Theory of local k-mer selection with applications to long-read alignment

Sketching Methods with Small Window Guarantee Using Minimum Decycling Sets

Most sequence sketching methods work by selecting specific k-mers from sequences so that the similarity between two sequences can be estimated using only the sketches. Because estimating sequence similarity is much faster using sketches than using sequence alignment, sketching methods are used to reduce the computational requirements of computational biology software. Applications using sketches often rely on properties of the k-mer selection procedure to ensure that using a sketch does not degrade the quality of the results compared with using sequence alignment. Two important examples of such properties are locality and window guarantees, the latter of which ensures that no long region of the sequence goes unrepresented in the sketch. A sketching method with a window guarantee, implicitly or explicitly, corresponds to a decycling set of the de Bruijn graph, which is a set of unavoidable k-mers. Any long enough sequence, by definition, must contain a k-mer from any decycling set (hence, the unavoidable property). Conversely, a decycling set also defines a sketching method by choosing the k-mers from the set as representatives. Although current methods use one of a small number of sketching method families, the space of decycling sets is much larger and largely unexplored. Finding decycling sets with desirable characteristics (e.g., small remaining path length) is a promising approach to discovering new sketching methods with improved performance (e.g., with small window guarantee). The Minimum Decycling Sets (MDSs) are of particular interest because of their minimum size. Only two algorithms, by Mykkeltveit and Champarnaud, are previously known to generate two particular MDSs, although there are typically a vast number of alternative MDSs. We provide a simple method to enumerate MDSs. This method allows one to explore the space of MDSs and to find MDSs optimized for desirable properties. We give evidence that the Mykkeltveit sets are close to optimal regarding one particular property, the remaining path length. A number of conjectures and computational and theoretical evidence to support them are presented. Code available at https://github.com/Kingsford-Group/mdsscope.

Application and Comparison of Machine Learning and Database-Based Methods in Taxonomic Classification of High-Throughput Sequencing Data

The advent of high-throughput sequencing technologies has not only revolutionized the field of bioinformatics but has also heightened the demand for efficient taxonomic classification. Despite technological advancements, efficiently processing and analyzing the deluge of sequencing data for precise taxonomic classification remains a formidable challenge. Existing classification approaches primarily fall into two categories, database-based methods and machine learning methods, each presenting its own set of challenges and advantages. On this basis, the aim of our study was to conduct a comparative analysis between these two methods while also investigating the merits of integrating multiple database-based methods. Through an in-depth comparative study, we evaluated the performance of both methodological categories in taxonomic classification by utilizing simulated data sets. Our analysis revealed that database-based methods excel in classification accuracy when backed by a rich and comprehensive reference database. Conversely, while machine learning methods show superior performance in scenarios where reference sequences are sparse or lacking, they generally show inferior performance compared with database methods under most conditions. Moreover, our study confirms that integrating multiple database-based methods does, in fact, enhance classification accuracy. These findings shed new light on the taxonomic classification of high-throughput sequencing data and bear substantial implications for the future development of computational biology. For those interested in further exploring our methods, the source code of this study is publicly available on https://github.com/LoadStar822/Genome-Classifier-Performance-Evaluator. Additionally, a dedicated webpage showcasing our collected database, data sets, and various classification software can be found at http://lab.malab.cn/~tqz/project/taxonomic/.

Screening Host Genomic Data for Wolbachia Infections

Less than a decade ago, the production of Wolbachia genomic assemblies was tedious, time-consuming, and expensive. The production of Wolbachia genomic DNA free of contamination from host DNA, as required for Wolbachia-targeted sequencing, was then only possible after the amplification and extraction of a large amount of clonal Wolbachia DNA. However, as an endosymbiotic bacterium, Wolbachia does not grow outside the host cell environment, and large-scale recovery of the bacteria required mass rearing of their host, preferably clones of a single individual to avoid strain genetic diversity, or amplification of cell cultures infected with a single Wolbachia strain. Bacterial DNA could be separated from host DNA based on genomic size. Nowadays, the production of full Wolbachia genomes does not require the physical isolation of the bacterial strains from their respective hosts, and the bacterium is often sequenced as a by-catch of host genomic projects. Here, we provide a step-by-step protocol to (1) identify whether host genome projects contain reads from associated Wolbachia and (2) isolate/retrieve the Wolbachia reads from the rest of the sequenced material. We hope this simple protocol will support many projects aiming at studying diverse Wolbachia genome assemblies.

Density and Conservation Optimization of the Generalized Masked-Minimizer Sketching Scheme

Minimizers and syncmers are sketching methods that sample representative k-mer seeds from a long string. The minimizer scheme guarantees a well-spread k-mer sketch (high coverage) while seeking to minimize the sketch size (low density). The syncmer scheme yields sketches that are more robust to base substitutions (high conservation) on random sequences, but do not have the coverage guarantee of minimizers. These sketching metrics are generally adversarial to one another, especially in the context of sketch optimization for a specific sequence, and thus are difficult to be simultaneously achieved. The parameterized syncmer scheme was recently introduced as a generalization of syncmers with more flexible sampling rules and empirically better coverage than the original syncmer variants. However, no approach exists to optimize parameterized syncmers. To address this shortcoming, we introduce a new scheme called masked minimizers that generalizes minimizers in manner analogous to how parameterized syncmers generalize syncmers and allows us to extend existing optimization techniques developed for minimizers. This results in a practical algorithm to optimize the masked minimizer scheme with respect to both density and conservation. We evaluate the optimization algorithm on various benchmark genomes and show that our algorithm finds sketches that are overall more compact, well-spread, and robust to substitutions than those found by previous methods. Our implementation is released at https://github.com/Kingsford-Group/maskedminimizer. This new technique will enable more efficient and robust genomic analyses in the many settings where minimizers and syncmers are used.

Creating and Using Minimizer Sketches in Computational Genomics

Processing large data sets has become an essential part of computational genomics. Greatly increased availability of sequence data from multiple sources has fueled breakthroughs in genomics and related fields but has led to computational challenges processing large sequencing experiments. The minimizer sketch is a popular method for sequence sketching that underlies core steps in computational genomics such as read mapping, sequence assembling, k-mer counting, and more. In most applications, minimizer sketches are constructed using one of few classical approaches. More recently, efforts have been put into building minimizer sketches with desirable properties compared with the classical constructions. In this survey, we review the history of the minimizer sketch, the theories developed around the concept, and the plethora of applications taking advantage of such sketches. We aim to provide the readers a comprehensive picture of the research landscape involving minimizer sketches, in anticipation of better fusion of theory and application in the future.

Sketching methods with small window guarantee using minimum decycling sets

Most sequence sketching methods work by selecting specific k -mers from sequences so that the similarity between two sequences can be estimated using only the sketches. Because estimating sequence similarity is much faster using sketches than using sequence alignment, sketching methods are used to reduce the computational requirements of computational biology software packages. Applications using sketches often rely on properties of the k -mer selection procedure to ensure that using a sketch does not degrade the quality of the results compared with using sequence alignment. Two important examples of such properties are locality and window guarantees, the latter of which ensures that no long region of the sequence goes unrepresented in the sketch. A sketching method with a window guarantee, implicitly or explicitly, corresponds to a Decycling Set, an unavoidable sets of k -mers. Any long enough sequence, by definition, must contain a k -mer from any decycling set (hence, it is unavoidable). Conversely, a decycling set also defines a sketching method by choosing the k -mers from the set as representatives. Although current methods use one of a small number of sketching method families, the space of decycling sets is much larger, and largely unexplored. Finding decycling sets with desirable characteristics (e.g., small remaining path length) is a promising approach to discovering new sketching methods with improved performance (e.g., with small window guarantee). The Minimum Decycling Sets (MDSs) are of particular interest because of their minimum size. Only two algorithms, by Mykkeltveit and Champarnaud, are previously known to generate two particular MDSs, although there are typically a vast number of alternative MDSs. We provide a simple method to enumerate MDSs. This method allows one to explore the space of MDSs and to find MDSs optimized for desirable properties. We give evidence that the Mykkeltveit sets are close to optimal regarding one particular property, the remaining path length. A number of conjectures and computational and theoretical evidence to support them are presented. Code available at https://github.com/Kingsford-Group/mdsscope.

Fast and robust metagenomic sequence comparison through sparse chaining with skani

Sequence comparison tools for metagenome-assembled genomes (MAGs) struggle with high-volume or low-quality data. We present skani ( https://github.com/bluenote-1577/skani ), a method for determining average nucleotide identity (ANI) via sparse approximate alignments. skani outperforms FastANI in accuracy and speed (>20× faster) for fragmented, incomplete MAGs. skani can query genomes against >65,000 prokaryotic genomes in seconds and 6 GB memory. skani unlocks higher-resolution insights for extensive, noisy metagenomic datasets.

Minmers are a generalization of minimizers that enable unbiased local Jaccard estimation

MOTIVATION

The Jaccard similarity on k-mer sets has shown to be a convenient proxy for sequence identity. By avoiding expensive base-level alignments and comparing reduced sequence representations, tools such as MashMap can scale to massive numbers of pairwise comparisons while still providing useful similarity estimates. However, due to their reliance on minimizer winnowing, previous versions of MashMap were shown to be biased and inconsistent estimators of Jaccard similarity. This directly impacts downstream tools that rely on the accuracy of these estimates.

RESULTS

To address this, we propose the minmer winnowing scheme, which generalizes the minimizer scheme by use of a rolling minhash with multiple sampled k-mers per window. We show both theoretically and empirically that minmers yield an unbiased estimator of local Jaccard similarity, and we implement this scheme in an updated version of MashMap. The minmer-based implementation is over 10 times faster than the minimizer-based version under the default ANI threshold, making it well-suited for large-scale comparative genomics applications.

AVAILABILITY AND IMPLEMENTATION

MashMap3 is available at https://github.com/marbl/MashMap.

Proving sequence aligners can guarantee accuracy in almost O(m log n) time through an average-case analysis of the seed-chain-extend heuristic

Seed-chain-extend with k-mer seeds is a powerful heuristic technique for sequence alignment used by modern sequence aligners. Although effective in practice for both runtime and accuracy, theoretical guarantees on the resulting alignment do not exist for seed-chain-extend. In this work, we give the first rigorous bounds for the efficacy of seed-chain-extend with k-mers in expectation Assume we are given a random nucleotide sequence of length ∼n that is indexed (or seeded) and a mutated substring of length ∼m ≤ n with mutation rate θ < 0.206. We prove that we can find a k = Θ(log n) for the k-mer size such that the expected runtime of seed-chain-extend under optimal linear-gap cost chaining and quadratic time gap extension is O(mn f (θ) log n), where f(θ) < 2.43 · θ holds as a loose bound. The alignment also turns out to be good; we prove that more than [Formula: see text] fraction of the homologous bases is recoverable under an optimal chain. We also show that our bounds work when k-mers are sketched, that is, only a subset of all k-mers is selected, and that sketching reduces chaining time without increasing alignment time or decreasing accuracy too much, justifying the effectiveness of sketching as a practical speedup in sequence alignment. We verify our results in simulation and on real noisy long-read data and show that our theoretical runtimes can predict real runtimes accurately. We conjecture that our bounds can be improved further, and in particular, f(θ) can be further reduced.

A survey of mapping algorithms in the long-reads era

It has been over a decade since the first publication of a method dedicated entirely to mapping long-reads. The distinctive characteristics of long reads resulted in methods moving from the seed-and-extend framework used for short reads to a seed-and-chain framework due to the seed abundance in each read. The main novelties are based on alternative seed constructs or chaining formulations. Dozens of tools now exist, whose heuristics have evolved considerably. We provide an overview of the methods used in long-read mappers. Since they are driven by implementation-specific parameters, we develop an original visualization tool to understand the parameter settings ( http://bcazaux.polytech-lille.net/Minimap2/ ).

Minmers are a generalization of minimizers that enable unbiased local Jaccard estimation

Motivation

The Jaccard similarity on k -mer sets has shown to be a convenient proxy for sequence identity. By avoiding expensive base-level alignments and comparing reduced sequence representations, tools such as MashMap can scale to massive numbers of pairwise comparisons while still providing useful similarity estimates. However, due to their reliance on minimizer winnowing, previous versions of MashMap were shown to be biased and inconsistent estimators of Jaccard similarity. This directly impacts downstream tools that rely on the accuracy of these estimates.

Results

To address this, we propose the minmer winnowing scheme, which generalizes the minimizer scheme by use of a rolling minhash with multiple sampled k -mers per window. We show both theoretically and empirically that minmers yield an unbiased estimator of local Jaccard similarity, and we implement this scheme in an updated version of MashMap. The minmer-based implementation is over 10 times faster than the minimizer-based version under the default ANI threshold, making it well-suited for large-scale comparative genomics applications.

How to optimally sample a sequence for rapid analysis

MOTIVATION

We face an increasing flood of genetic sequence data, from diverse sources, requiring rapid computational analysis. Rapid analysis can be achieved by sampling a subset of positions in each sequence. Previous sequence-sampling methods, such as minimizers, syncmers and minimally overlapping words, were developed by heuristic intuition, and are not optimal.

RESULTS

We present a sequence-sampling approach that provably optimizes sensitivity for a whole class of sequence comparison methods, for randomly evolving sequences. It is likely near-optimal for a wide range of alignment-based and alignment-free analyses. For real biological DNA, it increases specificity by avoiding simple repeats. Our approach generalizes universal hitting sets (which guarantee to sample a sequence at least once) and polar sets (which guarantee to sample a sequence at most once). This helps us understand how to do rapid sequence analysis as accurately as possible.

AVAILABILITY AND IMPLEMENTATION

Source code is freely available at https://gitlab.com/mcfrith/noverlap.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Strobealign: flexible seed size enables ultra-fast and accurate read alignment

Read alignment is often the computational bottleneck in analyses. Recently, several advances have been made on seeding methods for fast sequence comparison. We combine two such methods, syncmers and strobemers, in a novel seeding approach for constructing dynamic-sized fuzzy seeds and implement the method in a short-read aligner, strobealign. The seeding is fast to construct and effectively reduces repetitiveness in the seeding step, as shown using a novel metric E-hits. strobealign is several times faster than traditional aligners at similar and sometimes higher accuracy while being both faster and more accurate than more recently proposed aligners for short reads of lengths 150nt and longer. Availability: https://github.com/ksahlin/strobealign.