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1. The minimizer Jaccard estimator is biased and inconsistent

   https://doi.org/10.1093/bioinformatics/btac244  

   Belbasi, Mahdi ; Blanca, Antonio ; Harris, Robert S. ; Koslicki, David ; Medvedev, Paul ( June 2022 , Bioinformatics)

   Sketching is now widely used in bioinformatics to reduce data size and increase data processing speed. Sketching approaches entice with improved scalability but also carry the danger of decreased accuracy and added bias. In this article, we investigate the minimizer sketch and its use to estimate the Jaccard similarity between two sequences.

   We show that the minimizer Jaccard estimator is biased and inconsistent, which means that the expected difference (i.e. the bias) between the estimator and the true value is not zero, even in the limit as the lengths of the sequences grow. We derive an analytical formula for the bias as a function of how the shared k-mers are laid out along the sequences. We show both theoretically and empirically that there are families of sequences where the bias can be substantial (e.g. the true Jaccard can be more than double the estimate). Finally, we demonstrate that this bias affects the accuracy of the widely used mashmap read mapping tool.

   Scripts to reproduce our experiments are available at https://github.com/medvedevgroup/minimizer-jaccard-estimator/tree/main/reproduce.

   Supplementary data are available at Bioinformatics online.

    

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2. Seeding with minimized subsequence

   https://doi.org/10.1093/bioinformatics/btad218  

   Li, Xiang ; Shi, Qian ; Chen, Ke ; Shao, Mingfu ( June 2023 , Bioinformatics)

   Modern methods for computation-intensive tasks in sequence analysis (e.g. read mapping, sequence alignment, genome assembly, etc.) often first transform each sequence into a list of short, regular-length seeds so that compact data structures and efficient algorithms can be employed to handle the ever-growing large-scale data. Seeding methods using kmers (substrings of length k) have gained tremendous success in processing sequencing data with low mutation/error rates. However, they are much less effective for sequencing data with high error rates as kmers cannot tolerate errors.

   We propose SubseqHash, a strategy that uses subsequences, rather than substrings, as seeds. Formally, SubseqHash maps a string of length n to its smallest subsequence of length k, k < n, according to a given order overall length-k strings. Finding the smallest subsequence of a string by enumeration is impractical as the number of subsequences grows exponentially. To overcome this barrier, we propose a novel algorithmic framework that consists of a specifically designed order (termed ABC order) and an algorithm that computes the minimized subsequence under an ABC order in polynomial time. We first show that the ABC order exhibits the desired property and the probability of hash collision using the ABC order is close to the Jaccard index. We then show that SubseqHash overwhelmingly outperforms the substring-based seeding methods in producing high-quality seed-matches for three critical applications: read mapping, sequence alignment, and overlap detection. SubseqHash presents a major algorithmic breakthrough for tackling the high error rates and we expect it to be widely adapted for long-reads analysis.

   SubseqHash is freely available at https://github.com/Shao-Group/subseqhash.

    

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3. Genome-wide alignment-free phylogenetic distance estimation under a no strand-bias model

   https://doi.org/10.1093/bioadv/vbac055  

   Balaban, Metin ; Bristy, Nishat Anjum ; Faisal, Ahnaf ; Bayzid, Md Shamsuzzoha ; Mirarab, Siavash ; Lengauer, ed., Thomas ( August 2022 , Bioinformatics Advances)

   Summary: While alignment has been the dominant approach for determining homology prior to phylogenetic inference, alignment-free methods can simplify the analysis, especially when analyzing genome-wide data. Furthermore, alignment-free methods present the only option for emerging forms of data, such as genome skims, which do not permit assembly. Despite the appeal, alignment-free methods have not been competitive with alignment-based methods in terms of accuracy. One limitation of alignment-free methods is their reliance on simplified models of sequence evolution such as Jukes–Cantor. If we can estimate frequencies of base substitutions in an alignment-free setting, we can compute pairwise distances under more complex models. However, since the strand of DNA sequences is unknown for many forms of genome-wide data, which arguably present the best use case for alignment-free methods, the most complex models that one can use are the so-called no strand-bias models. We show how to calculate distances under a four-parameter no strand-bias model called TK4 without relying on alignments or assemblies. The main idea is to replace letters in the input sequences and recompute Jaccard indices between k-mer sets. However, on larger genomes, we also need to compute the number of k-mer mismatches after replacement due to random chance as opposed to homology. We show in simulation that alignment-free distances can be highly accurate when genomes evolve under the assumed models and study the accuracy on assembled and unassembled biological data.

   Our software is available open source at https://github.com/nishatbristy007/NSB.

   Supplementary data are available at Bioinformatics Advances online.

    

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4. CMash: fast, multi-resolution estimation of k-mer-based Jaccard and containment indices

   https://doi.org/10.1093/bioinformatics/btac237  

   Liu, Shaopeng ; Koslicki, David ( June 2022 , Bioinformatics)

   K-mer-based methods are used ubiquitously in the field of computational biology. However, determining the optimal value of k for a specific application often remains heuristic. Simply reconstructing a new k-mer set with another k-mer size is computationally expensive, especially in metagenomic analysis where datasets are large. Here, we introduce a hashing-based technique that leverages a kind of bottom-m sketch as well as a k-mer ternary search tree (KTST) to obtain k-mer-based similarity estimates for a range of k values. By truncating k-mers stored in a pre-built KTST with a large k=kmax value, we can simultaneously obtain k-mer-based estimates for all k values up to kmax. This truncation approach circumvents the reconstruction of new k-mer sets when changing k values, making analysis more time and space-efficient.

   We derived the theoretical expression of the bias factor due to truncation. And we showed that the biases are negligible in practice: when using a KTST to estimate the containment index between a RefSeq-based microbial reference database and simulated metagenome data for 10 values of k, the running time was close to 10× faster compared to a classic MinHash approach while using less than one-fifth the space to store the data structure.

   A python implementation of this method, CMash, is available at https://github.com/dkoslicki/CMash. The reproduction of all experiments presented herein can be accessed via https://github.com/KoslickiLab/CMASH-reproducibles.

   Supplementary data are available at Bioinformatics online.

    

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5. A space and time-efficient index for the compacted colored de Bruijn graph

   https://doi.org/10.1093/bioinformatics/bty292  

   Almodaresi, Fatemeh ; Sarkar, Hirak ; Srivastava, Avi ; Patro, Rob ( June 2018 , Bioinformatics)

   Indexing reference sequences for search—both individual genomes and collections of genomes—is an important building block for many sequence analysis tasks. Much work has been dedicated to developing full-text indices for genomic sequences, based on data structures such as the suffix array, the BWT and the FM-index. However, the de Bruijn graph, commonly used for sequence assembly, has recently been gaining attention as an indexing data structure, due to its natural ability to represent multiple references using a graphical structure, and to collapse highly-repetitive sequence regions. Yet, much less attention has been given as to how to best index such a structure, such that queries can be performed efficiently and memory usage remains practical as the size and number of reference sequences being indexed grows large.

   We present a novel data structure for representing and indexing the compacted colored de Bruijn graph, which allows for efficient pattern matching and retrieval of the reference information associated with each k-mer. As the popularity of the de Bruijn graph as an index has increased over the past few years, so have the number of proposed representations of this structure. Existing structures typically fall into two categories; those that are hashing-based and provide very fast access to the underlying k-mer information, and those that are space-frugal and provide asymptotically efficient but practically slower pattern search. Our representation achieves a compromise between these two extremes. By building upon minimum perfect hashing and making use of succinct representations where applicable, our data structure provides practically fast lookup while greatly reducing the space compared to traditional hashing-based implementations. Further, we describe a sampling scheme for this index, which provides the ability to trade off query speed for a reduction in the index size. We believe this representation strikes a desirable balance between speed and space usage, and allows for fast search on large reference sequences.

   Finally, we describe an application of this index to the taxonomic read assignment problem. We show that by adopting, essentially, the approach of Kraken, but replacing k-mer presence with coverage by chains of consistent unique maximal matches, we can improve the space, speed and accuracy of taxonomic read assignment.

   pufferfish is written in C++11, is open source, and is available at https://github.com/COMBINE-lab/pufferfish.

   Supplementary data are available at Bioinformatics online.

    

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