Algorithms for Colinear Chaining with Overlaps and Gap Costs

Jain, Chirag; Gibney, Daniel; Thankachan, Sharma V.

doi:10.1089/cmb.2022.0266

Cited by 13 publications

(34 citation statements)

References 30 publications

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“…We only use k-mer seeds in this study, although other types of seeds are possible (Keich et al, 2004; Kiełbasa et al, 2011). An optimal increasing subsequence of possibly overlapping anchors based on some score is then collected into a chain , where increasing is defined with the standard precedence relationship (Jain et al, 2022) between k-mer anchors (See Figure 5a and Chaining below). The chain is extended into a full alignment by aligning between anchor gaps in the chain.…”

Section: Resultsmentioning

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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Section: Resultsmentioning

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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“…Co-linear chaining is a mathematically rigorous approach to do clustering of anchors. It is well studied for the case of sequence-to-sequence alignment [1,11,12,16,26,28,32], and is widely used in present-day long read to reference sequence aligners [18,21,35,37,38]. For the sequence-to-sequence alignment case, the input to the chaining problem is a set of N weighted anchors where each anchor is a pair of intervals in the two sequences that match exactly.…”

Section: Introductionmentioning

confidence: 99%

“…However, the problem formulations in these works did not include gap cost. Without penalizing gaps, chaining is less effective [16]. A challenge in enforcing gap cost is that measuring gap between two loci in a DAG is not a simple arithmetic operation like in a sequence [20].…”

Section: Introductionmentioning

confidence: 99%

Sequence to graph alignment using gap-sensitive co-linear chaining

Chandra

Jain

2022

Preprint

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Co-linear chaining is a widely used technique in sequence alignment tools that follow seed-filter-extend methodology. It is a mathematically rigorous approach to combine small exact matches. For co-linear chaining between two sequences, efficient subquadratic-time chaining algorithms are well-known for linear, concave and convex gap cost functions [Eppstein et al. JACM'92]. However, developing extensions of chaining algorithms for DAGs (directed acyclic graphs) has been challenging. Recently, a new sparse dynamic programming framework was introduced that exploits small path cover of pangenome reference DAGs, and enables efficient chaining [Makinen et al. TALG'19, RECOMB'18]. However, the underlying problem formulation did not consider gap cost which makes chaining less effective in practice. To address this, we develop novel problem formulations and optimal chaining algorithms that support a variety of gap cost functions. We demonstrate empirically the ability of our provably-good chaining implementation to align long reads more precisely in comparison to existing aligners. For mapping simulated long reads from human genome to a pangenome DAG of 95 human haplotypes, we achieve 98.7% precision while leaving < 2% reads unmapped. Implementation: https://github.com/at-cg/minichain

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“…For long reads, there has been a recent breakthrough by sampling and indexing only a relatively small number of short potential seeds from the reference genome, which has led to faster and more accurate mapping tools, e.g., [24] and [16]. Chaining consists of finding maximal subsets of seeds that all agree on a certain genomic location [14]; seeds often have spurious matches due to their short lengths.…”

Section: Introductionmentioning

confidence: 99%

“…We also show for the first time that indexing only the long minimizer-space seeds ( k -min-mers) that occur uniquely in the genome is sufficient for sensitive and specific mapping. Another major conceptual advance is that by leveraging the high specificity of these seeds, we can devise a provably 𝒪( n ) time (heuristic) pseudo-chaining algorithm, which improves upon the subsequent best 𝒪( n log n ) runtime of all other known colinear chaining methods [14], without loss of performance in practice. We further study why simply using longer k -mers would be suboptimal.…”

Section: Introductionmentioning

confidence: 99%

mapquik: Efficient low-divergence mapping of long reads in minimizer space

Ekim

Sahlin

Medvedev

et al. 2022

Preprint

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DNA sequencing data continues to progress towards longer reads with increasingly lower sequencing error rates. We focus on the critical problem of mapping, or aligning, low-divergence sequences from long reads (PacBio HiFi) to a reference genome, which poses challenges in terms of accuracy and computational resources when using cutting-edge read mapping approaches that are designed for all types of alignments. A natural idea would be to optimize efficiency with longer seeds to reduce the probability of extraneous matches; however, contiguous exact seeds quickly reach a sensitivity limit. We introduce mapquik, a novel strategy that creates accurate longer seeds by anchoring alignments through matches of k consecutively-sampled minimizers (k-min-mers) and only indexing k-min-mers that occur once in the reference genome, thereby unlocking ultra-fast mapping while retaining high sensitivity. We demonstrate that mapquik significantly accelerates the seeding and chaining steps - fundamental bottlenecks to read mapping - for both the human and maize genomes with > 96% sensitivity and near-perfect specificity. On the human genome, mapquik achieves a 30x speed-up over the state-of-the-art tool minimap2, and on the maize genome, a 350x speed-up over minimap2, making mapquik the fastest mapper to date. These accelerations are enabled not only by minimizer-space seeding but also a novel heuristic O(n) pseudo-chaining algorithm, which improves over the long-standing O(n log n) bound. Minimizer-space computation builds the foundation for achieving real-time analysis of long-read sequencing data.

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Algorithms for Colinear Chaining with Overlaps and Gap Costs

Cited by 13 publications

References 30 publications

Sequence aligners can guarantee accuracy in almostO(mlogn) time: a rigorous 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

Sequence to graph alignment using gap-sensitive co-linear chaining

mapquik: Efficient low-divergence mapping of long reads in minimizer space

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