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Sequence to Graph Alignment Using Gap-Sensitive Co-linear Chaining

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Research in Computational Molecular Biology (RECOMB 2023)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 13976))


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 short 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 directed acyclic graphs (DAGs) 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.


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  1. Abouelhoda, M., Ohlebusch, E.: Chaining algorithms for multiple genome comparison. J. Discrete Algorithms 3(2–4), 321–341 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Baaijens, J.A., et al.: Computational graph pangenomics: a tutorial on data structures and their applications. Nat. Comput. 21, 81–108 (2022).

    Article  MathSciNet  Google Scholar 

  3. Backurs, A., Indyk, P.: Edit distance cannot be computed in strongly subquadratic time (unless SETH is false). In: Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing, pp. 51–58 (2015)

    Google Scholar 

  4. de Berg, M., Cheong, O., van Kreveld, M.J., Overmars, M.H.: Computational Geometry: Algorithms and Applications, 3rd edn. Springer, Heidelberg (2008).

    Book  MATH  Google Scholar 

  5. Cáceres, M., Cairo, M., Mumey, B., Rizzi, R., Tomescu, A.I.: Sparsifying, shrinking and splicing for minimum path cover in parameterized linear time. In: Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 359–376. SIAM (2022)

    Google Scholar 

  6. Chandra, G., Jain, C.: Sequence to graph alignment using gap-sensitive co-linear chaining. BioRxiv (2022).

  7. Computational Pan-Genomics Consortium: Computational pan-genomics: status, promises and challenges. Brief. Bioinform. 19(1), 118–135 (2018)

    Google Scholar 

  8. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press, Cambridge (2022)

    MATH  Google Scholar 

  9. Dvorkina, T., Antipov, D., Korobeynikov, A., Nurk, S.: SPAligner: alignment of long diverged molecular sequences to assembly graphs. BMC Bioinform. 21(12), 1–14 (2020)

    Google Scholar 

  10. Eggertsson, H.P., Jonsson, H., Kristmundsdottir, S., et al.: Graphtyper enables population-scale genotyping using pangenome graphs. Nat. Genet. 49(11), 1654–1660 (2017)

    Article  Google Scholar 

  11. Eizenga, J.M., et al.: Pangenome graphs. Annu. Rev. Genomics Hum. Genet. 21, 139 (2020)

    Article  Google Scholar 

  12. Eppstein, D., Galil, Z., Giancarlo, R., Italiano, G.F.: Sparse dynamic programming I: linear cost functions. J. ACM 39(3), 519–545 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  13. Eppstein, D., Galil, Z., Giancarlo, R., Italiano, G.F.: Sparse dynamic programming II: convex and concave cost functions. J. ACM 39(3), 546–567 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  14. Garg, S., Rautiainen, M., Novak, A.M., et al.: A graph-based approach to diploid genome assembly. Bioinformatics 34(13), i105–i114 (2018)

    Article  Google Scholar 

  15. Illumina: DRAGEN v3.10.4 software release notes. Accessed 08 Aug 2022

  16. Ivanov, P., Bichsel, B., Vechev, M.: Fast and optimal sequence-to-graph alignment guided by seeds. In: Pe’er, I. (ed.) RECOMB 2022. LNBI, vol. 13278, pp. 306–325. Springer, Cham (2022).

    Chapter  Google Scholar 

  17. Jain, C., Gibney, D., Thankachan, S.V.: Co-linear chaining with overlaps and gap costs. In: Pe’er, I. (ed.) RECOMB 2022. LNBI, vol. 13278, pp. 246–262. Springer, Cham (2022).

    Chapter  Google Scholar 

  18. Jain, C., Misra, S., Zhang, H., Dilthey, A., Aluru, S.: Accelerating sequence alignment to graphs. In: 2019 IEEE International Parallel and Distributed Processing Symposium (IPDPS), pp. 451–461. IEEE (2019)

    Google Scholar 

  19. Jain, C., Rhie, A., Hansen, N.F., Koren, S., Phillippy, A.M.: Long-read mapping to repetitive reference sequences using Winnowmap2. Nat. Methods 19(6), 705–710 (2022)

    Article  Google Scholar 

  20. Jain, C., et al.: Weighted minimizer sampling improves long read mapping. Bioinformatics 36(Supplement_1), i111–i118 (2020)

    Google Scholar 

  21. Jain, C., Zhang, H., Dilthey, A., Aluru, S.: Validating paired-end read alignments in sequence graphs. In: 19th International Workshop on Algorithms in Bioinformatics (WABI 2019). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2019)

    Google Scholar 

  22. Li, H.: Minimap2: pairwise alignment for nucleotide sequences. Bioinformatics 34(18), 3094–3100 (2018).

    Article  Google Scholar 

  23. Li, H., Feng, X., Chu, C.: The design and construction of reference pangenome graphs with minigraph. Genome Biol. 21(1), 265 (2020).

    Article  Google Scholar 

  24. Li, H., Ruan, J., Durbin, R.: Mapping short DNA sequencing reads and calling variants using mapping quality scores. Genome Res. 18(11), 1851–1858 (2008)

    Article  Google Scholar 

  25. Liao, W.W., et al.: A draft human pangenome reference. BioRxiv (2022).

  26. Ma, J., Cáceres, M., Salmela, L., Mäkinen, V., Tomescu, A.I.: GraphChainer: co-linear chaining for accurate alignment of long reads to variation graphs. BioRxiv (2022)

    Google Scholar 

  27. Mäkinen, V., Sahlin, K.: Chaining with overlaps revisited. In: 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Schloss Dagstuhl-Leibniz-Zentrum für Informatik (2020)

    Google Scholar 

  28. Mäkinen, V., Tomescu, A.I., Kuosmanen, A., Paavilainen, T., Gagie, T., Chikhi, R.: Sparse dynamic programming on DAGs with small width. ACM Trans. Algorithms 15(2), 1–21 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  29. Myers, G., Miller, W.: Chaining multiple-alignment fragments in sub-quadratic time. In: SODA, vol. 95, pp. 38–47 (1995)

    Google Scholar 

  30. Navarro, G.: Improved approximate pattern matching on hypertext. Theor. Comput. Sci. 237(1–2), 455–463 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  31. Nurk, S., Koren, S., Rhie, A., Rautiainen, M., et al.: The complete sequence of a human genome. Science 376(6588), 44–53 (2022).

    Article  Google Scholar 

  32. Ono, Y., Asai, K., Hamada, M.: PBSIM2: a simulator for long-read sequencers with a novel generative model of quality scores. Bioinformatics 37(5), 589–595 (2020).

    Article  Google Scholar 

  33. Otto, C., Hoffmann, S., Gorodkin, J., Stadler, P.F.: Fast local fragment chaining using sum-of-pair gap costs. Algorithms Mol. Biol. 6(1), 4 (2011).

    Article  Google Scholar 

  34. Paten, B., Novak, A.M., Eizenga, J.M., Garrison, E.: Genome graphs and the evolution of genome inference. Genome Res. 27(5), 665–676 (2017)

    Article  Google Scholar 

  35. Rautiainen, M., Marschall, T.: GraphAligner: rapid and versatile sequence-to-graph alignment. Genome Biol. 21(1), 1–28 (2020).

    Article  Google Scholar 

  36. Ren, J., Chaisson, M.J.: lra: a long read aligner for sequences and contigs. PLoS Comput. Biol. 17(6), e1009078 (2021)

    Article  Google Scholar 

  37. Roberts, M., Hayes, W., Hunt, B.R., Mount, S.M., Yorke, J.A.: Reducing storage requirements for biological sequence comparison. Bioinformatics 20(18), 3363–3369 (2004).

    Article  Google Scholar 

  38. Sahlin, K., Baudeau, T., Cazaux, B., Marchet, C.: A survey of mapping algorithms in the long-reads era. BioRxiv (2022)

    Google Scholar 

  39. Sahlin, K., Mäkinen, V.: Accurate spliced alignment of long RNA sequencing reads. Bioinformatics 37(24), 4643–4651 (2021)

    Article  Google Scholar 

  40. Salmela, L., Rivals, E.: LoRDEC: accurate and efficient long read error correction. Bioinformatics 30(24), 3506–3514 (2014)

    Article  Google Scholar 

  41. Sirén, J., Monlong, J., Chang, X., et al.: Pangenomics enables genotyping of known structural variants in 5202 diverse genomes. Science 374(6574), abg8871 (2021)

    Google Scholar 

  42. Wang, T., Antonacci-Fulton, L., Howe, K., et al.: The human pangenome project: a global resource to map genomic diversity. Nature 604(7906), 437–446 (2022)

    Article  Google Scholar 

  43. Zhang, H., Wu, S., Aluru, S., Li, H.: Fast sequence to graph alignment using the graph wavefront algorithm. arXiv preprint arXiv:2206.13574 (2022)

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This work was supported by funding from the National Supercomputing Mission, India under DST/NSM/R &D_HPC_Applications. We used computing resources provided by the C-DAC National PARAM Supercomputing Facility, India, and the National Energy Research Scientific Computing Center, USA.

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Correspondence to Chirag Jain .

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Chandra, G., Jain, C. (2023). Sequence to Graph Alignment Using Gap-Sensitive Co-linear Chaining. In: Tang, H. (eds) Research in Computational Molecular Biology. RECOMB 2023. Lecture Notes in Computer Science(), vol 13976. Springer, Cham.

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