Sparse Dynamic Programming on DAGs with Small Width

The minimum path cover problem asks us to find a minimum-cardinality set of paths that cover all the nodes of a directed acyclic graph (DAG). We study the case when the size k of a minimum path cover is small, that is, when the DAG has a small width. This case is motivated by applications in pan-genomics, where the genomic variation of a population is expressed as a DAG. We observe that classical alignment algorithms exploiting sparse dynamic programming can be extended to the sequence-against-DAG case by mimicking the algorithm for sequences on each path of a minimum path cover and handling an evaluation order anomaly with reachability queries. Namely, we introduce a general framework for DAG-extensions of sparse dynamic programming. This framework produces algorithms that are slower than their counterparts on sequences only by a factor k. We illustrate this on two classical problems extended to DAGs: longest increasing subsequence and longest common subsequence. For the former, we obtain an algorithm with running time O(k vertical bar E vertical bar log vertical bar V vertical bar). This matches the optimal solution to the classical problem variant when the input sequence is modeled as a path. We obtain an analogous result for the longest common subsequence problem. We then apply this technique to the co-linear chaining problem, which is a generalization of the above two problems. The algorithm for this problem turns out to be more involved, needing further ingredients, such as an FM-index tailored for large alphabets and a two-dimensional range search tree modified to support range maximum queries. We also study a general sequence-to-DAG alignment formulation that allows affine gap costs in the sequence. The main ingredient of the proposed framework is a new algorithm for finding a minimum path cover of a DAG (V, E) in O(k vertical bar E vertical bar log vertical bar V vertical bar) time, improving all known time-bounds when k is small and the DAG is not too dense. In addition to boosting the sparse dynamic programming framework, an immediate consequence of this new minimum path cover algorithm is an improved space/time tradeoff for reachability queries in arbitrary directed graphs.Peer reviewe

Accurate spliced alignment of long RNA sequencing reads

Motivation: Long-read RNA sequencing technologies are establishing themselves as the primary techniques to detect novel isoforms, and many such analyses are dependent on read alignments. However, the error rate and sequencing length of the reads create new challenges for accurately aligning them, particularly around small exons. Results: We present an alignment method uLTRA for long RNA sequencing reads based on a novel two-pass collinear chaining algorithm. We show that uLTRA produces higher accuracy over state-of-the-art aligners with substantially higher accuracy for small exons on simulated and synthetic data. On simulated data, uLTRA achieves an accuracy of about 60% for exons of length 10 nucleotides or smaller and close to 90% accuracy for exons of length between 11 and 20 nucleotides. On biological data where true read location is unknown, we show several examples where uLTRA aligns to known and novel isoforms containing small exons that are not detected with other aligners. While uLTRA obtains its accuracy using annotations, it can also be used as a wrapper around minimap2 to align reads outside annotated regions.Peer reviewe

Fast local fragment chaining using sum-of-pair gap costs

<p>Abstract</p> <p>Background</p> <p>Fast seed-based alignment heuristics such as <monospace>BLAST</monospace> and <monospace>BLAT</monospace> have become indispensable tools in comparative genomics for all studies aiming at the evolutionary relations of proteins, genes, and non-coding RNAs. This is true in particular for the large mammalian genomes. The sensitivity and specificity of these tools, however, crucially depend on parameters such as seed sizes or maximum expectation values. In settings that require high sensitivity the amount of short local match fragments easily becomes intractable. Then, fragment chaining is a powerful leverage to quickly connect, score, and rank the fragments to improve the specificity.</p> <p>Results</p> <p>Here we present a fast and flexible fragment chainer that for the first time also supports a sum-of-pair gap cost model. This model has proven to achieve a higher accuracy and sensitivity in its own field of application. Due to a highly time-efficient index structure our method outperforms the only existing tool for fragment chaining under the linear gap cost model. It can easily be applied to the output generated by alignment tools such as <monospace>segemehl</monospace> or <monospace>BLAST</monospace>. As an example we consider homology-based searches for human and mouse snoRNAs demonstrating that a highly sensitive <monospace>BLAST</monospace> search with subsequent chaining is an attractive option. The sum-of-pair gap costs provide a substantial advantage is this context.</p> <p>Conclusions</p> <p>Chaining of short match fragments helps to quickly and accurately identify regions of homology that may not be found using local alignment heuristics alone. By providing both the linear and the sum-of-pair gap cost model, a wider range of application can be covered. The software clasp is available at <url>http://www.bioinf.uni-leipzig.de/Software/clasp/</url>.</p

Fast scaffolding with small independent mixed integer programs

Peer reviewe

Chaining with Overlaps Revisited

Chaining algorithms aim to form a semi-global alignment of two sequences based on a set of anchoring local alignments as input. Depending on the optimization criteria and the exact definition of a chain, there are several O(n log n) time algorithms to solve this problem optimally, where n is the number of input anchors. In this paper, we focus on a formulation allowing the anchors to overlap in a chain. This formulation was studied by Shibuya and Kurochkin (WABI 2003), but their algorithm comes with no proof of correctness. We revisit and modify their algorithm to consider a strict definition of precedence relation on anchors, adding the required derivation to convince on the correctness of the resulting algorithm that runs in O(n log2 n) time on anchors formed by exact matches. With the more relaxed definition of precedence relation considered by Shibuya and Kurochkin or when anchors are non-nested such as matches of uniform length (k-mers), the algorithm takes O(n log n) time. We also establish a connection between chaining with overlaps and the widely studied longest common subsequence problem. 2012 ACM Subject Classification Theory of computation ! Pattern matching; Theory of computation ! Dynamic programming; Applied computing ! Genomics.Peer reviewe

Cgaln: fast and space-efficient whole-genome alignment

<p>Abstract</p> <p>Background</p> <p>Whole-genome sequence alignment is an essential process for extracting valuable information about the functions, evolution, and peculiarities of genomes under investigation. As available genomic sequence data accumulate rapidly, there is great demand for tools that can compare whole-genome sequences within practical amounts of time and space. However, most existing genomic alignment tools can treat sequences that are only a few Mb long at once, and no state-of-the-art alignment program can align large sequences such as mammalian genomes directly on a conventional standalone computer.</p> <p>Results</p> <p>We previously proposed the CGAT (Coarse-Grained AlignmenT) algorithm, which performs an alignment job in two steps: first at the block level and then at the nucleotide level. The former is "coarse-grained" alignment that can explore genomic rearrangements and reduce the sizes of the regions to be analyzed in the next step. The latter is detailed alignment within limited regions. In this paper, we present an update of the algorithm and the open-source program, Cgaln, that implements the algorithm. We compared the performance of Cgaln with those of other programs on whole genomic sequences of several bacteria and of some mammalian chromosome pairs. The results showed that Cgaln is several times faster and more memory-efficient than the best existing programs, while its sensitivity and accuracy are comparable to those of the best programs. Cgaln takes less than 13 hours to finish an alignment between the whole genomes of human and mouse in a single run on a conventional desktop computer with a single CPU and 2 GB memory.</p> <p>Conclusions</p> <p>Cgaln is not only fast and memory efficient but also effective in coping with genomic rearrangements. Our results show that Cgaln is very effective for comparison of large genomes, especially of intact chromosomal sequences. We believe that Cgaln provides novel viewpoint for reducing computational complexity and will contribute to various fields of genome science.</p

Third-generation RNA-sequencing analysis : graph alignment and transcript assembly with long reads

The information contained in the genome of an organism, its DNA, is expressed through transcription of its genes to RNA, in quantities determined by many internal and external factors. As such, studying the gene expression can give valuable information for e.g. clinical diagnostics. A common analysis workflow of RNA-sequencing (RNA-seq) data consists of mapping the sequencing reads to a reference genome, followed by the transcript assembly and quantification based on these alignments. The advent of second-generation sequencing revolutionized the field by reducing the sequencing costs by 50,000-fold. Now another revolution is imminent with the third-generation sequencing platforms producing an order of magnitude higher read lengths. However, higher error rate, higher cost and lower throughput compared to the second-generation sequencing bring their own challenges. To compensate for the low throughput and high cost, hybrid approaches using both short second-generation and long third-generation reads have gathered recent interest. The first part of this thesis focuses on the analysis of short-read RNA-seq data. As short-read mapping is an already well-researched field, we focus on giving a literature review of the topic. For transcript assembly we propose a novel (at the time of the publication) approach of using minimum-cost flows to solve the problem of covering a graph created from the read alignments with a set of paths with the minimum cost, under some cost model. Various network-flow-based solutions were proposed in parallel to, as well as after, ours. The second part, where the main contributions of this thesis lie, focuses on the analysis of long-read RNA-seq data. The driving point of our research has been the Minimum Path Cover with Subpath Constraints (MPC-SC) model, where transcript assembly is modeled as a minimum path cover problem, with the addition that each of the chains of exons (subpath constraints) created from the long reads must be completely contained in a solution path. In addition to implementing this concept, we experimentally studied different approaches on how to find the exon chains in practice. The evaluated approaches included aligning the long reads to a graph created from short read alignments instead of the reference genome, which led to our final contribution: extending a co-linear chaining algorithm from between two sequences to between a sequence and a directed acyclic graph.Transkriptiossa organismin geenien mallin mukaan luodaan RNA-molekyyleja. Lukuisat tekijät, sekä solun sisäiset että ulkoiset, määrittävät mitä geenejä transkriptoidaan, ja missä määrin. Tämän prosessin tutkiminen antaa arvokasta tietoa esimerkiksi lääketieteelliseen diagnostiikkaan. Yksi yleisistä RNA-sekvensointidatan analyysitavoista koostuu kolmesta osasta: lukujaksojen (read sequences) linjaus referenssigenomiin, transkriptien kokoaminen, ja transkriptien ekspressiotasojen määrittäminen. Toisen sukupolven sekvensointiteknologian kehityksen myötä sekvensoinnin hinta laski huomattavasti, mikä salli RNA-sekvensointidatan käytön yhä useampaan tarkoitukseen. Nyt kolmannen sukupolven sekvensointiteknologiat tarjoavat kertaluokkaa pidempiä lukujaksoja, mikä laajentaa analysointimahdollisuuksia. Kuitenkin suurempi virhemäärä, korkeampi hinta ja pienempi määrä tuotettua dataa tuovat omat haasteensa. Toisen ja kolmannen sukupolven teknologioiden käyttäminen yhdessä, ns. hybridilähestymistapa, on tutkimussuunta joka on kerännyt paljon kiinnostusta viimeaikoina. Tämän tutkielman ensimmäinen osa keskittyy toisen sukupolven, eli ns. lyhyiden RNA-lukujaksojen (short read), analyysiin. Näiden lyhyiden lukujaksojen linjausta referenssigenomiin on tutkittu jo 2000-luvulla, joten tällä alueella keskitymme olemassaolevaan kirjallisuuteen. Transkriptien kokoamisen alalta esittelemme metodin, joka käyttää vähimmäiskustannusvirtauksen (minimum-cost flow) mallia. Vähimmäiskustannusvirtauksen mallissa lukujaksoista luotu verkko peitetään joukolla polkuja, joiden kustannus on pienin mahdollinen. Virtausmalleja on käytetty myös muiden tutkijoiden kehittämissä analyysityökaluissa. Tämän tutkielman suurin kontribuutio on toisessa osassa, joka keskittyy ns. pitkien RNA-lukujaksojen (long read) analysointiin. Tutkimuksemme lähtökohtana on ollut malli, jossa pienimmän polkupeitteen (Minimum Path Cover) ongelmaan lisätään alipolkurajoitus (subpath constraint). Jokainen alipolkurajoitus vastaa eksoniketjua (exon chain), jotka jokin pitkä lukujakso peittää, ja jokaisen alipolkurajoituksen täytyy sisältyä kokonaan johonkin polkupeitteen polkuun. Tämän konseptin toteuttamisen lisäksi testasimme kokeellisesti erilaisia lähestymistapoja eksoniketjujen löytämiseksi. Näihin testattaviin lähestymistapoihin kuului pitkien lukujaksojen linjaaminen suoraan lyhyistä lukujaksoista luotuun verkkoon referenssigenomin sijaan. Tämä lähestymistapa johti tämän tutkielman viimeiseen kontribuutioon: kolineaarisen ketjun (co-linear chaining) algoritmin yleistäminen kahden sekvenssin sijasta sekvenssiin ja suunnattuun syklittömään verkkoon