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BMC Mol BiolBMC Molecular Biology1471-2199BioMed Central 1471-2199-5-141533314010.1186/1471-2199-5-14Research ArticleSequence periodicity of Escherichia coli is concentrated in intergenic regions Hosid Sergey 1hosid@research.haifa.ac.ilTrifonov Edward N 1trifonov@research.haifa.ac.ilBolshoy Alexander 1bolshoy@research.haifa.ac.il1 Genome Diversity Center, Institute of Evolution, University of Haifa, Mt. Carmel 31905 ISRAEL2004 26 8 2004 5 14 14 31 12 2003 26 8 2004 Copyright © 2004 Hosid et al; licensee BioMed Central Ltd.2004Hosid et al; licensee BioMed Central Ltd.This is an open-access article distributed under the terms of the Creative Commons Attribution License (), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Background
Sequence periodicity with a period close to the DNA helical repeat is a very basic genomic property. This genomic feature was demonstrated for many prokaryotic genomes. The Escherichia coli sequences display the period close to 11 base pairs.

Results
Here we demonstrate that practically only ApA/TpT dinucleotides contribute to overall dinucleotide periodicity in Escherichia coli. The noncoding sequences reveal this periodicity much more prominently compared to protein-coding sequences. The sequence periodicity of ApC/GpT, ApT and GpC dinucleotides along the Escherichia coli K-12 is found to be located as well mainly within the intergenic regions.

Conclusions
The observed concentration of the dinucleotide sequence periodicity in the intergenic regions of E. coli suggests that the periodicity is a typical property of prokaryotic intergenic regions. We suppose that this preferential distribution of dinucleotide periodicity serves many biological functions; first of all, the regulation of transcription.
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Background
DNA sequence periodicity with the period about 10–11 base pairs (bp) has been long known in eukaryotic DNA sequences. It was discovered recently in prokaryotic sequences as well [1-6]. The periodicity in Eubacteria sequences usually shows the period close to 11 bp [1]. This period is clearly different from the structural helical period of 10.5–10.6 bp/turn [7,8]. The difference was interpreted [1,2] as a possible reflection of the sequence dependent writhe of prokaryotic DNA. In the work [9] it was demonstrated that the periodicity in the bacterial genomes, in E. coli as well, is distributed in a non-uniform way, in scattered segments of the size 100–150 bases. It was also known for a long time that quite a few DNA promoter regions of E. coli possess the sequence periodicity of AA and TT dinucleotides [10].

The sequence periodicity of AA/TT dinucleotides is frequently associated with sequence-dependent DNA curvature, which is known to play an important role in the initiation of transcription of many genes (for reviews, see [11-15]). Using different models and approaches for prediction of intrinsic DNA curvature it was shown that many E. coli promoters have upstream curved sequences [16,17]. Pedersen et al. [18] showed that promoter area frequently has an unusual sequence structure. This region possesses higher DNA curvature, more rigid and less stable. Moreover, in our study of prokaryotic terminators of transcription (Hosid and Bolshoy, submitted) we have found that in E. coli DNA curvature peaks are frequently located downstream of the CDS.

Since the dinucleotide periodicity with the period close to the helical repeat is associated with DNA intrinsic curvature [19-23], the curvature distribution along DNA would suggest similar distribution of DNA sequence periodicity.

In this work, the sequence dinucleotide periodicity in E. coli and its distribution along the genome are systematically analyzed. A strong preference of intergenic regions to express the sequence periodicity of AA, AC, GC, and TT dinucleotides is discovered.

Results and Discussion
Positional autocorrelation analysis of the nucleotide sequences is an appropriate tool to detect all major characteristic distances in the sequences, the periodicities in particular. The complete genome of E. coli, as well as its coding and noncoding regions, was subjected to this procedure. Resulting autocorrelation profiles for all 16 dinucleotides (data not shown) were further analyzed by Fourier transform. In Fig. 1 the corresponding spectra are shown. The analysis demonstrates presence of the sequence periodicity of AA and TT dinucleotides with a period close to 11 bp mostly in intergenic regions, and weaker periodicity of AC and GC notably exclusively in intergenic regions. All 16 dinucleotides show periodicity of 3 bp, a well-known characteristics of the coding sequences, e.g. [24,25]. Weak 2 bp periodicity of AT and TA is also observed in intergenic regions. It indicates, perhaps, presence of tandem ApT repeats. A weak 10 bp periodicity of GC in intergenic regions, probably, corresponds to terminator regions (work in progress). The amplitudes of the 11 bp periodicity of AA and TT are the highest, even comparable with 3 bp coding periodicity. We, thus, focused on AA and TT distributions.

Figure 1 Periodograms of the distance distributions of 16 dinucleotides in E. coli genome. The complete nucleotide sequence of E. coli, as well as subsets of its coding and noncoding regions, was subjected to the positional autocorrelation analysis for all 16 dinucleotides separately. Resulting autocorrelation profiles were after that analyzed by Fourier transform. The black lines correspond to the whole genome, the blue curves – to the coding sequences, and the red curves – to the noncoding sequences.

To screen the genome of E. coli and find out where the periodical regions are located, we chose the period 11.2 bp [1,2,5] and this study (Fig. 1); and the window of 150 bp [9,26]. We used periodical AA and TT probes with the above periodicity to correlate with the E. coli genome sequence and to detect the periodical sites. This calculation shows that the periodicity is not evenly distributed along the E. coli genome.

In Fig. 2, the typical maps for several large segments of the E. coli genome are shown. The periodicity is distinctly located in certain regions. Many of the peaks observed are found to correspond to the intergenic regions (indicated by the black bars at the top). For example, two such peaks of periodicity in Fig. 2a correspond to the intergenic regions. Three such maxima are observed in Fig. 2b, three in Fig. 2c, and two in Fig. 2d. For the genome sections in Fig. 2 about 2/3 of the intergenic regions are associated with the local periodicity.

Figure 2 Four examples of periodicity maps for fragments of E. coli genome. The maps were smoothed by running average with window 51 bp. The black bars on the top of the plot correspond to positions of intergenic regions.

To verify the apparent strong correlation between the intergenic regions and AA/TT periodicity, we split intergenic regions in several families by size and analyzed the subsets separately by aligning (centering) the regions and summing up the respective local periodicity distributions. The combined maps for intergenic regions with a size from 50 to 150 bp, from 150 to 250 bp, from 250 to 350 bp, from 350 to 450 bp, and from 450 to 550 bp are shown in Fig. 3. This figure demonstrates, indeed, that intergenic regions are typically periodic, irrespective of the size. The average amplitudes of the observed periodicities – 0.1–0.25 units – are comparable with the amplitudes in Fig. 2, which indicates that, indeed a large proportion of the intergenic regions are periodical.

Figure 3 The averaged maps of periodicity are synchronized at the centers of intergenic regions and smoothed by a running average of 51 bp. Five families of the intergenic regions with different lengths are presented: a) 100 ± 50, bp 1073 sequences, b) 200 ± 50 bp, 602 sequences, c) 300 ± 50 bp, 319 sequences, d) 400 ± 50 bp, 160 sequences, and e) 500 ± 50 bp, 78 sequences. The black bars at the bottom of the each figure correspond to the average intergenic region. The gray bands around black dashed lines correspond to standard deviations around randomized background.

To verify the choice of the period 11.2 bases, we calculated the periodicity maps for highly populated group of the regions of the size 200 ± 50 bp, by assuming different periods in the range 10.5–12.5 bases. The resonance 3D plot in Fig. 4 indicates that the best-fit period is 11.3 ± 0.4 bp, which confirms earlier estimates of the E. coli DNA sequence periodicity.

Figure 4 The 3D resonance plot for the intergenic regions of length 200 ± 50 bp. The maximum of resonance the plot corresponds to period 11.3 ± 0.4 bp. The contour around the maximum is also shown as a projection at the base line level.

The spectral analysis (Fig. 1) and examples of the periodicity distribution maps (Fig. 2) show that apart from described correlation among the intergenic regions and AA/TT periodicity, there are numerous sites of periodicity located within coding sequences. Work is in progress to find out the functional relevance, if any, of these sites.

Conclusions
The observed concentration of the sequence periodicity in the intergenic regions corroborates earlier results and suggests that the periodicity is a typical property of the intergenic regions.

Methods
Genome data
The sequence of the whole genome of Escherichia coli K-12 MG1655, locus U00096, 4639221 base pairs, was taken from the National Center of Biotechnology Information . Intergenic regions were identified in accordance with the annotation to this genome of E. coli and gathered in a separate dataset.

Fourier transform of positional autocorrelation function
Autocorrelation profile X was calculated for each dinucleotide separately. For the calculation of ApA autocorrelation, for example, we calculated the number of occurrences of pairs ApA – ApA in a distance k, and designated it by Xk. Spectral analysis of autocorrelation profile X was obtained using the following formulae:



where fp is normalized wave-function amplitude of period p, X is an autocorrelation profile for one chosen dinucleotide, Xi is its value in position i,  is its average value, and W is a maximal considered autocorrelation distance (in our case 100 bp).

Sequence periodicity
As a probe of periodicity the sine waves with period T were taken to describe idealized periodical distribution of AA and TT dinucleotides within window W. The probes were correlated with E. coli sequences by moving the probes along the sequences and calculating the value C for every position.



where i is an index of a dinucleotide position in the window W and



The value Cmax is introduced for the normalization purposes. It is calculated as follows:



where i is a position in the window W and



Ideally periodical sequence segments would be, therefore, described by C = 1, while segments with no periodicity would correspond to C = 0. The results of these calculations are presented as maps of the sequence periodicity. The four sample maps are shown in Fig. 2a,2b,2c,2d.

Synchronization of the maps
The maps around intergenic regions were combined (summed) separately for the groups of similar sizes of the intergenic regions. Five such groups were analyzed: 100 ± 50 bp, 200 ± 50 bp, 300 ± 50 bp, 400 ± 50 bp, and 500 ± 50 bp. For each group the maps were synchronized at the respective intergenic centers and the sums of the maps were calculated and smoothed by a running average within 51 bp. The standard deviations for the combined plots were estimated by generating random sequences of the same size and dinucleotides composition for each group separately and averaging the respective periodicity maps.

The resonance plot
The resonance 3D plot for the intergenic regions of length 200 ± 50 bp was built from calculations with different periods T in the interval 10–12.5 bp. One-third (202) of the most periodic maps of this group was taken for the calculation. The maps for different periods T were smoothed five times by a running average over 51 bp. The baselines were set to 0. The surface of 3D plot was smoothed 3 times by a running average over 9 point square elements, on the grid with separations 0.1 bp for T, and 20 bp for sequence position.

Competing interests
None declared.

Authors' contributions
SH carried out all graphics. ENT and AB participated in the design of the study and analysis of results. All authors drafted the manuscript. All authors read and approved the final manuscript.

Acknowledgments
We thank V. Kirzhner and all members of the Genome Diversity Center for fruitful discussions and critical comments on the paper. A.B. is grateful to Professors T. Ratiu and J.H. Maddocks from the Bernoulli Institute at the Swiss Federal Institute of Technology for the kind invitation to visit "Centre Bernoulli" for two months. S.H. and A.B. are partially supported by the FIRST Foundation of the Israel Academy of Science and Humanities.
==== Refs
Herzel H Weiss O Trifonov EN  Sequence periodicity in complete genomes of Archaea suggests positive supercoiling J Biomol Struct Dyn 1998 16 341 345 9833672 
Herzel H Weiss O Trifonov EN  10–11 bp periodicities in complete genomes reflect protein structure and DNA folding Bioinformatics 1999 15 187 193 10222405 10.1093/bioinformatics/15.3.187 
Ozoline ON Deev AA Trifonov EN  DNA bendability – a novel feature in E-coli promoter recognition J Biomol Struct Dyn 1999 16 825 831 10217452 
Tomita M Wada M Kawashima Y  ApA dinucleotide periodicity in prokaryote, eukaryote, and organelle genomes J Mol Evol 1999 49 182 192 10441670 
Worning P Jensen LJ Nelson KE Brunak S Ussery DW  Structural analysis of DNA sequence: evidence for lateral gene transfer in Thermotoga maritima Nucleic Acids Res 2000 28 706 709 10637321 10.1093/nar/28.3.706 
Petersen L Larsen TS Ussery DW On SLW Krogh A  RpoD promoters in Campylobacter jejuni exhibit a strong periodic signal instead of a-35 box J Mol Biol 2003 326 1361 1372 12595250 10.1016/S0022-2836(03)00034-2 
Strauss F Gaillard C Prunell A  Helical Periodicity of DNA, Poly(Da) . Poly(Dt) and Poly(Da-Dt) . Poly(Da-Dt) in Solution Eur J Biochem 1981 118 215 222 7285918 
Peck LJ Wang JC  Sequence Dependence of the Helical Repeat of DNA in Solution Nature 1981 292 375 378 6265793 
Tolstorukov MY Virnik K Adhya S Zhurkin VB  Genome-wide A-tract distribution and DNA packaging in pro-and eukaryotes [abstract] J Biomol Struct Dyn 2003 20 869 870 
Plaskon RR Wartell RM  Sequence Distributions Associated with DNA Curvature Are Found Upstream of Strong Escherichia-Coli Promoters Nucleic Acids Res 1987 15 785 796 3547329 
Trifonov EN  Curved DNA Crc Critical Reviews in Biochemistry 1985 19 89 106 3905255 
Hagerman PJ  Sequence-directed curvature of DNA Annu Rev Biochem 1990 59 755 781 2197990 10.1146/annurev.bi.59.070190.003543 
Harrington RE  DNA Curving and Bending in Protein DNA Recognition Mol Microbiol 1992 6 2549 2555 1333034 
Perez-Martin J Rojo F de Lorenzo V  Promoters responsive to DNA bending: a common theme in prokaryotic gene expression Microbiol Rev 1994 58 268 290 8078436 
Gabrielian A Pongor S  Correlation of intrinsic DNA curvature with DNA property periodicity FEBS Lett 1996 393 65 68 8804425 10.1016/0014-5793(96)00855-1 
Lisser S Margalit H  Determination of Common Structural Features in Escherichia-Coli Promoters by Computer-Analysis Eur J Biochem 1994 223 823 830 8055959 
Gabrielian AE Landsman D Bolshoy A  Curved DNA in promoter sequences In Silico Biol 2000 1 183 196 
Pedersen AG Jensen LJ Brunak S Staerfeldt HH Ussery DW  A DNA structural atlas for Escherichia coli J Mol Biol 2000 299 907 930 10843847 10.1006/jmbi.2000.3787 
Marini JC Levene SD Crothers DM Englund PT  Bent Helical Structure in Kinetoplast DNA Proc Natl Acad Sci U S A 1982 79 7664 7668 16593261 
Hagerman PJ  Evidence for the existence of stable curvature of DNA in solution Proc Natl Acad Sci U S A 1984 81 4632 4636 6087336 
Hagerman PJ  Sequence dependence of the curvature of DNA – a test of the phasing hypothesis Biochemistry 1985 24 7033 7037 4084556 
Koo HS Wu HM Crothers DM  DNA bending at adenine . thymine tracts Nature 1986 320 501 506 3960133 
Ulanovsky L Bodner M Trifonov EN Choder M  Curved DNA – Design, Synthesis, and Circularization Proc Natl Acad Sci U S A 1986 83 862 866 3456570 
Trifonov EN  Translation Framing Code and Frame-Monitoring Mechanism as Suggested by the Analysis of Messenger-RNA and 16 S Ribosomal-RNA Nucleotide-Sequences J Mol Biol 1987 194 643 652 2443708 
Trifonov EN  3-, 10.5-, 200-and 400-base periodicities in genome sequences Physica A 1998 249 511 516 10.1016/S0378-4371(97)00510-4 
Bolshoy A Nevo E  Ecologic genomics of DNA: upstream bending in prokaryotic promoters Genome Res 2000 10 1185 1193 10958636 10.1101/gr.10.8.1185

