Ancestral sequence reconstruction is an important task in bioinformatics, with applications ranging from protein engineering to the study of genome evolution. When sequences can only undergo substitutions, optimal reconstructions can be efficiently computed using well-known algorithms. However, accounting for indels in ancestral reconstructions is much harder. First, for biologically-relevant problem formulations, no polynomial-time exact algorithms are available. Second, multiple reconstructions are often equally parsimonious or likely, making it crucial to correctly display uncertainty in the results. Here, we consider a parsimony approach where only deletions are allowed, while addressing the aforementioned limitations. First, we describe an exact algorithm to obtain all the optimal solutions. The algorithm runs in polynomial time if only one solution is sought. Second, we show that all possible optimal reconstructions for a fixed node can be represented using a graph computable in polynomial time. While previous studies have proposed graph-based representations of ancestral reconstructions, this result is the first to offer a solid mathematical justification for this approach. Finally we provide arguments for the relevance of the deletion-only case for the general case.

Consider words of length n. The set of all periods of a word of length n is a subset of {0,1,2,…,n-1}. However, any subset of {0,1,2,…,n-1} is not necessarily a valid set of periods. In a seminal paper in 1981, Guibas and Odlyzko proposed to encode the set of periods of a word into an n long binary string, called an autocorrelation, where a one at position i denotes the period i. They considered the question of recognizing a valid period set, and also studied the number of valid period sets for strings of length n, denoted κ_n. They conjectured that ln(κ_n) asymptotically converges to a constant times ln²(n). Although improved lower bounds for ln(κ_n)/ln²(n) were proposed in 2001, the question of a tight upper bound has remained open since Guibas and Odlyzko’s paper. Here, we exhibit an upper bound for this fraction, which implies its convergence and closes this longstanding conjecture. Moreover, we extend our result to find similar bounds for the number of correlations: a generalization of autocorrelations which encodes the overlaps between two strings.

MOTIVATION: Seeking probabilistic motifs in a sequence is a common task to annotate putative transcription factor binding sites or other RNA/DNA binding sites. Useful motif representations include position weight matrices (PWMs), dinucleotide PWMs (di-PWMs), and hidden Markov models (HMMs). Dinucleotide PWMs not only combine the simplicity of PWMs-a matrix form and a cumulative scoring function-but also incorporate dependency between adjacent positions in the motif (unlike PWMs which disregard any dependency). For instance to represent binding sites, the HOCOMOCO database provides di-PWM motifs derived from experimental data. Currently, two programs, SPRy-SARUS and MOODS, can search for occurrences of di-PWMs in sequences. RESULTS: We propose a Python package called dipwmsearch, which provides an original and efficient algorithm for this task (it first enumerates matching words for the di-PWM, and then searches these all at once in the sequence, even if the latter contains IUPAC codes). The user benefits from an easy installation via Pypi or conda, a comprehensive documentation, and executable scripts that facilitate the use of di-PWMs. AVAILABILITY AND IMPLEMENTATION: dipwmsearch is available at https://pypi.org/project/dipwmsearch/ and https://gite.lirmm.fr/rivals/dipwmsearch/ under Cecill license.

MOTIVATION: Phylogenetic placement enables phylogenetic analysis of massive collections of newly sequenced DNA, when de novo tree inference is too unreliable or inefficient. Assuming that a high-quality reference tree is available, the idea is to seek the correct placement of the new sequences in that tree. Recently, alignment-free approaches to phylogenetic placement have emerged, both to circumvent the need to align the new sequences and to avoid the calculations that typically follow the alignment step. A promising approach is based on the inference of k-mers that can be potentially related to the reference sequences, also called phylo-k-mers. However, its usage is limited by the time and memory-consuming stage of reference data preprocessing and the large numbers of k-mers to consider. RESULTS: We suggest a filtering method for selecting informative phylo-k-mers based on mutual information, which can significantly improve the efficiency of placement, at the cost of a small loss in placement accuracy. This method is implemented in IPK, a new tool for computing phylo-k-mers that significantly outperforms the software previously available. We also present EPIK, a new software for phylogenetic placement, supporting filtered phylo-k-mer databases. Our experiments on real-world data show that EPIK is the fastest phylogenetic placement tool available, when placing hundreds of thousands and millions of queries while still providing accurate placements. AVAILABILITY AND IMPLEMENTATION: IPK and EPIK are freely available at https://github.com/phylo42/IPK and https://github.com/phylo42/EPIK. Both are implemented in C++ and Python and supported on Linux and MacOS.

Gene expression is the synthesis of proteins from the information encoded on DNA. One of the two main steps of gene expression is the translation of messenger RNA (mRNA) into polypeptide sequences of amino acids. Here, by taking into account mRNA degradation, we model the motion of ribosomes along mRNA with a ballistic model where particles advance along a filament without excluded volume interactions. Unidirectional models of transport have previously been used to fit the average density of ribosomes obtained by the experimental ribo-sequencing (Ribo-seq) technique in order to obtain the kinetic rates. The degradation rate is not, however, accounted for and experimental data from different experiments are needed to have enough parameters for the fit. Here, we propose an entirely novel experimental setup and theoretical framework consisting in splitting the mRNAs into categories depending on the number of ribosomes from one to four. We solve analytically the ballistic model for a fixed number of ribosomes per mRNA, study the different regimes of degradation, and propose a criterion for the quality of the inverse fit. The proposed method provides a high sensitivity to the mRNA degradation rate. The additional equations coming from using the monosome (single ribosome) and polysome (arbitrary number) ribo-seq profiles enable us to determine all the kinetic rates in terms of the experimentally accessible mRNA degradation rate.

Finding the correct position of new sequences within an established phylogenetic tree is an increasingly relevant problem in evolutionary bioinformatics and metagenomics. Recently, alignment-free approaches for this task have been proposed. One such approach is based on the concept of phylogenetically-informative k-mers or phylo- k-mers for short. In practice, phylo- k-mers are inferred from a set of related reference sequences and are equipped with scores expressing the probability of their appearance in different locations within the input reference phylogeny. Computing phylo- k-mers, however, represents a computational bottleneck to their applicability in real-world problems such as the phylogenetic analysis of metabarcoding reads and the detection of novel recombinant viruses. Here we consider the problem of phylo- k-mer computation: how can we efficiently find all k-mers whose probability lies above a given threshold for a given tree node? We describe and analyze algorithms for this problem, relying on branch-and-bound and divide-and-conquer techniques. We exploit the redundancy of adjacent windows of the alignment to save on computation. Besides computational complexity analyses, we provide an empirical evaluation of the relative performance of their implementations on simulated and real-world data. The divide-and-conquer algorithms are found to surpass the branch-and-bound approach, especially when many phylo- k-mers are found.

The hierarchical overlap graph (HOG) is a graph that encodes overlaps from a given set P of n strings, as the overlap graph does. A best known algorithm constructs HOG in O(||P|| log n) time and O(||P||) space, where ||P|| is the sum of lengths of the strings in P. In this paper we present a new algorithm to construct HOG in O(||P||) time and space. Hence, the construction time and space of HOG are better than those of the overlap graph, which are O(||P|| + n^2).

MOTIVATION: Phylogenetic placement (PP) is a process of taxonomic identification for which several tools are now available. However, it remains difficult to assess which tool is more adapted to particular genomic data or a particular reference taxonomy. We developed Placement Evaluation WOrkflows (PEWO), the first benchmarking tool dedicated to PP assessment. Its automated workflows can evaluate PP at many levels, from parameter optimization for a particular tool, to the selection of the most appropriate genetic marker when PP-based species identifications are targeted. Our goal is that PEWO will become a community effort and a standard support for future developments and applications of PP. AVAILABILITY AND IMPLEMENTATION: https://github.com/phylo42/PEWO. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Novel recombinant viruses may have important medical and evolutionary significance, as they sometimes display new traits not present in the parental strains. This is particularly concerning when the new viruses combine fragments coming from phylogenetically distinct viral types. Here, we consider the task of screening large collections of sequences for such novel recombinants. A number of methods already exist for this task. However, these methods rely on complex models and heavy computations that are not always practical for a quick scan of a large number of sequences. RESULTS: We have developed SHERPAS, a new program to detect novel recombinants and provide a first estimate of their parental composition. Our approach is based on the precomputation of a large database of 'phylogenetically-informed k-mers', an idea recently introduced in the context of phylogenetic placement in metagenomics. Our experiments show that SHERPAS is hundreds to thousands of times faster than existing software, and enables the analysis of thousands of whole genomes, or long-sequencing reads, within minutes or seconds, and with limited loss of accuracy. AVAILABILITY AND IMPLEMENTATION: The source code is freely available for download at https://github.com/phylo42/sherpas. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The boom of genomic sequencing makes compression of sets of sequences inescapable. This underlies the need for multi-string indexing data structures that helps compressing the data. The most prominent example of such data structures is the Burrows-Wheeler Transform (BWT), a reversible permutation of a text that improves its compressibility. A similar data structure, the eXtended Burrows-Wheeler Transform (XBW), is able to index a tree labelled with alphabet symbols. A link between a multi-string BWT and the Aho-Corasick automaton has already been found and led to a way to build a XBW from a multi-string BWT. We exhibit a stronger link between a multi-string BWT and a XBW by using the order of the concatenation in the multi-string. This bijective link has several applications: first, it allows one to build one data structure from the other; second, it enables one to compute an ordering of the input strings that optimises a Run-Length measure (i.e., the compressibility) of the BWT or of the XBW.

MOTIVATION: The visualization and interpretation of evolutionary spatiotemporal scenarios is broadly and increasingly used in infectious disease research, ecology or agronomy. Using probabilistic frameworks, well-known tools can infer from molecular data ancestral traits for internal nodes in a phylogeny, and numerous phylogenetic rendering tools can display such evolutionary trees. However, visualizing such ancestral information and its uncertainty on the tree remains tedious. For instance, ancestral nodes can be associated to several geographical annotations with close probabilities and thus, several migration or transmission scenarios exist. RESULTS: We expose a web-based tool, named AQUAPONY, that facilitates such operations. Given an evolutionary tree with ancestral (e.g. geographical) annotations, the user can easily control the display of ancestral information on the entire tree or a subtree, and can view alternative phylogeographic scenarios along a branch according to a chosen uncertainty threshold. AQUAPONY interactively visualizes the tree and eases the objective interpretation of evolutionary scenarios. AQUAPONY's implementation makes it highly responsive to user interaction, and instantaneously updates the tree visualizations even for large trees (which can be exported as image files). AVAILABILITY AND IMPLEMENTATION: AQUAPONY is coded in JavaScript/HTML, available under Cecill license, and can be freely used at http://www.atgc-montpellier.fr/aquapony/.

DNA sequencing technologies have tremendously increased their throughput, and hence complicated DNA assembly. Numerous assembly programs use de Bruijn graphs (dBG) built from short reads to merge these into contigs, which represent putative DNA segments. In a dBG of order k, nodes are substrings of length k of reads (or k-mers), while arcs are their k+1-mers. As analysing reads often require to index all their substrings, it is interesting to exhibit algorithms that directly build a dBG from a pre-existing index, and especially a contracted dBG, where non-branching paths are condensed into single nodes. Here, we exhibit linear time algorithms for constructing the full or contracted dBGs from suffix trees, suffix arrays, and truncated suffix trees. With the latter the construction uses a space that is linear in the size of the dBG. Finally, we also provide algorithms to dynamically update the order of the graph without reconstructing it.

A superstring of a set of words P = {s_1, ..., s_p } is a string that contains each word of P as substring. Given P, the well known Shortest Linear Superstring problem (SLS), asks for a shortest superstring of P. In a variant of SLS, called Multi-SLS, each word s_i comes with an integer m(i), its multiplicity, that sets a constraint on its number of occurrences, and the goal is to find a shortest superstring that contains at least m(i) occurrences of s_i. Multi-SLS generalizes SLS and is obviously as hard to solve, but it has been studied only in special cases (with words of length 2 or with a fixed number of words). The approximability of Multi-SLS in the general case remains open. Here, we study the approximability of Multi-SLS and that of the companion problem Multi-SCCS, which asks for a shortest cyclic cover instead of shortest superstring. First, we investigate the approximation of a greedy algorithm for maximizing the compression offered by a superstring or by a cyclic cover: the approximation ratio is 1/2 for Multi-SLS and 1 for Multi-SCCS. Then, we exhibit a linear time approximation algorithm, Concat-Greedy, and show it achieves a ratio of 4 regarding the superstring length. This demonstrates that for both measures Multi-SLS belongs to the class of APX problems.

For analysing text algorithms, for computing superstrings, or for testing random number generators, one needs to compute all overlaps between any pairs of words in a given set. The positions of overlaps of a word onto itself, or of two words, are needed to compute the absence probability of a word in a random text, or the numbers of common words shared by two random texts. In all these contexts, one needs to compute or to query overlaps between pairs of words in a given set. For this sake, we designed COvI, a compressed overlap index that supports multiple queries on overlaps: like computing the correlation of two words, or listing pairs of words whose longest overlap is maximal among all possible pairs. COvI stores overlaps in a hierarchical and non-redundant manner. We propose an implementation that can handle datasets of millions of words and still answer queries efficiently. Comparison with a baseline solution - called FullAC - relying on the Aho-Corasick automaton shows that COvI provides significant advantages. For similar construction times, COvI requires half the memory FullAC, and still solves complex queries much faster.

A superstring of a set of words is a string that contains each input word as a substring. Given such a set, the Shortest Superstring Problem (SSP) asks for a superstring of minimum length. SSP is an important theoretical problem related to the Asymmetric Travelling Salesman Problem, and also has practical applications in data compression and in bioinformatics. Indeed, it models the question of assembling a genome from a set of sequencing reads. Unfortunately, SSP is known to be NP-hard even on a binary alphabet and also hard to approximate with respect to the superstring length or to the compression achieved by the superstring. Even the variant in which all words share the same length r, called r-SSP, is NP-hard whenever r>2. Numerous involved approximation algorithms achieve approximation ratio above 2 for the superstring, but remain difficult to implement in practice. In contrast the greedy conjecture asked in 1988 whether a simple greedy algorithm achieves ratio of 2 for SSP. Here, we present a novel approach to bound the superstring approximation ratio with the compression ratio, which, when applied to the greedy algorithm, shows a 2 approximation ratio for 3-SSP, and also that greedy achieves ratios smaller than 2. This leads to a new version of the greedy conjecture.

The Suffix Tree, a crucial and versatile data structure for string analysis of large texts, is often used in pattern matching and in bioinformatics applications. The Affix Tree generalizes the Suffix Tree in that it supports full tree functionalities in both search directions. The bottleneck of Affix Trees is their space requirement for storing the data structure. Here, we discuss existing representations and classify them into two categories: Synchronous and Asynchronous. We design Compressed Affix Tree indexes in both categories and explored how to support all tree operations bidirectionally. This work compares alternative approaches for compressing the Affix Tree, measuring their space and time trade-offs for different operations. Moreover, to our knowledge, this is the first work that compares all Compressed Affix Tree implementations offering a practical benchmark for this structure.

Motivation: New long read sequencing technologies, like PacBio SMRT and Oxford NanoPore, can produce sequencing reads up to 50 000 bp long but with an error rate of at least 15%. Reducing the error rate is necessary for subsequent utilization of the reads in, e.g. de novo genome assembly. The error correction problem has been tackled either by aligning the long reads against each other or by a hybrid approach that uses the more accurate short reads produced by second generation sequencing technologies to correct the long reads. Results: We present an error correction method that uses long reads only. The method consists of two phases: first, we use an iterative alignment-free correction method based on de Bruijn graphs with increasing length of k -mers, and second, the corrected reads are further polished using long-distance dependencies that are found using multiple alignments. According to our experiments, the proposed method is the most accurate one relying on long reads only for read sets with high coverage. Furthermore, when the coverage of the read set is at least 75×, the throughput of the new method is at least 20% higher. Availability and Implementation: LoRMA is freely available at http://www.cs.helsinki.fi/u/lmsalmel/LoRMA/ . Contact: [email protected].

For a set of input words, finding a superstring (a string containing each word of the set as a substring) of minimal length is hard. Most approximation algorithms solve the Shortest Cyclic Cover problem before merging the cyclic strings into a linear superstring. A cyclic cover is a set of cyclic strings in which the input words occur as a substring. We investigate a variant of the Shortest Cyclic Cover problem for the case of DNA. Because the two strands that compose DNA have a reverse complementary sequence, and because the sequencing process often overlooks the strand of a read, each read or its reverse complement must occur as a substring in a cyclic cover. We exhibit a linear time algorithm based on graphs for solving the Shortest DNA Cyclic Cover problem and propose compressed data structures for storing the underlying graphs. All results and algorithms can be adapted to the case where strings are simply reversed but not complemented (e.g. in pattern recognition).

BACKGROUND: Next Generation Sequencing (NGS) has dramatically enhanced our ability to sequence genomes, but not to assemble them. In practice, many published genome sequences remain in the state of a large set of contigs. Each contig describes the sequence found along some path of the assembly graph, however, the set of contigs does not record all the sequence information contained in that graph. Although many subsequent analyses can be performed with the set of contigs, one may ask whether mapping reads on the contigs is as informative as mapping them on the paths of the assembly graph. Currently, one lacks practical tools to perform mapping on such graphs. RESULTS: Here, we propose a formal definition of mapping on a de Bruijn graph, analyse the problem complexity which turns out to be NP-complete, and provide a practical solution. We propose a pipeline called GGMAP (Greedy Graph MAPping). Its novelty is a procedure to map reads on branching paths of the graph, for which we designed a heuristic algorithm called BGREAT (de Bruijn Graph REAd mapping Tool). For the sake of efficiency, BGREAT rewrites a read sequence as a succession of unitigs sequences. GGMAP can map millions of reads per CPU hour on a de Bruijn graph built from a large set of human genomic reads. Surprisingly, results show that up to 22 % more reads can be mapped on the graph but not on the contig set. CONCLUSIONS: Although mapping reads on a de Bruijn graph is complex task, our proposal offers a practical solution combining efficiency with an improved mapping capacity compared to assembly-based mapping even for complex eukaryotic data.

BACKGROUND: Comparing and aligning genomes is a key step in analyzing closely related genomes. Despite the development of many genome aligners in the last 15 years, the problem is not yet fully resolved, even when aligning closely related bacterial genomes of the same species. In addition, no procedures are available to assess the quality of genome alignments or to compare genome aligners. RESULTS: We designed an original method for pairwise genome alignment, named YOC, which employs a highly sensitive similarity detection method together with a recent collinear chaining strategy that allows overlaps. YOC improves the reliability of collinear genome alignments, while preserving or even improving sensitivity. We also propose an original qualitative evaluation criterion for measuring the relevance of genome alignments. We used this criterion to compare and benchmark YOC with five recent genome aligners on large bacterial genome datasets, and showed it is suitable for identifying the specificities and the potential flaws of their underlying strategies. CONCLUSIONS: The YOC prototype is available at https://github.com/ruricaru/YOC . It has several advantages over existing genome aligners: (1) it is based on a simplified two phase alignment strategy, (2) it is easy to parameterize, (3) it produces reliable genome alignments, which are easier to analyze and to use.

MOTIVATION: PacBio single molecule real-time sequencing is a third-generation sequencing technique producing long reads, with comparatively lower throughput and higher error rate. Errors include numerous indels and complicate downstream analysis like mapping or de novo assembly. A hybrid strategy that takes advantage of the high accuracy of second-generation short reads has been proposed for correcting long reads. Mapping of short reads on long reads provides sufficient coverage to eliminate up to 99% of errors, however, at the expense of prohibitive running times and considerable amounts of disk and memory space. RESULTS: We present LoRDEC, a hybrid error correction method that builds a succinct de Bruijn graph representing the short reads, and seeks a corrective sequence for each erroneous region in the long reads by traversing chosen paths in the graph. In comparison, LoRDEC is at least six times faster and requires at least 93% less memory or disk space than available tools, while achieving comparable accuracy. Availability and implementaion: LoRDEC is written in C++, tested on Linux platforms and freely available at http://atgc.lirmm.fr/lordec.

We consider the problem of inferring approximate common intervals of multiple genomes. Genomes are modelled as sequences of homologous genes families identifiers, and approximate common intervals represent conserved regions possibly showing rearrangements, as well as repetitions, or insertions/deletions. This problem is already known, but existing approaches are not incremental and somehow limited to special cases. We adopt a simple, classical graph-based approach, where the vertices of the graph represent the exact common intervals of the sequences (i.e., regions containing the same gene set), and where edges link vertices that differ by less than δ elements (with δ being parameter). With this model, approximate gene clusters are maximal cliques of the graph: computing them can exploit known and well designed algorithms. For a proof of concept, we applied the method to several datasets of bacterial genomes and compared the two maximal cliques algorithms, a static and a dynamic one. While being quite flexible, this approach opens the way to a combinatorial characterization of genomic rearrangements in terms of .

BACKGROUND: High Throughput Sequencing (HTS) is now heavily exploited for genome (re-) sequencing, metagenomics, epigenomics, and transcriptomics and requires different, but computer intensive bioinformatic analyses. When a reference genome is available, mapping reads on it is the first step of this analysis. Read mapping programs owe their efficiency to the use of involved genome indexing data structures, like the Burrows-Wheeler transform. Recent solutions index both the genome, and the k-mers of the reads using hash-tables to further increase efficiency and accuracy. In various contexts (e.g. assembly or transcriptome analysis), read processing requires to determine the sub-collection of reads that are related to a given sequence, which is done by searching for some k-mers in the reads. Currently, many developments have focused on genome indexing structures for read mapping, but the question of read indexing remains broadly unexplored. However, the increase in sequence throughput urges for new algorithmic solutions to query large read collections efficiently. RESULTS: Here, we present a solution, named Gk arrays, to index large collections of reads, an algorithm to build the structure, and procedures to query it. Once constructed, the index structure is kept in main memory and is repeatedly accessed to answer queries like "given a k-mer, get the reads containing this k-mer (once/at least once)". We compared our structure to other solutions that adapt uncompressed indexing structures designed for long texts and show that it processes queries fast, while requiring much less memory. Our structure can thus handle larger read collections. We provide examples where such queries are adapted to different types of read analysis (SNP detection, assembly, RNA-Seq). CONCLUSIONS: Gk arrays constitute a versatile data structure that enables fast and more accurate read analysis in various contexts. The Gk arrays provide a flexible brick to design innovative programs that mine efficiently genomics, epigenomics, metagenomics, or transcriptomics reads. The Gk arrays library is available under Cecill (GPL compliant) license from http://www.atgc-montpellier.fr/ngs/.

BACKGROUND: Microsatellites are short, tandemly-repeated DNA sequences which are widely distributed among genomes. Their structure, role and evolution can be analyzed based on exhaustive extraction from sequenced genomes. Several dedicated algorithms have been developed for this purpose. Here, we compared the detection efficiency of five of them (TRF, Mreps, Sputnik, STAR, and RepeatMasker). RESULTS: Our analysis was first conducted on the human X chromosome, and microsatellite distributions were characterized by microsatellite number, length, and divergence from a pure motif. The algorithms work with user-defined parameters, and we demonstrate that the parameter values chosen can strongly influence microsatellite distributions. The five algorithms were then compared by fixing parameters settings, and the analysis was extended to three other genomes (Saccharomyces cerevisiae, Neurospora crassa and Drosophila melanogaster) spanning a wide range of size and structure. Significant differences for all characteristics of microsatellites were observed among algorithms, but not among genomes, for both perfect and imperfect microsatellites. Striking differences were detected for short microsatellites (below 20 bp), regardless of motif. CONCLUSION: Since the algorithm used strongly influences empirical distributions, studies analyzing microsatellite evolution based on a comparison between empirical and theoretical size distributions should therefore be considered with caution. We also discuss why a typological definition of microsatellites limits our capacity to capture their genomic distributions.

MOTIVATION: Tandem repeats consist in approximate and adjacent repetitions of a DNA motif. Such repeats account for large portions of eukaryotic genomes and have also been found in other life kingdoms. Owing to their polymorphism, tandem repeats have proven useful in genome cartography, forensic and population studies, etc. Nevertheless, they are not systematically detected nor annotated in genome projects. Partially because of this lack of data, their evolution is still poorly understood. RESULTS: In this work, we design an exact algorithm to locate approximate tandem repeats (ATR) of a motif in a DNA sequence. Given a motif and a DNA sequence, our method named STAR, identifies all segments of the sequence that correspond to significant approximate tandem repetitions of the motif. In our model, an Exact Tandem Repeat (ETR) comes from the tandem duplication of the motif and an ATR derives from an ETR by a series of point mutations. An ATR can then be encoded as a number of duplications of the motif together with a list of mutations. Consequently, any sequence that is not an ATR cannot be encoded efficiently by this description, while a true ATR can. Our method uses the minimum description length criterion to identify which sequence segments are ATR. Our optimization procedure guarantees that STAR finds a combination of ATR that minimizes this criterion. AVAILABILITY: for use at http://atgc.lirmm.fr/star

Long version of Recomb paper

With the increasing amount of DNA sequence information deposited in public databases, searching for similarity to a query sequence has become a basic operation in molecular biology.But even today's fast algorithms reach their limits when applied to all-versus-all comparisons of large databases.Here we present a new database searching algorithm called QUASAR (Q-gram Alignment based on Suffix ARrays) which was designed to quickly detect sequences with strong similarity to the query in a context where many searches are conducted on one database.Our algorithm applies a modification of q-tuple filtering implemented on top of a suffix array.Two versions were developed, one for a RAM resident suffix array and one for access to the suffix array on disk.We compared our implementation with BLAST and found that our approach is an order of magnitude faster.It is, however, restricted to the search for strongly similar DNA sequences as is typically required, e.g., in the context of clustering expressed sequence tags (ESTs).

MOTIVATION: Evolution acts in several ways on DNA: either by mutating a base, or by inserting, deleting or copying a segment of the sequence (Ruddle, 1997; Russell, 1994; Li and Grauer, 1991). Classical alignment methods deal with point mutations (Waterman, 1995), genome-level mutations are studied using genome rearrangement distances (Bafna and Pevzner, 1993, 1995; Kececioglu and Sankoff, 1994; Kececioglu and Ravi, 1995). The latter distances generally operate, not on the sequences, but on an ordered list of genes. To our knowledge, no measure of distance attempts to compare sequences using a general set of segment-based operations. RESULTS: Here we define a new family of distances, called transformation distances, which quantify the dissimilarity between two sequences in terms of segment-based events. We focus on the case where segment-copy, -reverse-copy and -insertion are allowed in our set of operations. Those events are weighted by their description length, but other sets of weights are possible when biological information is available. The transformation distance from sequence S to sequence T is then the Minimum Description Length among all possible scripts that build T knowing S with segment-based operations. The underlying idea is related to Kolmogorov complexity theory. We present an algorithm which, given two sequences S and T, computes exactly and efficiently the transformation distance from S to T. Unlike alignment methods, the method we propose does not necessarily respect the order of the residues within the compared sequences and is therefore able to account for duplications and translocations that cannot be properly described by sequence alignment. A biological application on Tnt1 tobacco retrotransposon is presented. AVAILABILITY: The algorithm and the graphical interface can be downloaded at http://www.lifl.fr/ approximately varre/TD

MOTIVATION: Compression algorithms can be used to analyse genetic sequences. A compression algorithm tests a given property on the sequence and uses it to encode the sequence: if the property is true, it reveals some structure of the sequence which can be described briefly, this yields a description of the sequence which is shorter than the sequence of nucleotides given in extenso. The more a sequence is compressed by the algorithm, the more significant is the property for that sequence. RESULTS: We present a compression algorithm that tests the presence of a particular type of dosDNA (defined ordered sequence-DNA): approximate tandem repeats of small motifs (i.e. of lengths < 4). This algorithm has been experimented with on four yeast chromosomes. The presence of approximate tandem repeats seems to be a uniform structural property of yeast chromosomes.

We present a text compression scheme dedicated to DNA sequences. The exponential growing of the number of sequences creates a real need for analyzing tools. A specific need emerges for methods that perform sequences classification upon various criteria, one of which is the sequence repetitiveness. A good lossless compression scheme is able to distinguish between "random" and "significative" repeats. Theoretical bases for this statement are found in Kolmogorov complexity theory.