The genome median problem is a central computational problem in comparative genomics, as it models the reconstruction of an ancestral genome from a set of related genomes. Given 𝓁 genomes and a distance measure, the problem asks for a genome that minimizes the sum of the distances to the input genomes. Two classical distances are the breakpoint distance and the double-cut-and-join (DCJ) distance. For multichromosomal circular genomes, the median problem is polynomial-time solvable under the breakpoint distance, whereas it is NP-hard under the DCJ distance. For even integer k ≥ 2, the σ_k distance interpolates between these two extremes: σ₂ corresponds to the breakpoint distance, while σ_∞ corresponds to the DCJ distance. A central open problem in this setting is the (3,4)-Median problem, which asks for a median of three genomes under the σ₄ distance, the first intermediate distance after the breakpoint distance. Motivated by this question, we study the more general (𝓁,k)-Median problem, in which 𝓁 is the number of input genomes and k determines the σ_k distance. We prove that (𝓁,6)-Median for every 𝓁 ≥ 4 and (3,12)-Median are NP-complete. We then extend the hardness of (𝓁,6)-Median to (𝓁,k)-Median for all even k ≥ 6, and the hardness of (3,12)-Median to (3,k)-Median for all even k ≥ 12. These results identify broad hardness regions in the (𝓁,k) parameter space and delimit the remaining open cases around the fundamental (3,4)-Median problem.

Genome rearrangement has been an active area of research in computational comparative genomics for the last three decades. While initially mostly an interesting algorithmic endeavor, now the practical application of rearrangement distance methods and more advanced phylogenetic tasks is becoming common practice, given the availability of many completely sequenced genomes. Several genome rearrangement models have been developed over time, sometimes with surprising computational properties. A prominent example is the fact that computing the reversal distance of two signed permutations is possible in linear time, while for two unsigned permutations it is NP-hard. Therefore one has to always be careful about the precise problem formulation and complexity analysis of rearrangement problems in order not to be fooled. The double distance is the minimum number of genomic rearrangements between a singular and a duplicated genome that - in addition to rearrangements - are separated by a whole genome duplication. At the same time it allows to assign the genes of the duplicated genome to the two paralogous chromosome copies that existed right after the duplication event. Computing the double distance is another example of a tricky hardness landscape: If the distance measure underlying the double distance is the simple breakpoint distance, the problem can be solved in linear time, while with the more elaborate DCJ distance it is NP-hard. Indeed, there is a whole family of distance measures, parameterized by an even number $k$, between the breakpoint distance ($k=2$) at the one end and the DCJ distance ($k=\infty$) at the other end. Only little was known about the hardness border that lies somewhere on the way between these two extremes. Precisely, beneath the two border cases the (linear) problem complexity was known only for $k=4$ and $k=6$. In this paper we close the gap, giving a full picture of the hardness landscape when computing the double distance.

MOTIVATION: Using a single linear reference genome poses a limitation to exploring the full genomic diversity of a species. The release of a draft human pangenome underscores the increasing relevance of pangenomics to overcome these limitations. Pangenomes are commonly represented as graphs, which can represent billions of base pairs of sequence. Presently, there is a lack of scalable software able to perform key tasks on pangenomes, such as quantifying universally shared sequence across genomes (the core genome) and measuring the extent of genomic variability as a function of sample size (pangenome growth). RESULTS: We introduce Panacus (pangenome-abacus), a tool designed to rapidly perform these tasks and visualize the results in interactive plots. Panacus can process GFA files, the accepted standard for pangenome graphs, and is able to analyze a human pangenome graph with 110 million nodes in <1 h. AVAILABILITY AND IMPLEMENTATION: Panacus is implemented in Rust and is published as Open Source software under the MIT license. The source code and documentation are available at https://github.com/marschall-lab/panacus. Panacus can be installed via Bioconda at https://bioconda.github.io/recipes/panacus/README.html.

MOTIVATION: Increasing amounts of individual genomes sequenced per species motivate the usage of pangenomic approaches. Pangenomes may be represented as graphical structures, e.g. compacted colored de Bruijn graphs, which offer a low memory usage and facilitate reference-free sequence comparisons. While sequence-to-graph mapping to graphical pangenomes has been studied for some time, no local alignment search tool in the vein of BLAST has been proposed yet. RESULTS: We present a new heuristic method to find maximum scoring local alignments of a DNA query sequence to a pangenome represented as a compacted colored de Bruijn graph. Our approach additionally allows a comparison of similarity among sequences within the pangenome. We show that local alignment scores follow an exponential-tail distribution similar to BLAST scores, and we discuss how to estimate its parameters to separate local alignments representing sequence homology from spurious findings. An implementation of our method is presented, and its performance and usability are shown. Our approach scales sublinearly in running time and memory usage with respect to the number of genomes under consideration. This is an advantage over classical methods that do not make use of sequence similarity within the pangenome. AVAILABILITY AND IMPLEMENTATION: Source code and test data are available from https://gitlab.ub.uni-bielefeld.de/gi/plast. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Tumors contain multiple subpopulations of genetically distinct cancer cells. Reconstructing their evolutionary history can improve our understanding of how cancers develop and respond to treatment. Subclonal reconstruction methods cluster mutations into groups that co-occur within the same subpopulations, estimate the frequency of cells belonging to each subpopulation, and infer the ancestral relationships among the subpopulations by constructing a clone tree. However, often multiple clone trees are consistent with the data and current methods do not efficiently capture this uncertainty; nor can these methods scale to clone trees with a large number of subclonal populations. Here, we formalize the notion of a partially-defined clone tree (partial clone tree for short) that defines a subset of the pairwise ancestral relationships in a clone tree, thereby implicitly representing the set of all clone trees that have these defined pairwise relationships. Also, we introduce a special partial clone tree, the Maximally-Constrained Ancestral Reconstruction (MAR), which summarizes all clone trees fitting the input data equally well. Finally, we extend commonly used clone tree validity conditions to apply to partial clone trees and describe SubMARine, a polynomial-time algorithm producing the subMAR, which approximates the MAR and guarantees that its defined relationships are a subset of those present in the MAR. We also extend SubMARine to work with subclonal copy number aberrations and define equivalence constraints for this purpose. Further, we extend SubMARine to permit noise in the estimates of the subclonal frequencies while retaining its validity conditions and guarantees. In contrast to other clone tree reconstruction methods, SubMARine runs in time and space that scale polynomially in the number of subclones. We show through extensive noise-free simulation, a large lung cancer dataset and a prostate cancer dataset that the subMAR equals the MAR in all cases where only a single clone tree exists and that it is a perfect match to the MAR in most of the other cases. Notably, SubMARine runs in less than 70 seconds on a single thread with less than one Gb of memory on all datasets presented in this paper, including ones with 50 nodes in a clone tree. On the real-world data, SubMARine almost perfectly recovers the previously reported trees and identifies minor errors made in the expert-driven reconstructions of those trees. The freely-available open-source code implementing SubMARine can be downloaded at https://github.com/morrislab/submarine.

The inversion distance, that is the distance between two unichromosomal genomes with the same content allowing only inversions of DNA segments, can be exactly computed thanks to a pioneering approach of Hannenhalli and Pevzner from 1995. In 2000, El-Mabrouk extended the inversion model to perform the comparison of unichromosomal genomes with unequal contents, combining inversions with insertions and deletions (indels) of DNA segments, giving rise to the inversion-indel distance. However, only a heuristic was provided for its computation. In 2005, Yancopoulos, Attie and Friedberg started a new branch of research by introducing the generic double cut and join (DCJ) operation, that can represent several genome rearrangements (including inversions). In 2006, Bergeron, Mixtacki and Stoye showed that the DCJ distance can be computed in linear time with a very simple procedure. As a consequence, in 2010 we gave a linear-time algorithm to compute the DCJ-indel distance. This result allowed the inversion-indel model to be revisited from another angle. In 2013, we could show that, when the diagram that represents the relation between the two compared genomes has no bad components, the inversion-indel distance is equal to the DCJ-indel distance. In the present work we complete the study of the inversion-indel distance by giving the first algorithm to compute it exactly even in the presence of bad components.

Recent large-scale community sequencing efforts allow at an unprecedented level of detail the identification of genomic regions that show signatures of natural selection. Traditional methods for identifying such regions from individuals' haplotype data, however, require excessive computing times and therefore are not applicable to current datasets. In 2019, Cunha et al. (Proceedings of BSB 2019) suggested the maximal perfect haplotype block as a very simple combinatorial pattern, forming the basis of a new method to perform rapid genome-wide selection scans. The algorithm they presented for identifying these blocks, however, had a worst-case running time quadratic in the genome length. It was posed as an open problem whether an optimal, linear-time algorithm exists. In this paper we give two algorithms that achieve this time bound, one conceptually very simple one using suffix trees and a second one using the positional Burrows-Wheeler Transform, that is very efficient also in practice.

BACKGROUND: The genomic similarity is a large-scale measure for comparing two given genomes. In this work we study the (NP-hard) problem of computing the genomic similarity under the DCJ model in a setting that does not assume that the genes of the compared genomes are grouped into gene families. This problem is called family-free DCJ similarity. RESULTS: We propose an exact ILP algorithm to solve the family-free DCJ similarity problem, then we show its APX-hardness and present four combinatorial heuristics with computational experiments comparing their results to the ILP. CONCLUSIONS: We show that the family-free DCJ similarity can be computed in reasonable time, although for larger genomes it is necessary to resort to heuristics. This provides a basis for further studies on the applicability and model refinement of family-free whole genome similarity measures.

Ancestral genome reconstruction is an important task to analyze the evolution of genomes. Recent progress in sequencing ancient DNA led to the publication of so-called paleogenomes and allows the integration of this sequencing data in genome evolution analysis. However, the de novo assembly of ancient genomes is usually fragmented due to DNA degradation over time among others. Integrated phylogenetic assembly addresses the issue of genome fragmentation in the ancient DNA assembly while aiming to improve the reconstruction of all ancient genomes in the phylogeny simultaneously. The fragmented assembly of the ancient genome can be represented as an assembly graph, indicating contradicting ordering information of contigs. In this setting, our approach is to compare the ancient data with extant finished genomes. We generalize a reconstruction approach minimizing the Single-Cut-or-Join rearrangement distance towards multifurcating trees and include edge lengths to improve the reconstruction in practice. This results in a polynomial time algorithm that includes additional ancient DNA data at one node in the tree, resulting in consistent reconstructions of ancestral genomes.

Important papers have appeared recently on the problem of indexing binary strings for jumbled pattern matching, and further lowering the time bounds in terms of the input size would now be a breakthrough with broad implications. We can still make progress on the problem, however, by considering other natural parameters. Badkobeh et al. (IPL, 2013) and Amir et al. (TCS, 2016) gave algorithms that index a binary string in O(n + r^2 log r) time, where n is the length and r is the number of runs, and Giaquinta and Grabowski (IPL, 2013) gave one that runs in O(n + r^2) time. In this paper we propose a new and very simple algorithm that also runs in O(n + r^2) time and can be extended either so that the index returns the position of a match (if there is one), or so that the algorithm uses only O(n) bits of space instead of O(n) words.

Rearrangements are mutations that can change the organization of a genome, but not its content. Examples are inversions of DNA segments, translocations of chromosome ends, fusions and fissions of chromosomes. All mentioned rearrangements can be represented by the generic Double Cut and Join (DCJ) operation. However, the DCJ operation also allows circular chromosomes to be created at intermediate steps, even if the compared genomes are linear. In this case it is more plausible to consider a restriction in which the reincorporation of a circular chromosome has to be done immediately after its creation. We call these two consecutive operations an ER composition. It has been shown that an ER composition mimics either an internal block interchange (when two segments in the same chromosome exchange their positions), or an internal transposition (the special case of a block interchange when the two segments are adjacent). The DCJ distance of two genomes is the same, regardless of this restriction, and can be computed in linear time. For comparing two genomes with unequal contents, in addition to rearrangements we have to allow insertions and deletions of DNA segments-named indels. It is already known that the distance in the model combining DCJ and indel operations can be exactly computed. Again, for linear genomes it would be more plausible to adopt a restricted version with ER compositions. This model was studied recently by da Silva et al. (BMC Bioinformatics 13, Suppl. 19, S14, 2012), but only an upper bound for the restricted DCJ-indel distance was provided. Here we first solve an open problem posed in that paper and present a very simple proof showing that the distance, which can be computed in linear time, is the same for both the unrestricted and the restricted DCJ-indel models. We then give a simpler algorithm for computing an optimal restricted DCJ-indel sorting scenario in O(n log n) time. We also relate the DCJ-indel distance to the restricted DCJ-substitution distance, which instead of indels considers a more powerful operation that allows the substitution of a DNA segment by another DNA segment. We show that the DCJ-indel distance is a 2-approximation for the restricted DCJ-substitution distance.

MOTIVATION: Fast algorithms and well-arranged visualizations are required for the comprehensive analysis of the ever-growing size of genomic and transcriptomic next-generation sequencing data. RESULTS: ReadXplorer is a software offering straightforward visualization and extensive analysis functions for genomic and transcriptomic DNA sequences mapped on a reference. A unique specialty of ReadXplorer is the quality classification of the read mappings. It is incorporated in all analysis functions and displayed in ReadXplorer's various synchronized data viewers for (i) the reference sequence, its base coverage as (ii) normalizable plot and (iii) histogram, (iv) read alignments and (v) read pairs. ReadXplorer's analysis capability covers RNA secondary structure prediction, single nucleotide polymorphism and deletion-insertion polymorphism detection, genomic feature and general coverage analysis. Especially for RNA-Seq data, it offers differential gene expression analysis, transcription start site and operon detection as well as RPKM value and read count calculations. Furthermore, ReadXplorer can combine or superimpose coverage of different datasets. AVAILABILITY AND IMPLEMENTATION: ReadXplorer is available as open-source software at http://www.readxplorer.org along with a detailed manual.

MOTIVATION: Comprehensive 2D gas chromatography-mass spectrometry is an established method for the analysis of complex mixtures in analytical chemistry and metabolomics. It produces large amounts of data that require semiautomatic, but preferably automatic handling. This involves the location of significant signals (peaks) and their matching and alignment across different measurements. To date, there exist only a few openly available algorithms for the retention time alignment of peaks originating from such experiments that scale well with increasing sample and peak numbers, while providing reliable alignment results. RESULTS: We describe BiPACE 2D, an automated algorithm for retention time alignment of peaks from 2D gas chromatography-mass spectrometry experiments and evaluate it on three previously published datasets against the mSPA, SWPA and Guineu algorithms. We also provide a fourth dataset from an experiment studying the H2 production of two different strains of Chlamydomonas reinhardtii that is available from the MetaboLights database together with the experimental protocol, peak-detection results and manually curated multiple peak alignment for future comparability with newly developed algorithms. AVAILABILITY AND IMPLEMENTATION: BiPACE 2D is contained in the freely available Maltcms framework, version 1.3, hosted at http://maltcms.sf.net, under the terms of the L-GPL v3 or Eclipse Open Source licenses. The software used for the evaluation along with the underlying datasets is available at the same location. The C.reinhardtii dataset is freely available at http://www.ebi.ac.uk/metabolights/MTBLS37.

Environmental shotgun sequencing (ESS) has potential to give greater insight into microbial communities than targeted sequencing of 16S regions, but requires much higher sequence coverage. The advent of next-generation sequencing has made it feasible for the Human Microbiome Project and other initiatives to generate ESS data on a large scale, but computationally efficient methods for analysing such data sets are needed.Here we present metaBEETL, a fast taxonomic classifier for environmental shotgun sequences. It uses a Burrows-Wheeler Transform (BWT) index of the sequencing reads and an indexed database of microbial reference sequences. Unlike other BWT-based tools, our method has no upper limit on the number or the total size of the reference sequences in its database. By capturing sequence relationships between strains, our reference index also allows us to classify reads which are not unique to an individual strain but are nevertheless specific to some higher phylogenetic order.Tested on datasets with known taxonomic composition, metaBEETL gave results that are competitive with existing similarity-based tools: due to normalization steps which other classifiers lack, the taxonomic profile computed by metaBEETL closely matched the true environmental profile. At the same time, its moderate running time and low memory footprint allow metaBEETL to scale well to large data sets.Code to construct the BWT indexed database and for the taxonomic classification is part of the BEETL library, available as a github repository at [email protected]:BEETL/BEETL.git.

BACKGROUND: Genes occurring co-localized in multiple genomes can be strong indicators for either functional constraints on the genome organization or remnant ancestral gene order. The computational detection of these patterns, which are usually referred to as gene clusters, has become increasingly sensitive over the past decade. The most powerful approaches allow for various types of imperfect cluster conservation: Cluster locations may be internally rearranged. The individual cluster locations may contain only a subset of the cluster genes and may be disrupted by uninvolved genes. Moreover cluster locations may not at all occur in some or even most of the studied genomes. The detection of such low quality clusters increases the risk of mistaking faint patterns that occur merely by chance for genuine findings. Therefore, it is crucial to estimate the significance of computational gene cluster predictions and discriminate between true conservation and coincidental clustering. RESULTS: In this paper, we present an efficient and accurate approach to estimate the significance of gene cluster predictions under the approximate common intervals model. Given a single gene cluster prediction, we calculate the probability to observe it with the same or a higher degree of conservation under the null hypothesis of random gene order, and add a correction factor to account for multiple testing. Our approach considers all parameters that define the quality of gene cluster conservation: the number of genomes in which the cluster occurs, the number of involved genes, the degree of conservation in the different genomes, as well as the frequency of the clustered genes within each genome. We apply our approach to evaluate gene cluster predictions in a large set of well annotated genomes.

BACKGROUND: The inversion distance, that is the distance between two unichromosomal genomes with the same content allowing only inversions of DNA segments, can be computed thanks to a pioneering approach of Hannenhalli and Pevzner in 1995. In 2000, El-Mabrouk extended the inversion model to allow the comparison of unichromosomal genomes with unequal contents, thus insertions and deletions of DNA segments besides inversions. However, an exact algorithm was presented only for the case in which we have insertions alone and no deletion (or vice versa), while a heuristic was provided for the symmetric case, that allows both insertions and deletions and is called the inversion-indel distance. In 2005, Yancopoulos, Attie and Friedberg started a new branch of research by introducing the generic double cut and join (DCJ) operation, that can represent several genome rearrangements (including inversions). Among others, the DCJ model gave rise to two important results. First, it has been shown that the inversion distance can be computed in a simpler way with the help of the DCJ operation. Second, the DCJ operation originated the DCJ-indel distance, that allows the comparison of genomes with unequal contents, considering DCJ, insertions and deletions, and can be computed in linear time. RESULTS: In the present work we put these two results together to solve an open problem, showing that, when the graph that represents the relation between the two compared genomes has no bad components, the inversion-indel distance is equal to the DCJ-indel distance. We also give a lower and an upper bound for the inversion-indel distance in the presence of bad components.

SUMMARY: UniMoG is a software combining five genome rearrangement models: double cut and join (DCJ), restricted DCJ, Hannenhalli and Pevzner (HP), inversion and translocation. It can compute the pairwise genomic distances and a corresponding optimal sorting scenario for an arbitrary number of genomes. All five models can be unified through the DCJ model, thus the implementation is based on DCJ and, where reasonable, uses the most efficient existing algorithms for each distance and sorting problem. Both textual and graphical output is possible for visualizing the operations. AVAILABILITY AND IMPLEMENTATION: The software is available through the Bielefeld University Bioinformatics Web Server at http://bibiserv.techfak.uni-bielefeld.de/dcj with instructions and example data. CONTACT: [email protected].

BACKGROUND: The comparison of relative gene orders between two genomes offers deep insights into functional correlations of genes and the evolutionary relationships between the corresponding organisms. Methods for gene order analyses often require prior knowledge of homologies between all genes of the genomic dataset. Since such information is hard to obtain, it is common to predict homologous groups based on sequence similarity. These hypothetical groups of homologous genes are called gene families. RESULTS: This manuscript promotes a new branch of gene order studies in which prior assignment of gene families is not required. As a case study, we present a new similarity measure between pairs of genomes that is related to the breakpoint distance. We propose an exact and a heuristic algorithm for its computation. We evaluate our methods on a dataset comprising 12 γ-proteobacteria from the literature. CONCLUSIONS: In evaluating our algorithms, we show that the exact algorithm is suitable for computations on small genomes. Moreover, the results of our heuristic are close to those of the exact algorithm. In general, we demonstrate that gene order studies can be improved by direct, gene family assignment-free comparisons.

BACKGROUND: Modern analytical methods in biology and chemistry use separation techniques coupled to sensitive detectors, such as gas chromatography-mass spectrometry (GC-MS) and liquid chromatography-mass spectrometry (LC-MS). These hyphenated methods provide high-dimensional data. Comparing such data manually to find corresponding signals is a laborious task, as each experiment usually consists of thousands of individual scans, each containing hundreds or even thousands of distinct signals. In order to allow for successful identification of metabolites or proteins within such data, especially in the context of metabolomics and proteomics, an accurate alignment and matching of corresponding features between two or more experiments is required. Such a matching algorithm should capture fluctuations in the chromatographic system which lead to non-linear distortions on the time axis, as well as systematic changes in recorded intensities. Many different algorithms for the retention time alignment of GC-MS and LC-MS data have been proposed and published, but all of them focus either on aligning previously extracted peak features or on aligning and comparing the complete raw data containing all available features. RESULTS: In this paper we introduce two algorithms for retention time alignment of multiple GC-MS datasets: multiple alignment by bidirectional best hits peak assignment and cluster extension (BIPACE) and center-star multiple alignment by pairwise partitioned dynamic time warping (CeMAPP-DTW). We show how the similarity-based peak group matching method BIPACE may be used for multiple alignment calculation individually and how it can be used as a preprocessing step for the pairwise alignments performed by CeMAPP-DTW. We evaluate the algorithms individually and in combination on a previously published small GC-MS dataset studying the Leishmania parasite and on a larger GC-MS dataset studying grains of wheat (Triticum aestivum). CONCLUSIONS: We have shown that BIPACE achieves very high precision and recall and a very low number of false positive peak assignments on both evaluation datasets. CeMAPP-DTW finds a high number of true positives when executed on its own, but achieves even better results when BIPACE is used to constrain its search space. The source code of both algorithms is included in the OpenSource software framework Maltcms, which is available from http://maltcms.sf.net. The evaluation scripts of the present study are available from the same source.

BACKGROUND: Mancheron, Uricaru and Rivals (Nucleic Acids Res. 39:e101, 2011) recently introduced a new approach in the context of multiple genome comparison that allows to detect regions of strong overlaps in a set of pairwise local alignments between several reference genomes and one target genome. Such overlap regions are an important source of information in genome annotation. RESULTS: In this paper we introduce a series of algorithms that improve over the approach of Mancheron et al., both in terms of computational complexity and in practical runtime. We also extend the problem definition such that overlaps to different reference genomes can be rated differently and regions overlapping only a subset of the reference genomes are detected.

MOTIVATION: The introduction of next-generation sequencing techniques and especially the high-throughput systems Solexa (Illumina Inc.) and SOLiD (ABI) made the mapping of short reads to reference sequences a standard application in modern bioinformatics. Short-read alignment is needed for reference based re-sequencing of complete genomes as well as for gene expression analysis based on transcriptome sequencing. Several approaches were developed during the last years allowing for a fast alignment of short sequences to a given template. Methods available to date use heuristic techniques to gain a speedup of the alignments, thereby missing possible alignment positions. Furthermore, most approaches return only one best hit for every query sequence, thus losing the potentially valuable information of alternative alignment positions with identical scores. RESULTS: We developed SARUMAN (Semiglobal Alignment of short Reads Using CUDA and NeedleMAN-Wunsch), a mapping approach that returns all possible alignment positions of a read in a reference sequence under a given error threshold, together with one optimal alignment for each of these positions. Alignments are computed in parallel on graphics hardware, facilitating an considerable speedup of this normally time-consuming step. Combining our filter algorithm with CUDA-accelerated alignments, we were able to align reads to microbial genomes in time comparable or even faster than all published approaches, while still providing an exact, complete and optimal result. At the same time, SARUMAN runs on every standard Linux PC with a CUDA-compatible graphics accelerator. AVAILABILITY: http://www.cebitec.uni-bielefeld.de/brf/saruman/saruman.html.

BACKGROUND: The distance between two genomes is often computed by comparing only the common markers between them. Some approaches are also able to deal with non-common markers, allowing the insertion or the deletion of such markers. In these models, a deletion and a subsequent insertion that occur at the same position of the genome count for two sorting steps. RESULTS: Here we propose a new model that sorts non-common markers with substitutions, which are more powerful operations that comprehend insertions and deletions. A deletion and an insertion that occur at the same position of the genome can be modeled as a substitution, counting for a single sorting step. CONCLUSIONS: Comparing genomes with unequal content, but without duplicated markers, we give a linear time algorithm to compute the genomic distance considering substitutions and double-cut-and-join (DCJ) operations. This model provides a parsimonious genomic distance to handle genomes free of duplicated markers, that is in practice a lower bound to the real genomic distances. The method could also be used to refine orthology assignments, since in some cases a substitution could actually correspond to an unannotated orthology.

BACKGROUND: Classical approaches to compute the genomic distance are usually limited to genomes with the same content, without duplicated markers. However, differences in the gene content are frequently observed and can reflect important evolutionary aspects. A few polynomial time algorithms that include genome rearrangements, insertions and deletions (or substitutions) were already proposed. These methods often allow a block of contiguous markers to be inserted, deleted or substituted at once but result in distance functions that do not respect the triangular inequality and hence do not constitute metrics. RESULTS: In the present study we discuss the disruption of the triangular inequality in some of the available methods and give a framework to establish an efficient correction for two models recently proposed, one that includes insertions, deletions and double cut and join (DCJ) operations, and one that includes substitutions and DCJ operations. CONCLUSIONS: We show that the proposed framework establishes the triangular inequality in both distances, by summing a surcharge on indel operations and on substitutions that depends only on the number of markers affected by these operations. This correction can be applied a posteriori, without interfering with the already available formulas to compute these distances. We claim that this correction leads to distances that are biologically more plausible.

BACKGROUND: The center string (or closest string) problem is a classic computer science problem with important applications in computational biology. Given k input strings and a distance threshold d, we search for a string within Hamming distance at most d to each input string. This problem is NP complete. RESULTS: In this paper, we focus on exact methods for the problem that are also swift in application. We first introduce data reduction techniques that allow us to infer that certain instances have no solution, or that a center string must satisfy certain conditions. We describe how to use this information to speed up two previously published search tree algorithms. Then, we describe a novel iterative search strategy that is efficient in practice, where some of our reduction techniques can also be applied. Finally, we present results of an evaluation study for two different data sets from a biological application. CONCLUSIONS: We find that the running time for computing the optimal center string is dominated by the subroutine calls for d = dopt -1 and d = dopt. Our data reduction is very effective for both, either rejecting unsolvable instances or solving trivial positions. We find that this speeds up computations considerably.

SUMMARY: Recent parallel pyrosequencing methods and the increasing number of finished genomes encourage the sequencing and investigation of closely related strains. Although the sequencing itself becomes easier and cheaper with each machine generation, the finishing of the genomes remains difficult. Instead of the desired whole genomic sequence, a set of contigs is the result of the assembly. In this applications note, we present the tool r2cat (related reference contig arrangement tool) that helps in the task of comparative assembly and also provides an interactive visualization for synteny inspection.

High-throughput sequencing (HTS) technologies are revolutionizing the way biologists acquire and analyze genomic data. HTS instruments, such as the Illumina Genomic Analyzer and the Applied Biosystems SOLiD System, are currently able to sequence tens of gigabases per week, at a cost of 200-fold less than previous methods, potentially enabling the routine sequencing of human and other genomes. Over the last few years the promise of HTS technologies has become a reality, however, realizing that the full promise of these technologies requires the development of computational methods that can analyze the resulting datasets to infer biological meaning. HTS can be used to study many biological problems, including assembling genomes of new organisms, identifying genome variation within a population, discovering novel transcripts, analyzing gene expression, discerning the regulatory mechanisms behind the expression levels and profiling the metagenome of a community. While many HTS datasets are readily available, the main bottleneck in the analysis is the dearth of computational methods that are able to directly answer biologists' questions from these datasets. The Special Interest Group on Short Read Sequencing and Algorithms (Short-SIG), held in conjunction with the Intelligent Systems in Molecular Biology (ISMB) conference, is a meeting that brings together computational biologists interested in analyzing these HTS datasets. The first Short-SIG, held in Toronto in 2008, brought together over 120 attendees, and featured 18 podium presentations, with many of them addressing the computational problems of read mapping—the alignment of reads to a larger reference genome—and assembly—the de novo generation of the genome of an organism from short read data. During the year that followed, significant progress has been made in these fields, and the topic of the 2009 meeting, held in Stockholm on June 28, concentrated on the development of methods that can analyze the resulting read mappings and assemblies to infer biological meaning. The meeting brought together over 200 researchers, and featured 17 platform presentations selected from 27 abstracts and 17 full paper submissions. The keynote address at the SIG was delivered by Dr Edwin Cuppen of the Hubrecht Laboratory (Utrecht, The Netherlands). The paper submissions were handled in coordination with the Bioinformatics journal, and a physical copy of the Bioinformatics ‘virtual issue’ on HTS, featuring papers published on this topic in Bioinformatics over the past year, was presented to all meeting attendees. Bioinformatics also sponsored a best paper award for the conference, given to Kai Ye and his co-authors for the paper ‘Pindel: a pattern growth approach to detect break points of large deletions and medium sized insertions from paired-end short reads’, as well as an award for a paper chosen from the ‘virtual issue’, that was given to Cole Trapnell and colleagues for ‘TopHat: discovering splice junctions with RNA-Seq’. One of the most prominent applications of HTS is the resequencing of human genomes. Genomic variants are discovered by mapping reads from a donor genome to a reference human genome (typically the NCBI assembly), and the resulting mappings are then analyzed to identify differences between the donor and the reference. The SIG saw eight presentations on variation identification, including variants of all sizes—from SNPs to larger, structural variants. From the SNP discovery perspective, Adrian Dalca presented VARiD, a generalized framework for calling SNPs from both regular (letter-space) reads and di-base encoded (color-space) data. Sohrab Shah presented SNVmix, a Bayesian mixture model-based method for discovering single nucleotide variants from somatic tissues, where the observed alleles and their ratios may vary due to adjacent tissues being present in a biopsy. There were also presentations on variation discovery methods from the two leading HTS technology manufacturers, Illumina and Life Technologies (Applied Biosystems). Dirk Evers of Illumina spoke of recent improvements to the CASAVA framework that allows for more accurate discovery of variants from long reads, especially indel and copy number variants. He presented the results of CASAVA on recently sequenced paired tumor/normal genomes from a melanoma cell line. Fiona C. L. Hyland, from Life Technologies, described diBayes, a Bayesian framework for SNP discovery from color-space data, and presented an extensive analysis of a SOLiD human dataset, including discovered SNPs, small indels and larger structural variants. The advent of high-throughput sequencing has for the first time allowed large, cost-effective studies to detect larger, structural variants. Such variation has been associated with numerous diseases, including autism, schizophrenia and cancer, making their discovery an important challenge for computational biologists. Several talks at the SIG focused on the development of novel methods for discovery of such variants. Kai Ye presented a method called Pindel, which, by anchoring the mates of nonmapping reads to a genomic location, was able to use split-mapping to detect deletion events as large as 10 kb with base-level precision (Ye et al., 2009). This paper was the winner of the best SIG paper award, sponsored by Bioinformatics. Seunghak Lee and Weldon Whitener showed how to detect smaller indels from pair-end data by using the distribution of insert sizes of all matepairs that span each genomic location. Paul Medvedev described a way that the depth-of-coverage signal can be combined with pair-end mapping-based techniques to detect copy number variants within segmental duplications. Overall, this year has seen the detection of structural variation come to the forefront of algorithmic research, and the next year will hopefully bring about more fully developed biologist-friendly tools. Another exciting application of HTS technologies is RNA sequencing. RNA sequencing is currently used for several applications, including RNA expression, de novo transcriptome sequencing for nonmodel organisms and novel transcript discovery; however, computational methods for the analysis of this data are in their infancy. For RNA and microRNA expression profiling, HTS has significant advantages compared with microarray methods in that it is better able to identify quantities of very common and very rare transcripts. Short-SIG featured five talks addressing various computational problems in RNA sequencing. Cole Trapnell presented his work on BowTie (Trapnell et al., 2009), a tool to map reads from RNA sequencing to a reference genome, while allowing for split-reads where the two ends of a read map in different locations (due to exon splicing). While the original paper was published as part of the ‘virtual issue’, the presentation included new improvements to the tool. Jan Prins presented MapSplice, a RNA mapping tool that is similar to TopHat, but includes the ability to consider noncanonical splice sites. Inanc Birol presented a version of the ABySS assembler for de novo mRNA assembly. ABySS was the first tool to attempt de novo assembly of the human genome, and in their presentation they presented the first results on de novo assembly of human transcriptome data. Finally, three presentations demonstrated methods to mine RNA-seq data for specific biomedical phenomena: Regina Bohnert presented an algorithm for identifying alternative transcripts and their expression levels, Chol-Hee Jung presented an analysis of combining multiple Drosophila RNA-seq datasets in order to discover novel noncoding RNAs, and Gerald Quon showed that using the ISOLATE framework (Quon and Morris, 2009), mRNA expression levels can be used to identify the tissue of origin in metastasized tumors. The final session of the SIG was devoted to a variety of classical and newly upcoming HTS applications. Bas Dutilh presented a method for mapping metagenomic reads to a reference genome, where the reference is changed during the mapping process to more accurately represent the community consensus genome, thus allowing a larger fraction of reads to map (Dutilh et al., 2009). Juliane Klein presented LOCAS, an assembler for short read data that is targeted toward low-coverage datasets, and significantly outperforms previous methods in this context. The last two presentations addressed the statistical issues underlying HTS. Su Yeon Kim described statistical foundation of designing association studies with HTS, specifically the use of a combination of pooled and unpooled samples from a number of individuals to design association studies. Adam Kowalczyk showed that it is possible to develop univariate statistical tests to compute the likelihood that two distributions of short read datasets are identical (P-values) based on the Poisson approximation to the binomial distribution. The SIG ended with a keynote address by Dr Edwin Cuppen of the Hubrecht Laboratory, in Utrecht, The Netherlands. His presentation demonstrated both some interesting advantage of short read sequencing, such as the ability of CHiP-seq experiments to identify which genes are regulated by specific distal enhancers, and some key limitations, for example, that RNA-seq, while capable of profiling relative transcript levels in different conditions, is unable to reconstruct actual transcript levels due to biases introduced during sample preparation. In addition to the podium presentations, many Short-SIG attendees used the opportunity to discuss collaborations and the general direction of the field. Clearly, the increase in read length (only 25–35 bp 2 years ago and 50–100 bp today) is making it difficult to develop timely tools, as the problems associated with different length reads are quite dissimilar. Illumina and SOLiD reads will very soon be as long as 454 reads were a few years ago, and this dynamics is forcing bioinformaticians to rethink algorithms developed only a year ago. Similarly, the increasing throughput of the sequencing platforms is requiring the scaling of the algorithms to larger datasets. Bioinformatics remains one of the key bottlenecks in HTS data analysis, with datasets created at a faster rate than can be effectively analyzed, and few tools providing ‘one stop shopping’ for the complete analysis of a single dataset. Addressing these shortcomings is a key step to realizing the full promise of HTS technologies. Conflict of Interest: none declared.

SUMMARY: We describe ChromA, a web-based alignment tool for chromatography-mass spectrometry data from the metabolomics and proteomics domains. Users can supply their data in open and standardized file formats for retention time alignment using dynamic time warping with different configurable local distance and similarity functions. Additionally, user-defined anchors can be used to constrain and speedup the alignment. A neighborhood around each anchor can be added to increase the flexibility of the constrained alignment. ChromA offers different visualizations of the alignment for easier qualitative interpretation and comparison of the data. For the multiple alignment of more than two data files, the center-star approximation is applied to select a reference among input files to align to. AVAILABILITY: ChromA is available at http://bibiserv.techfak.uni-bielefeld.de/chroma. Executables and source code under the L-GPL v3 license are provided for download at the same location.

BACKGROUND: Metagenomics is a new field of research on natural microbial communities. High-throughput sequencing techniques like 454 or Solexa-Illumina promise new possibilities as they are able to produce huge amounts of data in much shorter time and with less efforts and costs than the traditional Sanger technique. But the data produced comes in even shorter reads (35-100 basepairs with Illumina, 100-500 basepairs with 454-sequencing). CARMA is a new software pipeline for the characterisation of species composition and the genetic potential of microbial samples using short, unassembled reads. RESULTS: In this paper, we introduce WebCARMA, a refined version of CARMA available as a web application for the taxonomic and functional classification of unassembled (ultra-)short reads from metagenomic communities. In addition, we have analysed the applicability of ultra-short reads in metagenomics. CONCLUSIONS: We show that unassembled reads as short as 35 bp can be used for the taxonomic classification of a metagenome. The web application is freely available at http://webcarma.cebitec.uni-bielefeld.de.

The order of genes in genomes provides extensive information. In comparative genomics, differences or similarities of gene orders are determined to predict functional relations of genes or phylogenetic relations of genomes. For this purpose, various combinatorial models can be used to identify gene clusters--groups of genes that are colocated in a set of genomes. We introduce a unified approach to model gene clusters and define the problem of labeling the inner nodes of a given phylogenetic tree with sets of gene clusters. Our optimization criterion in this context combines two properties: parsimony, i.e., the number of gains and losses of gene clusters has to be minimal, and consistency, i.e., for each ancestral node, there must exist at least one potential gene order that contains all the reconstructed clusters. We present and evaluate an exact algorithm to solve this problem. Despite its exponential worst-case time complexity, our method is suitable even for large-scale data. We show the effectiveness and efficiency on both simulated and real data.

MOTIVATION: The recent advances in metabolomics have created the potential to measure the levels of hundreds of metabolites which are the end products of cellular regulatory processes. The automation of the sample acquisition and subsequent analysis in high-throughput instruments that are capable of measuring metabolites is posing a challenge on the necessary systematic storage and computational processing of the experimental datasets. Whereas a multitude of specialized software systems for individual instruments and preprocessing methods exists, there is clearly a need for a free and platform-independent system that allows the standardized and integrated storage and analysis of data obtained from metabolomics experiments. Currently there exists no such system that on the one hand supports preprocessing of raw datasets but also allows to visualize and integrate the results of higher level statistical analyses within a functional genomics context. RESULTS: To facilitate the systematic storage, analysis and integration of metabolomics experiments, we have implemented MeltDB, a web-based software platform for the analysis and annotation of datasets from metabolomics experiments. MeltDB supports open file formats (netCDF, mzXML, mzDATA) and facilitates the integration and evaluation of existing preprocessing methods. The system provides researchers with means to consistently describe and store their experimental datasets. Comprehensive analysis and visualization features of metabolomics datasets are offered to the community through a web-based user interface. The system covers the process from raw data to the visualization of results in a knowledge-based background and is integrated into the context of existing software platforms of genomics and transcriptomics at Bielefeld University. We demonstrate the potential of MeltDB by means of a sample experiment where we dissect the influence of three different carbon sources on the gram-negative bacterium Xanthomonas campestris pv. campestris on the level of measured metabolites. Experimental data are stored, analyzed and annotated within MeltDB and accessible via the public MeltDB web server. AVAILABILITY: The system is publicly available at http://meltdb.cebitec.uni-bielefeld.de.

Abstract The suffix array of a string is a permutation of all starting positions of the string's suffixes that are lexicographically sorted. We present a practical algorithm for suffix array construction that consists of two easy‐to‐implement components. First it sorts the suffixes with respect to a fixed length prefix; then it refines each bucket of suffixes sharing the same prefix using the order of already sorted suffixes. Other suffix array construction algorithms follow more complex strategies. Moreover, we achieve a very fast construction for common strings as well as for worst case strings by enhancing our algorithm with further techniques. Copyright © 2006 John Wiley & Sons, Ltd.

MOTIVATION: The first version of the graphical multiple sequence alignment environment QAlign was published in 2003. Heavy response from the molecular-biological user community clearly demonstrated the need for such a platform. RESULTS: Panta rhei extends QAlign by several features. Major redesigns on the user interface, for instance, allow users to flexibily compose views for multiple projects. The new sequence viewer handles datasets with arbitrarily many and arbitrarily large sequences that may still be edited by guided block moving. More distance-based algorithms are available to interactively reconstruct phylogenetic trees which can now also be zoomed and navigated graphicaly. AVAILABILITY: Executables and the JAVA source code are available under the Apache license at http://gi.cebitec.uni-bielefeld.de/qalign CONTACT: [email protected].

Traditional sequence comparison by alignment employs a mutation model comprised of two events, substitutions and indels (insertions or deletions) of single positions. However, modern genetic analysis knows a variety of more complex mutation events (e.g., duplications, excisions, and rearrangements), especially regarding DNA. With ever more DNA sequence data becoming available, the need to accurately compare sequences which have clearly undergone more complicated types of mutational processes is becoming critical. Herein we introduce a new method for pairwise alignment and comparison of sequences with respect to the special evolution of tandem repeats: substitutions and indels of single positions and, additionally, duplications and excisions of variable degree (i.e., of one or more repeat copies simultaneously) are taken into account. To evaluate our method, we apply it to the spa VNTR (variable number of tandem repeats) cluster of Staphylococcus aureus, a bacterium of high medical importance.

SUMMARY: We provide the graphical tool BACCardI for the construction of virtual clone maps from standard assembler output files or BLAST based sequence comparisons. This new tool has been applied to numerous genome projects to solve various problems including (a) validation of whole genome shotgun assemblies, (b) support for contig ordering in the finishing phase of a genome project, and (c) intergenome comparison between related strains when only one of the strains has been sequenced and a large insert library is available for the other. The BACCardI software can seamlessly interact with various sequence assembly packages. MOTIVATION: Genomic assemblies generated from sequence information need to be validated by independent methods such as physical maps. The time-consuming task of building physical maps can be circumvented by virtual clone maps derived from read pair information of large insert libraries.

BACKGROUND: Searching a biological sequence database with a query sequence looking for homologues has become a routine operation in computational biology. In spite of the high degree of sophistication of currently available search routines it is still virtually impossible to identify quickly and clearly a group of sequences that a given query sequence belongs to. RESULTS: We report on our developments in grouping all known protein sequences hierarchically into superfamily and family clusters. Our graph-based algorithms take into account the topology of the sequence space induced by the data itself to construct a biologically meaningful partitioning. We have applied our clustering procedures to a non-redundant set of about 1,000,000 sequences resulting in a hierarchical clustering which is being made available for querying and browsing at http://systers.molgen.mpg.de/. CONCLUSIONS: Comparisons with other widely used clustering methods on various data sets show the abilities and strengths of our clustering methods in producing a biologically meaningful grouping of protein sequences.

BACKGROUND: Numerous tools have been developed to align genomic sequences. However, their relative performance in specific applications remains poorly characterized. Alignments of protein-coding sequences typically have been benchmarked against "correct" alignments inferred from structural data. For noncoding sequences, where such independent validation is lacking, simulation provides an effective means to generate "correct" alignments with which to benchmark alignment tools. RESULTS: Using rates of noncoding sequence evolution estimated from the genus Drosophila, we simulated alignments over a range of divergence times under varying models incorporating point substitution, insertion/deletion events, and short blocks of constrained sequences such as those found in cis-regulatory regions. We then compared "correct" alignments generated by a modified version of the ROSE simulation platform to alignments of the simulated derived sequences produced by eight pairwise alignment tools (Avid, BlastZ, Chaos, ClustalW, DiAlign, Lagan, Needle, and WABA) to determine the off-the-shelf performance of each tool. As expected, the ability to align noncoding sequences accurately decreases with increasing divergence for all tools, and declines faster in the presence of insertion/deletion evolution. Global alignment tools (Avid, ClustalW, Lagan, and Needle) typically have higher sensitivity over entire noncoding sequences as well as in constrained sequences. Local tools (BlastZ, Chaos, and WABA) have lower overall sensitivity as a consequence of incomplete coverage, but have high specificity to detect constrained sequences as well as high sensitivity within the subset of sequences they align. Tools such as DiAlign, which generate both local and global outputs, produce alignments of constrained sequences with both high sensitivity and specificity for divergence distances in the range of 1.25-3.0 substitutions per site. CONCLUSION: For species with genomic properties similar to Drosophila, we conclude that a single pair of optimally diverged species analyzed with a high performance alignment tool can yield accurate and specific alignments of functionally constrained noncoding sequences. Further algorithm development, optimization of alignment parameters, and benchmarking studies will be necessary to extract the maximal biological information from alignments of functional noncoding DNA.

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.

Abstract We present an efficient implementation of a write‐only top‐down construction for suffix trees. Our implementation is based on a new, space‐efficient representation of suffix trees that requires only 12 bytes per input character in the worst case, and 8.5 bytes per input character on average for a collection of files of different type. We show how to efficiently implement the lazy evaluation of suffix trees such that a subtree is evaluated only when it is traversed for the first time. Our experiments show that for the problem of searching many exact patterns in a fixed input string, the lazy top‐down construction is often faster and more space efficient than other methods. Copyright © 2003 John Wiley & Sons, Ltd.

In physical mapping, one orders a set of genetic landmarks or a library of cloned fragments of DNA according to their position in the genome. Our approach to physical mapping divides the problem into smaller and easier subproblems by partitioning the probe set into independent parts (probe contigs). For this purpose we introduce a new distance function between probes, the averaged rank distance (ARD) derived from bootstrap resampling of the raw data. The ARD measures the pairwise distances of probes within a contig and smoothes the distances of probes across different contigs. It shows distinct jumps at contig borders. This makes it appropriate for contig selection by clustering. We have designed a physical mapping algorithm that makes use of these observations and seems to be particularly well suited to the delineation of reliable contigs. We evaluated our method on data sets from two physical mapping projects. On data from the recently sequenced bacterium Xylella fastidiosa, the probe contig set produced by the new method was evaluated using the probe order derived from the sequence information. Our approach yielded a basically correct contig set. On this data we also compared our method to an approach which uses the number of supporting clones to determine contigs. Our map is much more accurate. In comparison to a physical map of Pasteurella haemolytica that was computed using simulated annealing, the newly computed map is considerably cleaner. The results of our method have already proven helpful for the design of experiments aimed at further improving the quality of a map.

Abstract Motivation: Multiple sequence alignment is an important tool in computational biology. In order to solve the task of computing multiple alignments in affordable time, the most commonly used multiple alignment methods have to use heuristics. Nevertheless, the computation of optimal multiple alignments is important in its own right, and it provides a means of evaluating heuristic approaches or serves as a subprocedure of heuristic alignment methods. Results: We present an algorithm that uses the divide-and-conquer alignment approach together with recent results on search space reduction to speed up the computation of multiple sequence alignments. The method is adaptive in that depending on the time one wants to spend on the alignment, a better, up to optimal alignment can be obtained. To speed up the computation in the optimal alignment step, we apply the \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(\mathcal{A}^{*}\) \end{document}algorithm which leads to a procedure provably more efficient than previous exact algorithms. We also describe our implementation of the algorithm and present results showing the effectiveness and limitations of the procedure. Availability: http://bibiserv.techfak.uni-bielefeld.de/oma/ Contact: [email protected] To whom correspondence should be addressed. **** Present address: mediaWays GmbH, Hülshorstweg 30, 33415 Verl, Germany.

A pair in a string is the occurrence of the same substring twice. A pair is maximal if the two occurrences of the substring cannot be extended to the left and right without making them different. The gap of a pair is the number of characters between the two occurrences of the substring. In this paper we present methods for finding all maximal pairs under various constraints on the gap. In a string of length n we can find all maximal pairs with gap in an upper and lower bounded interval in time O(n log n + z) where z is the number of reported pairs. If the upper bound is removed the time reduces to O(n+z). Since a tandem repeat is a pair where the gap is zero, our methods can be seen as a generalization of finding tandem repeats. The running time of our methods equals the running time of well known methods for finding tandem repeats.

MOTIVATION: We present a new probabilistic model of the evolution of RNA-, DNA-, or protein-like sequences and a software tool, Rose, that implements this model. Guided by an evolutionary tree, a family of related sequences is created from a common ancestor sequence by insertion, deletion and substitution of characters. During this artificial evolutionary process, the 'true' history is logged and the 'correct' multiple sequence alignment is created simultaneously. The model also allows for varying rates of mutation within the sequences, making it possible to establish so-called sequence motifs. RESULTS: The data created by Rose are suitable for the evaluation of methods in multiple sequence alignment computation and the prediction of phylogenetic relationships. It can also be useful when teaching courses in or developing models of sequence evolution and in the study of evolutionary processes. AVAILABILITY: Rose is available on the Bielefeld Bioinformatics WebServer under the following URL: http://bibiserv.TechFak.Uni-Bielefeld.DE/rose/ The source code is available upon request. CONTACT: [email protected]

MOTIVATION: DCA is a new computer program for multiple sequence alignment which utilizes a 'divide-and-conquer' type of heuristic approach. AVAILABILITY: The algorithm is freely available from http://bibiserv.TechFak.Uni-Bielefeld.DE/dca/.