114] has been proposed as a very powerful technique for fractal analysis of DNA sequences [102,115] (see also Ref. [116] where the WT is used as a tool for visualizing regular patterns in DNA sequences). As already experienced in various fields, the WT can be seen as a mathematical microscope that is well suited for characterizing the scaling properties of fractal objects and this even in the presence of some polynomial component [113,117,118,119,120].…”

Section: Introductionmentioning

confidence: 99%

Wavelet Analysis of DNA Bending Profiles reveals Structural Constraints on the Evolution of Genomic Sequences

Audit

Vaillant

Arnéodo

et al. 2004

Journal of Biological Physics

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Abstract. Analyses of genomic DNA sequences have shown in previous works that base pairs are correlated at large distances with scale-invariant statistical properties. We show in the present study that these correlations between nucleotides (letters) result in fact from long-range correlations (LRC) between sequence-dependent DNA structural elements (words) involved in the packaging of DNA in chromatin. Using the wavelet transform technique, we perform a comparative analysis of the DNA text and of the corresponding bending profiles generated with curvature tables based on nucleosome positioning data. This exploration through the optics of the so-called 'wavelet transform microscope' reveals a characteristic scale of 100 − 200 bp that separates two regimes of different LRC. We focus here on the existence of LRC in the small-scale regime ( 200 bp). Analysis of genomes in the three kingdoms reveals that this regime is specifically associated to the presence of nucleosomes. Indeed, small scale LRC are observed in eukaryotic genomes and to a less extent in archaeal genomes, in contrast with their absence in eubacterial genomes. Similarly, this regime is observed in eukaryotic but not in bacterial viral DNA genomes. There is one exception for genomes of Poxviruses, the only animal DNA viruses that do not replicate in the cell nucleus and do not present small scale LRC. Furthermore, no small scale LRC are detected in the genomes of all examined RNA viruses, with one exception in the case of retroviruses. Altogether, these results strongly suggest that small-scale LRC are a signature of the nucleosomal structure. Finally, we discuss possible interpretations of these small-scale LRC in terms of the mechanisms that govern the positioning, the stability and the dynamics of the nucleosomes along the DNA chain. This paper is maily devoted to a pedagogical presentation of the theoretical concepts and physical methods which are well suited to perform a statistical analysis of genomic sequences. We review the results obtained with the so-called waveletbased multifractal analysis when investigating the DNA sequences of various organisms in the three kingdoms. Some of these results have been announced in B. Audit et al. [1,2].

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Section: Introductionmentioning

confidence: 99%

Wavelet Analysis of DNA Bending Profiles reveals Structural Constraints on the Evolution of Genomic Sequences

Audit

Vaillant

Arnéodo

et al. 2004

Journal of Biological Physics

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“…Thus, spectral density of the longer periods should not be distributed onto the shorter periods, as occurs in the case of symbolical sequence decomposition into a certain set of numerical sequences and following the use of Fourier transformation [9][10][11][12][13][14][15][16][17].…”

Section: Methods and Algorithmsmentioning

confidence: 99%

“…The direct transformation of a symbolical text to a numerical sequence with replacement of symbols by numbers is not an adequate transformation, because we actually introduce weights for symbols, leading to distortion of statistical properties of the initial symbolical sequence. Earlier, several approaches were used for solving this problem [9][10][11][12][13][14][15][16][17]. The most widely used is the method involving construction from the given symbolical sequence of m sequences consisting of the numbers zero and one, formed according to the law: x(i,j)=1, if the symbol a i occupies a site j, and x(i,j)=0 in all other cases.…”

Section: Introductionmentioning

confidence: 99%

Information decomposition method to analyze symbolical sequences

Korotkov

Korotkova²,

Kudryashov³

2003

Physics Letters A

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We developed a non-parametric method of Information Decomposition (ID) of a content of any symbolical sequence. The method is based on the calculation of Shannon mutual information between analyzed and artificial symbolical sequences, and allows the revealing of latent periodicity in any symbolical sequence. We show the stability of the ID method in the case of a large number of random letter changes in an analyzed symbolic sequence. We demonstrate the possibilities of the method, analyzing both poems, and DNA and protein sequences. In DNA and protein sequences we show the existence of many DNA and amino acid sequences with different types and lengths of latent periodicity. The possible origin of latent periodicity for different symbolical sequences is discussed.

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“…В частности, скрытые тандемные повторы без вставок и делеций получили название нечетких тандемных повторов (FTR) [3,4]. Проблема выявления такой скрытой периодичности в биологической последовательности (строке) актуальна для поиска древних микро-и минисателлитов, генотипирования микроорганизмов с помощью VNTR (Variable Number Tandem Repeats) районов в их геномах [5][6][7][8][9], определения участков генетической нестабильности и анализа их влияния на проявление заболеваний [10][11][12] 21 поиска функциональных регулярных структур в белках [13][14][15][16], и для других подобных задач.…”

Section: Introductionunclassified

“…Для выявления периодичности в биологических строках ранее широко использовались методы Фурье-и вейвлет-анализа [17][18][19][20][21], комбинаторные методы и методы динамического программирования [1, 3,4,[22][23][24], различные статистические критерии проверки однородности строк [25][26][27][28][29] и др., см., например, обзор [30]. Однако по сравнению со статистическими критериями Фурье-анализ имеет плохую чувствительность к паттернам периодичности, размер которых в несколько раз превышает размер алфавита анализируемой строки [26].…”

Section: Introductionunclassified

Joint Use of Different Homogeneity Testing Criteria for Latent Periodicity Revelation in Biological Sequences

Чалей¹,

Chaley²

2007

Math.Biol.Bioinf.

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Fourier and Wavelet Transform Analysis, a Tool for Visualizing Regular Patterns in DNA Sequences

Cited by 105 publications

References 13 publications

Wavelet Analysis of DNA Bending Profiles reveals Structural Constraints on the Evolution of Genomic Sequences

Wavelet Analysis of DNA Bending Profiles reveals Structural Constraints on the Evolution of Genomic Sequences

Information decomposition method to analyze symbolical sequences

Joint Use of Different Homogeneity Testing Criteria for Latent Periodicity Revelation in Biological Sequences

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