BackgroundThrough 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.ResultsIn 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.ConclusionsWe 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/.

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 | E |log | V |). 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 | E |log | V |) 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.

High-throughput sequencing has revolutionised the field of biological sequence analysis. Its application has enabled researchers to address important biological questions, often for the first time. This book provides an integrated presentation of the fundamental algorithms and data structures that power modern sequence analysis workflows. The topics covered range from the foundations of biological sequence analysis (alignments and hidden Markov models), to classical index structures (k-mer indexes, suffix arrays and suffix trees), Burrows–Wheeler indexes, graph algorithms and a number of advanced omics applications. The chapters feature numerous examples, algorithm visualisations, exercises and problems, each chosen to reflect the steps of large-scale sequencing projects, including read alignment, variant calling, haplotyping, fragment assembly, alignment-free genome comparison, transcript prediction and analysis of metagenomic samples. Each biological problem is accompanied by precise formulations, providing graduate students and researchers in bioinformatics and computer science with a powerful toolkit for the emerging applications of high-throughput sequencing.