The Positional Burrows-Wheeler Transform (PBWT) is a data structure designed for efficiently representing and querying large collections of sequences, such as haplotype panels in genomics. Forward and backward stepping operations - analogues to LF- and FL-mapping in the traditional BWT - are fundamental to the PBWT, underpinning many algorithms based on the PBWT for haplotype matching and related analyses. Although the run-length encoded variant of the PBWT (also known as the μ-PBWT) achieves O(r̃)-word space usage, where r̃ is the total number of runs, no data structure supporting both forward and backward stepping in constant time within this space bound was previously known. In this paper, we consider the multi-allelic PBWT that is extended from its original binary form to a general ordered alphabet {0, … , σ-1}. We first establish bounds on the size r̃ and then introduce a new O(r̃)-word data structure built over a list of haplotypes {S_1, … , S_h}, each of length w, that supports constant-time forward and backward stepping. We further revisit two key applications - haplotype retrieval and prefix search - leveraging our efficient forward stepping technique. Specifically, we design an O(r̃)-word space data structure that supports haplotype retrieval in O(log log_w h + w) time. For prefix search, we present an O(h + r̃)-word data structure that answers queries in O(m' log log_w σ + occ) time, where m' denotes the length of the longest common prefix returned and occ denotes the number of haplotypes prefixed the longest prefix.

Recently, Cenzato et al. proposed a new text index, called the suffixient array, which is a subset of the suffix array and supports locating a single pattern occurrence or finding its maximal exact matches (MEMs), assuming random access to the input text T[1..n] is available. They show that, given the suffix array, the longest common prefix array, and the Burrows-Wheeler transform (BWT) of the reverse of T[1..n] over an alphabet {1,…,σ}, a suffixient array can be constructed in linear time. However, their construction algorithms require multiple scans of these arrays. When restricted to a single pass over the arrays, they present an alternative construction algorithm running in O(n + r log σ) time, where r is the number of runs in the BWT of the reversed text. In this paper, we present a new one-pass algorithm that constructs a suffixient array in linear time under the standard RAM model.

Minimizer sketches summarize sequences with the main purpose of keeping the smallest footprint to be used for the sequence comparison of multiple reads: they are based on the notion of the smallest lexicographic k-mer in a window. Building on the concept of Lyndon factorization and a compact representation of sequences, called fingerprints, that correspond to the length of the factors in the factorization, we extend the notion of minimizer sketches to read fingerprints. By leveraging the conservation property of Lyndon factorization, we propose a novel approach for a fast comparison of long reads, to detect overlapping read pairs. An experimental evaluation of assemblies produced using the overlaps computed by our approach shows that it is competitive with the state-of-the-art tool minimap2 in terms of quality, while being up to 5 times faster at higher coverage levels.

Abstract Several computational methods for the differential analysis of alternative splicing (AS) events among RNA-Seq samples typically rely on estimating isoform-level gene expression. However, these approaches are often error-prone due to the interplay of individual AS events, which results in different isoforms with locally similar sequences. Moreover, methods based on isoform-level quantification usually need annotated transcripts. In this work, we leverage the ability of deep learning networks to learn features from images and propose , a novel method for event-based AS differential analysis between two RNA-Seq samples. Our method does not rely on isoform abundance estimation, neither on a specific annotation. employs an image embedding scheme to represent the alignments of the two samples on the same region and utilizes a residual neural network to predict the AS events possibly expressed within that region. To our knowledge, is the first deep learning approach for performing an event-based AS analysis of RNA-Seq samples. To validate , we also address the lack of high quality AS benchmark datasets. For this purpose, we manually curated a set of regions exhibiting AS events. These regions were used for training our model and for assessing the predictions of our method. Our results highlight that achieves higher precision at the expense of a small reduction in sensitivity. The tool and the manually curated regions are available at https://github.com/sciccolella/deepSpecas .

The notion of Lyndon word and Lyndon factorization has shown to have unexpected applications in theory as well in developing novel algorithms on words. A counterpart to these notions are those of inverse Lyndon word and inverse Lyndon factorization. Differently from the Lyndon words, the inverse Lyndon words may be bordered. The relationship between the two factorizations is related to the inverse lexicographic ordering, and has only been recently explored. More precisely, a main open question is how to get an inverse Lyndon factorization from a classical Lyndon factorization under the inverse lexicographic ordering, named CFLin. In this paper we reveal a strong connection between these two factorizations where the border plays a relevant role. More precisely, we show two main results. We say that a factorization has the border property if a nonempty border of a factor cannot be a prefix of the next factor. First we show that there exists a unique inverse Lyndon factorization having the border property. Then we show that this unique factorization with the border property is the so-called canonical inverse Lyndon factorization, named ICFL. By showing that ICFL is obtained by compacting factors of the Lyndon factorization over the inverse lexicographic ordering, we provide a linear time algorithm for computing ICFL from CFLin.

MOTIVATION: Bacterial genomes present more variability than human genomes, which requires important adjustments in computational tools that are developed for human data. In particular, bacteria exhibit a mosaic structure due to homologous recombinations, but this fact is not sufficiently captured by standard read mappers that align against linear reference genomes. The recent introduction of pangenomics provides some insights in that context, as a pangenome graph can represent the variability within a species. However, the concept of sequence-to-graph alignment that captures the presence of recombinations has not been previously investigated. RESULTS: In this paper, we present the extension of the notion of sequence-to-graph alignment to a variation graph that incorporates a recombination, so that the latter are explicitly represented and evaluated in an alignment. Moreover, we present a dynamic programming approach for the special case where there is at most a recombination-we implement this case as RecGraph. From a modelling point of view, a recombination corresponds to identifying a new path of the variation graph, where the new arc is composed of two halves, each extracted from an original path, possibly joined by a new arc. Our experiments show that RecGraph accurately aligns simulated recombinant bacterial sequences that have at most a recombination, providing evidence for the presence of recombination events. AVAILABILITY AND IMPLEMENTATION: Our implementation is open source and available at https://github.com/AlgoLab/RecGraph.

BACKGROUND: The construction of a pangenome graph is a fundamental task in pangenomics. A natural theoretical question is how to formalize the computational problem of building an optimal pangenome graph, making explicit the underlying optimization criterion and the set of feasible solutions. Current approaches build a pangenome graph with some heuristics, without assuming some explicit optimization criteria. Thus it is unclear how a specific optimization criterion affects the graph topology and downstream analysis, like read mapping and variant calling. RESULTS: In this paper, by leveraging the notion of maximal block in a Multiple Sequence Alignment (MSA), we reframe the pangenome graph construction problem as an exact cover problem on blocks called Minimum Weighted Block Cover (MWBC). Then we propose an Integer Linear Programming (ILP) formulation for the MWBC problem that allows us to study the most natural objective functions for building a graph. We provide an implementation of the ILP approach for solving the MWBC and we evaluate it on SARS-CoV-2 complete genomes, showing how different objective functions lead to pangenome graphs that have different properties, hinting that the specific downstream task can drive the graph construction phase. CONCLUSION: We show that a customized construction of a pangenome graph based on selecting objective functions has a direct impact on the resulting graphs. In particular, our formalization of the MWBC problem, based on finding an optimal subset of blocks covering an MSA, paves the way to novel practical approaches to graph representations of an MSA where the user can guide the construction.

Pangenomes are becoming a powerful framework to perform many bioinformatics analyses taking into account the genetic variability of a population, thus reducing the bias introduced by a single reference genome. With the wider diffusion of pangenomes, integrating genetic variability with transcriptome diversity is becoming a natural extension that demands specific methods for its exploration. In this work, we extend the notion of spliced pangenomes to that of annotated spliced pangenomes; this allows us to introduce a formal definition of Alternative Splicing (AS) events on a graph structure. To investigate the usage of graph pangenomes for the quantification of AS events across conditions, we developed pantas, the first pangenomic method for the detection and differential analysis of AS events from short RNA-Seq reads. A comparison with state-of-the-art linear reference-based approaches proves that pantas achieves competitive accuracy, making spliced pangenomes effective for conducting AS events quantification and opening future directions for the analysis of population-based transcriptomes.

MOTIVATION: The Positional Burrows-Wheeler Transform (PBWT) is a data structure that indexes haplotype sequences in a manner that enables finding maximal haplotype matches in h sequences containing w variation sites in O(hw) time. This represents a significant improvement over classical quadratic-time approaches. However, the original PBWT data structure does not allow for queries over Biobank panels that consist of several millions of haplotypes, if an index of the haplotypes must be kept entirely in memory. RESULTS: In this article, we leverage the notion of r-index proposed for the BWT to present a memory-efficient method for constructing and storing the run-length encoded PBWT, and computing set maximal matches (SMEMs) queries in haplotype sequences. We implement our method, which we refer to as μ-PBWT, and evaluate it on datasets of 1000 Genome Project and UK Biobank data. Our experiments demonstrate that the μ-PBWT reduces the memory usage up to a factor of 20% compared to the best current PBWT-based indexing. In particular, μ-PBWT produces an index that stores high-coverage whole genome sequencing data of chromosome 20 in about a third of the space of its BCF file. μ-PBWT is an adaptation of techniques for the run-length compressed BWT for the PBWT (RLPBWT) and it is based on keeping in memory only a succinct representation of the RLPBWT that still allows the efficient computation of set maximal matches (SMEMs) over the original panel. AVAILABILITY AND IMPLEMENTATION: Our implementation is open source and available at https://github.com/dlcgold/muPBWT. The binary is available at https://bioconda.github.io/recipes/mupbwt/README.html.

Abstract Computational pangenomics is an emerging research field that is changing the way computer scientists are facing challenges in biological sequence analysis. In past decades, contributions from combinatorics, stringology, graph theory and data structures were essential in the development of a plethora of software tools for the analysis of the human genome. These tools allowed computational biologists to approach ambitious projects at population scale, such as the 1000 Genomes Project. A major contribution of the 1000 Genomes Project is the characterization of a broad spectrum of genetic variations in the human genome, including the discovery of novel variations in the South Asian, African and European populations—thus enhancing the catalogue of variability within the reference genome. Currently, the need to take into account the high variability in population genomes as well as the specificity of an individual genome in a personalized approach to medicine is rapidly pushing the abandonment of the traditional paradigm of using a single reference genome. A graph-based representation of multiple genomes, or a graph pangenome, is replacing the linear reference genome. This means completely rethinking well-established procedures to analyze, store, and access information from genome representations. Properly addressing these challenges is crucial to face the computational tasks of ambitious healthcare projects aiming to characterize human diversity by sequencing 1M individuals (Stark et al. 2019). This tutorial aims to introduce readers to the most recent advances in the theory of data structures for the representation of graph pangenomes. We discuss efficient representations of haplotypes and the variability of genotypes in graph pangenomes, and highlight applications in solving computational problems in human and microbial (viral) pangenomes.

MOTIVATION: The latest advances in cancer sequencing, and the availability of a wide range of methods to infer the evolutionary history of tumors, have made it important to evaluate, reconcile and cluster different tumor phylogenies. Recently, several notions of distance or similarities have been proposed in the literature, but none of them has emerged as the golden standard. Moreover, none of the known similarity measures is able to manage mutations occurring multiple times in the tree, a circumstance often occurring in real cases. RESULTS: To overcome these limitations, in this article, we propose MP3, the first similarity measure for tumor phylogenies able to effectively manage cases where multiple mutations can occur at the same time and mutations can occur multiple times. Moreover, a comparison of MP3 with other measures shows that it is able to classify correctly similar and dissimilar trees, both on simulated and on real data. AVAILABILITY AND IMPLEMENTATION: An open source implementation of MP3 is publicly available at https://github.com/AlgoLab/mp3treesim. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: In recent years, the well-known Infinite Sites Assumption has been a fundamental feature of computational methods devised for reconstructing tumor phylogenies and inferring cancer progressions. However, recent studies leveraging single-cell sequencing (SCS) techniques have shown evidence of the widespread recurrence and, especially, loss of mutations in several tumor samples. While there exist established computational methods that infer phylogenies with mutation losses, there remain some advancements to be made. RESULTS: We present Simulated Annealing Single-Cell inference (SASC): a new and robust approach based on simulated annealing for the inference of cancer progression from SCS datasets. In particular, we introduce an extension of the model of evolution where mutations are only accumulated, by allowing also a limited amount of mutation loss in the evolutionary history of the tumor: the Dollo-k model. We demonstrate that SASC achieves high levels of accuracy when tested on both simulated and real datasets and in comparison with some other available methods. AVAILABILITY AND IMPLEMENTATION: The SASC tool is open source and available at https://github.com/sciccolella/sasc. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Recent advances in high-throughput RNA-Seq technologies allow to produce massive datasets. When a study focuses only on a handful of genes, most reads are not relevant and degrade the performance of the tools used to analyze the data. Removing irrelevant reads from the input dataset leads to improved efficiency without compromising the results of the study. RESULTS: We introduce a novel computational problem, called gene assignment and we propose an efficient alignment-free approach to solve it. Given an RNA-Seq sample and a panel of genes, a gene assignment consists in extracting from the sample, the reads that most probably were sequenced from those genes. The problem becomes more complicated when the sample exhibits evidence of novel alternative splicing events. We implemented our approach in a tool called Shark and assessed its effectiveness in speeding up differential splicing analysis pipelines. This evaluation shows that Shark is able to significantly improve the performance of RNA-Seq analysis tools without having any impact on the final results. AVAILABILITY AND IMPLEMENTATION: The tool is distributed as a stand-alone module and the software is freely available at https://github.com/AlgoLab/shark. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Being able to efficiently call variants from the increasing amount of sequencing data daily produced from multiple viral strains is of the utmost importance, as demonstrated during the COVID-19 pandemic, in order to track the spread of the viral strains across the globe. RESULTS: We present MALVIRUS, an easy-to-install and easy-to-use application that assists users in multiple tasks required for the analysis of a viral population, such as the SARS-CoV-2. MALVIRUS allows to: (1) construct a variant catalog consisting in a set of variations (SNPs/indels) from the population sequences, (2) efficiently genotype and annotate variants of the catalog supported by a read sample, and (3) when the considered viral species is the SARS-CoV-2, assign the input sample to the most likely Pango lineages using the genotyped variations. CONCLUSIONS: Tests on Illumina and Nanopore samples proved the efficiency and the effectiveness of MALVIRUS in analyzing SARS-CoV-2 strain samples with respect to publicly available data provided by NCBI and the more complete dataset provided by GISAID. A comparison with state-of-the-art tools showed that MALVIRUS is always more precise and often have a better recall.

Single cell sequencing (SCS) technologies provide a level of resolution that makes it indispensable for inferring from a sequenced tumor, evolutionary trees or phylogenies representing an accumulation of cancerous mutations. A drawback of SCS is elevated false negative and missing value rates, resulting in a large space of possible solutions, which in turn makes it difficult, sometimes infeasible using current approaches and tools. One possible solution is to reduce the size of an SCS instance - usually represented as a matrix of presence, absence, and uncertainty of the mutations found in the different sequenced cells - and to infer the tree from this reduced-size instance. In this work, we present a new clustering procedure aimed at clustering such categorical vector, or matrix data - here representing SCS instances, called celluloid. We show that celluloid clusters mutations with high precision: never pairing too many mutations that are unrelated in the ground truth, but also obtains accurate results in terms of the phylogeny inferred downstream from the reduced instance produced by this method. We demonstrate the usefulness of a clustering step by applying the entire pipeline (clustering + inference method) to a real dataset, showing a significant reduction in the runtime, raising considerably the upper bound on the size of SCS instances which can be solved in practice. Our approach, celluloid: clustering single cell sequencing data around centroids is available at https://github.com/AlgoLab/celluloid/ under an MIT license, as well as on the Python Package Index (PyPI) at https://pypi.org/project/celluloid-clust/.

The last decade brought a significant increase in the amount of data and a variety of new inference methods for reconstructing the detailed evolutionary history of various cancers. This brings the need of designing efficient procedures for comparing rooted trees representing the evolution of mutations in tumor phylogenies. Bernardini et al. [CPM 2019] recently introduced a notion of the rearrangement distance for fully-labelled trees motivated by this necessity. This notion originates from two operations: one that permutes the labels of the nodes, the other that affects the topology of the tree. Each operation alone defines a distance that can be computed in polynomial time, while the actual rearrangement distance, that combines the two, was proven to be NP-hard. We answer two open question left unanswered by the previous work. First, what is the complexity of computing the permutation distance? Second, is there a constant-factor approximation algorithm for estimating the rearrangement distance between two arbitrary trees? We answer the first one by showing, via a two-way reduction, that calculating the permutation distance between two trees on n nodes is equivalent, up to polylogarithmic factors, to finding the largest cardinality matching in a sparse bipartite graph. In particular, by plugging in the algorithm of Liu and Sidford [ArXiv 2020], we obtain an 𝒪̃(n^{4/3+o(1}) time algorithm for computing the permutation distance between two trees on n nodes. Then we answer the second question positively, and design a linear-time constant-factor approximation algorithm that does not need any assumption on the trees.

SUMMARY: Retroviruses and their vector derivatives integrate semi-randomly in the genome of host cells and are inherited by their progeny as stable genetic marks. The retrieval and mapping of the sequences flanking the virus-host DNA junctions allows the identification of insertion sites in gene therapy or virally infected patients, essential for monitoring the evolution of genetically modified cells in vivo. However, since ∼30% of insertions land in low complexity or repetitive regions of the host cell genome, they cannot be correctly assigned and are currently discarded, limiting the accuracy and predictive power of clonal tracking studies. Here, we present γ-TRIS, a new graph-based genome-free alignment tool for identifying insertion sites even if embedded in low complexity regions. By using γ-TRIS to reanalyze clinical studies, we observed improvements in clonal quantification and tracking. AVAILABILITY AND IMPLEMENTATION: Source code at https://bitbucket.org/bereste/g-tris. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Cancer progression reconstruction is an important development stemming from the phylogenetics field. In this context, the reconstruction of the phylogeny representing the evolutionary history presents some peculiar aspects that depend on the technology used to obtain the data to analyze: Single Cell DNA Sequencing data have great specificity, but are affected by moderate false negative and missing value rates. Moreover, there has been some recent evidence of back mutations in cancer: this phenomenon is currently widely ignored. RESULTS: We present a new tool, gpps, that reconstructs a tumor phylogeny from Single Cell Sequencing data, allowing each mutation to be lost at most a fixed number of times. The General Parsimony Phylogeny from Single cell (gpps) tool is open source and available at https://github.com/AlgoLab/gpps . CONCLUSIONS: gpps provides new insights to the analysis of intra-tumor heterogeneity by proposing a new progression model to the field of cancer phylogeny reconstruction on Single Cell data.

Circular splicing systems are a mathematical model, inspired by a recombinant behaviour of circular DNA. They are defined by a finite alphabet A, an initial set I of circular words, and a set R of rules. A circular splicing language is a language generated by a circular splicing system. An open pro blem is to characterize regular circular splicing languages and the corresponding circular splicing systems. In this framework an important role is played by unavoidable sets. These sets have been considered in several contexts. In particular, Ehrenfeucht, Haussler and Rozenberg (1983) proved the following generalization of a famous Higman’s theorem: the quasi-order induced by insertions of words from a fixed finite set is a well-quasi-order if and only if the finite set is unavoidable. In this paper we survey the known relations between unavoidable sets and regular circular languages. Motivated by these connections we give an alternative and simpler proof of the Ehrenfeucht, Haussler and Rozenberg result. Our proof is strongly based on a known characterization of unavoidable sets in terms of graphs associated with them.

The problem of comparing trees representing the evolutionary histories of cancerous tumors has turned out to be crucial, since there is a variety of different methods which typically infer multiple possible trees. A departure from the widely studied setting of classical phylogenetics, where trees are leaf-labelled, tumoral trees are fully labelled, i.e., every vertex has a label. In this paper we provide a rearrangement distance measure between two fully-labelled trees. This notion originates from two operations: one which modifies the topology of the tree, the other which permutes the labels of the vertices, hence leaving the topology unaffected. While we show that the distance between two trees in terms of each such operation alone can be decided in polynomial time, the more general notion of distance when both operations are allowed is NP-hard to decide. Despite this result, we show that it is fixed-parameter tractable, and we give a 4-approximation algorithm when one of the trees is binary.

Most of the evolutionary history reconstruction approaches are based on the infinite sites assumption, which states that mutations appear once in the evolutionary history. The Perfect Phylogeny model is the result of the infinite sites assumption and has been widely used to infer cancer evolution. Nonetheless, recent results show that recurrent and back mutations are present in the evolutionary history of tumors, hence the Perfect Phylogeny model might be too restrictive. We propose an approach that allows losing previously acquired mutations and multiple acquisitions of a character. Moreover, we provide an ILP formulation for the evolutionary tree reconstruction problem. Our formulation allows us to tackle both the Incomplete Directed Phylogeny problem and the Clonal Reconstruction problem when general evolutionary models are considered. The latter problem is fundamental in cancer genomics, the goal is to study the evolutionary history of a tumor considering as input data the fraction of cells having a certain mutation in a set of cancer samples. For the Clonal Reconstruction problem, an experimental analysis shows the advantage of allowing mutation losses. Namely, by analyzing real and simulated datasets, our ILP approach provides a better interpretation of the evolutionary history than a Perfect Phylogeny. The software is at https://github.com/AlgoLab/gppf.

BACKGROUND: Haplotype assembly is the process of assigning the different alleles of the variants covered by mapped sequencing reads to the two haplotypes of the genome of a human individual. Long reads, which are nowadays cheaper to produce and more widely available than ever before, have been used to reduce the fragmentation of the assembled haplotypes since their ability to span several variants along the genome. These long reads are also characterized by a high error rate, an issue which may be mitigated, however, with larger sets of reads, when this error rate is uniform across genome positions. Unfortunately, current state-of-the-art dynamic programming approaches designed for long reads deal only with limited coverages. RESULTS: Here, we propose a new method for assembling haplotypes which combines and extends the features of previous approaches to deal with long reads and higher coverages. In particular, our algorithm is able to dynamically adapt the estimated number of errors at each variant site, while minimizing the total number of error corrections necessary for finding a feasible solution. This allows our method to significantly reduce the required computational resources, allowing to consider datasets composed of higher coverages. The algorithm has been implemented in a freely available tool, HapCHAT: Haplotype Assembly Coverage Handling by Adapting Thresholds. An experimental analysis on sequencing reads with up to 60 × coverage reveals improvements in accuracy and recall achieved by considering a higher coverage with lower runtimes. CONCLUSIONS: Our method leverages the long-range information of sequencing reads that allows to obtain assembled haplotypes fragmented in a lower number of unphased haplotype blocks. At the same time, our method is also able to deal with higher coverages to better correct the errors in the original reads and to obtain more accurate haplotypes as a result. AVAILABILITY: HapCHAT is available at http://hapchat.algolab.eu under the GNU Public License (GPL).

BACKGROUND: While the reconstruction of transcripts from a sample of RNA-Seq data is a computationally expensive and complicated task, the detection of splicing events from RNA-Seq data and a gene annotation is computationally feasible. This latter task, which is adequate for many transcriptome analyses, is usually achieved by aligning the reads to a reference genome, followed by comparing the alignments with a gene annotation, often implicitly represented by a graph: the splicing graph. RESULTS: We present ASGAL (Alternative Splicing Graph ALigner): a tool for mapping RNA-Seq data to the splicing graph, with the specific goal of detecting novel splicing events, involving either annotated or unannotated splice sites. ASGAL takes as input the annotated transcripts of a gene and a RNA-Seq sample, and computes (1) the spliced alignments of each read in input, and (2) a list of novel events with respect to the gene annotation. CONCLUSIONS: An experimental analysis shows that ASGAL allows to enrich the annotation with novel alternative splicing events even when genes in an experiment express at most one isoform. Compared with other tools which use the spliced alignment of reads against a reference genome for differential analysis, ASGAL better predicts events that use splice sites which are novel with respect to a splicing graph, showing a higher accuracy. To the best of our knowledge, ASGAL is the first tool that detects novel alternative splicing events by directly aligning reads to a splicing graph. AVAILABILITY: Source code, documentation, and data are available for download at http://asgal.algolab.eu .

The perfect phylogeny is a widely used model in phylogenetics, since it provides an effective representation of evolution of binary characters in several contexts, such as for example in haplotype inference. The model, which is conceptually the simplest among those actually used, is based on the in finite sites assumption, that is no character can mutate more than once in the whole tree. Since a large number of biological phenomena cannot be modeled by the perfect phylogeny, it becomes important to find generalizations that retain the computational tractability of the original model, but are more flexible in modeling biological data when the infinite site assumption is violated, e.g. because of back mutations. In this paper, we introduce a new model—called species-driven persistent phylogeny—and we study the relations between three different formulations: perfect phylogeny, persistent phylogeny, galled trees, and species-driven persistent phylogeny. The species-driven persistent phylogeny model is intermediate between the perfect and the persistent phylogeny, since a perfect phylogeny allows no back mutations and a persistent phylogeny allows each character to back mutate only once. We describe an algorithm to compute a species-driven persistent phylogeny and we prove that every matrix admitting a galled-tree also admits a species-driven persistent phylogeny.

MOTIVATION: Haplotype assembly is the computational problem of reconstructing haplotypes in diploid organisms and is of fundamental importance for characterizing the effects of single-nucleotide polymorphisms on the expression of phenotypic traits. Haplotype assembly highly benefits from the advent of 'future-generation' sequencing technologies and their capability to produce long reads at increasing coverage. Existing methods are not able to deal with such data in a fully satisfactory way, either because accuracy or performances degrade as read length and sequencing coverage increase or because they are based on restrictive assumptions. RESULTS: By exploiting a feature of future-generation technologies-the uniform distribution of sequencing errors-we designed an exact algorithm, called HapCol, that is exponential in the maximum number of corrections for each single-nucleotide polymorphism position and that minimizes the overall error-correction score. We performed an experimental analysis, comparing HapCol with the current state-of-the-art combinatorial methods both on real and simulated data. On a standard benchmark of real data, we show that HapCol is competitive with state-of-the-art methods, improving the accuracy and the number of phased positions. Furthermore, experiments on realistically simulated datasets revealed that HapCol requires significantly less computing resources, especially memory. Thanks to its computational efficiency, HapCol can overcome the limits of previous approaches, allowing to phase datasets with higher coverage and without the traditional all-heterozygous assumption. AVAILABILITY AND IMPLEMENTATION: Our source code is available under the terms of the GNU General Public License at http://hapcol.algolab.eu/ CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The Minimum Path Cover (MinPC) problem on directed acyclic graphs (DAGs) is a classical problem in graph theory that provides a clear and simple mathematical formulation for several applications in computational biology. In this paper, we study the computational complexity of three constrained variants of MinPC motivated by the recent introduction of Next-Generation Sequencing technologies. The first variant (MinRPC), given a DAG and a set of pairs of vertices, asks for a minimum-cardinality set of (not necessarily disjoint) paths such that both vertices of each pair belong to the same path. For this problem, we establish a sharp tractability borderline depending on the ‘overlapping degree’ of the instance, a natural parameter in some applications of the problem. The second variant we consider (MinPCRP), given a DAG and a set of pairs of vertices, asks for a minimum-cardinality set of (not necessarily disjoint) paths ‘covering’ all the vertices of the graph and such that both vertices of each pair belong to the same path. For this problem, we show that, while it is NP-hard to compute if there exists a solution consisting of at most three paths, it is possible to decide in polynomial time whether a solution consisting of at most two paths exists. The third variant (MaxRPSP), given a DAG and a set of pairs of vertices, asks for a single path containing the maximum number of the given pairs of vertices. We show that MaxRPSP is W[1]-hard when parameterized by the number of covered pairs and we give a fixed-parameter algorithm when the parameter is the maximum overlapping degree.

MOTIVATION: TANGO is one of the most accurate tools for the taxonomic assignment of sequence reads. However, because of the differences in the taxonomy structures, performing a taxonomic assignment on different reference taxonomies will produce divergent results. RESULTS: We have improved the TANGO pipeline to be able to perform the taxonomic assignment of a metagenomic sample using alternative reference taxonomies, coming from different sources. We highlight the novel pre-processing step, necessary to accomplish this task, and describe the improvements in the assignment process. We present the new TANGO pipeline in details, and, finally, we show its performance on four real metagenomic datasets and also on synthetic datasets. AVAILABILITY: The new version of TANGO, including implementation improvements and novel developments to perform the assignment on different reference taxonomies, is freely available at http://sourceforge.net/projects/taxoassignment/.

Next-generation sequencing (NGS) technologies allow new methodologies for alternative splicing (AS) analysis. Current computational methods for AS from NGS data are mainly focused on predicting splice site junctions or de novo assembly of full-length transcripts. These methods are computationally expensive and produce a huge number of full-length transcripts or splice junctions, spanning the whole genome of organisms. Thus summarizing such data into the different gene structures and AS events of the expressed genes is an hard task. To face this issue in this paper we investigate the computational problem of reconstructing from NGS data, in absence of the genome, a gene structure for each gene that is represented by the isoform graph: we introduce such graph and we show that it uniquely summarizes the gene transcripts. We define the computational problem of reconstructing the isoform graph and provide some conditions that must be met to allow such reconstruction. Finally, we describe an efficient algorithmic approach to solve this problem, validating our approach with both a theoretical and an experimental analysis.

BACKGROUND: A challenging issue in designing computational methods for predicting the gene structure into exons and introns from a cluster of transcript (EST, mRNA) sequences, is guaranteeing accuracy as well as efficiency in time and space, when large clusters of more than 20,000 ESTs and genes longer than 1 Mb are processed. Traditionally, the problem has been faced by combining different tools, not specifically designed for this task. RESULTS: We propose a fast method based on ad hoc procedures for solving the problem. Our method combines two ideas: a novel algorithm of proved small time complexity for computing spliced alignments of a transcript against a genome, and an efficient algorithm that exploits the inherent redundancy of information in a cluster of transcripts to select, among all possible factorizations of EST sequences, those allowing to infer splice site junctions that are largely confirmed by the input data. The EST alignment procedure is based on the construction of maximal embeddings, that are sequences obtained from paths of a graph structure, called embedding graph, whose vertices are the maximal pairings of a genomic sequence T and an EST P. The procedure runs in time linear in the length of P and T and in the size of the output.The method was implemented into the PIntron package. PIntron requires as input a genomic sequence or region and a set of EST and/or mRNA sequences. Besides the prediction of the full-length transcript isoforms potentially expressed by the gene, the PIntron package includes a module for the CDS annotation of the predicted transcripts. CONCLUSIONS: PIntron, the software tool implementing our methodology, is available at http://www.algolab.eu/PIntron under GNU AGPL. PIntron has been shown to outperform state-of-the-art methods, and to quickly process some critical genes. At the same time, PIntron exhibits high accuracy (sensitivity and specificity) when benchmarked with ENCODE annotations.

Haplotype Inference (HI) is a computational challenge of crucial importance in a range of genetic studies. Pedigrees allow to infer haplotypes from genotypes more accurately than population data, since Mendelian inheritance restricts the set of possible solutions. In this work, we define a new HI problem on pedigrees, called MINIMUM-CHANGE HAPLOTYPE CONFIGURATION (MCHC) problem, that allows two types of genetic variation events: recombinations and mutations. Our new formulation extends the MINIMUM-RECOMBINANT HAPLOTYPE CONFIGURATION (MRHC) problem, that has been proposed in the literature to overcome the limitations of classic statistical haplotyping methods. Our contribution is twofold. First, we prove that the MCHC problem is APX-hard under several restrictions. Second, we propose an efficient and accurate heuristic algorithm for MCHC based on an L-reduction to a well-known coding problem. Our heuristic can also be used to solve the original MRHC problem and can take advantage of additional knowledge about the input genotypes. Moreover, the L-reduction proves for the first time that MCHC and MRHC are O(nm/(log nm))-approximable on general pedigrees, where n is the pedigree size and m is the genotype length. Finally, we present an extensive experimental evaluation and comparison of our heuristic algorithm with several other state-of-the-art methods for HI on pedigrees.

The MINIMUM-RECOMBINANT HAPLOTYPE CONFIGURATION problem (MRHC) has been highly successful in providing a sound combinatorial formulation for the important problem of genotype phasing on pedigrees. Despite several algorithmic advances that have improved the efficiency, its applicability to real data sets has been limited since it does not take into account some important phenomena such as mutations, genotyping errors, and missing data. In this work, we propose the MINIMUM-RECOMBINANT HAPLOTYPE CONFIGURATION WITH BOUNDED ERRORS problem (MRHCE), which extends the original MRHC formulation by incorporating the two most common characteristics of real data: errors and missing genotypes (including untyped individuals). We describe a practical algorithm for MRHCE that is based on a reduction to the well-known Satisfiability problem (SAT) and exploits recent advances in the constraint programming literature. An experimental analysis demonstrates the biological soundness of the phasing model and the effectiveness (on both accuracy and performance) of the algorithm under several scenarios. The analysis on real data and the comparison with state-of-the-art programs reveals that our approach couples better scalability to large and complex pedigrees with the explicit inclusion of genotyping errors into the model.

We propose a new formalism for generating picture languages based on an assembly mechanism of tiles that uses rules having a context and a replacement site. More precisely, a picture language will be generated from a finite set of initial pictures by iteratively applying rewriting rules from a given finite set of rules, called a tiling rule system (TRuS system). We prove that the TRuS systems have a greater generative capacity than the tiling systems of Giammarresi and Restivo. This is due mainly to the use of the notion of replacement site, but we further characterize the difference between these systems by comparing them to Wang systems.

The haplotype resolution from xor-genotype data has been recently formulated as a new model for genetic studies. The xor-genotype data is a cheaply obtainable type of data distinguishing heterozygous from homozygous sites without identifying the homozygous alleles. In this paper, we propose a formulation based on a well-known model used in haplotype inference: pure parsimony. We exhibit exact solutions of the problem by providing polynomial time algorithms for some restricted cases and a fixed-parameter algorithm for the general case. These results are based on some interesting combinatorial properties of a graph representation of the solutions. Furthermore, we show that the problem has a polynomial time k-approximation, where k is the maximum number of xor-genotypes containing a given single nucleotide polymorphisms (SNP). Finally, we propose a heuristic and produce an experimental analysis showing that it scales to real-world large instances taken from the HapMap project.

MOTIVATION: Alternative splicing has recently emerged as a key mechanism responsible for the expansion of transcriptome and proteome complexity in human and other organisms. Although several online resources devoted to alternative splicing analysis are available they may suffer from limitations related both to the computational methodologies adopted and to the extent of the annotations they provide that prevent the full exploitation of the available data. Furthermore, current resources provide limited query and download facilities. RESULTS: ASPicDB is a database designed to provide access to reliable annotations of the alternative splicing pattern of human genes and to the functional annotation of predicted splicing isoforms. Splice-site detection and full-length transcript modeling have been carried out by a genome-wide application of the ASPic algorithm, based on the multiple alignments of gene-related transcripts (typically a Unigene cluster) to the genomic sequence, a strategy that greatly improves prediction accuracy compared to methods based on independent and progressive alignments. Enhanced query and download facilities for annotations and sequences allow users to select and extract specific sets of data related to genes, transcripts and introns fulfilling a combination of user-defined criteria. Several tabular and graphical views of the results are presented, providing a comprehensive assessment of the functional implication of alternative splicing in the gene set under investigation. ASPicDB, which is regularly updated on a monthly basis, also includes information on tissue-specific splicing patterns of normal and cancer cells, based on available EST sequences and their library source annotation. AVAILABILITY: www.caspur.it/ASPicDB

In this paper, we investigate the computational and approximation complexity of the Exemplar Longest Common Subsequence of a set of sequences (ELCS problem), a generalization of the Longest Common Subsequence problem, where the input sequences are over the union of two disjoint sets of symbols, a set of mandatory symbols and a set of optional symbols. We show that different versions of the problem are APX-hard even for instances with two sequences. Moreover, we show that the related problem of determining the existence of a feasible solution of the Exemplar Longest Common Subsequence of two sequences is NP-hard. On the positive side, we first present an efficient algorithm for the ELCS problem over instances of two sequences where each mandatory symbol can appear in total at most three times in the sequences. Furthermore, we present two fixed-parameter algorithms for the ELCS problem over instances of two sequences where the parameter is the number of mandatory symbols.

BACKGROUND: Currently available methods to predict splice sites are mainly based on the independent and progressive alignment of transcript data (mostly ESTs) to the genomic sequence. Apart from often being computationally expensive, this approach is vulnerable to several problems--hence the need to develop novel strategies. RESULTS: We propose a method, based on a novel multiple genome-EST alignment algorithm, for the detection of splice sites. To avoid limitations of splice sites prediction (mainly, over-predictions) due to independent single EST alignments to the genomic sequence our approach performs a multiple alignment of transcript data to the genomic sequence based on the combined analysis of all available data. We recast the problem of predicting constitutive and alternative splicing as an optimization problem, where the optimal multiple transcript alignment minimizes the number of exons and hence of splice site observations. We have implemented a splice site predictor based on this algorithm in the software tool ASPIC (Alternative Splicing PredICtion). It is distinguished from other methods based on BLAST-like tools by the incorporation of entirely new ad hoc procedures for accurate and computationally efficient transcript alignment and adopts dynamic programming for the refinement of intron boundaries. ASPIC also provides the minimal set of non-mergeable transcript isoforms compatible with the detected splicing events. The ASPIC web resource is dynamically interconnected with the Ensembl and Unigene databases and also implements an upload facility. CONCLUSION: Extensive bench marking shows that ASPIC outperforms other existing methods in the detection of novel splicing isoforms and in the minimization of over-predictions. ASPIC also requires a lower computation time for processing a single gene and an EST cluster. The ASPIC web resource is available at http://aspic.algo.disco.unimib.it/aspic-devel/.