How to optimally sample a sequence for rapid analysis

Frith, Martin C.; Shaw, Jim; Spouge, John L.

doi:10.1093/bioinformatics/btad057

Cited by 5 publications

(3 citation statements)

References 36 publications

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“…This theorem is the reason we use open syncmers and is crucial to our proofs. The spacing property makes selected open syncmers a polar set ( Zheng et al 2021 ); other methods also give rise to polar sets ( Frith et al 2021 , 2023 ) but open syncmers seem to perform well empirically ( Dutta et al 2022 ; Shaw and Yu 2022 ; Frith et al 2023 ) and are easy to describe. For the rest of the section, we will assume c = k − s + 1 is odd, so

.…”

Section: Methodsmentioning

confidence: 99%

Proving sequence aligners can guarantee accuracy in almostO(mlogn) time through an average-case analysis of the seed-chain-extend heuristic

Shaw

2023

Genome Res.

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Seed-chain-extend withk-mer seeds is a powerful heuristic technique for sequence alignment employed by modern sequence aligners. While 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 withk-mers in expectation. Assume we are given a random nucleotide sequence of length ∼nthat is indexed (or seeded) and a mutated substring of length ∼m≤nwith mutation rate θ < 0.206. We prove that we can find ak= Θ(log n) for thek-mer size such that the expected runtime of seed-chain-extend under optimal linear gap cost chaining and quadratic time gap extension is O(mnf(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 1 − O( 1/√m ) fraction of the homologous bases are recoverable under an optimal chain. We also show that our bounds work whenk-mers are sketched, i.e. only a subset of allk-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.

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.…”

Section: Methodsmentioning

confidence: 99%

Proving sequence aligners can guarantee accuracy in almostO(mlogn) time through an average-case analysis of the seed-chain-extend heuristic

Shaw

2023

Genome Res.

Self Cite

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show abstract

“…This theorem is the reason we use open syncmers and is crucial to our proofs. The spacing property makes selected open syncmers a polar set (Zheng et al, 2021); other methods also give rise to polar sets (Frith et al, 2020, 2022) but open syncmers seem to perform well empirically (Shaw and Yu, 2022; Frith et al, 2022; Dutta et al, 2022) and are easy to describe. For the rest of the section, we will assume c = k – s + 1 is odd, so .…”

Section: Methodsmentioning

confidence: 99%

Sequence aligners can guarantee accuracy in almostO(mlogn) time: a rigorous average-case analysis of the seed-chain-extend heuristic

Shaw

2022

Preprint

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Seed-chain-extend with k-mer seeds is a powerful heuristic technique for sequence alignment employed by modern sequence aligners. While 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(mnf(θ)log n) where f(θ) < 2.43·θ holds as a loose bound. In fact, for reasonable θ = 0.05, f(θ) < 0.08, indicating nearly quasilinear running time in practice. The alignment also turns out to be good; we prove that more than 1 − O(1/√m) fraction of the homologous bases are recoverable under an optimal chain. We also show that our bounds work when k-mers are sketched, i.e. only a subset of all k-mers is selected. Under the open syncmer sketching method, one can sketch with decreasing density as a function of n and achieve asymptotically smaller chaining time, yet the same bounds for extension time and recoverability hold. In other words, 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 conjecture that f(θ) can be further reduced.

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“…These seeding constructs have been referred to as dynamic seeds (Sahlin, Baudeau, et al 2022) as they are neither fixed in length nor in the number of CPU cycles for their construction. There are also seeding constructs known as subsampling methods that aim to use only a subsample of k-mers as seeds due to their redundant 2 nature using, e.g., minimizers (Roberts et al 2004) or later subsampling techniques (DeBlasio et al 2019;Frith, Noé, et al 2020;Ekim, Berger, and Orenstein 2020;Zheng et al 2021;Edgar 2021;Frith, Shaw, et al 2023). For an extensive study of subsampling techniques, see (Shaw and Yu 2021).…”

Section: Other Seed Constructsmentioning

confidence: 99%

Entropy predicts sensitivity of pseudorandom seeds

Maier

Sahlin

2023

Genome Res.

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Seed design is important for sequence similarity search applications such as read mapping and average nucleotide identity (ANI) estimation. Whilek-mers and spacedk-mers are likely the most well-known and used seeds, sensitivity suffers at high error rates, particularly when indels are present. Recently, we developed a pseudo-random seeding construct, strobemers, which were empirically demonstrated to have high sensitivity also at high indel rates. However, the study lacked a deeper understanding of why. In this study, we propose a model to estimate the entropy of a seed and find that seeds with high entropy, according to our model, in most cases have high match sensitivity. Our discovered seed randomness-sensitivity relationship explains why some seeds perform better than others, and the relationship provides a framework for designing even more sensitive seeds. We also present three new strobemer seed constructs, mixedstrobes, altstrobes, and multistrobes. We use both simulated and biological data to demonstrate that our new seed constructs improve sequence-matching sensitivity to other strobemers. We show that the three new seed constructs are useful for read mapping and ANI estimation. For read mapping, we implement strobemers into minimap2 and observe 30% faster alignment time and 0.2% higher accuracy than usingk-mers when mapping reads at high error rates. As for ANI-estimation, we find that higher entropy seeds have a higher rank correlation between estimated and true ANI.

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How to optimally sample a sequence for rapid analysis

Cited by 5 publications

References 36 publications

Proving sequence aligners can guarantee accuracy in almostO(mlogn) time through an average-case analysis of the seed-chain-extend heuristic

Proving sequence aligners can guarantee accuracy in almostO(mlogn) time through an average-case analysis of the seed-chain-extend heuristic

Sequence aligners can guarantee accuracy in almostO(mlogn) time: a rigorous average-case analysis of the seed-chain-extend heuristic

Entropy predicts sensitivity of pseudorandom seeds

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