Among grammar-based compression techniques, RePair is a notable offline encoding scheme known for its simplicity and powerful combinatorial properties, producing compact grammars by repeatedly replacing the most frequent adjacent pairs of symbols, known as bigrams. However, RePair’s memory usage scales poorly with input size, as it loads the entire text into memory. In contrast, Relative Lempel-Ziv (RLZ) parsing offers a scalable and lightweight online encoding scheme that losslessly represents a text in terms of phrases that refer to a reference string, but it often fails to expose deeper structural patterns. We introduce an algorithm that produces a RePair grammar from the RLZ parse of the input, leveraging the strengths of both methods. Our method, RLZ-RePair, performs bigram replacements systematically, preserving the integrity of the RLZ phrases throughout the RePair iterations. When the reference is well chosen, our method achieves the same grammar as standard RePair while significantly reducing both memory usage and the number of bigram replacements. In particular, we show that RLZ-RePair can reduce memory usage by more than 80% while incurring only a modest runtime increase compared to RePair. To our knowledge, RLZ-RePair is one of the first scalable methods that constructs exact RePair grammars, resulting in a grammar-based compressor that is both practical for large datasets and faithful to the theoretical elegance of RePair.

We clarify the design principles and evaluation choices underlying Syotti, a robust and scalable probe-design tool developed to support large, heterogeneous bacterial datasets with minimal parameter tuning. We highlight Syotti's ability to perform simultaneous large-scale designs and its effectiveness as a reliable alternative when existing tools such as CATCH are not well suited to the problem setting.

MOTIVATION: Multiplex PCR-based enrichment is widely used in viral genome sequencing and pathogen surveillance. However, designing large sets of primers that maximize genome coverage while minimizing primer-primer interactions remains a major computational challenge. Existing methods such as SADDLE and Olivar use heuristics to optimize a Badness score for primer dimers but lack theoretical guarantees on solution quality. RESULTS: We introduce PRISM, a new framework that formulates multiplex primer design as a constrained submodular maximization problem. Our method defines an objective that balances genome coverage and dimer risk, and applies a local search algorithm with a constant-factor approximation guarantee. Evaluations on viral genome datasets demonstrate that PRISM consistently achieves lower Badness scores compared to PrimalScheme, Olivar, and primerJinn. These results highlight the scalability and theoretical rigor of submodular optimization in primer design. AVAILABILITY: PRISM is open-source and available at https://github.com/yhhan19/PRISM-new. The experimental data, scripts, and results used in this paper are archived on Figshare at https://doi.org/10.6084/m9.figshare.32806499.

How do user-defined gestures for mixed reality change when users’ hands are engaged in tasks? To address this question, we conducted a gesture elicitation study to understand user preferences and the characteristics of gestures conceptualized in three scenarios with varying levels of hand constraints, namely: "both hands free", "one hand fixed", and "both hands busy". We analyzed these gestures across multiple dimensions and compared our findings with those from prior research. Our results indicate that when both hands are occupied, users tend to favor head gestures over those involving other body parts, such as the eyes or legs. Additionally, we found that most of the proposed gestures were metaphorical, with many influenced by legacy bias. These insights enhance our understanding of how hand constraints influence gesture choices in mixed reality scenarios.

While there is explosive growth in the creation of biological data, researchers rely on ad hoc verification methods such as testing with small simulated datasets. Due to their importance in biology and biomedicine, there is a critical need to verify these algorithms as well as their implementations to ensure that the results and conclusions are trustworthy. In this paper, we explore an effective combination of model checking and theorem proving of bioinformatics software, including BiopLib, BWA, Jellyfish, SDSL, Dashing, SPAdes, and MUMmer. We provide results for model checking for bioinfomatics software libraries and theorem proving for specific properties. Our model checking framework found several potential flaws in the two tools (BiopLib and BWA). We have also detected several failing cases in Succinct Data Structures Library (SDSL).

MOTIVATION: Antibiotic resistance in Mycobacterium tuberculosis (MTB) poses a significant challenge to global public health. Rapid and accurate prediction of antibiotic resistance can inform treatment strategies and mitigate the spread of resistant strains. In this study, we present a novel approach leveraging large language models (LLMs) to predict antibiotic resistance in MTB (LLMTB). Our model is trained and evaluated on genomic data from 12 185 CRyPTIC isolates and their associated resistance profiles, utilizing natural language processing techniques to capture patterns and mutations linked to resistance. The model's architecture integrates state-of-the-art transformer-based LLMs, enabling the analysis of complex genomic sequences and the extraction of critical features relevant to antibiotic resistance. RESULTS: We evaluate our model's performance using a comprehensive dataset of MTB strains, demonstrating its ability to achieve high performance in predicting resistance to various antibiotics. Unlike traditional machine learning methods, fine-tuning or few-shot learning opens avenues for LLMs to adapt to new or emerging drugs, thereby reducing reliance on extensive data curation. Beyond predictive accuracy, LLMTB uncovers deeper biological insights, identifying critical genes, intergenic regions, and novel resistance mechanisms. This method marks a transformative shift in resistance prediction and offers significant potential for enhancing diagnostic capabilities and guiding personalized treatment plans, ultimately contributing to the global effort to combat tuberculosis and antibiotic resistance. AVAILABILITY AND IMPLEMENTATION: All source code is publicly available at https://github.com/ctestagrose/LLMTB.

The FM-index is one of the main success stories of the field of compact data structures and is a key part of many important tools in bioinformatics. Its primary weakness is a lack of access locality, with each step in a backward search typically causing several cache misses. If the indexed text is more than about lg σ times the size of cache, where σ is the size of the alphabet, then the bitvector at each level of the wavelet tree over the Burrows-Wheeler Transform (BWT) of the text may by itself be larger than cache — causing a cache miss as we descend from each level of the wavelet tree to the next. The resulting slowdown can be enough to cause practitioners to switch from FM-indexes to compressed suffix arrays, which have somewhat better locality.

MOTIVATION: World Health Organization estimates that there were over 10 million cases of tuberculosis (TB) worldwide in 2019, resulting in over 1.4 million deaths, with a worrisome increasing trend yearly. The disease is caused by Mycobacterium tuberculosis (MTB) through airborne transmission. Treatment of TB is estimated to be 85% successful, however, this drops to 57% if MTB exhibits multiple antimicrobial resistance (AMR), for which fewer treatment options are available. RESULTS: We develop a robust machine-learning classifier using both linear and nonlinear models (i.e. LASSO logistic regression (LR) and random forests (RF)) to predict the phenotypic resistance of Mycobacterium tuberculosis (MTB) for a broad range of antibiotic drugs. We use data from the CRyPTIC consortium to train our classifier, which consists of whole genome sequencing and antibiotic susceptibility testing (AST) phenotypic data for 13 different antibiotics. To train our model, we assemble the sequence data into genomic contigs, identify all unique 31-mers in the set of contigs, and build a feature matrix M, where M[i, j] is equal to the number of times the ith 31-mer occurs in the jth genome. Due to the size of this feature matrix (over 350 million unique 31-mers), we build and use a sparse matrix representation. Our method, which we refer to as MTB++, leverages compact data structures and iterative methods to allow for the screening of all the 31-mers in the development of both LASSO LR and RF. MTB++ is able to achieve high discrimination (F-1 >80%) for the first-line antibiotics. Moreover, MTB++ had the highest F-1 score in all but three classes and was the most comprehensive since it had an F-1 score >75% in all but four (rare) antibiotic drugs. We use our feature selection to contextualize the 31-mers that are used for the prediction of phenotypic resistance, leading to some insights about sequence similarity to genes in MEGARes. Lastly, we give an estimate of the amount of data that is needed in order to provide accurate predictions. AVAILABILITY: The models and source code are publicly available on Github at https://github.com/M-Serajian/MTB-Pipeline.

The extended Burrows-Wheeler Transform (eBWT) was introduced by Mantaci et al. [TCS 2007] to extend the definition of the BWT to a collection of strings. As opposed to other commonly used BWT-variants for string collections, the eBWT is independent of the input order of the strings in the collection, while preserving the full functionality and compressibility of the classic BWT. In our prior work [Boucher et al. Computing the original eBWT faster, simpler, and with less memory, SPIRE 2021], we presented a linear-time algorithm for constructing the eBWT. The algorithm combines a modification of the Suffix Array Induced Sorting (SAIS) algorithm [Nong et al., IEEE Trans Comput 2011] with Prefix-Free Parsing [Boucher et al., Alg Mol Biol 2019; Kuhnle et. al., JCB 2020]. In this paper, we show how this construction can be extended for building the r-index of the eBWT, which we call extended r-index, an analogous data structure to the r-index of Gagie et al. [SODA 2018, JACM 2020], with the added value that circular pattern matching is also supported. Our data structure occupies O(r) words, where r is the number of runs of the eBWT of the input collection, and answers count and locate queries in time analogous to the original r-index. We also show how to efficiently support finding maximal exact matches (MEMs) using the extended r-index. We implemented the extended r-index and tested it on circular bacterial genomes and plasmids, comparing it to five state-of-the-art compressed text indexes, including the original r-index and several dictionary-based indexes. While our data structure maintains similar time and memory requirements for answering pattern matching queries as the original r-index, it is the only index in the literature that regards the strings as circular. So, it can naturally be used for both circular and linear input collections. This is an extended version of the conference paper Boucher et al., r-indexing the eBWT, SPIRE 2021.

In this paper, we present an algorithm for constructing the Lempel-Ziv 77 (LZ77) factorization using prefix-free parsing, an algorithm that was first developed as preprocessing algorithm for constructing the Burrows-Wheeler transform and the suffix array for input text. It was then demonstrated that the output of prefix-free parsing can be an effective data structure that emulates a compressed suffix tree (CST). PFP-LZ77 marries this data structure with the algorithm proposed by Karkkäinen et al. [CPM 2013]. In particular, we implemented a modification of the primitives used to support CST operations to enable previous smaller value and next smaller value queries on the suffix array of the text. This allow PFP-LZ77 to exploit the repetitiveness of the text, while building the LZ77 parse. We show that PFP-LZ77, SE-KKP, and ReLZ were the only methods capable of scaling to large datasets (e.g., 1024 copies of chromosome 19). And although SE-KKP and ReLZ performed well, SE-KKP was between 2.5 and 5 times slower, and used between 3 and 11 times more memory than PFP-LZ77 for reasonably large datasets (i.e., more than 16 copies of chromosome 19), and ReLZ only generates an LZ77 approximation. Our implementation is available at https://github.com/AaronHong1024/PFP_LZ77.

FM-indexes are a crucial data structure in DNA alignment, for example, but searching with them usually takes at least one random access per character in the query pattern. Ferragina and Fischer [5] observed in 2007 that word-based indexes often use fewer random accesses than character-based indexes, and thus support faster searches. Since DNA lacks natural word-boundaries, however, it is necessary to parse it somehow before applying word-based FM-indexing. Last year, Deng et al. [3] proposed parsing genomic data by induced suffix sorting, and showed the resulting word-based FM-indexes support faster counting queries than standard FM-indexes when patterns are a few thousand characters or longer. In this paper we show that using prefix-free parsing-which takes parameters that let us tune the average length of the phrases-instead of induced suffix sorting, gives a significant speedup for patterns of only a few hundred characters. We implement our method and demonstrate it is between 3 and 18 times faster than competing methods on queries to GRCh38. And was consistently faster on queries made to 25,000, 50,000 and 100,000 SARS-CoV-2 genomes. Hence, it is very clear that our method accelerates the performance of count over all state-of-the-art methods with a minor increase in the memory. The source code for PFP-FM is available at https://github.com/marco-oliva/afm.

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

Generating pangenomic datasets is becoming increasingly common but there are still few tools able to handle them and even fewer accessible to non-specialists. Building compressed suffix trees (CSTs) for pangenomic datasets is still a major challenge but could be enormously beneficial to the community. In this paper, we present a method, which we refer to as RePFP-CST, for building CSTs in a manner that is scalable. To accomplish this, we show how to build a CST directly from VCF files without decompressing them, and to prune from the prefix-free parse (PFP) phrase boundaries whose removal reduces the total size of the dictionary and the parse. We show that these improvements reduce the time and space required for the construction of the CST, and the memory footprint of the finished CST, enabling us to build a CST for a terabyte of DNA for the first time in the literature.

Antimicrobial resistance (AMR) is a growing threat to public health and farming at large. In clinical and veterinary practice, timely characterization of the antibiotic susceptibility profile of bacterial infections is a crucial step in optimizing treatment. High-throughput sequencing is a promising option for clinical point-of-care and ecological surveillance, opening the opportunity to develop genotyping-based AMR determination as a possibly faster alternative to phenotypic testing. In the present work, we compare the performance of state-of-the-art methods for detection of AMR using high-throughput sequencing data from clinical settings. We consider five computational approaches based on alignment (AMRPlusPlus), deep learning (DeepARG), k-mer genomic signatures (KARGA, ResFinder) or hidden Markov models (Meta-MARC). We use an extensive collection of 585 isolates with available AMR resistance profiles determined by phenotypic tests across nine antibiotic classes. We show how the prediction landscape of AMR classifiers is highly heterogeneous, with balanced accuracy varying from 0.40 to 0.92. Although some algorithms-ResFinder, KARGA and AMRPlusPlus-exhibit overall better balanced accuracy than others, the high per-AMR-class variance and related findings suggest that: (1) all algorithms might be subject to sampling bias both in data repositories used for training and experimental/clinical settings; and (2) a portion of clinical samples might contain uncharacterized AMR genes that the algorithms-mostly trained on known AMR genes-fail to generalize upon. These results lead us to formulate practical advice for software configuration and application, and give suggestions for future study designs to further develop AMR prediction tools from proof-of-concept to bedside.

MOTIVATION: Bait enrichment is a protocol that is becoming increasingly ubiquitous as it has been shown to successfully amplify regions of interest in metagenomic samples. In this method, a set of synthetic probes ('baits') are designed, manufactured and applied to fragmented metagenomic DNA. The probes bind to the fragmented DNA and any unbound DNA is rinsed away, leaving the bound fragments to be amplified for sequencing. Metsky et al. demonstrated that bait-enrichment is capable of detecting a large number of human viral pathogens within metagenomic samples. RESULTS: We formalize the problem of designing baits by defining the Minimum Bait Cover problem, show that the problem is NP-hard even under very restrictive assumptions, and design an efficient heuristic that takes advantage of succinct data structures. We refer to our method as Syotti. The running time of Syotti shows linear scaling in practice, running at least an order of magnitude faster than state-of-the-art methods, including the method of Metsky et al. At the same time, our method produces bait sets that are smaller than the ones produced by the competing methods, while also leaving fewer positions uncovered. Lastly, we show that Syotti requires only 25 min to design baits for a dataset comprised of 3 billion nucleotides from 1000 related bacterial substrains, whereas the method of Metsky et al. shows clearly super-linear running time and fails to process even a subset of 17% of the data in 72 h. AVAILABILITY AND IMPLEMENTATION: https://github.com/jnalanko/syotti. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

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

Optical mapping is a method for creating high resolution restriction maps of an entire genome. Optical mapping has been largely automated, and first produces single molecule restriction maps, called Rmaps, which are assembled to generate genome wide optical maps. Since the location and orientation of each Rmap is unknown, the first problem in the analysis of this data is finding related Rmaps, i.e., pairs of Rmaps that share the same orientation and have significant overlap in their genomic location. Although heuristics for identifying related Rmaps exist, they all require quantization of the data which leads to a loss in the precision. In this paper, we propose a Gaussian mixture modelling clustering based method, which we refer to as OMclust, that finds overlapping Rmaps without quantization. Using both simulated and real datasets, we show that OMclust substantially improves the precision (from 48.3% to 73.3%) over the state-of-the art methods while also reducing CPU time and memory consumption. Further, we integrated OMclust into the error correction methods (Elmeri and cOMet) to demonstrate the increase in the performance of these methods. When OMclust was combined with cOMet to error correct Rmap data generated from human DNA, it was able to error correct close to 3x more Rmaps, and reduced the CPU time by more than 35x. Our software is written in C++ and is publicly available under GNU General Public License at https://github.com/kingufl/OMclust.

Prefix-free parsing (PFP) was introduced by Boucher et al. (2019) as a preprocessing step to ease the computation of Burrows-Wheeler Transforms (BWTs) of genomic databases. Given a string S, it produces a dictionary D and a parse P of overlapping phrases such that BWT(S) can be computed from D and P in time and workspace bounded in terms of their combined size |PFP(S)|. In practice D and P are significantly smaller than S and computing BWT(S) from them is more efficient than computing it from S directly, at least when S is the concatenation of many genomes. In this paper, we consider PFP(S) as a data structure and show how it can be augmented to support full suffix tree functionality, still built and fitting within O(|PFP(S)|) space. This entails the efficient computation of various primitives to simulate the suffix tree: computing a longest common extension (LCE) of two positions in S; reading any cell of its suffix array (SA), of its inverse (ISA), of its BWT, and of its longest common prefix array (LCP); and computing minima over ranges and next/previous smaller value queries over the LCP. Our experimental results show that the PFP suffix tree can be efficiently constructed for very large repetitive datasets and that its operations perform competitively with other compressed suffix trees that can only handle much smaller datasets.

Computing the matching statistics of patterns with respect to a text is a fundamental task in bioinformatics, but a formidable one when the text is a highly compressed genomic database. Bannai et al. gave an efficient solution for this case, which Rossi et al. recently implemented, but it uses two passes over the patterns and buffers a pointer for each character during the first pass. In this paper, we simplify their solution and make it streaming, at the cost of slowing it down slightly. This means that, first, we can compute the matching statistics of several long patterns (such as whole human chromosomes) in parallel while still using a reasonable amount of RAM; second, we can compute matching statistics online with low latency and thus quickly recognize when a pattern becomes incompressible relative to the database. Our code is available at https://github.com/koeppl/phoni.

Large sequencing projects, such as GenomeTrakr and MetaSub, are updated frequently (sometimes daily, in the case of GenomeTrakr) with new data. Therefore, it is imperative that any data structure indexing such data supports efficient updates. Toward this goal, Bannai et al. (TCS, 2020) proposed a data structure named dynamic r-index which is suitable for large genome collections and supports incremental construction; however, it is still not powerful enough to support substantial updates. Here, we develop a novel algorithm for updating the r-index, which we refer to as RIMERGE. Fundamental to our algorithm is the combination of the basics of the dynamic r-index with a known algorithm for merging Burrows-Wheeler Transforms (BWTs). As a result, RIMERGE is capable of performing batch updates in a manner that exploits parallelism while keeping the memory overhead small. We compare our method to the dynamic r-index of Bannai et al. using two different datasets, and show that RIMERGE is between 1.88 to 5.34 times faster on reasonably large inputs.

MOTIVATION: The de Bruijn graph is one of the fundamental data structures for analysis of high throughput sequencing data. In order to be applicable to population-scale studies, it is essential to build and store the graph in a space- and time-efficient manner. In addition, due to the ever-changing nature of population studies, it has become essential to update the graph after construction, e.g. add and remove nodes and edges. Although there has been substantial effort on making the construction and storage of the graph efficient, there is a limited amount of work in building the graph in an efficient and mutable manner. Hence, most space efficient data structures require complete reconstruction of the graph in order to add or remove edges or nodes. RESULTS: In this article, we present DynamicBOSS, a succinct representation of the de Bruijn graph that allows for an unlimited number of additions and deletions of nodes and edges. We compare our method with other competing methods and demonstrate that DynamicBOSS is the only method that supports both addition and deletion and is applicable to very large samples (e.g. greater than 15 billion k-mers). Competing dynamic methods, e.g. FDBG cannot be constructed on large scale datasets, or cannot support both addition and deletion, e.g. BiFrost. AVAILABILITY AND IMPLEMENTATION: DynamicBOSS is publicly available at https://github.com/baharpan/dynboss. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Metagenomics refers to the study of complex samples containing of genetic contents of multiple individual organisms and, thus, has been used to elucidate the microbiome and resistome of a complex sample. The microbiome refers to all microbial organisms in a sample, and the resistome refers to all of the antimicrobial resistance (AMR) genes in pathogenic and non-pathogenic bacteria. Single-nucleotide polymorphisms (SNPs) can be effectively used to 'fingerprint' specific organisms and genes within the microbiome and resistome and trace their movement across various samples. However, to effectively use these SNPs for this traceability, a scalable and accurate metagenomics SNP caller is needed. Moreover, such an SNP caller should not be reliant on reference genomes since 95% of microbial species is unculturable, making the determination of a reference genome extremely challenging. In this article, we address this need. RESULTS: We present LueVari, a reference-free SNP caller based on the read-colored de Bruijn graph, an extension of the traditional de Bruijn graph that allows repeated regions longer than the k-mer length and shorter than the read length to be identified unambiguously. LueVari is able to identify SNPs in both AMR genes and chromosomal DNA from shotgun metagenomics data with reliable sensitivity (between 91% and 99%) and precision (between 71% and 99%) as the performance of competing methods varies widely. Furthermore, we show that LueVari constructs sequences containing the variation, which span up to 97.8% of genes in datasets, which can be helpful in detecting distinct AMR genes in large metagenomic datasets. AVAILABILITY AND IMPLEMENTATION: Code and datasets are publicly available at https://github.com/baharpan/cosmo/tree/LueVari. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Identification of motifs and quantification of their occurrences are important for the study of genetic diseases, gene evolution, transcription sites, and other biological mechanisms. Exact formulae for estimating count distributions of motifs under Markovian assumptions have high computational complexity and are impractical to be used on large motif sets. Approximated formulae, e.g. based on compound Poisson, are faster, but reliable p value calculation remains challenging. Here, we introduce 'motif_prob', a fast implementation of an exact formula for motif count distribution through progressive approximation with arbitrary precision. Our implementation speeds up the exact calculation, usually impractical, making it feasible and posit to substitute currently employed heuristics. RESULTS: We implement motif_prob in both Perl and C+ + languages, using an efficient error-bound iterative process for the exact formula, providing comparison with state-of-the-art tools (e.g. MoSDi) in terms of precision, run time benchmarks, along with a real-world use case on bacterial motif characterization. Our software is able to process a million of motifs (13-31 bases) over genome lengths of 5 million bases within the minute on a regular laptop, and the run times for both the Perl and C+ + code are several orders of magnitude smaller (50-1000× faster) than MoSDi, even when using their fast compound Poisson approximation (60-120× faster). In the real-world use cases, we first show the consistency of motif_prob with MoSDi, and then how the p-value quantification is crucial for enrichment quantification when bacteria have different GC content, using motifs found in antimicrobial resistance genes. The software and the code sources are available under the MIT license at https://github.com/DataIntellSystLab/motif_prob . CONCLUSIONS: The motif_prob software is a multi-platform and efficient open source solution for calculating exact frequency distributions of motifs. It can be integrated with motif discovery/characterization tools for quantifying enrichment and deviation from expected frequency ranges with exact p values, without loss in data processing efficiency.

Genome wide optical maps are high resolution restriction maps that give a unique numeric representation to a genome. They are produced by assembling hundreds of thousands of single molecule optical maps, which are called Rmaps. Unfortunately, there exists very few choices for assembling Rmap data. There exists only one publicly-available non-proprietary method for assembly and one proprietary method that is available via an executable. Furthermore, the publicly-available method, by Valouev et al. (2006), follows the overlap-layout-consensus (OLC) paradigm, and therefore, is unable to scale for relatively large genomes. The algorithm behind the proprietary method, Bionano Genomics' Solve, is largely unknown. In this paper, we extend the definition of bi-labels in the paired de Bruijn graph to the context of optical mapping data, and present the first de Bruijn graph based method for Rmap assembly. We implement our approach, which we refer to as rmapper, and compare its performance against the assembler of Valouev et al. (2006) and Solve by Bionano Genomics on data from three genomes - E. coli, human, and climbing perch fish (Anabas Testudineus). Our method was the only one able to successfully run on all three genomes. The method of Valouev et al. (2006) only successfully ran on E. coli and Bionano Solve successfully ran on E. coli and human but not on the fish genome. Moreover, on the human genome rmapper was at least 130 times faster than Bionano Solve, used five times less memory and produced the highest genome fraction with zero mis-assemblies.

MOTIVATION: Oxford Nanopore technologies (ONT) add miniaturization and real time to high-throughput sequencing. All available software for ONT data analytics run on cloud/clusters or personal computers. Instead, a linchpin to true portability is software that works on mobile devices of internet connections. Smartphones' and tablets' chipset/memory/operating systems differ from desktop computers, but software can be recompiled. We sought to understand how portable current ONT analysis methods are. RESULTS: Several tools, from base-calling to genome assembly, were ported and benchmarked on an Android smartphone. Out of 23 programs, 11 succeeded. Recompilation failures included lack of standard headers and unsupported instruction sets. Only DSK, BCALM2 and Kraken were able to process files up to 16 GB, with linearly scaling CPU-times. However, peak CPU temperatures were high. In conclusion, the portability scenario is not favorable. Given the fast market growth, attention of developers to ARM chipsets and Android/iOS is warranted, as well as initiatives to implement mobile-specific libraries. AVAILABILITY AND IMPLEMENTATION: The source code is freely available at: https://github.com/marco-oliva/portable-nanopore-analytics.

MOTIVATION: Optical mapping data is used in many core genomics applications, including structural variation detection, scaffolding assembled contigs and mis-assembly detection. However, the pervasiveness of spurious and deleted cut sites in the raw data, which are called Rmaps, make assembly and alignment of them challenging. Although there exists another method to error correct Rmap data, named cOMet, it is unable to scale to even moderately large sized genomes. The challenge faced in error correction is in determining pairs of Rmaps that originate from the same region of the same genome. RESULTS: We create an efficient method for determining pairs of Rmaps that contain significant overlaps between them. Our method relies on the novel and nontrivial adaption and application of spaced seeds in the context of optical mapping, which allows for spurious and deleted cut sites to be accounted for. We apply our method to detecting and correcting these errors. The resulting error correction method, referred to as Elmeri, improves upon the results of state-of-the-art correction methods but in a fraction of the time. More specifically, cOMet required 9.9 CPU days to error correct Rmap data generated from the human genome, whereas Elmeri required less than 15 CPU hours and improved the quality of the Rmaps by more than four times compared to cOMet. AVAILABILITY AND IMPLEMENTATION: Elmeri is publicly available under GNU Affero General Public License at https://github.com/LeenaSalmela/Elmeri. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Bioinformatics (2019) doi:10.1093/bioinformatics/btz663 Incorrect supplementary material was published alongside the above manuscript. This has now been replaced with the correct material.

MOTIVATION: There exist several large genomic and metagenomic data collection efforts, including GenomeTrakr and MetaSub, which are routinely updated with new data. To analyze such datasets, memory-efficient methods to construct and store the colored de Bruijn graph were developed. Yet, a problem that has not been considered is constructing the colored de Bruijn graph in a scalable manner that allows new data to be added without reconstruction. This problem is important for large public datasets as scalability is needed but also the ability to update the construction is also needed. RESULTS: We create a method for constructing the colored de Bruijn graph for large datasets that is based on partitioning the data into smaller datasets, building the colored de Bruijn graph using a FM-index based representation, and succinctly merging these representations to build a single graph. The last step, merging succinctly, is the algorithmic challenge which we solve in this article. We refer to the resulting method as VariMerge. This construction method also allows the graph to be updated with new data. We validate our approach and show it produces a three-fold reduction in working space when constructing a colored de Bruijn graph for 8000 strains. Lastly, we compare VariMerge to other competing methods-including Vari, Rainbowfish, Mantis, Bloom Filter Trie, the method of Almodaresi et al. and Multi-BRWT-and illustrate that VariMerge is the only method that is capable of building the colored de Bruijn graph for 16 000 strains in a manner that allows it to be updated. Competing methods either did not scale to this large of a dataset or do not allow for additions without reconstruction. AVAILABILITY AND IMPLEMENTATION: VariMerge is available at https://github.com/cosmo-team/cosmo/tree/VARI-merge under GPLv3 license. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Optical maps are high-resolution restriction maps (Rmaps) that give a unique numeric representation to a genome. Used in concert with sequence reads, they provide a useful tool for genome assembly and for discovering structural variations and rearrangements. Although they have been a regular feature of modern genome assembly projects, optical maps have been mainly used in post-processing step and not in the genome assembly process itself. Several methods have been proposed for pairwise alignment of single molecule optical maps-called Rmaps, or for aligning optical maps to assembled reads. However, the problem of aligning an Rmap to a graph representing the sequence data of the same genome has not been studied before. Such an alignment provides a mapping between two sets of data: optical maps and sequence data which will facilitate the usage of optical maps in the sequence assembly step itself. RESULTS: We define the problem of aligning an Rmap to a de Bruijn graph and present the first algorithm for solving this problem which is based on a seed-and-extend approach. We demonstrate that our method is capable of aligning 73% of Rmaps generated from the Escherichia coli genome to the de Bruijn graph constructed from short reads generated from the same genome. We validate the alignments and show that our method achieves an accuracy of 99.6%. We also show that our method scales to larger genomes. In particular, we show that 76% of Rmaps can be aligned to the de Bruijn graph in the case of human data. AVAILABILITY AND IMPLEMENTATION: The software for aligning optical maps to de Bruijn graph, omGraph is written in C++ and is publicly available under GNU General Public License at https://github.com/kingufl/omGraph. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We present Kohdista, which is an index-based algorithm for finding pairwise alignments between single molecule maps (Rmaps). The novelty of our approach is the formulation of the alignment problem as automaton path matching, and the application of modern index-based data structures. In particular, we combine the use of the Generalized Compressed Suffix Array (GCSA) index with the wavelet tree in order to build Kohdista. We validate Kohdista on simulated E. coli data, showing the approach successfully finds alignments between Rmaps simulated from overlapping genomic regions. Lastly, we demonstrate Kohdista is the only method that is capable of finding a significant number of high quality pairwise Rmap alignments for large eukaryote organisms in reasonable time. Kohdista is available at https://github.com/mmuggli/KOHDISTA/.

Motivation: The de Bruijn graph is fundamental to the analysis of next generation sequencing data and so, as datasets of DNA reads grow rapidly, it becomes more important to represent de Bruijn graphs compactly while still supporting fast assembly. Previous implementations of compact de Bruijn graphs have not supported node or edge deletion, however, which is important for pruning spurious elements from the graph. Results: Belazzougui et al. (2016b) recently proposed a compact and fully dynamic representation, which supports exact membership queries and insertions and deletions of both nodes and edges. In this paper, we give a practical implementation of their data structure, supporting exact membership queries and fully dynamic edge operations, as well as limited support for dynamic node operations. We demonstrate experimentally that its performance is comparable to that of state-of-the-art implementations based on Bloom filters. Availability and implementation: Our source-code is publicly available at https://github.com/csirac/dynamicDBG under an open-source license.

While long reads produced by third-generation sequencing technology from, e.g, Pacific Biosciences have been shown to increase the quality of draft genomes in repetitive regions, fundamental computational challenges remain in overcoming their high error rate and assembling them efficiently. In this paper we show that the de Bruijn graph built on the long reads can be efficiently and substantially disentangled using optical mapping data as auxiliary information. Fundamental to our approach is the use of the positional de Bruijn graph and a succinct data structure for constructing and traversing this graph. Our experimental results show that over 97.7% of directed cycles have been removed from the resulting positional de Bruijn graph as compared to its non-positional counterpart. Our results thus indicate that disentangling the de Bruijn graph using positional information is a promising direction for developing a simple and efficient assembly algorithm for long reads.

MOTIVATION: In 2012, Iqbal et al. introduced the colored de Bruijn graph, a variant of the classic de Bruijn graph, which is aimed at 'detecting and genotyping simple and complex genetic variants in an individual or population'. Because they are intended to be applied to massive population level data, it is essential that the graphs be represented efficiently. Unfortunately, current succinct de Bruijn graph representations are not directly applicable to the colored de Bruijn graph, which requires additional information to be succinctly encoded as well as support for non-standard traversal operations. RESULTS: Our data structure dramatically reduces the amount of memory required to store and use the colored de Bruijn graph, with some penalty to runtime, allowing it to be applied in much larger and more ambitious sequence projects than was previously possible. AVAILABILITY AND IMPLEMENTATION: https://github.com/cosmo-team/cosmo/tree/VARI. CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Although smartwatches are gaining popularity among mainstream consumers, the input space is limited due to their small form factor. The goal of this work is to explore how to design non-touchscreen gestures to extend the input space of smartwatches. We conducted an elicitation study eliciting gestures for 31 smartwatch tasks. From this study, we demonstrate that a consensus exists among the participants on the mapping of gesture to command and use this consensus to specify a user-defined gesture set. Using gestures collected during our study, we define a taxonomy describing the mapping and physical characteristics of the gestures. Lastly, we provide insights to inform the design of non-touchscreen gestures for smartwatch interaction.

The de Bruijn graph GK of a set of strings Sis a key data structure in genome assembly that represents overlaps between all the K-length substrings of S. Construction and navigation of the graph is a space and time bottleneck in practice and the main hurdle for assembling large genomes. This problem is compounded because state-of-the-art assemblers do not build the de Bruijn graph for a single order (value of K) but for multiple values of K: they builddde Bruijn graphs, each with a specific order, i.e., GK1, GK2, GKd. Al-though, this paradigm increases the quality of the assembly produce but it greatly increases runtime, because of the need to construct graphs instead of one. In this paper, we show how to augment a succinct de Bruijn graph representation by Bowe et al. (Proc. WABI, 2012) to support new operations that let us change order on the fly, effectively representing all de Bruijn graphs of order up to some maximum Kin a single data structure. Our experiments show our variable-order de Bruijn graph only modestly increases space usage, construction time, and navigation time compared to a single order graph.

MOTIVATION: A crucial problem in genome assembly is the discovery and correction of misassembly errors in draft genomes. We develop a method called misSEQuel that enhances the quality of draft genomes by identifying misassembly errors and their breakpoints using paired-end sequence reads and optical mapping data. Our method also fulfills the critical need for open source computational methods for analyzing optical mapping data. We apply our method to various assemblies of the loblolly pine, Francisella tularensis, rice and budgerigar genomes. We generated and used stimulated optical mapping data for loblolly pine and F.tularensis and used real optical mapping data for rice and budgerigar. RESULTS: Our results demonstrate that we detect more than 54% of extensively misassembled contigs and more than 60% of locally misassembled contigs in assemblies of F.tularensis and between 31% and 100% of extensively misassembled contigs and between 57% and 73% of locally misassembled contigs in assemblies of loblolly pine. Using the real optical mapping data, we correctly identified 75% of extensively misassembled contigs and 100% of locally misassembled contigs in rice, and 77% of extensively misassembled contigs and 80% of locally misassembled contigs in budgerigar. AVAILABILITY AND IMPLEMENTATION: misSEQuel can be used as a post-processing step in combination with any genome assembler and is freely available at http://www.cs.colostate.edu/seq/.

RNA splicing is a cellular process driven by the interaction between numerous regulatory sequences and binding sites, however, such interactions have been primarily explored by laboratory methods since computational tools largely ignore the relationship between different splicing elements. Current computational methods identify either splice sites or other regulatory sequences, such as enhancers and silencers. We present a novel approach for characterizing co-occurring relationships between splice site motifs and splicing enhancers. Our approach relies on an efficient algorithm for approximately solving Consensus Sequence with Outliers , an NP-complete string clustering problem. In particular, we give an algorithm for this problem that outputs near-optimal solutions in polynomial time. To our knowledge, this is the first formulation and computational attempt for detecting co-occurring sequence elements in RNA sequence data. Further, we demonstrate that SeeSite is capable of showing that certain ESEs are preferentially associated with weaker splice sites, and that there exists a co-occurrence relationship with splice site motifs.

MOTIVATION: Assemblies of next-generation sequencing (NGS) data, although accurate, still contain a substantial number of errors that need to be corrected after the assembly process. We develop SEQuel, a tool that corrects errors (i.e. insertions, deletions and substitution errors) in the assembled contigs. Fundamental to the algorithm behind SEQuel is the positional de Bruijn graph, a graph structure that models k-mers within reads while incorporating the approximate positions of reads into the model. RESULTS: SEQuel reduced the number of small insertions and deletions in the assemblies of standard multi-cell Escherichia coli data by almost half, and corrected between 30% and 94% of the substitution errors. Further, we show SEQuel is imperative to improving single-cell assembly, which is inherently more challenging due to higher error rates and non-uniform coverage; over half of the small indels, and substitution errors in the single-cell assemblies were corrected. We apply SEQuel to the recently assembled Deltaproteobacterium SAR324 genome, which is the first bacterial genome with a comprehensive single-cell genome assembly, and make over 800 changes (insertions, deletions and substitutions) to refine this assembly. AVAILABILITY: SEQuel can be used as a post-processing step in combination with any NGS assembler and is freely available at http://bix.ucsd.edu/SEQuel/.

Given a set S of n strings, each of length l, and a nonnegative value d, we define a center string as a string of length l that has Hamming distance at most d from each string in S. The #CLOSEST STRING problem aims to determine the number of center strings for a given set of strings S and input parameters n, l, and d. We show #CLOSEST STRING is impossible to solve exactly or even approximately in polynomial time, and that restricting #CLOSEST STRING so that any one of the parameters n, ‘, or d is fixed leads to a fully polynomial-time randomized approximation scheme (FPRAS). We show equivalent results for the problem of efficiently sampling center strings uniformly at random (u.a.r.).

BACKGROUND: Given n strings s1, …, sn each of length ℓ and a nonnegative integer d, the CLOSEST STRING problem asks to find a center string s such that none of the input strings has Hamming distance greater than d from s. Finding a common pattern in many--but not necessarily all--input strings is an important task that plays a role in many applications in bioinformatics. RESULTS: Although the closest string model is robust to the oversampling of strings in the input, it is severely affected by the existence of outliers. We propose a refined model, the closest string with outliers (CSWO) problem, to overcome this limitation. This new model asks for a center string s that is within Hamming distance d to at least n - k of the n input strings, where k is a parameter describing the maximum number of outliers. A CSWO solution not only provides the center string as a representative for the set of strings but also reveals the outliers of the set.We provide fixed parameter algorithms for CSWO when d and k are parameters, for both bounded and unbounded alphabets. We also show that when the alphabet is unbounded the problem is W[1]-hard with respect to n - k, ℓ, and d. CONCLUSIONS: Our refined model abstractly models finding common patterns in several but not all input strings. We initialize the study of the computability of this model and show that it is sensitive to different parameterizations. Lastly, we conclude by suggesting several open problems which warrant further investigation.

BACKGROUND: Improving the accuracy and efficiency of motif recognition is an important computational challenge that has application to detecting transcription factor binding sites in genomic data. Closely related to motif recognition is the CONSENSUS STRING decision problem that asks, given a parameter d and a set of l-length strings S = {s1, ..., sn}, whether there exists a consensus string that has Hamming distance at most d from any string in S. A set of strings S is pairwise bounded if the Hamming distance between any pair of strings in S is at most 2d. It is trivial to determine whether a set is pairwise bounded, and a set cannot have a consensus string unless it is pairwise bounded. We use CONSENSUS STRING to determine whether or not a pairwise bounded set has a consensus. Unfortunately, CONSENSUS STRING is NP-complete. The lack of an efficient method to solve the CONSENSUS STRING problem has caused it to become a computational bottleneck in MCL-WMR, a motif recognition program capable of solving difficult motif recognition problem instances. RESULTS: We focus on the development of a method for solving CONSENSUS STRING quickly with a small probability of error. We apply this heuristic to develop a new motif recognition program, sMCL-WMR, which has impressive accuracy and efficiency. We demonstrate the performance of sMCL-WMR in detecting weak motifs in large data sets and in real genomic data sets, and compare the performance to other leading motif recognition programs. In our preliminary discussion of our CONSENSUS STRING algorithm we give insight into the issue of sampling pairwise bounded sets, and discuss its relevance to motif recognition. CONCLUSION: Our novel heuristic gives birth to a state of the art program, sMCL-WMR, that is capable of detecting weak motifs in data sets with a large number of strings. sMCL-WMR is orders of magnitude faster than its predecessor MCL-WMR and is capable of solving previously unsolved synthetic motif recognition problems. Lastly, sMCL-WMR shows impressive accuracy in detecting transcription factor binding sites in the genomic data and used in the assessment of Tompa et al.