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

Abstract

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].

Influence of the genomic sequence on the primary structure of chromatin

“…As previously reported in subsection 'Modelling of in vivo nucleosome occupancy data in S. cerevisiae' (Figure 33), this statistical nucleosome ordering can also be diagnosed from the periodic modulations observed in the auto-correlation function C( s) = δY (s)δY (s + s) . But in addition and very importantly, when plotted in a logarithmic representation, the power spectrum displays a very convincing power law decay S(k) ∝ k −ν , with exponent ν = 2H − 1 = 0.74 ± 0.02 (H = 0.87) that is likely to be a direct consequence of the large-scale (low frequency k < 1/200) LRC regime observed in the yeast DNA bending profile in Audit et al (2001Audit et al ( , 2002Audit et al ( , 2004.…”

“…As illustrated in Figure 41(b), this simply means that nucleosomes adapt themselves better on sequences that display a 10 bp periodicity with AA/TT/AT that oscillate in phase with each other and facing the minor groove, and out of phase with GC facing the major groove. As originally pointed out in Audit et al (2001Audit et al ( , 2002Audit et al ( , 2004, when performing time-frequency analysis of eukaryotic genomic sequences using either dinucleotide codings or more elaborated di-or tri-nucleotide experimental tables coding for the structural and/or bending properties of the DNA double helix, there is no significant peak that emerges in the power spectrum at the frequency 1/10 bp −1 . This confirms that if locally the 10 bp periodicity sketched in Figure 41(b) can help to phase and position some nucleosomes, at the genome scale this periodicity is clearly not exploited to position the majority of well-defined nucleosomes observed in vivo.…”

“…But these periodically distributed motifs concern only 5% of sequences that present affinities for the histone octamer significantly larger than average (Lowary and Widom 1997) and cannot account for more than ∼20% of the in vivo nucleosome positioning above what is expected by chance (Peckham et al 2007;Yuan and Liu 2008). Alternatively, similar sequence motifs were shown to present long-range correlations (LRC) along the genome as the signature of the majority of nucleosomes that corresponds to 95% of bulk genomic DNA sequences having an affinity for the histone octamer similar to that of random sequences (Audit et al 2001(Audit et al , 2002(Audit et al , 2004Arneodo et al 2011). Hence, in contrast to the tight histone binding obtained with an adequate periodic ('deterministic') distribution of bending sites, LRC likely facilitate the formation of some large-scale intrinsic curvature due to a persistent distribution of DNA curvature sites that predisposes DNA to make small (random) loops favoring the positioning of the histone core throughout a major part of the genome (Vaillant et al 2005(Vaillant et al , 2006Moukhtar et al 2007Moukhtar et al , 2009Moukhtar et al , 2010Moukhtar et al , 2011.…”

Identification of higher-order functional domains in the human ENCODE regions

“…As such, wavelets are far better suited to detect domain-type behaviors that span discrete genomic intervals. Wavelets have been used for the analysis of genomic data to uncover local periodic patterns in DNA-bending profiles (Audit et al 2004) and gene-expression data (Allen et al 2003;Jeong et al 2004) to predict protein structures (Lio and Vannucci 2000) and to correlate a variety of genomic data on multiple scales in microbial genomes (Allen et al 2006), and a variety of other applications (Lio 2003).…”

Long-range Periodic Patterns in Microbial Genomes Indicate Significant Multi-scale Chromosomal Organization

“…In order to detect such long-range periodic patterns in inherently noisy chromosome positiondependent data, wavelet analysis has been used in several studies [13,15] (Figure 1). This method has previously been used to detect patterns in gene orientation [14], DNAbending profiles [16], and gene expression data [17,18] in prokaryotes, as well as GC/AT skew oscillations in human chromosomes [19]. These studies have revealed that genome sequences are generally nonrandom with respect to chromosome position, and that long-range correlations in certain properties (e.g., gene orientation; [14]) exist across many different length-scales.…”