Maximum likelihood estimates of pairwise rearrangement distances

Accurate estimation of evolutionary distances between taxa is important for many phylogenetic reconstruction methods. In the case of bacteria, distances can be estimated using a range of different evolutionary models, from single nucleotide polymorphisms to large-scale genome rearrangements. In the case of sequence evolution models (such as the Jukes-Cantor model and associated metric) have been used to correct pairwise distances. Similar correction methods for genome rearrangement processes are required to improve inference. Current attempts at correction fall into 3 categories: Empirical computational studies, Bayesian/MCMC approaches, and combinatorial approaches. Here we introduce a maximum likelihood estimator for the inversion distance between a pair of genomes, using the group-theoretic approach to modelling inversions introduced recently. This MLE functions as a corrected distance: in particular, we show that because of the way sequences of inversions interact with each other, it is quite possible for minimal distance and MLE distance to differently order the distances of two genomes from a third. This has obvious implications for the use of minimal distance in phylogeny reconstruction. The work also tackles the above problem allowing free rotation of the genome. Generally a frame of reference is locked, and all computation made accordingly. This work incorporates the action of the dihedral group so that distance estimates are free from any a priori frame of reference.Comment: 21 pages, 7 figures. To appear in the Journal of Theoretical Biolog

Dynamics of Genome Rearrangement in Bacterial Populations

Genome structure variation has profound impacts on phenotype in organisms ranging from microbes to humans, yet little is known about how natural selection acts on genome arrangement. Pathogenic bacteria such as Yersinia pestis, which causes bubonic and pneumonic plague, often exhibit a high degree of genomic rearrangement. The recent availability of several Yersinia genomes offers an unprecedented opportunity to study the evolution of genome structure and arrangement. We introduce a set of statistical methods to study patterns of rearrangement in circular chromosomes and apply them to the Yersinia. We constructed a multiple alignment of eight Yersinia genomes using Mauve software to identify 78 conserved segments that are internally free from genome rearrangement. Based on the alignment, we applied Bayesian statistical methods to infer the phylogenetic inversion history of Yersinia. The sampling of genome arrangement reconstructions contains seven parsimonious tree topologies, each having different histories of 79 inversions. Topologies with a greater number of inversions also exist, but were sampled less frequently. The inversion phylogenies agree with results suggested by SNP patterns. We then analyzed reconstructed inversion histories to identify patterns of rearrangement. We confirm an over-representation of “symmetric inversions”—inversions with endpoints that are equally distant from the origin of chromosomal replication. Ancestral genome arrangements demonstrate moderate preference for replichore balance in Yersinia. We found that all inversions are shorter than expected under a neutral model, whereas inversions acting within a single replichore are much shorter than expected. We also found evidence for a canonical configuration of the origin and terminus of replication. Finally, breakpoint reuse analysis reveals that inversions with endpoints proximal to the origin of DNA replication are nearly three times more frequent. Our findings represent the first characterization of genome arrangement evolution in a bacterial population evolving outside laboratory conditions. Insight into the process of genomic rearrangement may further the understanding of pathogen population dynamics and selection on the architecture of circular bacterial chromosomes

Group-theoretic models of the inversion process in bacterial genomes

The variation in genome arrangements among bacterial taxa is largely due to the process of inversion. Recent studies indicate that not all inversions are equally probable, suggesting, for instance, that shorter inversions are more frequent than longer, and those that move the terminus of replication are less probable than those that do not. Current methods for establishing the inversion distance between two bacterial genomes are unable to incorporate such information. In this paper we suggest a group-theoretic framework that in principle can take these constraints into account. In particular, we show that by lifting the problem from circular permutations to the affine symmetric group, the inversion distance can be found in polynomial time for a model in which inversions are restricted to acting on two regions. This requires the proof of new results in group theory, and suggests a vein of new combinatorial problems concerning permutation groups on which group theorists will be needed to collaborate with biologists. We apply the new method to inferring distances and phylogenies for published Yersinia pestis data.Comment: 19 pages, 7 figures, in Press, Journal of Mathematical Biolog

The genome of the medieval Black Death agent (extended abstract)

The genome of a 650 year old Yersinia pestis bacteria, responsible for the medieval Black Death, was recently sequenced and assembled into 2,105 contigs from the main chromosome. According to the point mutation record, the medieval bacteria could be an ancestor of most Yersinia pestis extant species, which opens the way to reconstructing the organization of these contigs using a comparative approach. We show that recent computational paleogenomics methods, aiming at reconstructing the organization of ancestral genomes from the comparison of extant genomes, can be used to correct, order and complete the contig set of the Black Death agent genome, providing a full chromosome sequence, at the nucleotide scale, of this ancient bacteria. This sequence suggests that a burst of mobile elements insertions predated the Black Death, leading to an exceptional genome plasticity and increase in rearrangement rate.Comment: Extended abstract of a talk presented at the conference JOBIM 2013, https://colloque.inra.fr/jobim2013_eng/. Full paper submitte

Characteristics of oligonucleotide frequencies across genomes: Conservation versus variation, strand symmetry, and evolutionary implications

One of the objectives of evolutionary genomics is to reveal the genetic information contained in the primordial genome (called the primary genetic information in this paper, with the primordial genome defined here as the most primitive nucleic acid genome for earth’s life) by searching for primitive traits or relics remained in modern genomes. As the shorter a sequence is, the less probable it would be modified during genome evolution. For that reason, some characteristics of very short nucleotide sequences would have considerable chances to persist during billions of years of evolution. Consequently, conservation of certain genomic features of mononucleotides, dinucleotides, and higher-order oligonucleotides across various genomes may exist; some, if not all, of these features would be relics of the primary genetic information. Based on this assumption, we analyzed the pattern of frequencies of mononucleotides, dinucleotides, and higher-order oligonucleotides of the whole-genome sequences from 458 species (including archaea, bacteria, and eukaryotes). Also, we studied the phenomenon of strand symmetry in these genomes. The results show that the conservation of frequencies of some dinucleotides and higher-order oligonucleotides across genomes does exist, and that strand symmetry is a ubiquitous and explicit phenomenon that may contribute to frequency conservation. We propose a new hypothesis for the origin of strand symmetry and frequency conservation as well as for the constitution of early genomes. We conclude that the phenomena of strand symmetry and the pattern of frequency conservation would be original features of the primary genetic information