Superbubbles, Ultrabubbles, and Cacti

Paten, Benedict; Eizenga, Jordan M.; Rosen, Yohei M.; Novak, Adam M.; Garrison, Erik; Hickey, Glenn

doi:10.1089/cmb.2017.0251

Cited by 56 publications

(77 citation statements)

References 18 publications

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“…Snarls can be computed in linear time using a cactus graph decomposition [24]. They can be computed once for a given graph using vg snarls , or on the y with vg call .…”

Section: Sv Genotyping Algorithmmentioning

confidence: 99%

“…Accordingly, variation graphs are constructed so as to encode haplotype sequences as walks through the graph. Variation between sequences shows up as bubbles in the graph [24].…”

Section: Supplementary Information Variation Graph and Structural Varmentioning

confidence: 99%

“…Reads are mapped to the graph and used to compute the read support for each node and edge (see Supplementary Information for a description of the graph formalism). Sites of variation within the graph are then identi ed using the snarl decomposition as described in [24]. These sites correspond to intervals along the reference paths (ex.…”

mentioning

confidence: 99%

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Genotyping structural variants in pangenome graphs using the vg toolkit

Hickey

Heller

Monlong

et al. 2019

Preprint

Self Cite

114

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Structural variants (SVs) remain challenging to represent and study relative to point mutations despite their demonstrated importance. We show that variation graphs, as implemented in the vg toolkit, provide an e ective means for leveraging SV catalogs for short-read SV genotyping experiments. We benchmarked vg against state-of-the-art SV genotypers using three sequence-resolved SV catalogs generated by recent long-read sequencing studies. In addition, we use assemblies from 12 yeast strains to show that graphs constructed directly from aligned de novo assemblies improve genotyping compared to graphs built from intermediate SV catalogs in the VCF format.real Illumina reads and a pangenome built from SVs discovered in recent long-read sequencing studies [21,22,23,5], We also compared vg's performance with state-of-the-art SV genotypers: SVTyper[3], Delly Genotyper[4], BayesTyper[19], Paragraph[20] and . Across the datasets we tested, which range in size from 26k to 97k SVs, vg is the best performing SV genotyper on real short-read data for all SV types in the majority of cases. Finally, we demonstrate that a pangenome graph built from the alignment of de novo assemblies of diverse Saccharomyces cerevisiae strains improves SV genotyping performance. Results Structural variation in vgWe used vg to implement a straightforward SV genotyping pipeline. Reads are mapped to the graph and used to compute the read support for each node and edge (see Supplementary Information for a description of the graph formalism). Sites of variation within the graph are then identi ed using the snarl decomposition as described in [24]. These sites correspond to intervals along the reference paths (ex. contigs or chromosomes) which are embedded in the graph. They also contain nodes and edges deviating from the reference path, which represent variation at the site. For each site, the two most supported paths spanning its interval (haplotypes) are determined, and their relative supports used to produce a genotype at that site (Figure 1a). The pipeline is described in detail in Methods. We rigorously evaluated the accuracy of our method on a variety of datasets, and present these results in the remainder of this section.

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“…Snarls can be computed in linear time using a cactus graph decomposition [24]. They can be computed once for a given graph using vg snarls , or on the y with vg call .…”

Section: Sv Genotyping Algorithmmentioning

confidence: 99%

“…Accordingly, variation graphs are constructed so as to encode haplotype sequences as walks through the graph. Variation between sequences shows up as bubbles in the graph [24].…”

Section: Supplementary Information Variation Graph and Structural Varmentioning

confidence: 99%

See 1 more Smart Citation

Genotyping structural variants in pangenome graphs using the vg toolkit

Hickey

Heller

Monlong

et al. 2019

Preprint

Self Cite

114

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“…The concept of a superbubble was extended to bi-directed and bi-edged graphs, called ultrabubble in [9–11]. The enumeration algorithm for ultrabubbles in [9] has a worst case complexity of , and hence does not provide an alternative for directed graphs.…”

Section: Introductionmentioning

confidence: 99%

Superbubbles revisited

Gärtner

Müller

Stadler

2018

Algorithms Mol Biol

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BackgroundSuperbubbles are distinctive subgraphs in direct graphs that play an important role in assembly algorithms for high-throughput sequencing (HTS) data. Their practical importance derives from the fact they are connected to their host graph by a single entrance and a single exit vertex, thus allowing them to be handled independently. Efficient algorithms for the enumeration of superbubbles are therefore of important for the processing of HTS data. Superbubbles can be identified within the strongly connected components of the input digraph after transforming them into directed acyclic graphs. The algorithm by Sung et al. (IEEE ACM Trans Comput Biol Bioinform 12:770–777, 2015) achieves this task in -time. The extraction of superbubbles from the transformed components was later improved to by Brankovic et al. (Theor Comput Sci 609:374–383, 2016) resulting in an overall -time algorithm.ResultsA re-analysis of the mathematical structure of superbubbles showed that the construction of auxiliary DAGs from the strongly connected components in the work of Sung et al. missed some details that can lead to the reporting of false positive superbubbles. We propose an alternative, even simpler auxiliary graph that solved the problem and retains the linear running time for general digraph. Furthermore, we describe a simpler, space-efficient -time algorithm for detecting superbubbles in DAGs that uses only simple data structures.ImplementationWe present a reference implementation of the algorithm that accepts many commonly used formats for the input graph and provides convenient access to the improved algorithm. https://github.com/Fabianexe/Superbubble.

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“…In previous work, we proposed a decomposition for sequence graphs that describes their common topological features [12]. A simple variant in a graph, such as an indel or SNP, will typically be represented as one or two nodes that represent the different alleles, flanked by two nodes representing conserved sequences.…”

Section: Snarl Decompositionmentioning

confidence: 99%

Distance Indexing and Seed Clustering in Sequence Graphs

Chang

Eizenga

Novak

et al. 2019

Preprint

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Graph representations of genomes are capable of expressing more genetic variation and can therefore better represent a population than standard linear genomes. However, due to the greater complexity of genome graphs relative to linear genomes, some functions that are trivial on linear genomes become more difficult in genome graphs. Calculating distance is one such function that is simple in a linear genome but much more complicated in a graph context. In read mapping algorithms, distance calculations are commonly used in a clustering step to determine if seed alignments could belong to the same mapping. Clustering algorithms are a bottleneck for some mapping algorithms due to the cost of repeated distance calculations. We have developed an algorithm for quickly calculating the minimum distance between positions on a sequence graph using a minimum distance index. We have also developed an algorithm that uses the distance index to cluster seeds on a graph. We demonstrate that our implementations of these algorithms are efficient and practical to use for mapping algorithms.

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Superbubbles, Ultrabubbles, and Cacti

Cited by 56 publications

References 18 publications

Genotyping structural variants in pangenome graphs using the vg toolkit

Genotyping structural variants in pangenome graphs using the vg toolkit

Superbubbles revisited

Distance Indexing and Seed Clustering in Sequence Graphs

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