Modern genomic analyses increasingly rely on pangenomes, that is, representations of the genome of entire populations. The simplest representation of a pangenome is a set of individual genome sequences. Compared to e.g. sequence graphs, this has the advantage that efficient exact search via indexes based on the Burrows-Wheeler Transform (BWT) is possible, that no chimeric sequences are created, and that the results are not influenced by heuristics. However, such an index may report a match in thousands of positions even if these all correspond to the same locus, making downstream analysis unnecessarily more expensive. For sufficiently similar sequences (e.g. human chromosomes), a multiple sequence alignment (MSA) can be computed. Since an MSA tends to group similar strings in the same columns, it is likely that a string occurring thousands of times in the pangenome can be described by very few columns in the MSA. We describe a method to tag entries in the BWT with the corresponding column in the MSA and develop an index that can map matches in the BWT to columns in the MSA in time proportional to the output. As a by-product, we can project a match to a designated reference genome, a capability that current pangenome aligners lack.

MOTIVATION: Since novel long read sequencing technologies allow for de novo assembly of many individuals of a species, high-quality assemblies are becoming widely available. For example, the recently published draft human pangenome reference was based on assemblies composed of contigs. There is an urgent need for a software-tool that is able to generate a multiple alignment of genomes of the same species because current multiple sequence alignment programs cannot deal with such a volume of data. RESULTS: We show that the combination of a well-known anchor-based method with the technique of prefix-free parsing yields an approach that is able to generate multiple alignments on a pangenomic scale, provided that large-scale structural variants are rare. Furthermore, experiments with real world data show that our software tool PANgenomic Anchor-based Multiple Alignment significantly outperforms current state-of-the art programs. AVAILABILITY AND IMPLEMENTATION: Source code is available at: https://gitlab.com/qwerzuiop/panama, archived at swh:1:dir:e90c9f664995acca9063245cabdd97549cf39694.

The suffix array is arguably one of the most important data structures in sequence analysis and consequently there is a multitude of suffix sorting algorithms. However, to this date the GSACA algorithm introduced in 2015 is the only known non-recursive linear-time suffix array construction algorithm (SACA). Despite its interesting theoretical properties, there has been little effort in improving GSACA ’s non-competitive real-world performance. There is a super-linear algorithm DSH , which relies on the same sorting principle and is faster than DivSufSort , the fastest SACA for over a decade. The purpose of this article is twofold: We analyse the sorting principle used in GSACA and DSH and exploit its properties to give an optimised linear-time algorithm, and we show that it can be very elegantly used to compute both the original extended Burrows-Wheeler transform ( eBWT ) and a bijective version of the Burrows-Wheeler transform ( BBWT ) in linear time. We call the algorithm “generic,” since it can be used to compute the regular suffix array and the variants used for the BBWT and eBWT . Our suffix array construction algorithm is not only significantly faster than GSACA but also outperforms DivSufSort and DSH . Our BBWT -algorithm is faster than or competitive with all other tested BBWT construction implementations on large or repetitive data, and our eBWT -algorithm is faster than all other programs on data that is not extremely repetitive.

MOTIVATION: A pangenome represents many diverse genome sequences of the same species. In order to cope with small variations as well as structural variations, recent research focused on the development of graph-based models of pangenomes. Mapping is the process of finding the original location of a DNA read in a reference sequence, typically a genome. Using a pangenome instead of a (linear) reference genome can, e.g. reduce mapping bias, the tendency to incorrectly map sequences that differ from the reference genome. Mapping reads to a graph, however, is more complex and needs more resources than mapping to a reference genome. Reducing the complexity of the graph by encoding simple variations like SNPs in a simple way can accelerate read mapping and reduce the memory requirements at the same time. RESULTS: We introduce graphs based on elastic-degenerate strings (ED strings, EDS) and the linearized form of these EDS graphs as a new representation for pangenomes. In this representation, small variations are encoded directly in the sequence. Structural variations are encoded in a graph structure. This reduces the size of the representation in comparison to sequence graphs. In the linearized form, mapping techniques that are known from ordinary strings can be applied with appropriate adjustments. Since most variations are expressed directly in the sequence, the mapping process rarely has to take edges of the EDS graph into account. We developed a prototypical software tool GED-MAP that uses this representation together with a minimizer index to map short reads to the pangenome. Our experiments show that the new method works on a whole human genome scale, taking structural variants properly into account. The advantage of GED-MAP, compared with other pangenomic short read mappers, is that the new representation allows for a simple indexing method. This makes GED-MAP fast and memory efficient. AVAILABILITY AND IMPLEMENTATION: Sources are available at: https://github.com/thomas-buechler-ulm/gedmap.

MOTIVATION: In resequencing experiments, a high-throughput sequencer produces DNA-fragments (called reads) and each read is then mapped to the locus in a reference genome at which it fits best. Currently dominant read mappers are based on the Burrows-Wheeler transform (BWT). A read can be mapped correctly if it is similar enough to a substring of the reference genome. However, since the reference genome does not represent all known variations, read mapping tends to be biased towards the reference and mapping errors may thus occur. To cope with this problem, Huang et al. encoded single nucleotide polymorphisms (SNPs) in a BWT by the International Union of Pure and Applied Chemistry (IUPAC) nucleotide code. In a different approach, Maciuca et al. provided a 'natural encoding' of SNPs and other genetic variations in a BWT. However, their encoding resulted in a significantly increased alphabet size (the modified alphabet can have millions of new symbols, which usually implies a loss of efficiency). Moreover, the two approaches do not handle all known kinds of variation. RESULTS: In this article, we propose a method that is able to encode many kinds of genetic variation (SNPs, multi-nucleotide polymorphisms, insertions or deletions, duplications, transpositions, inversions and copy-number variation) in a BWT. It takes the best of both worlds: SNPs are encoded by the IUPAC nucleotide code as in Huang et al. (2013, Short read alignment with populations of genomes. Bioinformatics, 29, i361-i370) and the encoding of the other kinds of genetic variation relies on the idea introduced in Maciuca et al. (2016, A natural encoding of genetic variation in a Burrows-Wheeler transform to enable mapping and genome inference. In: Proceedings of the 16th International Workshop on Algorithms in Bioinformatics, Volume 9838 of Lecture Notes in Computer Science, pp. 222-233. Springer). In contrast to Maciuca et al., however, we use only one additional symbol. This symbol marks variant sites in a chromosome and delimits multiple variants, which are added at the end of the 'marked chromosome'. We show how the backward search algorithm, which is used in BWT-based read mappers, can be modified in such a way that it can cope with the genetic variation encoded in the BWT. We implemented our method and compared it with BWBBLE and gramtools. AVAILABILITY AND IMPLEMENTATION: https://www.uni-ulm.de/in/theo/research/seqana/.

MOTIVATION: Low-cost genome sequencing gives unprecedented complete information about the genetic structure of populations, and a population graph captures the variations between many individuals of a population. Recently, Marcus et al. proposed to use a compressed de Bruijn graph for representing an entire population of genomes. They devised an O(n log g) time algorithm called splitMEM that constructs this graph directly (i.e. without using the uncompressed de Bruijn graph) based on a suffix tree, where n is the total length of the genomes and g is the length of the longest genome. Since the applicability of their algorithm is limited to rather small datasets, there is a strong need for space-efficient construction algorithms. RESULTS: We present two algorithms that outperform splitMEM in theory and in practice. The first implements a novel linear-time suffix tree algorithm by means of a compressed suffix tree. The second algorithm uses the Burrows-Wheeler transform to build the compressed de Bruijn graph in [Formula: see text] time, where σ is the size of the alphabet. To demonstrate the scalability of the algorithms, we applied it to seven human genomes. AVAILABILITY AND IMPLEMENTATION: https://www.uni-ulm.de/in/theo/research/seqana/.

The suffix tree is a very important data structure in string processing, but it suffers from a huge space consumption. In large-scale applications, compressed suffix trees (CSTs) are therefore used instead. A CST consists of three (compressed) components: the suffix array, the LCP-array, and data structures for simulating navigational operations on the suffix tree. The LCP-array stores the lengths of the longest common prefixes of lexicographically adjacent suffixes, and it can be computed in linear time. In this paper, we present new LCP-array construction algorithms that are fast and very space efficient. In practice, our algorithms outperform the currently best algorithms on large inputs.

SUMMARY: We implemented a software tool called GENESIS for three different genome rearrangement problems: Sorting a unichromosomal genome by weighted reversals and transpositions (SwRT), sorting a multichromosomal genome by reversals, translocations, fusions and fissions (SRTl), and sorting a multichromosomal genome by weighted reversals, translocations, fusions, fissions and transpositions (SwRTTl). AVAILABILITY: Source code can be obtained by the authors, or use the web interface http://www.uni-ulm.de/in/theo/research/genesis.html.

BACKGROUND: Comparative genomics is the analysis and comparison of genomes from different species. This area of research is driven by the large number of sequenced genomes and heavily relies on efficient algorithms and software to perform pairwise and multiple genome comparisons. RESULTS: Most of the software tools available are tailored for one specific task. In contrast, we have developed a novel system CoCoNUT (Computational Comparative geNomics Utility Toolkit) that allows solving several different tasks in a unified framework: (1) finding regions of high similarity among multiple genomic sequences and aligning them, (2) comparing two draft or multi-chromosomal genomes, (3) locating large segmental duplications in large genomic sequences, and (4) mapping cDNA/EST to genomic sequences. CONCLUSION: CoCoNUT is competitive with other software tools w.r.t. the quality of the results. The use of state of the art algorithms and data structures allows CoCoNUT to solve comparative genomics tasks more efficiently than previous tools. With the improved user interface (including an interactive visualization component), CoCoNUT provides a unified, versatile, and easy-to-use software tool for large scale studies in comparative genomics.

BACKGROUND: Due to recent progress in genome sequencing, more and more data for phylogenetic reconstruction based on rearrangement distances between genomes become available. However, this phylogenetic reconstruction is a very challenging task. For the most simple distance measures (the breakpoint distance and the reversal distance), the problem is NP-hard even if one considers only three genomes. RESULTS: In this paper, we present a new heuristic algorithm that directly constructs a phylogenetic tree w.r.t. the weighted reversal and transposition distance. Experimental results on previously published datasets show that constructing phylogenetic trees in this way results in better trees than constructing the trees w.r.t. the reversal distance, and recalculating the weight of the trees with the weighted reversal and transposition distance. An implementation of the algorithm can be obtained from the authors. CONCLUSION: The possibility of creating phylogenetic trees directly w.r.t. the weighted reversal and transposition distance results in biologically more realistic scenarios. Our algorithm can solve today's most challenging biological datasets in a reasonable amount of time.

A team at the Lawrence Livermore National Laboratory (LLNL) was given the task of using computational tools to speed up the development of DNA diagnostics for pathogen detection. This work will be described in another paper in this issue (see pages 133-149). To achieve this goal it was necessary to understand the merits and limitations of the various available comparative genomics tools. A review of some recent tools for multisequence/genome alignment and substring comparison is presented, within the general framework of applicability to a large-scale application. We note that genome alignments are important for many things, only one of which is pathogen detection. Understanding gene function, gene regulation, gene networks, phylogenetic studies and other aspects of evolution all depend on accurate nucleic acid and protein sequence alignment. Selecting appropriate tools can make a large difference in the quality of results obtained and the effort required.

Abstract Motivation: To allow a direct comparison of the genomic DNA sequences of sufficiently similar organisms, there is an urgent need for software tools that can align more than two genomic sequences. Results: We developed new algorithms and a software tool ‘Multiple Genome Aligner’ (MGA for short) that efficiently computes multiple genome alignments of large, closely related DNA sequences. For example, it can align 85% percent of the complete genomes of six human adenoviruses (average length 35305 bp.) in 159 seconds. An alignment of 74% of the complete genomes of three of strains of E. coli (lengths: 5528445; 5498450; 4639221~bp.) is produced in 30 minutes. Availability: The software MGA is available free of charge for non-commercial research institutions. For details see http://bibiserv.techfak.uni-bielefeld.de/mga/ Contact: [email protected]@techfak.uni-bielefeld.de Keywords: genome comparison; multiple alignment; efficient algorithms; graph algorithms; suffix trees.

On the one hand, the inclusion problem for nonerasing and erasing pattern languages is undecidable (see Jiang et al., 1995). On the other hand, the language equivalence problem for nonerasing pattern languages is trivially decidable (see Angluin, 1980) but the question of whether the same holds for erasing pattern languages is still open. It has been conjectured by Jiang et al. that the language equivalence problem for erasing pattern languages is also decidable. In this paper, we introduce a new normal form for patterns and show, using the normal form, that the language equivalence problem for erasing pattern languages is decidable in many special cases. We conjecture that our normal form procedure decides the problem in the general case, too. If the conjecture holds true, then the normal form is the shortest pattern generating a given erasing pattern language.