The study of evolution between species (phylogenetics) and the study of evolution within a species (population genetics) are highly related, as the same biological mechanisms are fundamental to both fields. Although both have been studied for a long time, their joint study in a unified setting has been prevented by the different time scales they consider and the different data types they employ. A similar discrepancy holds for their whole-genome specializations, comparative genomics and pangenomics. Two active areas in these fields are genome rearrangement studies and graphical pangenomics, respectively. Since the emergence of graphical pangenomics, these have existed as separate fields, despite observations that central data structures representing genomic variants in both fields are highly similar. While there exists a wealth of theoretical results for various rearrangement models in comparative genomics, the application to pangenomic data is hampered by the limitations of rearrangement problem formulations. On the practical side, pangenomes typically contain too many individual genomes for classical problems, such as the often NP-hard parsimony problems, to be solved, or for all-vs-all comparisons using rearrangement distances to be performed. On the theoretical side, some assumptions in the formulation of rearrangement problems, such as the assumption of an underlying tree, are inadequate for many pangenomes. In this work, we propose the Complete Ancestral Reconstruction for Pangenomes (CARP) problem, which overcomes these limitations while retaining intuitive relationships to both classical rearrangement problems and pangenome graphs.

Genomic rearrangements are major drivers of evolution and genetic disease. However, studying rearrangements requires segmenting the genomes of interest into conserved regions, called synteny blocks, that highlight structural differences between genomes. Synteny blocks are typically defined from annotated genes or derived as a by-product of whole-genome alignments. As these procedures are heuristic and do not explicitly model rearrangements, they can obscure real variation, create false similarities, and affect phylogenetic inference. The importance of synteny block definition has long been recognized, as shown for example by discussions on breakpoint reuse, where different definitions of synteny blocks led to different estimates of rearrangement complexity in mammalian genomes. We present a formal framework for deriving synteny blocks directly from sequence data by partitioning genomic elements into blocks that do not contain breakpoints. A breakpoint is defined between a pair of genomes as an adjacency of shared elements that occurs in one genome but not in the other. Synteny blocks are therefore not allowed to span such boundaries, ensuring that rearrangements are not obscured. The framework is fully agnostic to the type of genomic element and applies to any genome representation expressed as sequences of elements, such as non-overlapping alignments, exact matches (MUMs/MEMs), k -mers, unitigs or minimizers. We formalize two optimization problems: minimizing the total genome length after replacement by synteny blocks (the Minimum-Length Synteny Block Problem) and minimizing the number of distinct blocks (the Minimum-Size Synteny Block Problem). We show that both problems are NP-hard in general. However, when blocks are required to be collinear and to contain a shared element, we provide a linear-time algorithm with respect to the number of input elements that simultaneously minimizes both objectives. The resulting method is simple, efficient, and produces large synteny blocks without obscuring rearrangements.

Genome rearrangement has been an active area of research in computational comparative genomics for the last three decades. While initially mostly an interesting algorithmic endeavor, now the practical application of rearrangement distance methods and more advanced phylogenetic tasks is becoming common practice, given the availability of many completely sequenced genomes. Several genome rearrangement models have been developed over time, sometimes with surprising computational properties. A prominent example is the fact that computing the reversal distance of two signed permutations is possible in linear time, while for two unsigned permutations it is NP-hard. Therefore one has to always be careful about the precise problem formulation and complexity analysis of rearrangement problems in order not to be fooled. The double distance is the minimum number of genomic rearrangements between a singular and a duplicated genome that - in addition to rearrangements - are separated by a whole genome duplication. At the same time it allows to assign the genes of the duplicated genome to the two paralogous chromosome copies that existed right after the duplication event. Computing the double distance is another example of a tricky hardness landscape: If the distance measure underlying the double distance is the simple breakpoint distance, the problem can be solved in linear time, while with the more elaborate DCJ distance it is NP-hard. Indeed, there is a whole family of distance measures, parameterized by an even number $k$, between the breakpoint distance ($k=2$) at the one end and the DCJ distance ($k=\infty$) at the other end. Only little was known about the hardness border that lies somewhere on the way between these two extremes. Precisely, beneath the two border cases the (linear) problem complexity was known only for $k=4$ and $k=6$. In this paper we close the gap, giving a full picture of the hardness landscape when computing the double distance.

BACKGROUND:We study the classical problem of inferring ancestral genomes from a set of extant genomes under a given phylogeny, known as the Small Parsimony Problem (SPP). Genomes are represented as sequences of oriented markers, organized in one or more linear or circular chromosomes. Any marker may appear in several copies, without restriction on orientation or genomic location, known as the natural genomes model. Evolutionary events along the branches of the phylogeny encompass large scale rearrangements, including segmental inversions, translocations, gain and loss (DCJ-indel model). Even under simpler rearrangement models, such as the classical breakpoint model without duplicates, the SPP is computationally intractable. Nevertheless, the SPP for natural genomes under the DCJ-indel model has been studied recently, with limited success. METHODS:Building on prior work, we present a highly optimized ILP that is able to solve the SPP for sufficiently small phylogenies and gene families. A notable improvement w.r.t. the previous result is an optimized way of handling both circular and linear chromosomes. This is especially relevant to the SPP, since the chromosomal structure of ancestral genomes is unknown and the solution space for this chromosomal structure is typically large. RESULTS:We benchmark our method on simulated and real data. On simulated phylogenies we observe a considerable performance improvement on problems that include linear chromosomes. And even when the ground truth contains only one circular chromosome per genome, our method outperforms its predecessor due to its optimized handling of the solution space. The practical advantage becomes also visible in an analysis of seven Anopheles taxa.

MOTIVATION:Using a single linear reference genome poses a limitation to exploring the full genomic diversity of a species. The release of a draft human pangenome underscores the increasing relevance of pangenomics to overcome these limitations. Pangenomes are commonly represented as graphs, which can represent billions of base pairs of sequence. Presently, there is a lack of scalable software able to perform key tasks on pangenomes, such as quantifying universally shared sequence across genomes (the core genome) and measuring the extent of genomic variability as a function of sample size (pangenome growth). RESULTS:We introduce Panacus (pangenome-abacus), a tool designed to rapidly perform these tasks and visualize the results in interactive plots. Panacus can process GFA files, the accepted standard for pangenome graphs, and is able to analyze a human pangenome graph with 110 million nodes in <1 h. AVAILABILITY AND IMPLEMENTATION:Panacus is implemented in Rust and is published as Open Source software under the MIT license. The source code and documentation are available at https://github.com/marschall-lab/panacus. Panacus can be installed via Bioconda at https://bioconda.github.io/recipes/panacus/README.html.

Plasmids are a key vector of antibiotic resistance, but the current bioinformatics toolkit is not well suited to tracking them. The rapid structural changes seen in plasmid genomes present considerable challenges to evolutionary and epidemiological analysis. Typical approaches are either low resolution (replicon typing) or use shared k- mer content to define a genetic distance. However, this distance can both overestimate plasmid relatedness by ignoring rearrangements, and underestimate by overpenalizing gene gain/loss. Therefore a model is needed which captures the key components of how plasmid genomes evolve structurally - through gene/block gain or loss, and rearrangement. A secondary requirement is to prevent promiscuous transposable elements (TEs) leading to over- clustering of unrelated plasmids. We choose the 'Double Cut and Join Indel' (DCJ- Indel) model, in which plasmids are studied at a coarse level, as a sequence of signed integers (representing genes or aligned blocks), and the distance between two plasmids is the minimum number of rearrangement events or indels needed to transform one into the other. We show how this gives much more meaningful distances between plasmids. We introduce a software workflow pling (https://github.com/iqbal-lab-org/pling), which uses the DCJ- Indel model, to calculate distances between plasmids and then cluster them. In our approach, we combine containment distances and DCJ- Indel distances to build a TE- aware plasmid network. We demonstrate superior performance and interpretability to other plasmid clustering tools on the 'Russian Doll' dataset and a hospital transmission dataset.

Pangenomics is the study of related genomes collectively, usually from the same species or closely related taxa. Originally, pangenomes were defined for bacterial species. After the concept was extended to eukaryotic genomes, two definitions of pangenome evolved in parallel: the gene-based approach, which defines the pangenome as the union of all genes, and the sequence-based approach, which defines the pangenome as the set of all nonredundant genomic sequences. Estimating the total size of the pangenome for a given species has been subject of study since the very first mention of pangenomes. Traditionally, this is performed by predicting the ratio at which new genes are discovered, referred to as the openness of the species. Here, we abstract each genome as a set of items, which is entirely agnostic of the two approaches (gene-based, sequence-based). Genes are a viable option for items, but also other possibilities are feasible, e.g., genome sequence substrings of fixed length k (k-mers). In the present study, we investigate the use of k-mers to estimate the openness as an alternative to genes, and compare the results. An efficient implementation is also provided.

De novo genome assembly is the process of reconstructing a complete genomic sequence from countless small sequencing reads. Due to the complexity of this task, numerous genome assemblers have been developed to cope with different requirements and the different kinds of data provided by sequencers within the fast evolving field of next-generation sequencing technologies. In particular, the recently introduced generation of benchtop sequencers, like Illumina's MiSeq and Ion Torrent's Personal Genome Machine (PGM), popularized the easy, fast, and cheap sequencing of bacterial organisms to a broad range of academic and clinical institutions. With a strong pragmatic focus, here, we give a novel insight into the line of assembly evaluation surveys as we benchmark popular de novo genome assemblers based on bacterial data generated by benchtop sequencers. Therefore, single-library assemblies were generated, assembled, and compared to each other by metrics describing assembly contiguity and accuracy, and also by practice-oriented criteria as for instance computing time. In addition, we extensively analyzed the effect of the depth of coverage on the genome assemblies within reasonable ranges and the k-mer optimization problem of de Bruijn Graph assemblers. Our results show that, although both MiSeq and PGM allow for good genome assemblies, they require different approaches. They not only pair with different assembler types, but also affect assemblies differently regarding the depth of coverage where oversampling can become problematic. Assemblies vary greatly with respect to contiguity and accuracy but also by the requirement on the computing power. Consequently, no assembler can be rated best for all preconditions. Instead, the given kind of data, the demands on assembly quality, and the available computing infrastructure determines which assembler suits best. The data sets, scripts and all additional information needed to replicate our results are freely available at ftp://ftp.cebitec.uni-bielefeld.de/pub/GABenchToB.

Computational pangenomics deals with the joint analysis of all genomic sequences of a species. It has already been successfully applied to various tasks in many research areas. Further advances in DNA sequencing technologies constantly let more and more genomic sequences become available for many species, leading to an increasing attractiveness of pangenomic studies. At the same time, larger datasets also pose new challenges for data structures and algorithms that are needed to handle the data. Efficient methods oftentimes make use of the concept of k-mers.Core detection is a common way of analyzing a pangenome. The pangenome's core is defined as the subset of genomic information shared among all individual members. Classically, it is not only determined on the abstract level of genes but can also be described on the sequence level.In this chapter, we provide an overview of k-mer-based methods in the context of pangenomics studies. We first revisit existing software solutions for k-mer counting and k-mer set representation. Afterward, we describe the usage of two k-mer-based approaches, Pangrowth and Corer, for pangenomic core detection.

Abstract Background Two genomes $$\mathbb {A}$$ A and $$\mathbb {B}$$ B over the same set of gene families form a canonical pair when each of them has exactly one gene from each family. Denote by $$n_*$$ n ∗ the number of common families of $$\mathbb {A}$$ A and $$\mathbb {B}$$ B . Different distances of canonical genomes can be derived from a structure called breakpoint graph, which represents the relation between the two given genomes as a collection of cycles of even length and paths. Let $$c_i$$ c i and $$p_j$$ p j be respectively the numbers of cycles of length i and of paths of length j in the breakpoint graph of genomes $$\mathbb {A}$$ A and $$\mathbb {B}$$ B . Then, the breakpoint distance of $$\mathbb {A}$$ A and $$\mathbb {B}$$ B is equal to $$n_*-\left( c_2+\frac{p_0}{2}\right)$$ n ∗ - c 2 + p 0 2 . Similarly, when the considered rearrangements are those modeled by the double-cut-and-join (DCJ) operation, the rearrangement distance of $$\mathbb {A}$$ A and $$\mathbb {B}$$ B is $$n_*-\left( c+\frac{p_e }{2}\right)$$ n ∗ - c + p e 2 , where c is the total number of cycles and $$p_e$$ p e is the total number of paths of even length. Motivation The distance formulation is a basic unit for several other combinatorial problems related to genome evolution and ancestral reconstruction, such as median or double distance. Interestingly, both median and double distance problems can be solved in polynomial time for the breakpoint distance, while they are NP-hard for the rearrangement distance. One way of exploring the complexity space between these two extremes is to consider a $$\sigma _k$$ σ k distance, defined to be $$n_*-\left( c_2+c_4+\ldots +c_k+\frac{p_0+p_2+\ldots +p_{k-2}}{2}\right)$$ n ∗ - c 2 + c 4 + … + c k + p 0 + p 2 + … + p k - 2 2 , and increasingly investigate the complexities of median and double distance for the $$\sigma _4$$ σ 4 distance, then the $$\sigma _6$$ σ 6 distance, and so on. Results While for the median much effort was done in our and in other research groups but no progress was obtained even for the $$\sigma _4$$ σ 4 distance, for solving the double distance under $$\sigma _4$$ σ 4 and $$\sigma _6$$ σ 6 distances we could devise linear time algorithms, which we present here.

Microbes – bacteria, archaea, unicellular eukaryotes, and viruses – play an important role in human and environmental health. Growing awareness of this fact has led to a huge increase in microbiological research and applications in a variety of fields. Driven by technological advances that allow high-throughput molecular characterization of microbial species and communities, microbiological research now offers unparalleled opportunities to address current and emerging needs. As well as helping to address global health threats such as antimicrobial resistance and viral pandemics, it also has a key role to play in areas such as agriculture, waste management, water treatment, ecosystems remediation, and the diagnosis, treatment and prevention of various diseases. Reflecting this broad potential, billions of euros have been invested in microbiota research programs worldwide. Though run independently, many of these projects are closely related. However, Germany currently has no infrastructure to connect such projects or even compare their results. Thus, the potential synergy of data and expertise is being squandered. The goal of the NFDI4Microbiota consortium is to serve and connect this broad and heterogeneous research community by elevating the availability and quality of research results through dedicated training, and by facilitating the generation, management, interpretation, sharing, and reuse of microbial data. In doing so, we will also foster interdisciplinary interactions between researchers. NFDI4Microbiota will achieve this by creating a German microbial research network through training and community-building activities, and by creating a cloud-based system that will make the storage, integration and analysis of microbial data, especially omics data, consistent, reproducible, and accessible across all areas of life sciences. In addition to increasing the quality of microbial research in Germany, our training program will support widespread and proper usage of these services. Through this dual emphasis on education and services, NFDI4Microbiota will ensure that microbial research in Germany is synergistic and efficient, and thus excellent. By creating a central resource for German microbial research, NDFDI4Microbiota will establish a connecting hub for all NFDI consortia that work with microbiological data, including GHGA, NFDI4Biodiversity, NFDI4Agri and several others. NFDI4Microbiota will provide non-microbial specialists from these consortia with direct and easy access to the necessary expertise and infrastructure in microbial research in order to facilitate their daily work and enhance their research. The links forged through NFDI4Microbiota will not only increase the synergy between NFDI consortia, but also elevate the overall quality and relevance of microbial research in Germany.

Genomic regions under positive selection harbor variation linked for example to adaptation. Most tools for detecting positively selected variants have computational resource requirements rendering them impractical on population genomic datasets with hundreds of thousands of individuals or more. We have developed and implemented an efficient haplotype-based approach able to scan large datasets and accurately detect positive selection. We achieve this by combining a pattern matching approach based on the positional Burrows-Wheeler transform with model-based inference which only requires the evaluation of closed-form expressions. We evaluate our approach with simulations, and find it to be both sensitive and specific. The computational resource requirements quantified using UK Biobank data indicate that our implementation is scalable to population genomic datasets with millions of individuals. Our approach may serve as an algorithmic blueprint for the era of "big data" genomics: a combinatorial core coupled with statistical inference in closed form.

This work is about comparing two genomes 𝕊 and 𝔻 over the same set of gene families, such that 𝕊 is singular (has one gene per family), while 𝔻 is duplicated (has two genes per family). Considering some underlying model, that can be simply the minimization of breakpoints or finding the smallest sequence of mutations mimicked by the double-cut-and-join (DCJ) operation, the double distance of 𝕊 and 𝔻 aims to find the smallest distance between 𝔻 and any element from the set , that contains all possible genome configurations obtained by doubling the chromosomes of 𝕊 . The breakpoint double distance of 𝕊 and 𝔻 can be greedily solved in linear time. In contrast, the DCJ double distance of 𝕊 and 𝔻 was proven to be NP-hard. The complexity space between these two extremes can be explored with the help of an intermediate family of problems, the σ _k distances, defined for each k ∈{2,4,6,...,∞} , in a way such that the σ _2 distance equals the breakpoint distance and the σ _∞ distance equals the DCJ distance. With this class of problems it is possible to investigate the complexity of the double distance under the σ _k distance, increasing the value k in an attempt to identify the smallest value for which the double distance becomes NP-hard, indicating the point in which the complexity changes. In our more recent work we have proven that, for the particular case in which genomes can only be composed of circular chromosomes, both σ _4 and σ _6 double distances can be solved in linear time. Here we present a non-trivial extension of these results to genomes including linear chromosomes.

One of the most basic kinds of analysis to be performed on a pangenome is the detection of its core, i.e., the information shared among all members. Pangenomic core detection is classically done on the gene level and many tools focus exclusively on core detection in prokaryotes. Here, we present a new method for sequence-based pangenomic core detection. Our model generalizes from a strict core definition allowing us to flexibly determine suitable core properties depending on the research question and the dataset under consideration. We propose an algorithm based on a colored de Bruijn graph that runs in linear time with respect to the number of k-mers in the graph. An implementation of our method is called Corer. Because of the usage of a colored de Bruijn graph, it works alignment-free, is provided with a small memory footprint, and accepts as input assembled genomes as well as sequencing reads.

Feature embedding methods have been proposed in literature to represent sequences as numeric vectors to be used in some bioinformatics investigations, such as family classification and protein structure prediction. Recent theoretical results showed that the well-known Lyndon factorization preserves common factors in overlapping strings. Surprisingly, the fingerprint of a sequencing read, which is the sequence of lengths of consecutive factors in variants of the Lyndon factorization of the read, is effective in preserving sequence similarities, suggesting it as basis for the definition of novels representations of sequencing reads. We propose a novel feature embedding method for Next-Generation Sequencing (NGS) data using the notion of fingerprint. We provide a theoretical and experimental framework to estimate the behaviour of fingerprints and of the $k$-mers extracted from it, called $k$-fingers, as possible feature embeddings for sequencing reads. As a case study to assess the effectiveness of such embeddings, we use fingerprints to represent RNA-Seq reads and to assign them to the most likely gene from which they were originated as fragments of transcripts of the gene. We provide an implementation of the proposed method in the tool lyn2vec, which produces Lyndon-based feature embeddings of sequencing reads.

Two genomes over the same set of gene families form a canonical pair when each of them has exactly one gene from each family. A genome is circular when it contains only circular chromosomes. Different distances of canonical circular genomes can be derived from a structure called breakpoint graph , which represents the relation between the two given genomes as a collection of cycles of even length. Then, the breakpoint distance is equal to n − c 2 , where n is the number of genes and c 2 is the number of cycles of length 2. Similarly, when the considered rearrangements are those modeled by the double-cut-and-join (DCJ) operation, the rearrangement distance is n − c , where c is the total number of cycles. The distance problem is a basic unit for several other combinatorial problems related to genome evolution and ancestral reconstruction, such as median or double distance . Interestingly, both median and double distance problems can be solved in polynomial time for the breakpoint distance, while they are NP-hard for the rearrangement distance. One way of exploring the complexity space between these two extremes is to consider a σ k distance, defined to be n − ( c 2 + c 4 + . . . + c k ), and increasingly investigate the complexities of median and double distance for the σ 4 distance, then the σ 6 distance, and so on. While for the median much effort was done in our and in other research groups but no progress was obtained even for the σ 4 distance, for solving the double distance under σ 4 and σ 6 distances we could devise linear time algorithms, which we present here. distance, double-cut-and-join (DCJ) distance, double distance Acknowledgements We would like to thank Cedric Chauve for bringing our attention to the class of σ k distances as a means for studying the hardness bound between the breakpoint distance and the DCJ distance in combinatorial problems related to genome evolution. Thanks also to Eloi Araujo, Daniel Doerr and Fábio H. V. Martinez for helping us studying the median problem under this class. of a component G of a { 6 } -pruned ambiguous breakpoint graph. candidates optimal: τ G induces one 4- and one 6-cycle, while the alternative e s ( τ G ) induces two 6-cycles.

Representations of biological sequences facilitating sequence comparison are crucial in several bioinformatics tasks. Recently, the Lyndon factorization has been proved to preserve common factors in overlapping reads [6], thus leading to the idea of using factorizations of sequences to define measures of similarity between reads. In this paper we propose as a signature of sequencing reads the notion of fingerprint, i.e., the sequence of lengths of consecutive factors in Lyndon-based factorizations of the reads. Surprisingly, fingerprints of reads are effective in preserving sequence similarities while providing a compact representation of the read, and so, k-mers extracted from a fingerprint, called k-fingers, can be used to capture sequence similarity between reads. We first provide a probabilistic framework to estimate the behaviour of fingerprints. Then we experimentally evaluate the effectiveness of this representation for machine learning algorithms for classifying biological sequences. In particular, we considered the problem of assigning RNASeq reads to the most likely gene from which they were generated. Our results show that fingerprints can provide an effective machine learning interpretable representation, successfully preserving sequence similarity.