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cloudrnaSPAdes: isoform assembly using bulk barcoded RNA sequencing data. Bioinformatics 2024; 40:btad781. [PMID: 38262343 PMCID: PMC10868327 DOI: 10.1093/bioinformatics/btad781] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2023] [Revised: 12/09/2023] [Accepted: 01/18/2024] [Indexed: 01/25/2024] Open
Abstract
MOTIVATION Recent advancements in long-read RNA sequencing have enabled the examination of full-length isoforms, previously uncaptured by short-read sequencing methods. An alternative powerful method for studying isoforms is through the use of barcoded short-read RNA reads, for which a barcode indicates whether two short-reads arise from the same molecule or not. Such techniques included the 10x Genomics linked-read based SParse Isoform Sequencing (SPIso-seq), as well as Loop-Seq, or Tell-Seq. Some applications, such as novel-isoform discovery, require very high coverage. Obtaining high coverage using long reads can be difficult, making barcoded RNA-seq data a valuable alternative for this task. However, most annotation pipelines are not able to work with a set of short reads instead of a single transcript, also not able to work with coverage gaps within a molecule if any. In order to overcome this challenge, we present an RNA-seq assembler that allows the determination of the expressed isoform per barcode. RESULTS In this article, we present cloudrnaSPAdes, a tool for assembling full-length isoforms from barcoded RNA-seq linked-read data in a reference-free fashion. Evaluating it on simulated and real human data, we found that cloudrnaSPAdes accurately assembles isoforms, even for genes with high isoform diversity. AVAILABILITY AND IMPLEMENTATION cloudrnaSPAdes is a feature release of a SPAdes assembler and version used for this article is available at https://github.com/1dayac/cloudrnaSPAdes-release.
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A safety framework for flow decomposition problems via integer linear programming. Bioinformatics 2023; 39:btad640. [PMID: 37862229 PMCID: PMC10628435 DOI: 10.1093/bioinformatics/btad640] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2022] [Revised: 09/05/2023] [Accepted: 10/19/2023] [Indexed: 10/22/2023] Open
Abstract
MOTIVATION Many important problems in Bioinformatics (e.g. assembly or multiassembly) admit multiple solutions, while the final objective is to report only one. A common approach to deal with this uncertainty is finding "safe" partial solutions (e.g. contigs) which are common to all solutions. Previous research on safety has focused on polynomially time solvable problems, whereas many successful and natural models are NP-hard to solve, leaving a lack of "safety tools" for such problems. We propose the first method for computing all safe solutions for an NP-hard problem, "minimum flow decomposition" (MFD). We obtain our results by developing a "safety test" for paths based on a general integer linear programming (ILP) formulation. Moreover, we provide implementations with practical optimizations aimed to reduce the total ILP time, the most efficient of these being based on a recursive group-testing procedure. RESULTS Experimental results on transcriptome datasets show that all safe paths for MFDs correctly recover up to 90% of the full RNA transcripts, which is at least 25% more than previously known safe paths. Moreover, despite the NP-hardness of the problem, we can report all safe paths for 99.8% of the over 27 000 non-trivial graphs of this dataset in only 1.5 h. Our results suggest that, on perfect data, there is less ambiguity than thought in the notoriously hard RNA assembly problem. AVAILABILITY AND IMPLEMENTATION https://github.com/algbio/mfd-safety.
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Chaining for accurate alignment of erroneous long reads to acyclic variation graphs. Bioinformatics 2023; 39:btad460. [PMID: 37494467 PMCID: PMC10423031 DOI: 10.1093/bioinformatics/btad460] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2022] [Revised: 06/08/2023] [Accepted: 07/25/2023] [Indexed: 07/28/2023] Open
Abstract
MOTIVATION Aligning reads to a variation graph is a standard task in pangenomics, with downstream applications such as improving variant calling. While the vg toolkit [Garrison et al. (Variation graph toolkit improves read mapping by representing genetic variation in the reference. Nat Biotechnol 2018;36:875-9)] is a popular aligner of short reads, GraphAligner [Rautiainen and Marschall (GraphAligner: rapid and versatile sequence-to-graph alignment. Genome Biol 2020;21:253-28)] is the state-of-the-art aligner of erroneous long reads. GraphAligner works by finding candidate read occurrences based on individually extending the best seeds of the read in the variation graph. However, a more principled approach recognized in the community is to co-linearly chain multiple seeds. RESULTS We present a new algorithm to co-linearly chain a set of seeds in a string labeled acyclic graph, together with the first efficient implementation of such a co-linear chaining algorithm into a new aligner of erroneous long reads to acyclic variation graphs, GraphChainer. We run experiments aligning real and simulated PacBio CLR reads with average error rates 15% and 5%. Compared to GraphAligner, GraphChainer aligns 12-17% more reads, and 21-28% more total read length, on real PacBio CLR reads from human chromosomes 1, 22, and the whole human pangenome. On both simulated and real data, GraphChainer aligns between 95% and 99% of all reads, and of total read length. We also show that minigraph [Li et al. (The design and construction of reference pangenome graphs with minigraph. Genome Biol 2020;21:265-19.)] and minichain [Chandra and Jain (Sequence to graph alignment using gap-sensitive co-linear chaining. In: Proceedings of the 27th Annual International Conference on Research in Computational Molecular Biology (RECOMB 2023). Springer, 2023, 58-73.)] obtain an accuracy of <60% on this setting. AVAILABILITY AND IMPLEMENTATION GraphChainer is freely available at https://github.com/algbio/GraphChainer. The datasets and evaluation pipeline can be reached from the previous address.
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cloudrnaSPAdes: Isoform assembly using bulk barcoded RNA sequencing data. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.07.25.550587. [PMID: 37546844 PMCID: PMC10402000 DOI: 10.1101/2023.07.25.550587] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/08/2023]
Abstract
Motivation Recent advancements in long-read RNA sequencing have enabled the examination of full-length isoforms, previously uncaptured by short-read sequencing methods. An alternative powerful method for studying isoforms is through the use of barcoded short-read RNA reads, for which a barcode indicates whether two short-reads arise from the same molecule or not. Such techniques included the 10x Genomics linked-read based SParse Isoform Sequencing (SPIso-seq), as well as Loop-Seq, or Tell-Seq. Some applications, such as novel-isoform discovery, require very high coverage. Obtaining high coverage using long reads can be difficult, making barcoded RNA-seq data a valuable alternative for this task. However, most annotation pipelines are not able to work with a set of short reads instead of a single transcript, also not able to work with coverage gaps within a molecule if any. In order to overcome this challenge, we present an RNA-seq assembler allowing the determination of the expressed isoform per barcode. Results In this paper, we present cloudrnaSPAdes, a tool for assembling full-length isoforms from barcoded RNA-seq linked-read data in a reference-free fashion. Evaluating it on simulated and real human data, we found that cloudrnaSPAdes accurately assembles isoforms, even for genes with high isoform diversity. Availability cloudrnaSPAdes is a feature release of a SPAdes assembler and available at https://cab.spbu.ru/software/cloudrnaspades/.
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Sensitive inference of alignment-safe intervals from biodiverse protein sequence clusters using EMERALD. Genome Biol 2023; 24:168. [PMID: 37461051 DOI: 10.1186/s13059-023-03008-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2023] [Accepted: 07/05/2023] [Indexed: 07/20/2023] Open
Abstract
Sequence alignments are the foundations of life science research, but most innovation so far focuses on optimal alignments, while information derived from suboptimal solutions is ignored. We argue that one optimal alignment per pairwise sequence comparison is a reasonable approximation when dealing with very similar sequences but is insufficient when exploring the biodiversity of the protein universe at tree-of-life scale. To overcome this limitation, we introduce pairwise alignment-safety to uncover the amino acid positions robustly shared across all suboptimal solutions. We implement EMERALD, a software library for alignment-safety inference, and apply it to 400k sequences from the SwissProt database.
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Extremely fast construction and querying of compacted and colored de Bruijn graphs with GGCAT. Genome Res 2023; 33:1198-1207. [PMID: 37253540 PMCID: PMC10538363 DOI: 10.1101/gr.277615.122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2023] [Accepted: 05/16/2023] [Indexed: 06/01/2023]
Abstract
Compacted de Bruijn graphs are one of the most fundamental data structures in computational genomics. Colored compacted de Bruijn graphs are a variant built on a collection of sequences and associate to each k-mer the sequences in which it appears. We present GGCAT, a tool for constructing both types of graphs, based on a new approach merging the k-mer counting step with the unitig construction step, as well as on numerous practical optimizations. For compacted de Bruijn graph construction, GGCAT achieves speed-ups of 3× to 21× compared with the state-of-the-art tool Cuttlefish 2. When constructing the colored variant, GGCAT achieves speed-ups of 5× to 39× compared with the state-of-the-art tool BiFrost. Additionally, GGCAT is up to 480× faster than BiFrost for batch sequence queries on colored graphs.
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Matchtigs: minimum plain text representation of k-mer sets. Genome Biol 2023; 24:136. [PMID: 37296461 DOI: 10.1186/s13059-023-02968-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2021] [Accepted: 05/10/2023] [Indexed: 06/12/2023] Open
Abstract
We propose a polynomial algorithm computing a minimum plain-text representation of k-mer sets, as well as an efficient near-minimum greedy heuristic. When compressing read sets of large model organisms or bacterial pangenomes, with only a minor runtime increase, we shrink the representation by up to 59% over unitigs and 26% over previous work. Additionally, the number of strings is decreased by up to 97% over unitigs and 90% over previous work. Finally, a small representation has advantages in downstream applications, as it speeds up SSHash-Lite queries by up to 4.26× over unitigs and 2.10× over previous work.
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The omnitig framework can improve genome assembly contiguity in practice. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.01.30.526175. [PMID: 36778435 PMCID: PMC9915519 DOI: 10.1101/2023.01.30.526175] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
Despite the long history of genome assembly research, there remains a large gap between the theoretical and practical work. There is practical software with little theoretical underpinning of accuracy on one hand and theoretical algorithms which have not been adopted in practice on the other. In this paper we attempt to bridge the gap between theory and practice by showing how the theoretical safe-and-complete framework can be integrated into existing assemblers in order to improve contiguity. The optimal algorithm in this framework, called the omnitig algorithm, has not been used in practice due to its complexity and its lack of robustness to real data. Instead, we pursue a simplified notion of omnitigs, giving an efficient algorithm to compute them and demonstrating their safety under certain conditions. We modify two assemblers (wtdbg2 and Flye) by replacing their unitig algorithm with the simple omnitig algorithm. We test our modifications using real HiFi data from the Drosophilia melanogaster and the Caenorhabditis elegans genome. Our modified algorithms lead to a substantial improvement in alignment-based contiguity, with negligible computational costs and either no or a small increase in the number of misassemblies.
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Flow Decomposition With Subpath Constraints. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2023; 20:360-370. [PMID: 35104222 DOI: 10.1109/tcbb.2022.3147697] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
Flow network decomposition is a natural model for problems where we are given a flow network arising from superimposing a set of weighted paths and would like to recover the underlying data, i.e., decompose the flow into the original paths and their weights. Thus, variations on flow decomposition are often used as subroutines in multiassembly problems such as RNA transcript assembly. In practice, we frequently have access to information beyond flow values in the form of subpaths, and many tools incorporate these heuristically. But despite acknowledging their utility in practice, previous work has not formally addressed the effect of subpath constraints on the accuracy of flow network decomposition approaches. We formalize the flow decomposition with subpath constraints problem, give the first algorithms for it, and study its usefulness for recovering ground truth decompositions. For finding a minimum decomposition, we propose both a heuristic and an FPT algorithm. Experiments on RNA transcript datasets show that for instances with larger solution path sets, the addition of subpath constraints finds 13% more ground truth solutions when minimal decompositions are found exactly, and 30% more ground truth solutions when minimal decompositions are found heuristically.
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Improving RNA Assembly via Safety and Completeness in Flow Decompositions. J Comput Biol 2022; 29:1270-1287. [PMID: 36288562 PMCID: PMC9807076 DOI: 10.1089/cmb.2022.0261] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
Decomposing a network flow into weighted paths is a problem with numerous applications, ranging from networking, transportation planning, to bioinformatics. In some applications we look for a decomposition that is optimal with respect to some property, such as the number of paths used, robustness to edge deletion, or length of the longest path. However, in many bioinformatic applications, we seek a specific decomposition where the paths correspond to some underlying data that generated the flow. In these cases, no optimization criteria guarantee the identification of the correct decomposition. Therefore, we propose to instead report the safe paths, which are subpaths of at least one path in every flow decomposition. In this work, we give the first local characterization of safe paths for flow decompositions in directed acyclic graphs, leading to a practical algorithm for finding the complete set of safe paths. In addition, we evaluate our algorithm on RNA transcript data sets against a trivial safe algorithm (extended unitigs), the recently proposed safe paths for path covers (TCBB 2021) and the popular heuristic greedy-width. On the one hand, we found that besides maintaining perfect precision, our safe and complete algorithm reports a significantly higher coverage (≈50% more) compared with the other safe algorithms. On the other hand, the greedy-width algorithm although reporting a better coverage, it also reports a significantly lower precision on complex graphs (for genes expressing a large number of transcripts). Overall, our safe and complete algorithm outperforms (by ≈20%) greedy-width on a unified metric (F-score) considering both coverage and precision when the evaluated data set has a significant number of complex graphs. Moreover, it also has a superior time (4-5×) and space performance (1.2-2.2×), resulting in a better and more practical approach for bioinformatic applications of flow decomposition.
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Safety in Multi-Assembly via Paths Appearing in All Path Covers of a DAG. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2022; 19:3673-3684. [PMID: 34847041 DOI: 10.1109/tcbb.2021.3131203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
A multi-assembly problem asks to reconstruct multiple genomic sequences from mixed reads sequenced from all of them. Standard formulations of such problems model a solution as a path cover in a directed acyclic graph, namely a set of paths that together cover all vertices of the graph. Since multi-assembly problems admit multiple solutions in practice, we consider an approach commonly used in standard genome assembly: output only partial solutions (contigs, or safe paths), that appear in all path cover solutions. We study constrained path covers, a restriction on the path cover solution that incorporate practical constraints arising in multi-assembly problems. We give efficient algorithms finding all maximal safe paths for constrained path covers. We compute the safe paths of splicing graphs constructed from transcript annotations of different species. Our algorithms run in less than 15 seconds per species and report RNA contigs that are over 99% precise and are up to 8 times longer than unitigs. Moreover, RNA contigs cover over 70% of the transcripts and their coding sequences in most cases. With their increased length to unitigs, high precision, and fast construction time, maximal safe paths can provide a better base set of sequences for transcript assembly programs.
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Abstract
Minimum flow decomposition (MFD) is an NP-hard problem asking to decompose a network flow into a minimum set of paths (together with associated weights). Variants of it are powerful models in multiassembly problems in Bioinformatics, such as RNA assembly. Owing to its hardness, practical multiassembly tools either use heuristics or solve simpler, polynomial time-solvable versions of the problem, which may yield solutions that are not minimal or do not perfectly decompose the flow. Here, we provide the first fast and exact solver for MFD on acyclic flow networks, based on Integer Linear Programming (ILP). Key to our approach is an encoding of all the exponentially many solution paths using only a quadratic number of variables. We also extend our ILP formulation to many practical variants, such as incorporating longer or paired-end reads, or minimizing flow errors. On both simulated and real-flow splicing graphs, our approach solves any instance in <13 seconds. We hope that our formulations can lie at the core of future practical RNA assembly tools. Our implementations are freely available on Github.
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What are the keys to succeeding as a computational biologist in today's research climate? Cell Syst 2022; 13:781-785. [PMID: 36265464 DOI: 10.1016/j.cels.2022.09.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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MIPUP: minimum perfect unmixed phylogenies for multi-sampled tumors via branchings and ILP. Bioinformatics 2019; 35:769-777. [PMID: 30101335 PMCID: PMC6394401 DOI: 10.1093/bioinformatics/bty683] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2018] [Revised: 07/08/2018] [Accepted: 08/07/2018] [Indexed: 12/31/2022] Open
Abstract
Motivation Discovering the evolution of a tumor may help identify driver mutations and provide a more comprehensive view on the history of the tumor. Recent studies have tackled this problem using multiple samples sequenced from a tumor, and due to clinical implications, this has attracted great interest. However, such samples usually mix several distinct tumor subclones, which confounds the discovery of the tumor phylogeny. Results We study a natural problem formulation requiring to decompose the tumor samples into several subclones with the objective of forming a minimum perfect phylogeny. We propose an Integer Linear Programming formulation for it, and implement it into a method called MIPUP. We tested the ability of MIPUP and of four popular tools LICHeE, AncesTree, CITUP, Treeomics to reconstruct the tumor phylogeny. On simulated data, MIPUP shows up to a 34% improvement under the ancestor-descendant relations metric. On four real datasets, MIPUP’s reconstructions proved to be generally more faithful than those of LICHeE. Availability and implementation MIPUP is available at https://github.com/zhero9/MIPUP as open source. Supplementary information Supplementary data are available at Bioinformatics online.
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Safely Filling Gaps with Partial Solutions Common to All Solutions. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2019; 16:617-626. [PMID: 29994355 DOI: 10.1109/tcbb.2017.2785831] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Gap filling has emerged as a natural sub-problem of many de novo genome assembly projects. The gap filling problem generally asks for an $s$s-$t$t path in an assembly graph whose length matches the gap length estimate. Several methods have addressed it, but only few have focused on strategies for dealing with multiple gap filling solutions and for guaranteeing reliable results. Such strategies include reporting only unique solutions, or exhaustively enumerating all filling solutions and heuristically creating their consensus. Our main contribution is a new method for reliable gap filling: filling gaps with those sub-paths common to all gap filling solutions. We call these partial solutions safe, following the framework of (Tomescu and Medvedev, RECOMB 2016). We give an efficient safe algorithm running in $O(dm)$O(dm) time and space, where $d$d is the gap length estimate and $m$m is the number of edges of the assembly graph. To show the benefits of this method, we implemented this algorithm for the problem of filling gaps in scaffolds. Our experimental results on bacterial and on conservative human assemblies show that, on average, our method can retrieve over 73 percent more safe and correct bases as compared to previous methods, with a similar precision.
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Hardness of Covering Alignment: Phase Transition in Post-Sequence Genomics. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2019; 16:23-30. [PMID: 29994032 DOI: 10.1109/tcbb.2018.2831691] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Covering alignment problems arise from recent developments in genomics; so called pan-genome graphs are replacing reference genomes, and advances in haplotyping enable full content of diploid genomes to be used as basis of sequence analysis. In this paper, we show that the computational complexity will change for natural extensions of alignments to pan-genome representations and to diploid genomes. More broadly, our approach can also be seen as a minimal extension of sequence alignment to labelled directed acyclic graphs (labeled DAGs). Namely, we show that finding a covering alignment of two labeled DAGs is NP-hard even on binary alphabets. A covering alignment asks for two paths R1 (red) and G1 (green) in DAG D1 and two paths R2 (red) and G2 (green) in DAG D2 that cover the nodes of the graphs and maximize the sum of the global alignment scores: as(sp(R1),sp(R2))+as(sp(G1),sp(G2)), where sp(P) is the concatenation of labels on the path P. Pair-wise alignment of haplotype sequences forming a diploid chromosome can be converted to a two-path coverable labelled DAG, and then the covering alignment models the similarity of two diploids over arbitrary recombinations. We also give a reduction to the other direction, to show that such a recombination-oblivious diploid alignment is NP-hard on alphabets of size 3.
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A safe and complete algorithm for metagenomic assembly. Algorithms Mol Biol 2018; 13:3. [PMID: 29445416 PMCID: PMC5802251 DOI: 10.1186/s13015-018-0122-7] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2017] [Accepted: 01/20/2018] [Indexed: 11/10/2022] Open
Abstract
Background Reconstructing the genome of a species from short fragments is one of the oldest bioinformatics problems. Metagenomic assembly is a variant of the problem asking to reconstruct the circular genomes of all bacterial species present in a sequencing sample. This problem can be naturally formulated as finding a collection of circular walks of a directed graph G that together cover all nodes, or edges, of G. Approach We address this problem with the “safe and complete” framework of Tomescu and Medvedev (Research in computational Molecular biology—20th annual conference, RECOMB 9649:152–163, 2016). An algorithm is called safe if it returns only those walks (also called safe) that appear as subwalk in all metagenomic assembly solutions for G. A safe algorithm is called complete if it returns all safe walks of G. Results We give graph-theoretic characterizations of the safe walks of G, and a safe and complete algorithm finding all safe walks of G. In the node-covering case, our algorithm runs in time \documentclass[12pt]{minimal}
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\begin{document}$$O(m^2 + n^3)$$\end{document}O(m2+n3), and in the edge-covering case it runs in time \documentclass[12pt]{minimal}
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\begin{document}$$O(m^2n)$$\end{document}O(m2n); n and m denote the number of nodes and edges, respectively, of G. This algorithm constitutes the first theoretical tight upper bound on what can be safely assembled from metagenomic reads using this problem formulation.
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Complexity and Algorithms for Finding a Perfect Phylogeny from Mixed Tumor Samples. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2018; 15:96-108. [PMID: 28113405 DOI: 10.1109/tcbb.2016.2606620] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Hajirasouliha and Raphael (WABI 2014) proposed a model for deconvoluting mixed tumor samples measured from a collection of high-throughput sequencing reads. This is related to understanding tumor evolution and critical cancer mutations. In short, their formulation asks to split each row of a binary matrix so that the resulting matrix corresponds to a perfect phylogeny and has the minimum number of rows among all matrices with this property. In this paper, we disprove several claims about this problem, including an NP-hardness proof of it. However, we show that the problem is indeed NP-hard, by providing a different proof. We also prove NP-completeness of a variant of this problem proposed in the same paper. On the positive side, we propose an efficient (though not necessarily optimal) heuristic algorithm based on coloring co-comparability graphs, and a polynomial time algorithm for solving the problem optimally on matrix instances in which no column is contained in both columns of a pair of conflicting columns. Implementations of these algorithms are freely available at https://github.com/alexandrutomescu/MixedPerfectPhylogeny.
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Abstract
Contig assembly is the first stage that most assemblers solve when reconstructing a genome from a set of reads. Its output consists of contigs-a set of strings that are promised to appear in any genome that could have generated the reads. From the introduction of contigs 20 years ago, assemblers have tried to obtain longer and longer contigs, but the following question remains: given a genome graph G (e.g., a de Bruijn, or a string graph), what are all the strings that can be safely reported from G as contigs? In this article, we answer this question using a model in which the genome is a circular covering walk. We also give a polynomial-time algorithm to find such strings, which we call omnitigs. Our experiments show that omnitigs are 66%-82% longer on average than the popular unitigs, and 29% of dbSNP locations have more neighbors in omnitigs than in unitigs.
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Explaining a Weighted DAG with Few Paths for Solving Genome-Guided Multi-Assembly. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2015; 12:1345-1354. [PMID: 26671806 DOI: 10.1109/tcbb.2015.2418753] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
RNA-Seq technology offers new high-throughput ways for transcript identification and quantification based on short reads, and has recently attracted great interest. This is achieved by constructing a weighted DAG whose vertices stand for exons, and whose arcs stand for split alignments of the RNA-Seq reads to the exons. The task consists of finding a number of paths, together with their expression levels, which optimally explain the weights of the graph under various fitting functions, such as least sum of squared residuals. In (Tomescu et al. BMC Bioinformatics, 2013) we studied this genome-guided multi-assembly problem when the number of allowed solution paths was linear in the number of arcs. In this paper, we further refine this problem by asking for a bounded number k of solution paths, which is the setting of most practical interest. We formulate this problem in very broad terms, and show that for many choices of the fitting function it becomes NP-hard. Nevertheless, we identify a natural graph parameter of a DAG G, which we call arc-width and denote ⟨G⟩, and give a dynamic programming algorithm running in time O(W(k)⟨G⟩(k)(⟨G⟩+ k)n) , where n is the number of vertices and W is the maximum weight of G. This implies that the problem is fixed-parameter tractable (FPT) in the parameters W, ⟨G⟩, and k. We also show that the arc-width of DAGs constructed from simulated and real RNA-Seq reads is small in practice. Finally, we study the approximability of this problem, and, in particular, give a fully polynomial-time approximation scheme (FPTAS) for the case when the fitting function penalizes the maximum ratio between the weights of the arcs and their predicted coverage.
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SNV-PPILP: refined SNV calling for tumor data using perfect phylogenies and ILP. ACTA ACUST UNITED AC 2014; 31:1133-5. [PMID: 25398608 DOI: 10.1093/bioinformatics/btu755] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2014] [Accepted: 11/11/2014] [Indexed: 01/23/2023]
Abstract
MOTIVATION Recent studies sequenced tumor samples from the same progenitor at different development stages and showed that by taking into account the phylogeny of this development, single-nucleotide variant (SNV) calling can be improved. Accurate SNV calls can better reveal early-stage tumors, identify mechanisms of cancer progression or help in drug targeting. RESULTS We present SNV-PPILP, a fast and easy to use tool for refining GATK's Unified Genotyper SNV calls, for multiple samples assumed to form a phylogeny. We tested SNV-PPILP on simulated data, with a varying number of samples, SNVs, read coverage and violations of the perfect phylogeny assumption. We always match or improve the accuracy of GATK, with a significant improvement on low read coverage. AVAILABILITY AND IMPLEMENTATION SNV-PPILP, available at cs.helsinki.fi/gsa/snv-ppilp/, is written in Python and requires the free ILP solver lp_solve. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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Abstract
BACKGROUND Multi-assembly problems have gathered much attention in the last years, as Next-Generation Sequencing technologies have started being applied to mixed settings, such as reads from the transcriptome (RNA-Seq), or from viral quasi-species. One classical model that has resurfaced in many multi-assembly methods (e.g. in Cufflinks, ShoRAH, BRANCH, CLASS) is the Minimum Path Cover (MPC) Problem, which asks for the minimum number of directed paths that cover all the nodes of a directed acyclic graph. The MPC Problem is highly popular because the acyclicity of the graph ensures its polynomial-time solvability. RESULTS In this paper, we consider two generalizations of it dealing with integrating constraints arising from long reads or paired-end reads; these extensions have also been considered by two recent methods, but not fully solved. More specifically, we study the two problems where also a set of subpaths, or pairs of subpaths, of the graph have to be entirely covered by some path in the MPC. We show that in the case of long reads (subpaths), the generalized problem can be solved in polynomial-time by a reduction to the classical MPC Problem. We also consider the weighted case, and show that it can be solved in polynomial-time by a reduction to a min-cost circulation problem. As a side result, we also improve the time complexity of the classical minimum weight MPC Problem. In the case of paired-end reads (pairs of subpaths), the generalized problem becomes NP-hard, but we show that it is fixed-parameter tractable (FPT) in the total number of constraints. This computational dichotomy between long reads and paired-end reads is also a general insight into multi-assembly problems.
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A rank-based sequence aligner with applications in phylogenetic analysis. PLoS One 2014; 9:e104006. [PMID: 25133391 PMCID: PMC4136772 DOI: 10.1371/journal.pone.0104006] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2013] [Accepted: 07/09/2014] [Indexed: 01/17/2023] Open
Abstract
Recent tools for aligning short DNA reads have been designed to optimize the trade-off between correctness and speed. This paper introduces a method for assigning a set of short DNA reads to a reference genome, under Local Rank Distance (LRD). The rank-based aligner proposed in this work aims to improve correctness over speed. However, some indexing strategies to speed up the aligner are also investigated. The LRD aligner is improved in terms of speed by storing [Formula: see text]-mer positions in a hash table for each read. Another improvement, that produces an approximate LRD aligner, is to consider only the positions in the reference that are likely to represent a good positional match of the read. The proposed aligner is evaluated and compared to other state of the art alignment tools in several experiments. A set of experiments are conducted to determine the precision and the recall of the proposed aligner, in the presence of contaminated reads. In another set of experiments, the proposed aligner is used to find the order, the family, or the species of a new (or unknown) organism, given only a set of short Next-Generation Sequencing DNA reads. The empirical results show that the aligner proposed in this work is highly accurate from a biological point of view. Compared to the other evaluated tools, the LRD aligner has the important advantage of being very accurate even for a very low base coverage. Thus, the LRD aligner can be considered as a good alternative to standard alignment tools, especially when the accuracy of the aligner is of high importance. Source code and UNIX binaries of the aligner are freely available for future development and use at http://lrd.herokuapp.com/aligners. The software is implemented in C++ and Java, being supported on UNIX and MS Windows.
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Abstract
Background Through transcription and alternative splicing, a gene can be transcribed into different RNA sequences (isoforms), depending on the individual, on the tissue the cell is in, or in response to some stimuli. Recent RNA-Seq technology allows for new high-throughput ways for isoform identification and quantification based on short reads, and various methods have been put forward for this non-trivial problem. Results In this paper we propose a novel radically different method based on minimum-cost network flows. This has a two-fold advantage: on the one hand, it translates the problem as an established one in the field of network flows, which can be solved in polynomial time, with different existing solvers; on the other hand, it is general enough to encompass many of the previous proposals under the least sum of squares model. Our method works as follows: in order to find the transcripts which best explain, under a given fitness model, a splicing graph resulting from an RNA-Seq experiment, we find a min-cost flow in an offset flow network, under an equivalent cost model. Under very weak assumptions on the fitness model, the optimal flow can be computed in polynomial time. Parsimoniously splitting the flow back into few path transcripts can be done with any of the heuristics and approximations available from the theory of network flows. In the present implementation, we choose the simple strategy of repeatedly removing the heaviest path. Conclusions We proposed a new very general method based on network flows for a multiassembly problem arising from isoform identification and quantification with RNA-Seq. Experimental results on prediction accuracy show that our method is very competitive with popular tools such as Cufflinks and IsoLasso. Our tool, called Traph (Transcrips in gRAPHs), is available at: http://www.cs.helsinki.fi/gsa/traph/.
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Ranking, unranking and random generation of extensional acyclic digraphs. INFORM PROCESS LETT 2013. [DOI: 10.1016/j.ipl.2013.01.010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Set Graphs. III. Proof Pearl: Claw-Free Graphs Mirrored into Transitive Hereditarily Finite Sets. J Autom Reason 2012. [DOI: 10.1007/s10817-012-9272-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Abstract
SUMMARY The advent of high-throughput sequencers (HTS) introduced the need of new tools in order to analyse the large amount of data that those machines are able to produce. The mandatory first step for a wide range of analyses is the alignment of the sequences against a reference genome. We present a major update to our rNA (randomized Numerical Aligner) tool. The main feature of rNA is the fact that it achieves an accuracy greater than the majority of other tools in a feasible amount of time. rNA executables and source codes are freely downloadable at http://iga-rna.sourceforge.net/. CONTACT vezzi@appliedgenomics.org; delfabbro@appliedgenomics.org SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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