Resolving Multicopy Duplications de novo Using Polyploid Phasing

  • Mark J. Chaisson
  • Sudipto Mukherjee
  • Sreeram Kannan
  • Evan E. Eichler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10229)

Abstract

While the rise of single-molecule sequencing systems has enabled an unprecedented rise in the ability to assemble complex regions of the genome, long segmental duplications in the genome still remain a challenging frontier in assembly. Segmental duplications are at the same time both gene rich and prone to large structural rearrangements, making the resolution of their sequences important in medical and evolutionary studies. Duplicated sequences that are collapsed in mammalian de novo assemblies are rarely identical; after a sequence is duplicated, it begins to acquire paralog-specific variants. In this paper, we study the problem of resolving the variations in multicopy, long segmental duplications by developing and utilizing algorithms for polyploid phasing. We develop two algorithms: the first one is targeted at maximizing the likelihood of observing the reads given the underlying haplotypes using discrete matrix completion. The second algorithm is based on correlation clustering and exploits an assumption, which is often satisfied in these duplications, that each paralog has a sizable number of paralog-specific variants. We develop a detailed simulation methodology and demonstrate the superior performance of the proposed algorithms on an array of simulated datasets. We measure the likelihood score as well as reconstruction accuracy, i.e., what fraction of the reads are clustered correctly. In both the performance metrics, we find that our algorithms dominate existing algorithms on more than 93% of the datasets. While the discrete matrix completion performs better on likelihood score, the correlation-clustering algorithm performs better on reconstruction accuracy due to the stronger regularization inherent in the algorithm. We also show that our correlation-clustering algorithm can reconstruct on average 7.0 haplotypes in 10-copy duplication datasets whereas existing algorithms reconstruct less than one copy on average.

References

  1. 1.
    Aguiar, D., Istrail, S.: Haplotype assembly in polyploid genomes and identical by descent shared tracts. Bioinformatics 29(13), i352–i360 (2013)CrossRefGoogle Scholar
  2. 2.
    Ailon, N., Charikar, M., Newman, A.: Aggregating inconsistent information: ranking and clustering. J. ACM (JACM) 55(5), 23 (2008)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Mach. Learn. 56(1–3), 89–113 (2004)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Bansal, V., Bafna, V.: Hapcut: an efficient and accurate algorithm for the haplotype assembly problem. Bioinformatics 24(16), i153–i159 (2008)CrossRefGoogle Scholar
  5. 5.
    Berger, E., Yorukoglu, D., Peng, J., Berger, B.: Haptree: a novel Bayesian framework for single individual polyplotyping using NGS data. PLoS Comput. Biol. 10(3), e1003502 (2014)CrossRefGoogle Scholar
  6. 6.
    Berlin, K., Koren, S., Chin, C.-S., Drake, J.P., Landolin, J.M., Phillippy, A.M.: Assembling large genomes with single-molecule sequencing and locality-sensitive hashing. Nat. Biotechnol. 33(6), 623–630 (2015)CrossRefGoogle Scholar
  7. 7.
    Bonizzoni, P., Dondi, R., Klau, G.W., Pirola, Y., Pisanti, N., Zaccaria, S.: On the minimum error correction problem for haplotype assembly in diploid and polyploid genomes. J. Comput. Biol. 23, 718–736 (2016)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Cai, C., Sanghavi, S., Vikalo, H.: Structured low-rank matrix factorization for haplotype assembly. J. Sel. Top. Sig. Process. 10(4), 647–657 (2016)CrossRefGoogle Scholar
  9. 9.
    Cai, J.-F., Candès, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20(4), 1956–1982 (2010)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Candès, E.J., Recht, B.: Exact matrix completion via convex optimization. Commun. ACM 55(6), 111–119 (2012)CrossRefMATHGoogle Scholar
  11. 11.
  12. 12.
    Charikar, M., Guruswami, V., Wirth, A.: Clustering with qualitative information. In: Proceedings of 44th Annual IEEE Symposium on Foundations of Computer Science, pp. 524–533. IEEE (2003)Google Scholar
  13. 13.
    Chen, Y., Kamath, G., Suh, C., Tse, D.: Community recovery in graphs with locality (2016). arXiv preprint arXiv:1602.03828
  14. 14.
    Das, S., Vikalo, H.: SDhaP: haplotype assembly for diploids and polyploids via semi-definite programming. BMC Genom. 16(1), 4 (2015)CrossRefGoogle Scholar
  15. 15.
    Demaine, E.D., Immorlica, N.: Correlation clustering with partial information. In: Arora, S., Jansen, K., Rolim, J.D.P., Sahai, A. (eds.) APPROX/RANDOM -2003. LNCS, vol. 2764, pp. 1–13. Springer, Heidelberg (2003). doi:10.1007/978-3-540-45198-3_1 Google Scholar
  16. 16.
    Dempster, A.P.: Laird, N, M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Stat. Soc. Ser. B (Methodol.) 39, 1–38 (1977)Google Scholar
  17. 17.
    Dennis, M.Y., Nuttle, X., Sudmant, P.H., Antonacci, F., Graves, T.A., Nefedov, M., Rosenfeld, J.A., Sajjadian, S., Malig, M., Kotkiewicz, H., et al.: Evolution of human-specific neural SRGAP2 genes by incomplete segmental duplication. Cell 149(4), 912–922 (2012)CrossRefGoogle Scholar
  18. 18.
    Eichler, E.E.: Recent duplication, domain accretion and the dynamic mutation of the human genome. Trends Genet. 17(11), 661–669 (2001)CrossRefGoogle Scholar
  19. 19.
    Emanuel, D., Fiat, A.: Correlation clustering – minimizing disagreements on arbitrary weighted graphs. In: Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 208–220. Springer, Heidelberg (2003). doi:10.1007/978-3-540-39658-1_21 CrossRefGoogle Scholar
  20. 20.
    Fortunato, S.: Community detection in graphs. Phys. Rep. 486(3), 75–174 (2010)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Gordon, D., Huddleston, J., Chaisson, M.J.P., Hill, C.M., Kronenberg, Z.N., Munson, K.M., Malig, M., Raja, A., Fiddes, I., Hillier, L.W., et al.: Long-read sequence assembly of the gorilla genome. Science 352(6281), aae0344 (2016)CrossRefGoogle Scholar
  22. 22.
    Jain, P., Netrapalli, P., Sanghavi, S.: Low-rank matrix completion using alternating minimization. In: Proceedings of 45h Annual ACM Symposium on Theory of Computing, STOC 2013, pp. 665–674, ACM, New York (2013)Google Scholar
  23. 23.
    Jiang, Z., Tang, H., Ventura, M., Cardone, M.F., Marques-Bonet, T., She, X., Pevzner, P.A., Eichler, E.E.: Ancestral reconstruction of segmental duplications reveals punctuated cores of human genome evolution. Nat. Genet. 39(11), 1361–1368 (2007)CrossRefGoogle Scholar
  24. 24.
    Koren, S., Walenz, B.P., Berlin, K., Miller, J.R., Phillippy, A.M.: Canu: scalable and accurate long-read assembly via adaptive k-mer weighting and repeat separation. bioRxiv, p. 071282 (2016)Google Scholar
  25. 25.
    Lancia, G., Bafna, V., Istrail, S., Lippert, R., Schwartz, R.: SNPs problems, complexity, and algorithms. In: Heide, F.M. (ed.) ESA 2001. LNCS, vol. 2161, pp. 182–193. Springer, Heidelberg (2001). doi:10.1007/3-540-44676-1_15 CrossRefGoogle Scholar
  26. 26.
    Motahari, A., Ramchandran, K., Tse, D., Ma, N.: Optimal DNA shotgun sequencing: noisy reads are as good as noiseless reads (2013). arXiv preprint arXiv:1304.2798
  27. 27.
    Myers, E.W.: Toward simplifying and accurately formulating fragment assembly. J. Comput. Biol. 2(2), 275–290 (1995)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Myers, G.: Efficient local alignment discovery amongst noisy long reads. In: Brown, D., Morgenstern, B. (eds.) WABI 2014. LNCS, vol. 8701, pp. 52–67. Springer, Heidelberg (2014). doi:10.1007/978-3-662-44753-6_5 Google Scholar
  29. 29.
    Patterson, M., Marschall, T., Pisanti, N., Iersel, L., Stougie, L., Klau, G.W., Schönhuth, A.: WhatsHap: haplotype assembly for future-generation sequencing reads. In: Sharan, R. (ed.) RECOMB 2014. LNCS, vol. 8394, pp. 237–249. Springer, Cham (2014). doi:10.1007/978-3-319-05269-4_19 CrossRefGoogle Scholar
  30. 30.
    Pevzner, P.A.: Dna physical mapping and alternating Eulerian cycles in colored graphs. Algorithmica 13(1–2), 77–105 (1995)MathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Pevzner, P.A., Tang, H., Waterman, M.S.: An Eulerian path approach to DNA fragment assembly. Proc. Nat. Acad. Sci. 98(17), 9748–9753 (2001)MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Puljiz, Z., Vikalo, H.: Decoding genetic variations: communications-inspired haplotype assembly. IEEE/ACM Trans. Comput. Biol. Bioinform. 13(3), 518–530 (2016)CrossRefGoogle Scholar
  33. 33.
    Recht, B., Fazel, M., Parrilo, P.A.: Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Rev. 52(3), 471–501 (2010)MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Schwartz, R., et al.: Theory and algorithms for the haplotype assembly problem. Commun. Inf. Syst. 10(1), 23–38 (2010)MathSciNetMATHGoogle Scholar
  35. 35.
    Seo, J.-S., Rhie, A., Lee, S., Sohn, M.-H., Kim, C.-U., Hastie, A., Cao, H., Yun, J.-Y., Kim, J., et al.: De novo assembly and phasing of a Korean human genome. Nature 538, 243 (2016)CrossRefGoogle Scholar
  36. 36.
    Si, H., Vikalo, H., Vishwanath, S.: Haplotype assembly: an information theoretic view. In: 2014 IEEE Information Theory Workshop (ITW), pp. 182–186. IEEE (2014)Google Scholar
  37. 37.
    Stankiewicz, P., Lupski, J.R.: Genome architecture, rearrangements and genomic disorders. Trends Genet. 18(2), 74–82 (2002)CrossRefGoogle Scholar
  38. 38.
    Steinberg, K.M., Graves-Lindsay, T., Schneider, V.A., Chaisson, M.J.P., Tomlinson, C., Huddleston, J.L., Minx, P., Kremitzki, M., Albrecht, D., Magrini, V., et al.: High-quality assembly of an individual of Yoruban descent. bioRxiv, p. 067447 (2016)Google Scholar
  39. 39.
    Usher, C.L., Handsaker, R.E., Esko, T., Tuke, M.A., Weedon, M.N., Hastie, A.R., Cao, H., Moon, J.E., Kashin, S., Fuchsberger, C., et al.: Structural forms of the human amylase locus and their relationships to SNPs, haplotypes and obesity. Nat. Genet. 47(8), 921–925 (2015)CrossRefGoogle Scholar
  40. 40.
    Welling, M., Kurihara, K.: Bayesian k-means as a maximization-expectation algorithm (2007)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Mark J. Chaisson
    • 1
  • Sudipto Mukherjee
    • 2
  • Sreeram Kannan
    • 2
  • Evan E. Eichler
    • 1
    • 3
  1. 1.Department of Genome SciencesUniversity of WashingtonSeattleUSA
  2. 2.Department of Electrical EngineeringUniversity of WashingtonSeattleUSA
  3. 3.Howard Hughes Medical InstituteUniversity of WashingtonSeattleUSA

Personalised recommendations