Weighted Minimum-Length Rearrangement Scenarios

We present the first known model of genome rearrangement with an arbitrary real-valued weight function on the rearrangements. It is based on the dominant model for the mathematical and algorithmic study of genome rearrangement, Double Cut and Join (DCJ). Our objective function is the sum or product of the weights of the DCJs in an evolutionary scenario, and the function can be minimized or maximized. If the likelihood of observing an independent DCJ was estimated based on biological conditions, for example, then this objective function could be the likelihood of observing the independent DCJs together in a scenario. We present an O(n^4)-time dynamic programming algorithm solving the Minimum Cost Parsimonious Scenario (MCPS) problem for co-tailed genomes with n genes (or syntenic blocks). Combining this with our previous work on MCPS yields a polynomial-time algorithm for general genomes. The key theoretical contribution is a novel link between the parsimonious DCJ (or 2-break) scenarios and quadrangulations of a regular polygon. To demonstrate that our algorithm is fast enough to treat biological data, we run it on syntenic blocks constructed for Human paired with Chimpanzee, Gibbon, Mouse, and Chicken. We argue that the Human and Gibbon pair is a particularly interesting model for the study of weighted genome rearrangements

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 inference of gene trees with species trees

Molecular phylogeny has focused mainly on improving models for the reconstruction of gene trees based on sequence alignments. Yet, most phylogeneticists seek to reveal the history of species. Although the histories of genes and species are tightly linked, they are seldom identical, because genes duplicate, are lost or horizontally transferred, and because alleles can co-exist in populations for periods that may span several speciation events. Building models describing the relationship between gene and species trees can thus improve the reconstruction of gene trees when a species tree is known, and vice-versa. Several approaches have been proposed to solve the problem in one direction or the other, but in general neither gene trees nor species trees are known. Only a few studies have attempted to jointly infer gene trees and species trees. In this article we review the various models that have been used to describe the relationship between gene trees and species trees. These models account for gene duplication and loss, transfer or incomplete lineage sorting. Some of them consider several types of events together, but none exists currently that considers the full repertoire of processes that generate gene trees along the species tree. Simulations as well as empirical studies on genomic data show that combining gene tree-species tree models with models of sequence evolution improves gene tree reconstruction. In turn, these better gene trees provide a better basis for studying genome evolution or reconstructing ancestral chromosomes and ancestral gene sequences. We predict that gene tree-species tree methods that can deal with genomic data sets will be instrumental to advancing our understanding of genomic evolution.Comment: Review article in relation to the "Mathematical and Computational Evolutionary Biology" conference, Montpellier, 201

Phylogenetic assembly of paleogenomes integrating ancient DNA data

Luhmann N. Phylogenetic assembly of paleogenomes integrating ancient DNA data. Bielefeld: Universität Bielefeld; 2017.In comparative genomics, reconstructing the genomes of ancestral species in a given phylogeny is an important problem in order to analyze genome evolution over time. The diversity of present-day genomes in terms of local mutations and genome rearrangements allows to shed light on the dynamics of evolutionary processes that led from a common ancestor to a set of extant genomes. This speciation history is depicted in a phylogenetic tree. Comparative genome reconstruction methods aim to infer genomic features such as an order of markers (e.g. genes) for extinct species at internal nodes of the tree by applying different evolutionary models, relying only on the information available for the extant genomes at the leaves of the phylogenetic tree. Recently, the steady progress in sequencing technologies led to the emergence of the field of paleogenomics, where the study of ancient DNA (aDNA) found in conserved organic material is moving rapidly towards the sequencing and analysis of complete paleogenomes. Such ''genetic time travel'' allows direct insight into specific phases of the evolution of specific genomes that are not only implicitly inferred from extant DNA sequences. However, as DNA is naturally degraded over time after the death of an organism and environmental conditions interfere with the conservation of DNA material, an assembly of these paleogenomes is usually fragmented, preventing a detailed analysis of genome rearrangements along the branches of the phylogenetic tree. In this thesis, we aim to combine the study of aDNA and comparative ancestral reconstruction in a phylogenetic framework. The comparison with extant related genomes can naturally assist in scaffolding a fragmented aDNA assembly, while the aDNA sequencing data can be included as an additional source of information for comparative reconstruction methods to improve the reconstructions of all related genomes in the phylogenetic tree. Our first focus is on integrative methods to reconstruct marker orders globally in a phylogeny under the assumption of parsimony. An underlying rearrangement model can describe the evolutionary operations that occurred along the edges of the tree. However, as much as complex rearrangement scenarios can give insights into underlying biological mechanisms during evolution, from an computational point of view the ancestral reconstruction problem under rearrangement distances is an NP-hard problem. One exception is the Single-Cut-or-Join (SCJ) distance, that uses a marker order-based representation of the involved genomes to model the cut and join of marker adjacencies as evolutionary operations. We build upon this rearrangement model and describe parsimony-based reconstruction methods aiming to minimize the SCJ distance in the tree. In addition, we require the reconstructed solutions to be consistent, such that they represent linear or circular regions of the ancestral genome. Our first polynomial-time method is based on the Sankoff-Rousseau algorithm and directly includes an aDNA assembly graph at one internal node of the tree. We show that including branch lengths in the underlying tree can avoid ambiguity in practice. Our second approach follows a more general strategy and includes the aDNA sequencing data as local weights for adjacencies next to the SCJ distance in the objective. We describe a fixed-parameter-tractable algorithm that also allows to sample co-optimal solutions. Finally, we describe an approach to fill gaps between potentially adjacent markers by aDNA data to reconstruct the complete genome sequence of a paleogenome guided by the related extant genome sequences. In addition, this approach enables us to select the adjacencies that are supported by the sequencing information from sets of conflicting adjacencies. We evaluate our proposed models and algorithms on simulated and biological data. In particular, we integrate two aDNA sequencing data sets for ancient strains of the pathogen Yersinia pestis, that is understood to be the cause of several pandemics in medieval times. We show that the combination of aDNA sequencing reads and a parsimonious reconstruction in the phylogenetic tree reduces the fragmentation of an initial aDNA assembly substantially and explore alternative reconstructions to emphasize reliably reconstructed regions of the ancient genomes