Wavelet to predict bacterial ori and ter: a tendency towards a physical balance

Replication of the bacterial chromosomal DNA starts at the origin (ori) and the two replication forks (or replicores) propagate in opposite directions up to the terminus (ter) region, as demonstrated in Escherichia coli [1–7]. Obviously, the two replication forks need to reach the ter region at the same time to optimize the replication process. It is therefore reasonable to assume that ori and ter should have a physical balance between them, i.e., opposite to each other, on the chromosome to guarantee a synchronous completion of the bi-directional chromosomal replication. Based on this assumption, we hypothesize that lateral transfer of large blocks of DNA into a bacterial chromosome would disrupt such a balance, making necessary the rearrangements of the chromosome to restore the balance. We have observed and reported the large insertions and the striking chromosomal rearrangements in Salmonella typhi [8–10]. The 180° physical balance between ori and ter has been seen in the complete sequence of Escherichia coli K12 [11] and a number of other bacteria sequenced subsequently. To address the importance of such a physical balance of the bacterial chromosomes in evolution, we proposed a model of bacterial speciation, i.e., the Adopt-Adapt Model [12, 13]. However, some sequenced chromosomes, such as that of Bacillus subtilis [14], show significant deviation of ori and ter from the hypothesized 180° relationship. Additionally, in many of the sequenced bacterial chromosomes, the locations of ori and ter are not reported. In order to know whether a physical balance actually exists in, or is required for the stability of, the bacterial chromosome, we attempted to locate ori and ter in the chromosomes of the sequenced bacteria and then investigate their physical relationships.

One key difficulty in locating ori and ter is that bacterial ori and ter seem not to have conserved nucleotide sequences across different bacteria. However, some chromosomal features, including those that have resulted from asymmetric error rates of replication between the leading and lagging DNA strands [15] such as GC skew and oligomer skews, have proven useful to help in locating the ori and ter regions. Lobry observed that GC skew, i.e., G-C/G+C averaged over a sliding window, changes sign at the origin [16–18]. For the past few years, GC skew (GCS) and AT skew (A-T/A+T averaged over a sliding window, ATS) have been widely used in predicting the ori and ter sites in bacteria [11, 19–21] and viruses [22]. The advantage of GCS and ATS is that they show the turning points clearly. However, the shape of curves and the accuracy of the predicted sites by the conventional GCS analysis methods [16, 17]. are dependent on the window size: the larger the window, the less accurate the sites. Thus, for genomic analysis, the windowed indices may lead to the loss of some critical information.

Oligomer skew analysis, another sequence-based method that finds short oligomers highly skewed on opposite strands of the chromosome, overcomes the window problem [23]. Using this method, Salzberg and colleagues located origins of replication in all 10 bacterial and one of three archaeal genomes analyzed. In some of the bacterial genomes, such as Bacillus subtilis, E. coli, Borrelia burgdorferi, and Mycoplasma genitalium, large numbers of different oligomers showed a significant skew. Although these oligomers locate origin of replication at different sites, varying from 3823 kb to 4002 kb in E. coli K12, for example, combining method could bring the results from multiple oligomers together and locate the origin at a site that is very close to the experimentally determined origin of replication. Unfortunately, different bacteria may have vastly different numbers of skewed oligomers, with some having no detectable skew. Therefore, alternative chromosomal features would be desirable.

Freeman et al. [24] reported three integral functions: purine excess, keto excess and coding-strand excess, and used these three indices to detect the pattern of chromosomal organization in E. coli, H. influenzae, M. genitalium and Synechocystis. In every case where independent information is available, the minimum point in the purine excess curve corresponds to the ori site, and the maximum point of the excess curves correlates with the known or suspected ter site; the keto excess curve reflects the same correlation. The coding-strand excess has the same tendency but shows a more variable behavior compared to the keto and purine excesses (i.e., less unambiguous than the keto and purine excesses in such studies). The main advantage of these indices is that, as with oligomer skews, there are no window slides; in addition, because of their universal existence in bacterial genomes, these indices are at least complementary to the oligomer skew method in locating bacterial ori and ter sites. However, one problem remains: the curves are not sufficiently sharp and smooth, making it difficult to pinpoint the predicted loci and estimate the confidence intervals with significance tests on the statistics. Additionally, although significance tests are usually performed by the t or the χ² methods, both of these tests are based on the assumption of a normal distribution, while in fact the distributions of the four bases on the bacterial chromosome are neither normal nor uniform.

To address these issues and overcome all of these disadvantages, we assessed the use of wavelet transformation analysis [25], a non-parametric method, to locate the bacterial chromosomal ori and ter sites. This technique was introduced in DNA sequence analysis by A. Arneodo and his group in 1995 [26]. The basic idea of wavelet analysis is to decompose a sequence profile into several groups of coefficients, each group containing information about features of the profile at a different scale. Coefficients at coarse scales capture gross and global features and coefficients at fine scales reveal the local details of the profile. These features of wavelet analysis are ideal for genomic analysis. As one application, wavelet analysis has been used on the G+C patterns occurring in genomes [27–29]. More recently, this technique has also been shown to be very successful in extracting quantitative information on the structure and dynamics of the nucleosomes [30]. Unfortunately most studies using wavelet analysis did not perform statistical significance tests. In this study, we used wavelet transform to locate ori and ter by documenting GC skew, AT skew, keto excess, and purine excess on published bacterial chromosomes and performed statistical significance tests. We observed a strong tendency of the bacterial chromosomes towards a physical balance, with the minima and maxima corresponding to the known or putative ori and ter and being about half chromosome separated in most of the bacteria studied.

Using wavelet analysis, we evaluated the relevance of GC and AT skews and keto and purine excesses with the regions that correspond to replication origin, ori, and terminus, ter. Mechanisms, by which compositional biases are created, are complex and beyond the scope of this work; excellent reviews are available such as that by Frank and Lobry [31]. In this study, our objectives are to find further support to our physical balance hypothesis of the bacterial chromosomes by documenting the compositional biases with wavelet. As shown in the Results, in the cases where ori and ter are reported, the minima and maxima of the curves for the GC and AT skews and keto and purine excesses fall into the regions of ori and ter, respectively. We therefore assumed that the four indices would locate ori and ter also in the cases where ori and ter have not been experimentally determined. The four indices behaved differently, with some being strong and others being weak in different bacteria (Table 1). This may reflect different evolutionary forces affecting GC and AT skews differentially and, essentially, purine excess is equivalent to the sum of GC and AT skews and keto excess to their subtraction [32]. Supporting the Adopt-Adapt model [12, 13], our results show an obvious tendency of the bacterial chromosomes towards a physical balance between ori and ter (Table 1). However, there seemed to be some exceptions among the bacteria analyzed, such as Mycoplasma gentalium (Table 1), where the minimum and maximum of the curve are significantly off the predicted balanced positions (202 degrees vs 180 degrees with a range of plus or minus 15 degrees in all other bacteria listed in Table 1). We need to further clarify the situations in such cases to know whether a chromosomal balance does exist in these bacteria but will have to be revealed in a different way, or whether these bacteria, as intracellular parasites, would have undiscovered mechanisms to compensate for such imbalance.

Characterizations of ori and ter have been performed on very few bacteria so far, therefore very little is known about the common features of these chromosomal loci, especially the ter region. The most detailed information about ori and ter comes from Hill et al. on E. coli K12 [2, 3], who described the terminus region of the E. coli chromosome as being directly opposite to the origin of replication and containing two sites that inhibit the progression of the replication forks. These two sites, T1 and T2, are separated by a 352 kb DNA segment and are located at the two extremities of the terminus region. They also demonstrate that a trans-acting factor encoded by tus is required for replication fork inhibition at both T1 and T2 [3]. In addition, Hill et al. identified a 23 bp sequence common to the region containing T1 and T2, which is sufficient to signal replication fork inhibition in a ColE1-derrived plasmid, and the terminator signal sequence is dependent on its orientation in the plasmid and the presence of the trans-acting termination factor Tus. These findings indicate that the terminus site of DNA replication is a special region, extending for several hundred kb and including loci such as T1, T2, tus, etc. We searched for the positions of the 23 bp signal sequence in all analyzed genome sequences and found unequal numbers in E. coli and Salmonella strains, which were all very close to tus (data not shown). Therefore, it is rather surprising to find that the ter region in E. coli O157:H7 EDL933 (terA through terF, nucleotide positions 1101244 to 1105943) is so far away from tus (nucleotide positions 2359317 to 2360276) or from the supposedly balanced position. The situation is similar with the other sequenced E. coli O157:H7 strain, Sakai-VT2. This unexpected finding raises the question: should the chromosomal balance be between ori and ter (E. coli K12) or between ori and a newly created "ad hoc terminus" (E. coli O157:H7; does the "ad hoc terminus" exist and what is in it)? Our results in Figure 6 strongly suggest that chromosomal replication is symmetrical, i.e., a tendency towards a physical balance exists even when major genomic events may significantly displace the ori or ter region. Perna et al. [33] identified a very large insertion at the terminus region. This insert is likely due to a recent lateral gene transfer, which obviously would disrupt the physical balance of chromosomal replication, as indicated by the relative locations of ori and ter on the genomes of the E. coli O157:H7 strains, and also unbalance the GC/AT skew or purine/keto excess. Over time, this unbalanced skew or excess will probably balance itself out through a process known as amelioration, which has been described in detail by Lawrence and Ochman [34]. Results presented in Figure 10 show that the purine/keto excess could be rebalanced prior to the rebalancing of ori or ter. One important implication here is that termination of DNA replication is occurring in a new chromosomal region that is ca. 180° away from ori, not the annotated ter region. In this sense, the actual physical balance of the bacterial chromosome may be better revealed by the purine/keto excess than by the chromosomal location of ter in relation to ori. The features of the "ad hoc terminus" regions need to be further explored.

From Table 1, it is interesting to note that related bacteria have the same tendency of having strong or weak keto and purine excesses. This may reflect their common evolutionary history and may serve as useful chromosomal features for comparative studies. We also tried wavelet analysis on Archaea; however, none of the four indices was "strong" enough to reveal any minima or maxima that may possibly correspond to ori or ter (data not shown). This finding reflects fundamental differences between Bacteria and Archaea in their chromosomal composition and evolutionary routes.

In this study, we used wavelet transformation analysis for significance test of the predicted loci. Two methods are commonly used in signal data processing, Fourier transformation and wavelet transform analysis. Compared to wavelet analysis, the windowed Fourier transformation suffers from three major defects: (1) the shape of the curve is highly dependent on the window size; (2) in computing the Fourier transform each time using only the data within the window, the window Fourier transform (WFT) gives inconsistent treatment of different frequencies; and (3) the WFT relies on the assumption that the index signal can be decomposed into sinusoidal components. The wavelet method can avoid these defects by decomposing the series in scale and frequency simultaneously. Because of the unknown and uncertain distribution of the indices, for revealing chromosomal features one cannot do significance tests based on conventional statistical methods. Monte-Carlo simulations combined with wavelet analysis supply a useful tool to overcome these issues. The wavelet transformation analysis is particularly suitable for visualizing chromosomal patterns at all scales, from coarse to fine. For example, one might like to separate the shorter period fluctuations from the longer sequences, wavelet analysis will do this, regardless of whether the fluctuation repeats on a regular basis or otherwise. Overall, wavelet is providing a powerful tool for comparative genomics.

Wavelet analysis provides a powerful tool to predict ori and ter on bacterial chromosomes and has revealed a strong tendency of the bacterial chromosomes towards a physical balance between ori and ter.