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1. A space and time-efficient index for the compacted colored de Bruijn graph

   https://doi.org/10.1093/bioinformatics/bty292  

   Almodaresi, Fatemeh ; Sarkar, Hirak ; Srivastava, Avi ; Patro, Rob ( June 2018 , Bioinformatics)

   Indexing reference sequences for search—both individual genomes and collections of genomes—is an important building block for many sequence analysis tasks. Much work has been dedicated to developing full-text indices for genomic sequences, based on data structures such as the suffix array, the BWT and the FM-index. However, the de Bruijn graph, commonly used for sequence assembly, has recently been gaining attention as an indexing data structure, due to its natural ability to represent multiple references using a graphical structure, and to collapse highly-repetitive sequence regions. Yet, much less attention has been given as to how to best index such a structure, such that queries can be performed efficiently and memory usage remains practical as the size and number of reference sequences being indexed grows large.

   We present a novel data structure for representing and indexing the compacted colored de Bruijn graph, which allows for efficient pattern matching and retrieval of the reference information associated with each k-mer. As the popularity of the de Bruijn graph as an index has increased over the past few years, so have the number of proposed representations of this structure. Existing structures typically fall into two categories; those that are hashing-based and provide very fast access to the underlying k-mer information, and those that are space-frugal and provide asymptotically efficient but practically slower pattern search. Our representation achieves a compromise between these two extremes. By building upon minimum perfect hashing and making use of succinct representations where applicable, our data structure provides practically fast lookup while greatly reducing the space compared to traditional hashing-based implementations. Further, we describe a sampling scheme for this index, which provides the ability to trade off query speed for a reduction in the index size. We believe this representation strikes a desirable balance between speed and space usage, and allows for fast search on large reference sequences.

   Finally, we describe an application of this index to the taxonomic read assignment problem. We show that by adopting, essentially, the approach of Kraken, but replacing k-mer presence with coverage by chains of consistent unique maximal matches, we can improve the space, speed and accuracy of taxonomic read assignment.

   pufferfish is written in C++11, is open source, and is available at https://github.com/COMBINE-lab/pufferfish.

   Supplementary data are available at Bioinformatics online.

    

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2. Stacks 2: Analytical methods for paired‐end sequencing improve RADseq‐based population genomics

   https://doi.org/10.1111/mec.15253  

   Rochette, Nicolas C. ; Rivera‐Colón, Angel G. ; Catchen, Julian M. ( October 2019 , Molecular Ecology)

   For half a century population genetics studies have put type II restriction endonucleases to work. Now, coupled with massively‐parallel, short‐read sequencing, the family of RAD protocols that wields these enzymes has generated vast genetic knowledge from the natural world. Here, we describe the first software natively capable of using paired‐end sequencing to derive short contigs from de novo RAD data. Stacks version 2 employs a de Bruijn graph assembler to build and connect contigs from forward and reverse reads for each de novo RAD locus, which it then uses as a reference for read alignments. The new architecture allows all the individuals in a metapopulation to be considered at the same time as each RAD locus is processed. This enables a Bayesian genotype caller to provide precise SNPs, and a robust algorithm to phase those SNPs into long haplotypes, generating RAD loci that are 400–800 bp in length. To prove its recall and precision, we tested the software with simulated data and compared reference‐aligned and de novo analyses of three empirical data sets. Our study shows that the latest version of Stacks is highly accurate and outperforms other software in assembling and genotyping paired‐end de novo data sets.

    

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3. Unbiased pangenome graphs

   https://doi.org/10.1093/bioinformatics/btac743  

   Garrison, Erik ; Guarracino, Andrea ( November 2022 , Bioinformatics)

   Alkan, Can (Ed.)

   Abstract Motivation Pangenome variation graphs model the mutual alignment of collections of DNA sequences. A set of pairwise alignments implies a variation graph, but there are no scalable methods to generate such a graph from these alignments. Existing related approaches depend on a single reference, a specific ordering of genomes or a de Bruijn model based on a fixed k-mer length. A scalable, self-contained method to build pangenome graphs without such limitations would be a key step in pangenome construction and manipulation pipelines. Results We design the seqwish algorithm, which builds a variation graph from a set of sequences and alignments between them. We first transform the alignment set into an implicit interval tree. To build up the variation graph, we query this tree-based representation of the alignments to reduce transitive matches into single DNA segments in a sequence graph. By recording the mapping from input sequence to output graph, we can trace the original paths through this graph, yielding a pangenome variation graph. We present an implementation that operates in external memory, using disk-backed data structures and lock-free parallel methods to drive the core graph induction step. We demonstrate that our method scales to very large graph induction problems by applying it to build pangenome graphs for several species. Availability and implementation seqwish is published as free software under the MIT open source license. Source code and documentation are available at https://github.com/ekg/seqwish. seqwish can be installed via Bioconda https://bioconda.github.io/recipes/seqwish/README.html or GNU Guix https://github.com/ekg/guix-genomics/blob/master/seqwish.scm. 

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4. Constructing small genome graphs via string compression

   https://doi.org/10.1093/bioinformatics/btab281  

   Qiu, Yutong ; Kingsford, Carl ( July 2021 , Bioinformatics)

   The size of a genome graph—the space required to store the nodes, node labels and edges—affects the efficiency of operations performed on it. For example, the time complexity to align a sequence to a graph without a graph index depends on the total number of characters in the node labels and the number of edges in the graph. This raises the need for approaches to construct space-efficient genome graphs.

   We point out similarities in the string encoding mechanisms of genome graphs and the external pointer macro (EPM) compression model. We present a pair of linear-time algorithms that transform between genome graphs and EPM-compressed forms. The algorithms result in an upper bound on the size of the genome graph constructed in terms of an optimal EPM compression. To further reduce the size of the genome graph, we propose the source assignment problem that optimizes over the equivalent choices during compression and introduce an ILP formulation that solves that problem optimally. As a proof-of-concept, we introduce RLZ-Graph, a genome graph constructed based on the relative Lempel–Ziv algorithm. Using RLZ-Graph, across all human chromosomes, we are able to reduce the disk space to store a genome graph on average by 40.7% compared to colored compacted de Bruijn graphs constructed by Bifrost under the default settings. The RLZ-Graph scales well in terms of running time and graph sizes with an increasing number of human genome sequences compared to Bifrost and variation graphs produced by VGtoolkit.

   The RLZ-Graph software is available at: https://github.com/Kingsford-Group/rlzgraph.

   Supplementary data are available at Bioinformatics online.

    

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5. On the Hardness and Inapproximability of Recognizing Wheeler Graphs

   https://doi.org/10.4230/LIPIcs.ESA.2019.51  

   Gibney, Daniel ;  Thankachan, Sharma V. ( January 2019 , 27th Annual European Symposium on Algorithms (ESA) 2019)

   In recent years several compressed indexes based on variants of the Burrows-Wheeler transformation have been introduced. Some of these are used to index structures far more complex than a single string, as was originally done with the FM-index [Ferragina and Manzini, J. ACM 2005]. As such, there has been an increasing effort to better understand under which conditions such an indexing scheme is possible. This has led to the introduction of Wheeler graphs [Gagie et al., Theor. Comput. Sci., 2017]. Gagie et al. showed that de Bruijn graphs, generalized compressed suffix arrays, and several other BWT related structures can be represented as Wheeler graphs and that Wheeler graphs can be indexed in a way which is space-efficient. Hence, being able to recognize whether a given graph is a Wheeler graph, or being able to approximate a given graph by a Wheeler graph, could have numerous applications in indexing. Here we resolve the open question of whether there exists an efficient algorithm for recognizing if a given graph is a Wheeler graph. We present - The problem of recognizing whether a given graph G=(V,E) is a Wheeler graph is NP-complete for any edge label alphabet of size sigma >= 2, even when G is a DAG. This holds even on a restricted, subset of graphs called d-NFA's for d >= 5. This is in contrast to recent results demonstrating the problem can be solved in polynomial time for d-NFA's where d <= 2. We also show the recognition problem can be solved in linear time for sigma =1; - There exists an 2^{e log sigma + O(n + e)} time exact algorithm where n = |V| and e = |E|. This algorithm relies on graph isomorphism being computable in strictly sub-exponential time; - We define an optimization variant of the problem called Wheeler Graph Violation, abbreviated WGV, where the aim is to remove the minimum number of edges in order to obtain a Wheeler graph. We show WGV is APX-hard, even when G is a DAG, implying there exists a constant C >= 1 for which there is no C-approximation algorithm (unless P = NP). Also, conditioned on the Unique Games Conjecture, for all C >= 1, it is NP-hard to find a C-approximation; - We define the Wheeler Subgraph problem, abbreviated WS, where the aim is to find the largest subgraph which is a Wheeler Graph (the dual of the WGV). In contrast to WGV, we prove that the WS problem is in APX for sigma=O(1); The above findings suggest that most problems under this theme are computationally difficult. However, we identify a class of graphs for which the recognition problem is polynomial-time solvable, raising the open question of which parameters determine this problem's difficulty. 

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