Sequence Compositional Complexity of DNA through an Entropic Segmentation Method

Román-Roldán, Ramón; Bernaola‐Galván, Pedro; Oliver, José Luis Tejera

doi:10.1103/physrevlett.80.1344

Cited by 79 publications

(95 citation statements)

References 32 publications

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“…During the past ten years, there has been intense discussion about the existence, the nature and the origin of LRC in DNA sequences. Besides Fourier and autocorrelation analysis, different techniques including mutual information functions [61,71,77,78], DNA walk representation [64,75,79,80,81,82,83,84], Zipf analysis [85,86,87] and entropies [88,89,90,91] were used for statistical analysis of DNA sequences. A lot of effort has been spent to adress rather struggling questions.…”

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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“…Chose a second random number r ∈ [0, 1] and compare it to the value of the exit distance distribution q P U,n or q P Y,n depending on the current state on the chain. 4. If r ≤ q P U,n (or r ≤ q P Y,n ) then the sequence is extended by n units of P U (or P Y ).…”

Section: A Model Dnamentioning

confidence: 99%

“…The observed complexity of these nested sequences has been shaped during evolutionary time based on functional needs. Processes like single nucleotide mutations, insertion and deletion of segments, multiple repetitions of elements acting simultaneously over different length and time scales have shaped the complexity of current day genomes producing intriguing statistical properties [3][4][5][6][7][8]. In this latter setting early investigations have shown that the succession of bases along coding regions in higher organisms presents short range correlations, whereas non-coding regions exhibit long-range correlations [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

DNA viewed as an out-of-equilibrium structure

Provata

Nicolis

2014

Phys. Rev. E

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The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory and information theory. The use of chi-square tests shows that DNA cannot be described as a low order Markov chain of order up to r = 6. Although detailed balance seems to hold at the level of purine-pyrimidine notation it fails when all four basepairs are considered, suggesting spatial asymmetry and irreversibility. Furthermore, the block entropy does not increase linearly with the block size, reflecting the long range nature of the correlations in the human genomic sequences. To probe locally the spatial structure of the chain we study the exit distances from a specific symbol, the distribution of recurrence distances and the Hurst exponent, all of which show power law tails and long range characteristics. These results suggest that human DNA can be viewed as a non-equilibrium structure maintained in its state through interactions with a constantly changing environment. Based solely on the exit distance distribution accounting for the nonequilibrium statistics and using the Monte Carlo rejection sampling method we construct a model DNA sequence. This method allows to keep all long range and short range statistical characteristics of the original sequence. The model sequence presents the same characteristic exponents as the natural DNA but fails to capture point-to-point details. *

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“…We therefore do not introduce further segment boundaries. the first approach, the Jensen-Shannon divergences of new segment boundaries are tested for statistical significance against various χ 2 distributions with the appropriate degrees of freedom (Bernaola-Galván et al, 1996;Román-Roldán et al, 1998). When no new segment boundaries are more significant than the chosen confidence level p, the recursive segmentation terminates.…”

Section: Segmentationmentioning

confidence: 99%

“…To find the unknown segment boundaries t i,m i separating segments m i and m i + 1, we use the recursive segmentation scheme introduced by Bernaola-Galván et al (1996) and Román-Roldán et al (1998). In this segmentation scheme, we check how likely it is for the point t in the time series x = (x 1 , .…”

Section: Segmentationmentioning

confidence: 99%

The Japanese Economy in Crises: A Time Series Segmentation Study

et al. 2012

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The authors performed a comprehensive time series segmentation study on the 36 Nikkei Japanese industry indices from 1 January 1996 to 11 June 2010. From the temporal distributions of the clustered segments, we found that the Japanese economy never fully recovered from the extended 1997-2003 crisis, and responded to the most recent global financial crisis in five stages. Of these, the second and main stage affecting 21 industries lasted only 27 days, in contrast to the two-and-a-half-years acrossthe-board recovery from the 1997-2003 financial crisis. We constructed the minimum spanning trees (MSTs) to visualize the Pearson cross correlations between Japanese industries over five macroeconomic periods:

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Sequence Compositional Complexity of DNA through an Entropic Segmentation Method

Cited by 79 publications

References 32 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

DNA viewed as an out-of-equilibrium structure

The Japanese Economy in Crises: A Time Series Segmentation Study

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