Determinantal point processes (DPPs) have become prominent in data summarization and recommender system tasks for their ability to simultaneously model diversity as well as relevance. In practical applications, k-Determinantal point processes (k-DPPs) are used to yield a selection of k items from a set of size N that are the most representative of the set. In this paper, we study a special case of the diverse subset selection problem where a fixed set GO is already given as a forced recommendation and the task is to determine the remainder of the recommendation G1. The standard k-DPP optimization objectives here can suggest items that are close to optimal when considering only items in G1, but are arbitrarily close to items in G0, i.e., they might not be sufficiently diverse w.r.t. G0. We explore a semi-supervised k-DPP objective that simultaneously considers G0 and G1 and compares the difference between the two recommendations. We demonstrate our findings using multiple examples where the diverse subset selection problem with forced recommendation is important in practice.

BACKGROUND: Alignment-free methods are a popular approach for comparing biological sequences, including complete genomes. The methods range from probability distributions of sequence composition to first and higher-order Markov chains, where a k-th order Markov chain over DNA has [Formula: see text] formal parameters. To circumvent this exponential growth in parameters, variable-length Markov chains (VLMCs) have gained popularity for applications in molecular biology and other areas. VLMCs adapt the depth depending on sequence context and thus curtail excesses in the number of parameters. The scarcity of available fast, or even parallel software tools, prompted the development of a parallel implementation using lazy suffix trees and a hash-based alternative. RESULTS: An extensive evaluation was performed on genomes ranging from 12Mbp to 22Gbp. Relevant learning parameters were chosen guided by the Bayesian Information Criterion (BIC) to avoid over-fitting. Our implementation greatly improves upon the state-of-the-art even in serial execution. It exhibits very good parallel scaling with speed-ups for long sequences close to the optimum indicated by Amdahl's law of 3 for 4 threads and about 6 for 16 threads, respectively. CONCLUSIONS: Our parallel implementation released as open-source under the GPLv3 license provides a practically useful alternative to the state-of-the-art which allows the construction of VLMCs even for very large genomes significantly faster than previously possible. Additionally, our parameter selection based on BIC gives guidance to end-users comparing genomes.

Alternating Direction Method Of Multipliers (ADMM) is one of the promising frameworks for training Support Vector Machines (SVMs) on large-scale data in a distributed manner. In a consensus-based ADMM, nodes may only communicate with one-hop neighbors and this may cause slow convergence. In this paper, we investigate the impact of network topology on the convergence speed of ADMM-based SVMs using expander graphs. In particular, we investigate how much the expansion property of the network influence the convergence and which topology is preferable. Besides, we supply an implementation making these theoretical advances practically available. The results of the experiments show that graphs with large spectral gaps and higher degrees exhibit accelerated convergence.

BACKGROUND: Discovery of microRNAs (miRNAs) relies on predictive models for characteristic features from miRNA precursors (pre-miRNAs). The short length of miRNA genes and the lack of pronounced sequence features complicate this task. To accommodate the peculiarities of plant and animal miRNAs systems, tools for both systems have evolved differently. However, these tools are biased towards the species for which they were primarily developed and, consequently, their predictive performance on data sets from other species of the same kingdom might be lower. While these biases are intrinsic to the species, their characterization can lead to computational approaches capable of diminishing their negative effect on the accuracy of pre-miRNAs predictive models. We investigate in this study how 45 predictive models induced for data sets from 45 species, distributed in eight subphyla/classes, perform when applied to a species different from the species used in its induction. RESULTS: Our computational experiments show that the separability of pre-miRNAs and pseudo pre-miRNAs instances is species-dependent and no feature set performs well for all species, even within the same subphylum/class. Mitigating this species dependency, we show that an ensemble of classifiers reduced the classification errors for all 45 species. As the ensemble members were obtained using meaningful, and yet computationally viable feature sets, the ensembles also have a lower computational cost than individual classifiers that rely on energy stability parameters, which are of prohibitive computational cost in large scale applications. CONCLUSION: In this study, the combination of multiple pre-miRNAs feature sets and multiple learning biases enhanced the predictive accuracy of pre-miRNAs classifiers of 45 species. This is certainly a promising approach to be incorporated in miRNA discovery tools towards more accurate and less species-dependent tools. The material to reproduce the results from this paper can be downloaded from http://dx.doi.org/10.5281/zenodo.49754 .

By integrating Haar wavelets with Hidden Markov Models, we achieve drastically reduced running times for Bayesian inference using Forward-Backward Gibbs sampling. We show that this improves detection of genomic copy number variants (CNV) in array CGH experiments compared to the state-of-the-art, including standard Gibbs sampling. The method concentrates computational effort on chromosomal segments which are difficult to call, by dynamically and adaptively recomputing consecutive blocks of observations likely to share a copy number. This makes routine diagnostic use and re-analysis of legacy data collections feasible; to this end, we also propose an effective automatic prior. An open source software implementation of our method is available at http://schlieplab.org/Software/HaMMLET/ (DOI: 10.5281/zenodo.46262). This paper was selected for oral presentation at RECOMB 2016, and an abstract is published in the conference proceedings.

MOTIVATION: Counting the frequencies of k-mers in read libraries is often a first step in the analysis of high-throughput sequencing data. Infrequent k-mers are assumed to be a result of sequencing errors. The frequent k-mers constitute a reduced but error-free representation of the experiment, which can inform read error correction or serve as the input to de novo assembly methods. Ideally, the memory requirement for counting should be linear in the number of frequent k-mers and not in the, typically much larger, total number of k-mers in the read library. RESULTS: We present a novel method that balances time, space and accuracy requirements to efficiently extract frequent k-mers even for high-coverage libraries and large genomes such as human. Our method is designed to minimize cache misses in a cache-efficient manner by using a pattern-blocked Bloom filter to remove infrequent k-mers from consideration in combination with a novel sort-and-compact scheme, instead of a hash, for the actual counting. Although this increases theoretical complexity, the savings in cache misses reduce the empirical running times. A variant of method can resort to a counting Bloom filter for even larger savings in memory at the expense of false-negative rates in addition to the false-positive rates common to all Bloom filter-based approaches. A comparison with the state-of-the-art shows reduced memory requirements and running times. AVAILABILITY AND IMPLEMENTATION: The tools are freely available for download at http://bioinformatics.rutgers.edu/Software/Turtle and http://figshare.com/articles/Turtle/791582.

BACKGROUND: Computational discovery of microRNAs (miRNA) is based on pre-determined sets of features from miRNA precursors (pre-miRNA). Some feature sets are composed of sequence-structure patterns commonly found in pre-miRNAs, while others are a combination of more sophisticated RNA features. In this work, we analyze the discriminant power of seven feature sets, which are used in six pre-miRNA prediction tools. The analysis is based on the classification performance achieved with these feature sets for the training algorithms used in these tools. We also evaluate feature discrimination through the F-score and feature importance in the induction of random forests. RESULTS: Small or non-significant differences were found among the estimated classification performances of classifiers induced using sets with diversification of features, despite the wide differences in their dimension. Inspired in these results, we obtained a lower-dimensional feature set, which achieved a sensitivity of 90% and a specificity of 95%. These estimates are within 0.1% of the maximal values obtained with any feature set (SELECT, Section "Results and discussion") while it is 34 times faster to compute. Even compared to another feature set (FS2, see Section "Results and discussion"), which is the computationally least expensive feature set of those from the literature which perform within 0.1% of the maximal values, it is 34 times faster to compute. The results obtained by the tools used as references in the experiments carried out showed that five out of these six tools have lower sensitivity or specificity. CONCLUSION: In miRNA discovery the number of putative miRNA loci is in the order of millions. Analysis of putative pre-miRNAs using a computationally expensive feature set would be wasteful or even unfeasible for large genomes. In this work, we propose a relatively inexpensive feature set and explore most of the learning aspects implemented in current ab-initio pre-miRNA prediction tools, which may lead to the development of efficient ab-initio pre-miRNA discovery tools.The material to reproduce the main results from this paper can be downloaded from http://bioinformatics.rutgers.edu/Static/Software/discriminant.tar.gz.

MOTIVATION: Mapping billions of reads from next generation sequencing experiments to reference genomes is a crucial task, which can require hundreds of hours of running time on a single CPU even for the fastest known implementations. Traditional approaches have difficulties dealing with matches of large edit distance, particularly in the presence of frequent or large insertions and deletions (indels). This is a serious obstacle both in determining the spectrum and abundance of genetic variations and in personal genomics. RESULTS: For the first time, we adopt the approximate string matching paradigm of geometric embedding to read mapping, thus rephrasing it to nearest neighbor queries in a q-gram frequency vector space. Using the L(1) distance between frequency vectors has the benefit of providing lower bounds for an edit distance with affine gap costs. Using a cache-oblivious kd-tree, we realize running times, which match the state-of-the-art. Additionally, running time and memory requirements are about constant for read lengths between 100 and 1000 bp. We provide a first proof-of-concept that geometric embedding is a promising paradigm for read mapping and that L(1) distance might serve to detect structural variations. TreQ, our initial implementation of that concept, performs more accurate than many popular read mappers over a wide range of structural variants. AVAILABILITY AND IMPLEMENTATION: TreQ will be released under the GNU Public License (GPL), and precomputed genome indices will be provided for download at http://treq.sf.net. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Next-generation sequencing techniques have facilitated a large-scale analysis of human genetic variation. Despite the advances in sequencing speed, the computational discovery of structural variants is not yet standard. It is likely that many variants have remained undiscovered in most sequenced individuals. RESULTS: Here, we present a novel internal segment size based approach, which organizes all, including concordant, reads into a read alignment graph, where max-cliques represent maximal contradiction-free groups of alignments. A novel algorithm then enumerates all max-cliques and statistically evaluates them for their potential to reflect insertions or deletions. For the first time in the literature, we compare a large range of state-of-the-art approaches using simulated Illumina reads from a fully annotated genome and present relevant performance statistics. We achieve superior performance, in particular, for deletions or insertions (indels) of length 20-100 nt. This has been previously identified as a remaining major challenge in structural variation discovery, in particular, for insert size based approaches. In this size range, we even outperform split-read aligners. We achieve competitive results also on biological data, where our method is the only one to make a substantial amount of correct predictions, which, additionally, are disjoint from those by split-read aligners. AVAILABILITY: CLEVER is open source (GPL) and available from http://clever-sv.googlecode.com. CONTACT: [email protected] or [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Analyzing short time-courses is a frequent and relevant problem in molecular biology, as, for example, 90% of gene expression time-course experiments span at most nine time-points. The biological or clinical questions addressed are elucidating gene regulation by identification of co-expressed genes, predicting response to treatment in clinical, trial-like settings or classifying novel toxic compounds based on similarity of gene expression time-courses to those of known toxic compounds. The latter problem is characterized by irregular and infrequent sample times and a total lack of prior assumptions about the incoming query, which comes in stark contrast to clinical settings and requires to implicitly perform a local, gapped alignment of time series. The current state-of-the-art method (SCOW) uses a variant of dynamic time warping and models time series as higher order polynomials (splines). RESULTS: We suggest to model time-courses monitoring response to toxins by piecewise constant functions, which are modeled as left-right Hidden Markov Models. A Bayesian approach to parameter estimation and inference helps to cope with the short, but highly multivariate time-courses. We improve prediction accuracy by 7% and 4%, respectively, when classifying toxicology and stress response data. We also reduce running times by at least a factor of 140; note that reasonable running times are crucial when classifying response to toxins. In conclusion, we have demonstrated that appropriate reduction of model complexity can result in substantial improvements both in classification performance and running time. AVAILABILITY: A Python package implementing the methods described is freely available under the GPL from http://bioinformatics.rutgers.edu/Software/MVQueries/.

MOTIVATION: Changes in gene expression levels play a central role in tumors. Additional information about the distribution of gene expression levels and distances between adjacent genes on chromosomes should be integrated into the analysis of tumor expression profiles. RESULTS: We use a Hidden Markov Model with distance-scaled transition matrices (DSHMM) to incorporate chromosomal distances of adjacent genes on chromosomes into the identification of differentially expressed genes in breast cancer. We train the DSHMM by integrating prior knowledge about potential distributions of expression levels of differentially expressed and unchanged genes in tumor. We find that especially the combination of these data and to a lesser extent the modeling of distances between adjacent genes contribute to a substantial improvement of the identification of differentially expressed genes in comparison to other existing methods. This performance benefit is also supported by the identification of genes well known to be associated with breast cancer. That suggests applications of DSHMMs for screening of other tumor expression profiles. AVAILABILITY: The DSHMM is available as part of the open-source Java library Jstacs (www.jstacs.de/index.php/DSHMM).

BACKGROUND: Hidden Markov Models (HMM) are often used for analyzing Comparative Genomic Hybridization (CGH) data to identify chromosomal aberrations or copy number variations by segmenting observation sequences. For efficiency reasons the parameters of a HMM are often estimated with maximum likelihood and a segmentation is obtained with the Viterbi algorithm. This introduces considerable uncertainty in the segmentation, which can be avoided with Bayesian approaches integrating out parameters using Markov Chain Monte Carlo (MCMC) sampling. While the advantages of Bayesian approaches have been clearly demonstrated, the likelihood based approaches are still preferred in practice for their lower running times; datasets coming from high-density arrays and next generation sequencing amplify these problems. RESULTS: We propose an approximate sampling technique, inspired by compression of discrete sequences in HMM computations and by kd-trees to leverage spatial relations between data points in typical data sets, to speed up the MCMC sampling. CONCLUSIONS: We test our approximate sampling method on simulated and biological ArrayCGH datasets and high-density SNP arrays, and demonstrate a speed-up of 10 to 60 respectively 90 while achieving competitive results with the state-of-the art Bayesian approaches. AVAILABILITY: An implementation of our method will be made available as part of the open source GHMM library from http://ghmm.org.

For designing oligonucleotide tiling arrays popular, current methods still rely on simple criteria like Hamming distance or longest common factors, neglecting base stacking effects which strongly contribute to binding energies. Consequently, probes are often prone to cross-hybridization which reduces the signal-to-noise ratio and complicates downstream analysis. We propose the first computationally efficient method using hybridization energy to identify specific oligonucleotide probes. Our Cross-Hybridization Potential (CHP) is computed with a Nearest Neighbor Alignment, which efficiently estimates a lower bound for the Gibbs free energy of the duplex formed by two DNA sequences of bounded length. It is derived from our simplified reformulation of t-gap insertion-deletion-like metrics. The computations are accelerated by a filter using weighted ungapped q-grams to arrive at seeds. The computation of the CHP is implemented in our software OSProbes, available under the GPL, which computes sets of viable probe candidates. The user can choose a trade-off between running time and quality of probes selected. We obtain very favorable results in comparison with prior approaches with respect to specificity and sensitivity for cross-hybridization and genome coverage with high-specificity probes. The combination of OSProbes and our Tileomatic method, which computes optimal tiling paths from candidate sets, yields globally optimal tiling arrays, balancing probe distance, hybridization conditions, and uniqueness of hybridization.

BACKGROUND: Cluster analysis is an important technique for the exploratory analysis of biological data. Such data is often high-dimensional, inherently noisy and contains outliers. This makes clustering challenging. Mixtures are versatile and powerful statistical models which perform robustly for clustering in the presence of noise and have been successfully applied in a wide range of applications. RESULTS: PyMix - the Python mixture package implements algorithms and data structures for clustering with basic and advanced mixture models. The advanced models include context-specific independence mixtures, mixtures of dependence trees and semi-supervised learning. PyMix is licenced under the GNU General Public licence (GPL). PyMix has been successfully used for the analysis of biological sequence, complex disease and gene expression data. CONCLUSIONS: PyMix is a useful tool for cluster analysis of biological data. Due to the general nature of the framework, PyMix can be applied to a wide range of applications and data sets.

MOTIVATION: Personalized medicine based on molecular aspects of diseases, such as gene expression profiling, has become increasingly popular. However, one faces multiple challenges when analyzing clinical gene expression data; most of the well-known theoretical issues such as high dimension of feature spaces versus few examples, noise and missing data apply. Special care is needed when designing classification procedures that support personalized diagnosis and choice of treatment. Here, we particularly focus on classification of interferon-beta (IFNbeta) treatment response in Multiple Sclerosis (MS) patients which has attracted substantial attention in the recent past. Half of the patients remain unaffected by IFNbeta treatment, which is still the standard. For them the treatment should be timely ceased to mitigate the side effects. RESULTS: We propose constrained estimation of mixtures of hidden Markov models as a methodology to classify patient response to IFNbeta treatment. The advantages of our approach are that it takes the temporal nature of the data into account and its robustness with respect to noise, missing data and mislabeled samples. Moreover, mixture estimation enables to explore the presence of response sub-groups of patients on the transcriptional level. We clearly outperformed all prior approaches in terms of prediction accuracy, raising it, for the first time, >90%. Additionally, we were able to identify potentially mislabeled samples and to sub-divide the good responders into two sub-groups that exhibited different transcriptional response programs. This is supported by recent findings on MS pathology and therefore may raise interesting clinical follow-up questions. AVAILABILITY: The method is implemented in the GQL framework and is available at http://www.ghmm.org/gql. Datasets are available at http://www.cin.ufpe.br/ approximately igcf/MSConst. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Normalization before clustering is often needed for proximity indices, such as Euclidian distance, which are sensitive to differences in the magnitude or scales of the attributes. The goal is to equalize the size or magnitude and the variability of these features. This can also be seen as a way to adjust the relative weighting of the attributes. In this context, we present a first large scale data driven comparative study of three normalization procedures applied to cancer gene expression data. The results are presented in terms of the recovering of the true cluster structure as found by five different clustering algorithms.

We present a novel framework that applies a meta-learning approach to clustering algorithms. Given a dataset, our meta-learning approach provides a ranking for the candidate algorithms that could be used with that dataset. This ranking could, among other things, support non-expert users in the algorithm selection task. In order to evaluate the framework proposed, we implement a prototype that employs regression support vector machines as the meta-learner. Our case study is developed in the context of cancer gene expression micro-array datasets.

MOTIVATION: The regulation of proliferation and differentiation of embryonic and adult stem cells into mature cells is central to developmental biology. Gene expression measured in distinguishable developmental stages helps to elucidate underlying molecular processes. In previous work we showed that functional gene modules, which act distinctly in the course of development, can be represented by a mixture of trees. In general, the similarities in the gene expression programs of cell populations reflect the similarities in the differentiation path. RESULTS: We propose a novel model for gene expression profiles and an unsupervised learning method to estimate developmental similarity and infer differentiation pathways. We assess the performance of our model on simulated data and compare it with favorable results to related methods. We also infer differentiation pathways and predict functional modules in gene expression data of lymphoid development. CONCLUSIONS: We demonstrate for the first time how, in principal, the incorporation of structural knowledge about the dependence structure helps to reveal differentiation pathways and potentially relevant functional gene modules from microarray datasets. Our method applies in any area of developmental biology where it is possible to obtain cells of distinguishable differentiation stages. AVAILABILITY: The implementation of our method (GPL license), data and additional results are available at http://algorithmics.molgen.mpg.de/Supplements/InfDif/. SUPPLEMENTARY INFORMATION: Supplementary data is available at Bioinformatics online.

BACKGROUND: The use of clustering methods for the discovery of cancer subtypes has drawn a great deal of attention in the scientific community. While bioinformaticians have proposed new clustering methods that take advantage of characteristics of the gene expression data, the medical community has a preference for using "classic" clustering methods. There have been no studies thus far performing a large-scale evaluation of different clustering methods in this context. RESULTS/CONCLUSION: We present the first large-scale analysis of seven different clustering methods and four proximity measures for the analysis of 35 cancer gene expression data sets. Our results reveal that the finite mixture of Gaussians, followed closely by k-means, exhibited the best performance in terms of recovering the true structure of the data sets. These methods also exhibited, on average, the smallest difference between the actual number of classes in the data sets and the best number of clusters as indicated by our validation criteria. Furthermore, hierarchical methods, which have been widely used by the medical community, exhibited a poorer recovery performance than that of the other methods evaluated. Moreover, as a stable basis for the assessment and comparison of different clustering methods for cancer gene expression data, this study provides a common group of data sets (benchmark data sets) to be shared among researchers and used for comparisons with new methods. The data sets analyzed in this study are available at http://algorithmics.molgen.mpg.de/Supplements/CompCancer/.

The representation of a genome by oligonucleotide probes is a prerequisite for the analysis of many of its basic properties, such as transcription factor binding sites, chromosomal breakpoints, gene expression of known genes and detection of novel genes, in particular those coding for small RNAs. An ideal representation would consist of a high density set of oligonucleotides with similar melting temperatures that do not cross-hybridize with other regions of the genome and are equidistantly spaced. The implementation of such design is typically called a tiling array or genome array. We formulate the minimal cost tiling path problem for the selection of oligonucleotides from a set of candidates. Computing the selection of probes requires multi-criterion optimization, which we cast into a shortest path problem. Standard algorithms running in linear time allow us to compute globally optimal tiling paths from millions of candidate oligonucleotides on a standard desktop computer for most problem variants. The solutions to this multi-criterion optimization are spatially adaptive to the problem instance. Our formulation incorporates experimental constraints with respect to specific regions of interest and trade offs between hybridization parameters, probe quality and tiling density easily. A web application is available at http://tileomatic.org.

BACKGROUND: Gene expression measurements during the development of the fly Drosophila melanogaster are routinely used to find functional modules of temporally co-expressed genes. Complimentary large data sets of in situ RNA hybridization images for different stages of the fly embryo elucidate the spatial expression patterns. RESULTS: Using a semi-supervised approach, constrained clustering with mixture models, we can find clusters of genes exhibiting spatio-temporal similarities in expression, or syn-expression. The temporal gene expression measurements are taken as primary data for which pairwise constraints are computed in an automated fashion from raw in situ images without the need for manual annotation. We investigate the influence of these pairwise constraints in the clustering and discuss the biological relevance of our results. CONCLUSION: Spatial information contributes to a detailed, biological meaningful analysis of temporal gene expression data. Semi-supervised learning provides a flexible, robust and efficient framework for integrating data sources of differing quality and abundance.

BACKGROUND: Predicting protein complexes from experimental data remains a challenge due to limited resolution and stochastic errors of high-throughput methods. Current algorithms to reconstruct the complexes typically rely on a two-step process. First, they construct an interaction graph from the data, predominantly using heuristics, and subsequently cluster its vertices to identify protein complexes. RESULTS: We propose a model-based identification of protein complexes directly from the experimental observations. Our model of protein complexes based on Markov random fields explicitly incorporates false negative and false positive errors and exhibits a high robustness to noise. A model-based quality score for the resulting clusters allows us to identify reliable predictions in the complete data set. Comparisons with prior work on reference data sets shows favorable results, particularly for larger unfiltered data sets. Additional information on predictions, including the source code under the GNU Public License can be found at http://algorithmics.molgen.mpg.de/Static/Supplements/ProteinComplexes. CONCLUSION: We can identify complexes in the data obtained from high-throughput experiments without prior elimination of proteins or weak interactions. The few parameters of our model, which does not rely on heuristics, can be estimated using maximum likelihood without a reference data set. This is particularly important for protein complex studies in organisms that do not have an established reference frame of known protein complexes.

UNLABELLED: The Graphical Query Language (GQL) is a set of tools for the analysis of gene expression time-courses. They allow a user to pre-process the data, to query it for interesting patterns, to perform model-based clustering or mixture estimation, to include subsequent refinements of clusters and, finally, to use other biological resources to evaluate the results. Analyses are carried out in a graphical and interactive environment, allowing expert intervention in all stages of the data analysis. AVAILABILITY: The GQL package is freely available under the GNU general public license (GPL) at http://www.ghmm.org/gql

Measuring gene expression over time can provide important insights into basic cellular processes. Identifying groups of genes with similar expression time-courses is a crucial first step in the analysis. As biologically relevant groups frequently overlap, due to genes having several distinct roles in those cellular processes, this is a difficult problem for classical clustering methods. We use a mixture model to circumvent this principal problem, with hidden Markov models (HMMs) as effective and flexible components. We show that the ensuing estimation problem can be addressed with additional labeled data-partially supervised learning of mixtures-through a modification of the Expectation-Maximization (EM) algorithm. Good starting points for the mixture estimation are obtained through a modification to Bayesian model merging, which allows us to learn a collection of initial HMMs. We infer groups from mixtures with a simple information-theoretic decoding heuristic, which quantifies the level of ambiguity in group assignment. The effectiveness is shown with high-quality annotation data. As the HMMs we propose capture asynchronous behavior by design, the groups we find are also asynchronous. Synchronous subgroups are obtained from a novel algorithm based on Viterbi paths. We show the suitability of our HMM mixture approach on biological and simulated data and through the favorable comparison with previous approaches. A software implementing the method is freely available under the GPL from http://ghmm.org/gql.

MOTIVATION: DNA arrays are a very useful tool to quickly identify biological agents present in some given sample, e.g. to identify viruses causing disease, for quality control in the food industry, or to determine bacteria contaminating drinking water. The selection of specific oligos to attach to the array surface is a relevant problem in the experiment design process. Given a set S of genomic sequences (the target sequences), the task is to find at least one oligonucleotide, called probe, for each sequence in S. This probe will be attached to the array surface, and must be chosen in a way that it will not hybridize to any other sequence but the intended target. Furthermore, all probes on the array must hybridize to their intended targets under the same reaction conditions, most importantly at the temperature T at which the experiment is conducted. RESULTS: We present an efficient algorithm for the probe design problem. Melting temperatures are calculated for all possible probe-target interactions using an extended nearest-neighbor model, allowing for both non-Watson-Crick base-pairing and unpaired bases within a duplex. To compute temperatures efficiently, a combination of suffix trees and dynamic programming based alignment algorithms is introduced. Additional filtering steps during preprocessing increase the speed of the computation. The practicability of the algorithms is demonstrated by two case studies: The identification of HIV-1 subtypes, and of 28S rDNA sequences from >or=400 organisms.

MOTIVATION: It is widely believed that for two proteins Aand Ba sequence identity above some threshold implies structural similarity due to a common evolutionary ancestor. Since this is only a sufficient, but not a necessary condition for structural similarity, the question remains what other criteria can be used to identify remote homologues. Transitivity refers to the concept of deducing a structural similarity between proteins A and C from the existence of a third protein B, such that A and B as well as B and C are homologues, as ascertained if the sequence identity between A and B as well as that between B and C is above the aforementioned threshold. It is not fully understood if transitivity always holds and whether transitivity can be extended ad infinitum. RESULTS: We developed a graph-based clustering approach, where transitivity plays a crucial role. We determined all pair-wise similarities for the sequences in the SwissProt database using the Smith-Waterman local alignment algorithm. This data was transformed into a directed graph, where protein sequences constitute vertices. A directed edge was drawn from vertex A to vertex B if the sequences A and B showed similarity, scaled with respect to the self-similarity of A, above a fixed threshold. Transitivity was important in the clustering process, as intermediate sequences were used, limited though by the requirement of having directed paths in both directions between proteins linked over such sequences. The length dependency-implied by the self-similarity-of the scaling of the alignment scores appears to be an effective criterion to avoid clustering errors due to multi-domain proteins. To deal with the resulting large graphs we have developed an efficient library. Methods include the novel graph-based clustering algorithm capable of handling multi-domain proteins and cluster comparison algorithms. Structural Classification of Proteins (SCOP) was used as an evaluation data set for our method, yielding a 24% improvement over pair-wise comparisons in terms of detecting remote homologues. AVAILABILITY: The software is available to academic users on request from the authors. CONTACT: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]. SUPPLEMENTARY INFORMATION: http://www.zaik.uni-koeln.de/~schliep/ProtClust.html.