BACKGROUND
the higher-order structure of dna, including hairpin turns, bending and curvature, and precise chromatin topology, could provide novel metadata needed to explain genome complexity.
the overall effect of electromagnetic interactions in the dna molecule, described by various topological variables such as twist, slide, tilt and roll  <cit> , is to deviate the trajectory of the dna molecule from an ideal straight line to a curved one in some cases, depending on the sequence.
trifonov and sussman  <cit>  observed that the natural anisotropy of the dna molecule facilitates its smooth folding into chromatin, and proposed the initial concept that certain dna regions may be bent, especially in a-rich tracts.
the curvature of dna represents the tendency of the helix axis to follow a non-linear pathway over a substantial length.
the pioneering work of gabrielian et al.
<cit> , bolshoy  <cit>  and shpigelman et al.
<cit>  demonstrated that every organism has a characteristic dna curvature profile.
additional studies presented significant relationships between curvature and other factors such as centromeric sequence, amino acid composition and transcription regulation.
for instance, all sixteen centromeres of saccharomyces cerevisiae are curved  <cit> , and the centromere sequence parc of escherichia coli is strongly curved  <cit> ; the codon usage and the aminoacid composition of the proteome are correlated with the dna curvature profile  <cit> , and discrete dna curvature signals are conserved in regulatory regions of both eukaryote and prokaryote genes  <cit> .
recent data also shows that promoter regions are significantly more curved than coding regions or randomly permuted sequences  <cit> .
it has also been recently hypothesized that dna curvature could affect transcription termination in many prokaryotes either directly, through contacts with rna polymerase, or indirectly, via contacts with some regulatory proteins  <cit> .
a deeper understanding of the various orders of complexity of genomic dna structure has allowed the design of sophisticated biochemical and biophysical tools for its analysis and manipulation, which in turn, have yielded a better knowledge of the genome itself.
it has been shown that the inclusion of dna structural parameters in the analysis of genomic properties leads to a better understanding of the underlying mechanisms regulating various biological functions  <cit> .
various programs to calculate dna bending and curvature have been proposed since the initial description of the structural variables involved  <cit> .
in parallel, different models compiling the contributions of dna structural parameters have been made and compared, including a-tract based, dinucleotide, and trinucleotide models  <cit> .
in more recent times structural algorithms that predict the dna trajectory in 3d have been published and tested  <cit> .
furthermore, novel resources compiling reported structural parameter sets of the dna molecule, and facilitating their analysis have been recently published  <cit> .
the program "curvature"  <cit>  was among the first to allow the calculation of dna curvature of an arbitrarily long dna sequence, and provided a set of wedge angles as structural parameters estimated from experimental data.
it has since then been tested and validated in numerous publications, making it the optimal choice for our analysis.
comparative genome analyses have shown the existence of conserved gene orders  in the genomes of different plant and mammal species  <cit> .
rice  and arabidopsis  are model monocot and dicot genomes that have been fully sequenced  <cit> .
comparison of the rice and arabidopsis genomes and proteomes showed that 71% of predicted rice proteins were similar to arabidopsis proteins.
this promising and unexpected high similarity suggests that the cellular and biochemical functions of many rice genes can be interpreted through experiments conducted in arabidopsis.
yet, further analysis is needed to clarify the relationship between these two plants, which belong to two different classes.
cpg islands are clusters of cpg dinucleotides in gc-rich regions, usually ~ <dig> kb long  <cit> .
they have been identified in the promoter regions of approximately 50% of genes in different organisms and are considered as gene markers.
in  <dig>  gardiner-garden and frommer  <cit>  first proposed an algorithm for scanning cpg islands in a dna sequence, however, this algorithm significantly inflates the number of cpg islands because of the many repeats which are abundant in plant genomes.
to solve this problem, takai and jones  <cit>  performed a systematic evaluation of the three parameters in gardiner-garden and frommer's algorithm and provided an optimal set of parameters.
tandem repeats are ubiquitous sequence features in both prokaryotic and eukaryotic genomes.
a direct or tandem repeat is the same pattern recurring on the same strand in the same nucleotide order.
tandem repeats play significant structural and functional roles in dna.
they occur in abundance in structural areas such as telomeres, centromeres and histone binding regions  <cit> .
it has been suggested that the conserved 3' region of some types of centromere-specific repeats have significant potential to direct bending  <cit> .
these repeats also play a regulatory role when found near genes and perhaps even within genes.
short tandem repeats are used as a convenient tool for the genetic profiling of individuals or for genetic marker analysis in mapping studies.
thus, identification and analysis of repetitive dna is an active area of biological and computational research.
however, to the best of our knowledge, attempts have yet to be made to establish genome-scale relationships between dna curvature, cpg islands, tandem repeats and centromeric regions of any organism.
therefore, we conducted a comparative genome-scale analysis of the arabidopsis and rice genomes to identify possible relationships between their genomic curvature, cpg islands, tandem repeats and each chromosome's centromere, and additionally explored their biological significance.
RESULTS
the main objectives of repetitive pattern identification algorithms are to identify its periodicity, pattern structure, location and copy number.
the algorithmic challenges for the repeat pattern identification problem are lack of prior knowledge regarding the composition of the repeat pattern and presence of inexact and hidden repeats.
inexact repeats are formed due to mutations of exact repeats and are thought to be representations of historical events associated with sequence evolution.
thus, it is important for any repetitive pattern identification algorithm to identify inexact in addition to exact repeat structures in a dna sequence.
by applying the algorithms and programs described in the methods section, we obtained nine plots for each of the chromosomes in rice and arabidopsis genomes.
this set of graphical plots provided the opportunity to study the relationships between the three major factors, curvature, cpg islands, and tandem repeats in relation to each other.
these plots are:
• an average curvature plot along the whole chromosome
• two plots for position and length of cpg islands
• two tandem repeats plots; number of repeats  and length of repeats
• combined-plot of curvature and length of the cpg islands
• combined-plot of curvature and repeats
• combined-plot of repeats and cpg islands
• combined-plot of curvature, repeats and cpg islands
curvature landscape
the position of maximal curvature value  and centromeric physical position  in rice  and arabidopsis  chromosomes are shown together with the difference between these two positions.
chromosomes with exceptional features are in bold.
note that these numbers are the center of a physical range between  <dig> - <dig>  bp.
survey of tandem repeats and cpg islands
comparison of curvature and cpg islands
outlook of curvature and tandem repeats
one of the major features revealed by combined plots of arabidopsis chromosomes  <dig>   <dig> and  <dig> and rice chromosomes  <dig> to  <dig>   <dig>   <dig>  and  <dig> is that regions with maximal repeat values are located exactly in the centromeric regions and inside or adjacent to the regions with maxcv.
figure  <dig> shows the relationship between curvature and tandem repeats for arabidopsis chromosome  <dig> and rice chromosome  <dig>  chromosome  <dig> of arabidopsis  and chromosomes  <dig> and  <dig> of rice  do not follow any of these two patterns, instead these chromosomes show a significant mincv, and surprisingly it is located between two maximal tandem repeats.
tandem repeats are barely seen next to or inside minimal curvature regions.
also, as a general observation, as the repeat number increases, the value of curvature increases in both arabidopsis and rice chromosomes  <dig>  where in a plot of repeat number versus curvature, a cluster of high curvature points in the case of  <dig> or more repeats in a  <dig> kb window is clearly observed .
further studies of this chromosome's peculiar structure might shed light upon their origins and evolutionary history.
relationship between cpg islands and tandem repeats
analysis of the location of cpg islands with the distribution of tandem repeats across the chromosomes showed that regions enriched with repeats usually do not contain any cpg islands, but the opposite situation does not always happen, in which regions with few cpg islands do not necessarily have more repeats .
in this case, as a general observation, when repeat number increases, the total length of cpg islands decreases.
the plot of repeat number versus cpg length shows a lower length of cpg islands in the case of  <dig> or more repeats in a  <dig> kb window in comparison to repeats of  <dig> to  <dig> .
the exceptional chromosomes
chromosomes  <dig> and  <dig> in arabidopsis and chromosomes  <dig> and  <dig> in rice show different patterns for all the features analyzed .
this might indicate a different evolutionary history for these chromosomes, but the specific reasons for their exceptional characteristics need to be further elucidated.
a wider survey of different organisms, as their genomic sequences become available, might provide the necessary data to elucidate if these chromosomes' structure is present or conserved in other kingdoms.
whole chromosome curvature averages are shown, with the corresponding standard deviation .
curvature max.
indicates the highest curvature value found in each chromosome, for the cases where this value represented more than  <dig> standard deviation units  from the corresponding mean.
the z-score measures the distance in sdu from the mean to the maximal value.
chromosome  <dig> of arabidopsis and chromosomes  <dig> and  <dig> of rice do not present any curvature value above the described threshold.
comparison with other organisms
whole chromosome sequence data from the genomes of mus musculus  and saccharomyces cereviciae  was analyzed to establish if the structural features we describe here were conserved beyond the plant kingdom.
none of the chromosomes of these organisms presented a similar structure near/on the centromeric region.
it is worth noting that the mouse centromeres are telocentric, and so might have different structural requirements than the submetacentric centromeres in plants, but in the case of yeast, which also presents submetacentric centromeres, there is no indication of repeat regions or high curvature near the centromeres similar to the profiles found in plant chromosomes.
it is important to note that previous reports of dna curvature in the centromeres of yeast  <cit>  studied only fragments of  <dig> nucleotides for the calculations, describing a very localized feature; a bend in the middle of a dna fragment of  <dig> base pairs containing cen fragments.
such features are not detected by our approach as the use of the smoothing algorithm averages local variations in curvature to favor the identification of larger, more global features.
the negative relationship between cpg islands and curvature was evident also in mouse chromosomes, but not in yeast, where both cpg islands and repeat regions are very scarce.
multiple plots of dna curvature, repeats and cpg islands for all chromosomes of the aforementioned organisms are available in additional file  <dig> "yeast-mouse-plots".
CONCLUSIONS
this study presents a systematic genome-scale analysis of dna curvature, cpg islands and tandem repeats at the dna sequence level in rice and arabidopsis.
it reveals significant correlations between curvature and genomic features such as cpg islands and repeat distribution.
the detailed analysis of each feature and the results driven from the combined plots generally propose that, for most of the chromosomes, maximal dna curvature occurs adjacent to centromeric regions, which also happen to have high frequency of repeats .
in rice, it has been shown that the centromere is occupied by a centromere-specific retrotransposon  <cit> .
there is also a negative correlation between cpg islands and dna curvature value along the chromosomes and centromeric regions, where usually maximal curvature regions are free of cpg islands.
previous studies have shown correlations between at-content and curvature, which demonstrated that high at-content might be responsible for the high curvature values  <cit> .
although, later studies  <cit>  recall the question of the evolutionary constraints acting on these sequences and whether we should expect that dna curvature can result from sequence elements other than at tracts.
our results suggest a genome evolution scenario in which an increase in tandem repeats, both in length and repetition increases the dna curvature, which in turn decreases gc content and subsequently promotes loss of cpg islands.
maximal curvature usually occurs at centromeric regions, as it has been already suggested by previous studies in other organisms, which have shown similar features  <cit> .
here we extend these previous observations by describing these structural features in all complete chromosomes of two plant genomes and finding correlations between repeats, curvature and the centromere.
the most critical finding or question remaining in this work is that in contrast to other prokaryote and eukaryotes studied before, in plants some chromosomes , do not follow the same pattern or rules for structural features such as curvature value, cpg islands or distribution of tandem repeats.
this shows the need for further research at both experimental and computational levels to explain this discrepancy.

 the higher-order structure of dna, including hairpin turns, bending and curvature, and precise chromatin topology, could provide novel metadata needed to explain genome complexity. the overall effect of electromagnetic interactions in the dna molecule, described by various topological variables such as twist, slide, tilt and roll, is to deviate the trajectory of the dna molecule from an ideal straight line to a curved one in some cases, depending on the sequence. trifonov and sussman observed that the natural anisotropy of the dna molecule facilitates its smooth folding into chromatin, and proposed the initial concept that certain dna regions may be bent, especially in a-rich tracts. the curvature of dna represents the tendency of the helix axis to follow a non-linear pathway over a substantial length. the pioneering work of gabrielian et al., bolshoy and shpigelman et al. demonstrated that every organism has a characteristic dna curvature profile. additional studies presented significant relationships between curvature and other factors such as centromeric sequence, amino acid composition and transcription regulation. for instance, all sixteen centromeres of saccharomyces cerevisiae are curved, and the centromere sequence parc of escherichia coli is strongly curved; the codon usage and the aminoacid composition of the proteome are correlated with the dna curvature profile, and discrete dna curvature signals are conserved in regulatory regions of both eukaryote and prokaryote genes. recent data also shows that promoter regions are significantly more curved than coding regions or randomly permuted sequences. it has also been recently hypothesized that dna curvature could affect transcription termination in many prokaryotes either directly, through contacts with rna polymerase, or indirectly, via contacts with some regulatory proteins. a deeper understanding of the various orders of complexity of genomic dna structure has allowed the design of sophisticated biochemical and biophysical tools for its analysis and manipulation, which in turn, have yielded a better knowledge of the genome itself. it has been shown that the inclusion of dna structural parameters in the analysis of genomic properties leads to a better understanding of the underlying mechanisms regulating various biological functions. various programs to calculate dna bending and curvature have been proposed since the initial description of the structural variables involved. in parallel, different models compiling the contributions of dna structural parameters have been made and compared, including a-tract based, dinucleotide, and trinucleotide models. in more recent times structural algorithms that predict the dna trajectory in 3d have been published and tested. furthermore, novel resources compiling reported structural parameter sets of the dna molecule, and facilitating their analysis have been recently published. the program "curvature" was among the first to allow the calculation of dna curvature of an arbitrarily long dna sequence, and provided a set of wedge angles as structural parameters estimated from experimental data. it has since then been tested and validated in numerous publications, making it the optimal choice for our analysis. comparative genome analyses have shown the existence of conserved gene orders in the genomes of different plant and mammal species. rice and arabidopsis are model monocot and dicot genomes that have been fully sequenced. comparison of the rice and arabidopsis genomes and proteomes showed that 71% of predicted rice proteins were similar to arabidopsis proteins. this promising and unexpected high similarity suggests that the cellular and biochemical functions of many rice genes can be interpreted through experiments conducted in arabidopsis. yet, further analysis is needed to clarify the relationship between these two plants, which belong to two different classes. cpg islands are clusters of cpg dinucleotides in gc-rich regions, usually ~ kb long. they have been identified in the promoter regions of approximately 50% of genes in different organisms and are considered as gene markers. in gardiner-garden and frommer first proposed an algorithm for scanning cpg islands in a dna sequence, however, this algorithm significantly inflates the number of cpg islands because of the many repeats which are abundant in plant genomes. to solve this problem, takai and jones performed a systematic evaluation of the three parameters in gardiner-garden and frommer's algorithm and provided an optimal set of parameters. tandem repeats are ubiquitous sequence features in both prokaryotic and eukaryotic genomes. a direct or tandem repeat is the same pattern recurring on the same strand in the same nucleotide order. tandem repeats play significant structural and functional roles in dna. they occur in abundance in structural areas such as telomeres, centromeres and histone binding regions. it has been suggested that the conserved 3' region of some types of centromere-specific repeats have significant potential to direct bending. these repeats also play a regulatory role when found near genes and perhaps even within genes. short tandem repeats are used as a convenient tool for the genetic profiling of individuals or for genetic marker analysis in mapping studies. thus, identification and analysis of repetitive dna is an active area of biological and computational research. however, to the best of our knowledge, attempts have yet to be made to establish genome-scale relationships between dna curvature, cpg islands, tandem repeats and centromeric regions of any organism. therefore, we conducted a comparative genome-scale analysis of the arabidopsis and rice genomes to identify possible relationships between their genomic curvature, cpg islands, tandem repeats and each chromosome's centromere, and additionally explored their biological significance.  the main objectives of repetitive pattern identification algorithms are to identify its periodicity, pattern structure, location and copy number. the algorithmic challenges for the repeat pattern identification problem are lack of prior knowledge regarding the composition of the repeat pattern and presence of inexact and hidden repeats. inexact repeats are formed due to mutations of exact repeats and are thought to be representations of historical events associated with sequence evolution. thus, it is important for any repetitive pattern identification algorithm to identify inexact in addition to exact repeat structures in a dna sequence. by applying the algorithms and programs described in the methods section, we obtained nine plots for each of the chromosomes in rice and arabidopsis genomes. this set of graphical plots provided the opportunity to study the relationships between the three major factors, curvature, cpg islands, and tandem repeats in relation to each other. these plots are: • an average curvature plot along the whole chromosome • two plots for position and length of cpg islands • two tandem repeats plots; number of repeats and length of repeats • combined-plot of curvature and length of the cpg islands • combined-plot of curvature and repeats • combined-plot of repeats and cpg islands • combined-plot of curvature, repeats and cpg islands curvature landscape the position of maximal curvature value and centromeric physical position in rice and arabidopsis chromosomes are shown together with the difference between these two positions. chromosomes with exceptional features are in bold. note that these numbers are the center of a physical range between - bp. survey of tandem repeats and cpg islands comparison of curvature and cpg islands outlook of curvature and tandem repeats one of the major features revealed by combined plots of arabidopsis chromosomes and and rice chromosomes to and is that regions with maximal repeat values are located exactly in the centromeric regions and inside or adjacent to the regions with maxcv. figure shows the relationship between curvature and tandem repeats for arabidopsis chromosome and rice chromosome chromosome of arabidopsis and chromosomes and of rice do not follow any of these two patterns, instead these chromosomes show a significant mincv, and surprisingly it is located between two maximal tandem repeats. tandem repeats are barely seen next to or inside minimal curvature regions. also, as a general observation, as the repeat number increases, the value of curvature increases in both arabidopsis and rice chromosomes where in a plot of repeat number versus curvature, a cluster of high curvature points in the case of or more repeats in a kb window is clearly observed. further studies of this chromosome's peculiar structure might shed light upon their origins and evolutionary history. relationship between cpg islands and tandem repeats analysis of the location of cpg islands with the distribution of tandem repeats across the chromosomes showed that regions enriched with repeats usually do not contain any cpg islands, but the opposite situation does not always happen, in which regions with few cpg islands do not necessarily have more repeats. in this case, as a general observation, when repeat number increases, the total length of cpg islands decreases. the plot of repeat number versus cpg length shows a lower length of cpg islands in the case of or more repeats in a kb window in comparison to repeats of to. the exceptional chromosomes chromosomes and in arabidopsis and chromosomes and in rice show different patterns for all the features analyzed. this might indicate a different evolutionary history for these chromosomes, but the specific reasons for their exceptional characteristics need to be further elucidated. a wider survey of different organisms, as their genomic sequences become available, might provide the necessary data to elucidate if these chromosomes' structure is present or conserved in other kingdoms. whole chromosome curvature averages are shown, with the corresponding standard deviation. curvature max. indicates the highest curvature value found in each chromosome, for the cases where this value represented more than standard deviation units from the corresponding mean. the z-score measures the distance in sdu from the mean to the maximal value. chromosome of arabidopsis and chromosomes and of rice do not present any curvature value above the described threshold. comparison with other organisms whole chromosome sequence data from the genomes of mus musculus and saccharomyces cereviciae was analyzed to establish if the structural features we describe here were conserved beyond the plant kingdom. none of the chromosomes of these organisms presented a similar structure near/on the centromeric region. it is worth noting that the mouse centromeres are telocentric, and so might have different structural requirements than the submetacentric centromeres in plants, but in the case of yeast, which also presents submetacentric centromeres, there is no indication of repeat regions or high curvature near the centromeres similar to the profiles found in plant chromosomes. it is important to note that previous reports of dna curvature in the centromeres of yeast studied only fragments of nucleotides for the calculations, describing a very localized feature; a bend in the middle of a dna fragment of base pairs containing cen fragments. such features are not detected by our approach as the use of the smoothing algorithm averages local variations in curvature to favor the identification of larger, more global features. the negative relationship between cpg islands and curvature was evident also in mouse chromosomes, but not in yeast, where both cpg islands and repeat regions are very scarce. multiple plots of dna curvature, repeats and cpg islands for all chromosomes of the aforementioned organisms are available in additional file "yeast-mouse-plots".  this study presents a systematic genome-scale analysis of dna curvature, cpg islands and tandem repeats at the dna sequence level in rice and arabidopsis. it reveals significant correlations between curvature and genomic features such as cpg islands and repeat distribution. the detailed analysis of each feature and the results driven from the combined plots generally propose that, for most of the chromosomes, maximal dna curvature occurs adjacent to centromeric regions, which also happen to have high frequency of repeats. in rice, it has been shown that the centromere is occupied by a centromere-specific retrotransposon. there is also a negative correlation between cpg islands and dna curvature value along the chromosomes and centromeric regions, where usually maximal curvature regions are free of cpg islands. previous studies have shown correlations between at-content and curvature, which demonstrated that high at-content might be responsible for the high curvature values. although, later studies recall the question of the evolutionary constraints acting on these sequences and whether we should expect that dna curvature can result from sequence elements other than at tracts. our results suggest a genome evolution scenario in which an increase in tandem repeats, both in length and repetition increases the dna curvature, which in turn decreases gc content and subsequently promotes loss of cpg islands. maximal curvature usually occurs at centromeric regions, as it has been already suggested by previous studies in other organisms, which have shown similar features. here we extend these previous observations by describing these structural features in all complete chromosomes of two plant genomes and finding correlations between repeats, curvature and the centromere. the most critical finding or question remaining in this work is that in contrast to other prokaryote and eukaryotes studied before, in plants some chromosomes, do not follow the same pattern or rules for structural features such as curvature value, cpg islands or distribution of tandem repeats. this shows the need for further research at both experimental and computational levels to explain this discrepancy. 
more in depth knowledge of the various orders of complexity of genomic dna structure has allowed the design of sophisticated bioinformatics tools for its analysis and manipulation, which, in turn, have yielded a better understanding of the genome itself. this study represents the first systematic genome-scale analysis of dna curvature, cpg islands and tandem repeats at the dna sequence level in plant genomes, and finds that not all of the chromosomes in plants follow the same rules common to other eukaryote organisms, suggesting that some of these genomic properties might be considered as specific to plants. cpg islands and tandem repeats also play significant roles in the dynamics and evolution of genomes. further analysis of cpg islands shows a clear interdependence between curvature value, repeat frequencies and cpg islands. each cpg island appears in a local minimal curvature region, and cpg islands usually do not appear in the centromere or regions with high repeat frequency. by analyzing tandem repeats across the genome, we found that frequencies of repeats are higher in regions adjacent to those with high curvature value. due to its overarching role in genome function, sequence-dependent dna curvature continues to attract great attention. a genome-scale prediction of curvature distribution in rice and arabidopsis indicated that most of the chromosomes of both genomes have maximal chromosomal dna curvature adjacent to the centromeric region.
 due to its overarching role in genome function, sequence-dependent dna curvature continues to attract great attention. the dna double helix is not a rigid cylinder, but presents both curvature and flexibility in different regions, depending on the sequence. more in depth knowledge of the various orders of complexity of genomic dna structure has allowed the design of sophisticated bioinformatics tools for its analysis and manipulation, which, in turn, have yielded a better understanding of the genome itself. curved dna is involved in many biologically important processes, such as transcription initiation and termination, recombination, dna replication, and nucleosome positioning. cpg islands and tandem repeats also play significant roles in the dynamics and evolution of genomes.  in this study, we analyzed the relationship between these three structural features within rice and arabidopsis genomes. a genome-scale prediction of curvature distribution in rice and arabidopsis indicated that most of the chromosomes of both genomes have maximal chromosomal dna curvature adjacent to the centromeric region. by analyzing tandem repeats across the genome, we found that frequencies of repeats are higher in regions adjacent to those with high curvature value. further analysis of cpg islands shows a clear interdependence between curvature value, repeat frequencies and cpg islands. each cpg island appears in a local minimal curvature region, and cpg islands usually do not appear in the centromere or regions with high repeat frequency. a statistical evaluation demonstrates the significance and non-randomness of these features.  this study represents the first systematic genome-scale analysis of dna curvature, cpg islands and tandem repeats at the dna sequence level in plant genomes, and finds that not all of the chromosomes in plants follow the same rules common to other eukaryote organisms, suggesting that some of these genomic properties might be considered as specific to plants. 