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Introduction

Genome arrangement has profound effects on organismal phenotype. Genome arrangement likely impacts gene expression [1],[2],[3], and can result in total loss of gene function when a rearrangement breakpoint occurs inside a reading frame. Moreover, rearrangements are known to affect linkage and introduce genetic incompatibility in eukaryotes [4]. Similar recombination-stifling effects have been proposed in prokaryotes [5],[6], whose capacity for genetic exchange among divergent taxa has only recently been appreciated [7]. In naturally competent microbes which undergo frequent homologous recombination, genome arrangements themselves may be better indicators of vertical inheritance than other molecular characters.

Our ability to measure gene order and chromosome structure has undergone several revolutions, beginning with careful study of linkage maps [8], later moving towards direct observation by microscope, FISH, Radiation Hybrid, paired-end genome sequencing, and Optical Mapping techniques [9],[10],[11],[12]. The continued improvement in measurement technology has offered revelations regarding the pattern and extent of genome rearrangement in organisms ranging from bacteria [13] to mammals [14].

In circular bacterial chromosomes, DNA replication divides the circular chromosome into two domains called replichores. Replication begins when DNA polymerase holoenzymes anneal to the origin of replication (ori). Two holoenzymes then simultaneously copy the circular chromosome in opposite directions, and initially the DNA polymerase holoenzymes are co-localized in the cell in a so-called “replication factory” [15]. Each holoenzyme copies about half the chromosome, and they eventually meet each other in the Ter macrodomain. The Ter macrodomain spans a large portion of the chromosome opposite the origin of replication and contains several ter sites which bind proteins that halt procession of DNA polymerase [16]. In cases where homologous recombination has taken place during replication, the XerCD molecular machinery resolves the chromosome dimer at the dif site [17],[18]. Moreover, the predominant site of replication termination appears to be at or near the dif site [19]. We refer to each half of the chromosome, delineated by ori and dif, as a replichore. Hereafter we will use the word “terminus” or phrase “terminus of replication” to refer to the approximate location of the dif site.

Genome sequencing has revealed that rearrangements do not occur with uniformly distributed endpoints on circular prokaryotic chromosomes. Instead, a striking pattern of inversions with endpoints biased by the origin and terminus of replication has commonly been observed [20],[21],[22],[23]. Several explanations for the observed pattern have been devised, all of which focus on the nature of DNA replication in circular chromosomes.

An inter-replichore inversion refers to a chromosomal inversion with one endpoint in each replichore. Such inversions swap the relative orientations of the origin and terminus. If the inversion endpoints are equally distant from the origin, then replichore sizes remain unchanged—a so-called “symmetric inversion”. Previous genome analyses indicate that inversions typically occur with breakpoints in oppositely oriented repetitive elements [24],[25],[26]. When DNA damage occurs, the homology-dependent recombination-repair machinery recruits another copy of the repetitive element as a repair template. Inversions, deletions, and duplications occur when the resulting Holliday junction is incorrectly resolved. Whereas recombination among inverted repeats leads to inversions, recombination among direct repeats leads to deletion. When the recombination among direct repeats occurs during replication, the segment becomes deleted from one chromosome and duplicated in the other.

Bacterial DNA replication appears to induce a multitude of mutational biases and selective forces with respect to their chromosome architecture [27]. Chromosomes are thought to remain small due to a general deletion bias [28]. Strand-specific oligomers such as χ sites [29] assist with DNA repair, while KOPS/AIMS [30],[31] have roles in DNA replication and chromosome segregation. Such sequence signals would be disrupted by inversions within a single replichore, but not by inter-replichore inversions. Moreover, a large survey of Salmonella genomes in culture has provided evidence that genomes with equal-sized replichores (balanced replichores) may be under positive selection [32]. It is currently unknown whether symmetric inter-replichore inversions are frequently observed simply because they occur more frequently than other rearrangements (a recombination bias), or whether other patterns of rearrangement commonly occur but are strongly selected against [26].

The observed frequency of rearrangement relative to neutral substitution is highly variable in different organisms. The frequency of observed rearrangement in modern genomes correlates with the presence of repeats induced by mobile genetic elements [26],[33]. Interestingly, mobile genetic elements (IS elements/transposons) are also associated with the generation of pseudogenes, genome reduction, and adaptive evolution of niche change [34]. Large-scale inversion and deletion are both driven by homologous recombination among repeat elements. Taken together, these associations suggest that methods to predict episodes of ancient genome rearrangement may be able to uncover historical genome reduction and transitions in ecological niche.

Studies of Yersinia have revealed extensive genomic rearrangement relative to conspecific isolates, and IS elements have been implicated in the rearrangement process. The recent availability of several finished Yersinia genome sequences offers the possibility to investigate patterns and biases associated with genomic rearrangement. Yersinia pestis played a role as the causative agent of the three major plague epidemics which together resulted in millions of deaths over the past two millenia [35]. Previous molecular studies have indicated that Yersinia pestis is a recently emerged clone of Y. pseudotuberculosis, with an estimated divergence less than 20,000 years ago [36], although some ambiguity in the branching order of Y. pestis isolates remains [37].

Given its pathogenic lifestyle, Y. pestis population dynamics are different from those of non-pathogens and the effect of population dynamics on genome arrangement warrants consideration. Upon infection of a human host, Y. pestis likely undergoes expansive population growth. Transmission to a new host is usually mediated by a flea vector which can viably harbor only a small number of Yersinia cells compared to an infected human. As such, modern Y. pestis may have undergone several cycles of unconstrained population growth followed by extreme transmission bottlenecks. The unconstrained growth phase could permit generation of cell lines with genomic rearrangement, which are subsequently fixed by the transmission bottlenecks. Such population dynamics would serve to increase the observed rate of rearrangement.

Previous experimental work has characterized patterns of genome arrangement in isolates of E. coli and Salmonella whose genomes were artificially perturbed in the laboratory [38]. Our study represents the first attempt to quantify selection and recombination bias acting on genome arrangement in a naturally evolving population.

Results

Genome Arangement History of Yersinia

We apply a Bayesian MCMC sampler to investigate selection and recombination bias acting on genome rearrangements in sequenced Yersinia isolates. At the time of this study, nine finished Yersinia genomes were publicly available, listed in Table 1, and several more had been sequenced to draft quality. As the Yersinia pestis are very recently diverged, only a small number of nucleotide substitutions have been observed in fully sequenced genomes [39], and efforts to reconstruct the Yersinia phylogeny have consequently been forced to integrate presence/abscence patterns of IS elements and VNTR sequences [37].

Table 1. Fully sequenced Yersinia genomes analyzed for genome rearrangements.

doi:10.1371/journal.pgen.1000128.t001

Pairwise comparisons of Yersinia genomes have revealed a large number of genomic rearrangements [25],[40] which may be suitable phylogenetic characters. As large-scale genome rearrangement is thought to be a low-homoplasy molecular character [41] impervious to lateral exchange by homologous recombination, even a small number of rearrangements may suffice to resolve phylogenetic tree topology.

Genome Alignment and Replichore Sizes

In order to compute a rearrangement history, we require genomes to be encoded as a signed permutation matrix indicating order and orientation of homologous segments in each genome. We used the Mauve multiple genome alignment software to identify and align 84 Locally Collinear Blocks (LCBs) shared among the 9 Yersinia genomes. Differential gene content among Yersinia lineages precludes a nine-way alignment that completely covers each genome. On average 81.5% of each genome is contained within LCBs, and the remaining lineage-specific regions reside in breakpoint regions. The breakpoint regions cannot be unambiguously assigned to either neighboring LCB, and the uncertainty about their placement in ancestral genome arrangements causes corresponding uncertainty in ancestral replichore sizes.

While Y. pestis and Y. pseudotuberculosis share a majority of their gene content, Y. enterocolitica has substantial differential content relative to the other eight taxa [42]. To mitigate inference problems related to differential gene content (see Methods), we removed Y. enterocolitica from our analysis and computed an alignment on the remaining 8 taxa using a procedure described in Methods.

The alignment of eight Y. pestis and Y. pseudotuberculosis strains, shown in Figure 1, consists of 78 LCBs (79 before considering genome circularity) that cover an average of 93.3% of each genome. The distribution of LCB lengths (Figure 2) appears to be geometric, consistent with expectation under the Nadeau-Taylor random breakage model [14]. For the purpose of inferring ancestral replichore sizes, we divide each of the 78 breakpoint regions in half and assign each half to a neighboring LCB. The origin and terminus of replication in each genome were assigned on the basis of a consensus prediction and homology (see Methods).

Figure 1. A genome alignment of eight Yersinia isolates.

Whole genome alignment of eight Yersinia genomes using Mauve [77] reveals 78 locally collinear blocks conserved among all eight taxa. Each chromosome has been laid out horizontally and homologous blocks in each genome are shown as identically colored regions linked across genomes. Regions that are inverted relative to Y. pestis KIM are shifted below a genome's center axis. The origin of replication in each genome is approximately at coordinate 1 and the terminus dif sites are approximately midway through each genome, as marked by grey vertical bars. The termini were identified by sequence comparison with Y. pestis KIM, where they were characterized by extensive sequence analysis [25]. Figure generated by Mauve, free/open-source software available from http://gel.ahabs.wisc.edu/mauve.

doi:10.1371/journal.pgen.1000128.g001

Figure 2. Lengths of Locally Collinear Blocks shared by the eight Yersinia genomes.

Block lengths are taken from the Y. pestis KIM reference genome.

doi:10.1371/journal.pgen.1000128.g002

Bayesian Analysis of Rearrangement Phylogeny

We used a modified version of the BADGER 1.01b software to sample the posterior probability distribution of phylogenetic trees, mutation rate, and genome arrangement histories using inversions as mutation operations. The model treats all inversion events to be equally likely a priori, with no explicit preference for rearrangements that maintain or improve replichore balance. The prior distribution on branch lengths creates a strong preference for histories with fewer inversions. Like other Bayesian MCMC samplers for phylogenetics, the method used here creates an initial phylogenetic tree with mutation events mapped onto the branches, then repeatedly proposes modifications to the current tree topology, mutation history, and branch lengths. Any proposed modifications are accepted with probability dictated by the Metropolis-Hastings ratio [43],[44]. The initial proposed reconstruction of inversion history typically has very low likelihood and proposed modifications are generally accepted until the likelihood reaches a local maxima. The initial period of sampling is commonly referred to as burn-in. Samples taken during burn-in are discarded since the Markov-chain has not yet converged to the true posterior distribution.

As applied to the 78 Yersinia LCBs, we ran chains with 1,510,000 modification proposal steps, discarded the first 10,000 steps of each chain as burn-in and then subsampled every 50 steps (details in Methods). The resulting posterior sampling consists of 30,000 complete genome arrangement histories. Each sampled history contains a tree topology with inversion events mapped onto the branches. In total, the sampled histories contain 30,000 tree topology estimates and 2,520,185 genome arrangements, of which 2,280,185 are inferred ancestral arrangements and 240,000 are modern genome arrangements. Visualization of the posterior distribution of trees using SplitsTree v4 [45] reveals a small amount of topological ambiguity as a splits network (Figure 3). Contributing to topological ambiguity are seven different tree topologies with parsimonious inversion histories of 79 events. All seven parsimonious topologies differ in their grouping of Y. pestis isolates. Nonetheless, the Y. pestis are found to be monophyletic, with subgroupings that are consistent with previously published genome analyses [39]. Application of a maximum parsimony algorithm to reconstruct inversion phylogeny recovers one of the seven parsimonious topologies identified by BADGER, also with 79 inversions [46],[47]. Internal branches of the Y. pestis clade are very short relative to external branches, a phenomenon which could have numerous explanations including exponential population growth, population subdivision, an ancestral selective sweep, or recently accelerated mutation rates possibly associated with pathogen population dynamics or relaxed selection in culture. Of note, SNP phylogenies also exhibit short internal branches [39].

Figure 3. Consensus phylogenetic network of Yersinia based on inversions.

Consensus phylogenetic network for eight of the Yersinia listed in Table 1. Branch lengths are proportional to the average number of per-branch inversion events. Splits with Bayesian posterior probability (Bpp)>0.2 are shown in black, splits with Bpp between 0.1 and 0.2 in gray. To visualize the network at Bpp 0.2, imagine removing gray edges and straightening the black edges. The inversion phylogeny supports a Y. pestis clade, and at Bpp 0.2 it supports subclades which agree with SNP phylogenies [39]. Of note, internal branches in the Y. pestis are short relative to Y. pseudotuberculosis, suggesting either rapid population growth, subdivision, or other effects. Network visualization created using SplitsTree 4 [45].

doi:10.1371/journal.pgen.1000128.g003

Visualizing Inversion History

To quickly scan for patterns in the genome rearrangement history of Yersinia, we developed a 3D video system to visualize the series of rearrangement events. The posterior sampling of inversion history contains 30,000 samples. We selected the one history with maximum a posteriori probability and rendered the series of rearrangement events on each branch of the phylogeny using custom Java software. The chromosome is rendered as a torus with positions of the replication origin and terminus marked. The replichores present in an ancestral node of the tree are colored distinctively, left replichore in blue, right replichore in green. The intensity of the colors changes on a gradient from origin to terminus, such that segments near the origin in the ancestor are dark blue or green, while segments near the terminus are light.

Supplementary Videos S1, S2, S3, S4, S5, S6, S7, and S8 show the inversion history along each external branch of the maximum a posteriori tree estimate. Several striking patterns of rearrangement can be seen in the videos, especially those representing longer branches such as the branch leading to Y. pestis 91001 (Video S3). First, the terminus remains positioned mostly opposite the origin throughout the rearrangement history. Second, light-colored segments which were near the terminus in the ancestral genome arrangement tend to remain near the terminus. Third, when large inversions happen within a single replichore, they appear to be quickly followed by a second inversion that reverts the first. We now describe statistics to quantify the significance of these observations, along with other aspects of genome arrangement evolution that are not as easily recognizable through visualization.

Selection for Replichore Balance

When the terminus of replication lies opposite the origin on the circular chromosome, replichore sizes are equal and the genome is said to be balanced. If we assume the origin is at positions 0 and 1 on the circular chromosome and the terminus dif site lies at some position b where 0<b<1, we can quantify the degree of imbalance as the deviation from perfect balance: . Thus, a perfectly balanced genome with b = 0.5 will have 0 imbalance, and imbalance increases to 1 as the terminus dif site position b approaches 0 or 1.

Of the 2,520,185 sampled ancestral arrangements, 77.9% of the arrangements have a replichore within 20% of perfect balance, and 88.5% are within 30% of perfect balance. The full distribution of balance for ancestral arrangements can be gleaned from the historic terminus position plot in Figure 4A. To prove that the ancestral positioning of the terminus can not be explained by a series of inversions with arbitrary endpoints, we performed 30,000 simulations of replichore balance evolution in a genome that undergoes inversions with uniformly chosen endpoints. Comparison with the null model suggests it can not explain the observed data (KS test, median p-value<10⁻¹). Even when the simulated terminus dif site position is restricted to the range observed in modern genomes, the null model cannot explain the observed genomic balance (KS test, median p-value≈0.0001).

Figure 4. Historic replichore balance in Yersinia.

Historic position of terminus dif site relative to origin (A) and historic degree of imbalance (B) observed in all sampled ancestral genome arrangements of the eight Yersinia listed in Table 1. The histogram in (A) shows the replichore balance of all sampled ancestral and extant genome arrangements of the Yersinia. In (A) an arrangement with equal replichore size will have a terminus at position 0.5, indicating perfect replichore balance. The diagram shows that >88% of sampled genome arrangements have replichores within 30% of perfect balance. (B): Histograms showing the degree of imbalance for arrangements sampled on branches leading to modern genomes. Each histogram is labeled with the corresponding strain's name. Genomes with perfectly balanced replichores have 0% imbalance while a genome with the origin and terminus at the same locus would have 100% imbalance. Many, but not all, parsimonious inversion histories have imbalanced genome arrangements at common ancestors of Y. pseudotuberculosis and Y. pestis Pestoides F that contribute toward the observed imbalance in the posterior distribution for those taxa.

doi:10.1371/journal.pgen.1000128.g004

Not all modern genomes are balanced genomes. Y. pestis Pestoides F is conspicuously imbalanced, with a terminus position of 0.77 (54% imbalance). As such, we might ask whether the imbalance observed in ancestral genome arrangements is confined to the Y. pestis Pestoides F lineage. Figure 4B shows the imbalance observed on each external branch of the phylogeny, with internal branches pooled. Clearly all lineages undergo imbalance, although the Pestoides F isolate has a greater fraction of imbalanced genomes in its history. Surprisingly, the Y. pseudotuberculosis exhibit a high degree of imbalance as well. As they are sister taxa to Pestoides F, the imbalance could be attributed to imbalance at the common ancestor. In fact, the common ancestor is frequently predicted to have an imbalanced genome, and reconstructions with a balanced common ancestor require intermediate states of imbalance on branches leading to the modern Y. psuedotuberculosis genomes.

Alternative explanations for the unusual terminus position in Y. pestis Pestoides F could be entertained, one such explanation being assembly error. As the assembly has been validated using a 40 kb Fosmid library, we do not believe this to be the case (P. Chain, personal comm.). Another alternative is that the primary replication terminus has shifted to a different location in the Y. pestis Pestoides F lineage. Visual inspection of the rearrangement pattern for Y. pestis Pestoides F in Figure 1 reveals several instances of local overlapping inversions characteristic of symmetric inversion about the terminus (seen as a “fan” pattern of crossing lines). If Pestoides F has indeed switched to a new primary terminus site it would introduce some error in our calculation of the historic replichore balance distribution. However, since only about 10% of inversions occur on the branch leading to Y. pestis Pestoides F, the error would be negligible. The error would serve to overdisperse the estimated balance distribution and result in weaker apparent bias towards replichore balance.

Substantial ambiguity exists in the phylogenetic tree topology reconstructed from the Yersinia genome arrangements. BADGER found seven parsimonious topologies, and in total 48 unique topologies were sampled with inversion counts ranging from 79 to 87. Parsimony has enjoyed a long history as a guiding philosophy in evolutionary inference, so it is of interest to know whether parsimonious reconstructions agree with our expectation of replichore balance in genome arrangements. The mean estimate of imbalance turns out to be slightly smaller for parsimonious histories and the variance is much lower, as shown in Table 2. The difference in balance between parsimonious and other reconstructions is significant (KS test, p<2e-16) but the difference is small (KS D = 0.016). If we believe that strong selection for balanced genomes exists and inversions not affecting balance are neutral, then parsimonious reconstructions appear slightly more favorable.

Table 2. Degree of imbalance as a function of total number of inversions.

doi:10.1371/journal.pgen.1000128.t002

Symmetric Inversions

Previous studies have suggested that DNA replication introduces a recombination bias that favors inversions with endpoints that are equally distant from the origin of replication [22],[20], so-called symmetric inversions. Given our inferred inversion histories, we can formally test for an excess of symmetric inversions. To do so, we introduce the following notation. Let V be the ordered set of inversions mapped onto tree branches in a sampled reconstruction of the inversion history, and let v_i represent the i^th inversion. Then we define a symmetry statistic for inter-replichore inversions as:
(1)
where O_L(v_i) is the distance between the origin and the left-end of the i^th inter-replichore inversion, while O_L(v_i) is the distance between the origin and the inversion's right-end. Thus, the equation expresses the distance between inversion endpoints and the origin in each replichore, and computes the squared-difference of distances. Equation 1 assigns a perfectly symmetric inversion a value of zero, while asymmetric inversions take on large values. Incidentally, the symmetry statistic is agnostic to the choice of which replichore is the left or right.

We would like to know whether the observed inversions are more symmetric than expected by chance. To do so, we use permutation to generate a distribution of symmetry statistics that represent the null hypothesis of lack of symmetry. We compute the symmetry statistic on arbitrary pairs of left and right inversion endpoints from inter-replichore inversions, according to the following equation:
(2)

More formally, we compute a null distribution by sampling x and y uniformly without replacement from the set of possible inter-replichore inversions. O_L(v_x) represents the distance from the origin to the left-side of inversion x, and O_R(v_y) is the distance from the origin to the right-side of inversion y. If the inversion endpoints on the two replichores were independent from each other, then we would not see a significant deviation from the null distribution. Deviation towards larger values would imply fewer symmetric inversions than expected, whereas deviation towards smaller values implies more symmetric inversions than expected.

Comparison of symmetry statistics generated by Equations 1 and 2 demonstrates that within-replichore inversions are more likely to be symmetric than expected by chance (KS test, median p = 0.0001, mean D = 0.47). The observed symmetry statistic distribution and the corresponding null distribution are shown in Figure 5.

Figure 5. Inter-replichore inversions exhibit symmetry.

Inter-replichore inversions exhibit greater symmetry about the origin and terminus than expected under a null model. Symmetry for inter-replichore inversions has been quantified by Equation 1 and compared to a null distribution. The null distribution is created by applying the permutation statistic in Eqn 2 to each of the 30,000 sampled rearrangement histories. The pooled posterior samples and permutations are plotted here, statistical tests are done on a per sample basis.

doi:10.1371/journal.pgen.1000128.g005

Episodes of Imbalance

Our inference method does not estimate event times but only relative event ordering, thus we are unable to directly infer the actual amount of time ancestral genomes have spent in a balanced state. However, if we define a state of imbalance as a percentage deviation from perfect balance, say a 20% deviation, then we can quantify the number of imbalance episodes that the organisms have undergone. The posterior estimate of the number of imbalance episodes the eight Yersinia have undergone is 3.26 (σ = 1.82), not counting episodes which span a bifurcation event in the tree. The posterior distribution is shown at left in Figure 6. Similarly, we can define the duration of an imbalance episode as the number of mutation events (inversions) experienced before the chromosome returns to a balanced state. The length of imbalance episodes observed in our posterior sampling is shown at right in Figure 6.

Figure 6. Episodes of imbalance in Yersinia.

Left: The Bayesian posterior distribution of the number of imbalance episodes occurring entirely on branches of reconstructed inversion phylogenies, compared with permuted data. Right: Posterior distribution of the imbalance episode duration (in mutation events) observed on branches, compared with data permuted as described in the text. From the two plots we can conclude that transitions to imbalance are less frequent than expected under a null model, and that imbalance episodes last longer than expected under the null model.

doi:10.1371/journal.pgen.1000128.g006

If imbalance is strongly selected against, we might expect episodes of imbalance to be very short and more frequent than expected by chance given the total number of imbalanced arrangements. To determine whether the number and duration of imbalance episodes was unusual, we designed a permutation test in which the balance states along branches of reconstructed trees were randomly permuted (see the Methods section for details). The permutation gives a null model of an organism which freely transitions to and from balance, spending the same total amount of time in each state as the Yersinia genomes.

Surprisingly, we find the exact opposite of our initial expectation. There are fewer imbalance episodes than expected under the null model, and episodes of imbalance are longer than expected given the null model. The pattern is robust to choice of a particular balance threshold, as other thresholds up to 40% give similar results. Explanations might be that imbalance is only mildly detrimental, or that transmission bottlenecks periodically fix suboptimal genome arrangements in lineages of Y. pestis, despite their fitness disadvantage. Once imbalanced, several inversions typically occur before balance is restored. Given that the Y. pestis chromosome is littered with repetitive DNA, the observation is consistent with the notion that picking an arbitrary pair of oppositely oriented repeats is unlikely to yield an inversion that restores balance. Under such a hypothesis, the number of inversions occurring before restoration of balance should rise with the frequency of oppositely oriented repetitive DNA.

Inversion Length

Assuming that no selection or recombination bias acts on inversion length, the distribution of inversion lengths could be modeled as the distance between two uniformly chosen points on a circle with circumference 1. However, 46.3% of sampled inversions act within a single replichore and we might expect such inversions to be short relative to inter-replichore inversions. Although they do not affect balance, inversions within a replichore act to reverse the polarity of x sites [29], KOPS/AIMS [30],[31], and they also change leading/lagging strand A/T and G/C biases [48], relative gene density [27], and gene expression levels. As shown in Figure 7, the observed length distribution for within-replichore inversions does indeed indicate that they are shorter than inter-replichore inversions. However, we expect inter-replichore inversions to be longer than within-replichore by definition, because inter-replichore inversions must have one endpoint in each replichore.

Figure 7. The posterior distribution of inversion lengths in Yersinia.

Inversions have been classified as inter-replichore (those which span the origin) and within-replichore. The observed within-replichore inversions have a strong tendency to be short, whereas the inter-replichore inversions have a more uniform length distribution.

doi:10.1371/journal.pgen.1000128.g007

To determine whether within-replichore inversions are significantly shorter than inter-replichore inversions, we develop a null model of inversion length that accounts for replichores. Replichore sizes change as the position of the terminus dif site changes over the course of evolution, thus the expected length of within-replichore and inter-replichore inversions changes. We assume that inversion endpoints are uniformly distributed and that no inversion acts on more than half the chromosome, otherwise a shorter complementary inversion operates on the other side of the circular chromosome. We can then define the expected length of a within-replichore inversion as:
(3)

(4)
where 0<b<1 is the position of the terminus dif site relative to the origin of replication. We define a similar measure of expected length for inter-replichore inversions:
(5)

We provide a detailed derivation of these equations in the Methods section, and the values given by each equation for 0<b<1 are shown at left in Figure 8.

Figure 8. Inversions are shorter than expected.

Left: The expected length of within-replichore and inter-replichore inversions assuming that inversion endpoints are uniformly distributed. The expected length changes as a function of the positioning of the terminus dif site relative to the origin of replication. In general, within-replichore inversions are expected to be shorter than inter-replichore inversions. Right: The ratio of observed inversion length to expected length for all sampled within- and inter-replichore inversions. Both inter- and within-replichore inversions are shorter than expected, but within-replichore inversions are much more so than inter-replichore inversions.

doi:10.1371/journal.pgen.1000128.g008

Knowing the expected length for each inversion, we compute the ratio of observed length to expected length for each inversion in the posterior sampling. The distribution of ratios for within- and inter-replichore inversions is given at right in Figure 8. Both classes of inversion are shorter than would be expected under the null model. Comparison among within- and inter-replichore inversions reveals that within-replichore inversions are much more so than inter-replichore inversions (KS test, median p = 0.002, mean D = 0.41).

Selection on the Orientation of ori and dif

Previous study of Salmonella isolates has demonstrated that inversion of the origin relative to the terminus does not have a noticeable fitness impact, so long as balance is maintained [32]. Despite that, eight of the nine Yersinia genomes have the origin and terminus in identical relative orientation, which we term the canonical OriDif configuration (see Table 1). The configuration can be readily observed in Figure 1 by noticing that blocks containing the dif site (purple) are shifted upwards in every genome except Y. pseudotuberculosis IP31758, as are blocks containing the origin (extreme left and right in Figure 1). If the canonical OriDif offers no selective advantage over the non-canonical configuration, then observation of the canonical OriDif can be modeled with a binomial distribution. Under the binomial, the probability of observing eight of nine genomes with the canonical OriDif is 0.018, suggesting that a preference for the canonical OriDif configuration must exist. The genomes of Y. pestis Angola and Y. pseudotuberculosis YPIII were finished while this manuscript was under review and they too exhibit the canonical OriDif configuration, bringing the tally to 10/11 and p<0.01. Of note, studies of mutation patterns in diverse bacteria suggest that replication terminates near the dif site itself, despite the presence of many additional ter sites [19]. Although it is tempting to generalize the canonical OriDif idea to other bacterial genomes, a cursory examination of related heavily rearranged Shigella genomes did not reveal a preference for a canonical OriDif configuration.

That modern isolates favor the canonical OriDif configuration suggests that ancestral Yersinia would favor it as well, and probably also spend a noticeably greater amount of time in such a configuration. Most genome rearrangements in Yersinia (53.7%) are inter-replichore inversions which swap canonical and non-canonical OriDif configurations. As such, the number of arrangements with the canonical OriDif is not substantially different from those which have the non-canonical arrangement.

Given that modern genomes tend towards balance and a canonical OriDif, we might expect an association between balance and OriDif because an inversion that disrupts balance must also change the relative orientation of the origin and terminus. The left panel of Figure 9 shows overall balance of arrangements as a function of OriDif configuration. A significant association between balance and canonical OriDif can be seen (KS test, median p = 0.0015, mean D = 0.4). Interestingly, when arrangements at internal nodes of the phylogeny are compared to branch arrangements, the association between canonical OriDif and balance appears to be more pronounced (Figure 9 right). However, a comparison of balance at internal node arrangements with canonical OriDif versus branch arrangements with canonical OriDif fails to demonstrate a significant difference (KS test, median p = 0.67, mean D = 0.33). Failure to find a significant difference may be due to lack of inferential power, since each inversion history sample has only six internal node arrangements from which to estimate the balance distribution. Additional finished Yersinia genome sequences would provide greater statistical power.

Figure 9. Association between replichore balance and the relative orientation of ori and dif.

Left: Balance for canonical and non-canonical OriDif configurations. Right: Balance as a function of whether arrangements are at an internal node or along a branch. Arrangements at internal nodes of the phylogeny appear to be better balanced, but only when ori and dif are in the canonical orientation.

doi:10.1371/journal.pgen.1000128.g009

Hotspots of Rearrangement

The most-parsimonious inversion histories inferred by BADGER contain 79 inversion events, yet only 78 gene-order breakpoints exist in the Yersinia genomes. Clearly, some breakpoints must be used repeatedly. Previous breakpoint re-use studies [49],[50] have typically relied on inferring the mere existence of reuse rather than identifying rearrangement hotspots. To do so, we must shift focus from breakpoints to inversion endpoints. Every inversion event acts to reverse one or more consecutive LCBs. The left side of the left-most and right side of the right-most reversed LCBs constitute the inversion endpoints. As such, we can count the number of times a given LCB boundary is used in an inversion history. By definition, every LCB boundary must be the endpoint of at least one inversion, however some LCB boundaries may be used more than once.

Figure 10 shows the posterior estimate of usage for individual LCB boundaries, mapped according to their occurrence in the Yersinia pestis KIM genome. A striking pattern emerges in which inversion endpoints lie proximal to the origin of replication much more frequently than to the terminus. While inversions with endpoints near the terminus of replication do occur, they are comparatively rare.