Report

High Throughput Sequencing: Microscope in the Big Data Era David Tse EASIT Chinese University of Hong Kong July 7, 2014 Research supported by NSF Center for Science of Information. DNA sequencing …ACGTGACTGAGGACCGTG CGACTGAGACTGACTGGGT CTAGCTAGACTACGTTTTA TATATATATACGTCGTCGT ACTGATGACTAGATTACAG ACTGATTTAGATACCTGAC TGATTTTAAAAAAATATT… High throughput sequencing revolution tech. driver for communications Shotgun sequencing read Technologies Sequence Sanger r 3730xl 454 GS Mechanis m Dideoxy chain terminatio n Read length Ion Torrent SOLiDv4 Illumina Pac Bio HiSeq 2000 Pyrose Detection quencin of g hydrogen ion Ligation and twobase coding Reversi Single ble molecule Nucleoti real time des 400-900 bp 700 bp ~400 bp 50 + 50 bp 100 bp PE 1000~1000 0 bp Error Rate 0.001% 0.1% 2% 0.1% 2% 10-15% Output data (per run) 100 KB 1 GB 100 GB 100 GB 1 TB 10 GB High throughput sequencing: Microscope in the big data era Genomic variations, 3-D structures, transcription, translation, protein interaction, etc. The quantities measured can be dynamic and vary spatially. Example: RNA expression is different in different tissues and at different times. Computational problems for high throughput data measure data • Assembly (de Novo) • Variant calling (reference-based assembly) manage data • Compression utilize data • Genome wide association studies • Privacy • Phylogenetic tree reconstruction • Pathogen detection Scope of this tutorial Assembly: three points of view • Software engineering • Computational complexity theoretic • Information theoretic Assembly as a software engineering problem • A single sequencing experiment can generate 100’s of millions of reads, 10’s to 100’s gigabytes of data. • Primary concerns are to minimize time and memory requirements. • No guarantee on optimality of assembly quality and in fact no optimality criterion at all. Computational complexity view • Formulate the assembly problem as a combinatorial optimization problem: – Shortest common superstring (Kececioglu-Myers 95) – Maximum likelihood (Medvedev-Brudno 09) – Hamiltonian path on overlap graph (Nagarajan-Pop 09) • Typically NP-hard and even hard to approximate. • Does not address the question of when the solution reconstructs the ground truth. Information theoretic view Basic question: What is the quality and quantity of read data needed to reliably reconstruct? Tutorial outline I. De Novo DNA assembly. I. De Novo RNA assembly Themes • Interplay between information and computational complexity. • Role of empirical data in driving theory and algorithm development. Part I: De Novo DNA Assembly Shotgun sequencing model Basic model : uniformly sampled reads. Assembly problem: reconstruct the genome given the reads. A Gigantic Jigsaw Puzzle Challenges Read errors Long repeats log(# of `-repeats) 16 15 16.5 16 14 15.5 12 15 10 10 14.5 8 14 13.5 6 5 13 4 12.5 2 12 0 11.5 0 0 20 2 40 60 100080 6 500 4 1001500 8 120 140 10 2000 160 12 Human Chr 22 repeat length histogram ` Illumina read error profile Two-step approach • First, we assume the reads are noiseless • Derive fundamental limits and near-optimal assembly algorithms. • Then, we add noise and see how things change. Repeat statistics harder jigsaw puzzle easier jigsaw puzzle How exactly do the fundamental limits depend on repeat statistics? Lower bound: coverage • Introduced by Lander-Waterman in 1988. • What is the number of reads needed to cover the entire DNA sequence with probability 1-²? • NLW only provides a lower bound on the number of reads needed for reconstruction. • NLW does not depend on the DNA repeat statistics! Simple model: I.I.D. DNA, G ! 1 (Motahari, Bresler & Tse 12) normalized # of reads reconstructable by greedy algorithm coverage 1 many repeats of length L no repeats of length L no coverage read length L What about for finite real DNA? I.I.D. DNA vs real DNA (Bresler, Bresler & Tse 12) Example: human chromosome 22 (build GRCh37, G = 35M) log(# of `-repeats) 16 15 16.5 16 16 14 15 15.5 12 15 10 14 10 14.5 8 1314 13.5 6 12 5 13 4 11 12.5 2 12 10 0 11.5 0 0 i.i.d. fit 20 2 2 40 4 4 500 data 60 80 6 10006 8 100 8 120 10 1500 140 10 122000 160 12 14 ` Can we derive performance bounds on an individual sequence basis? Individual sequence performance bounds (Bresler, Bresler, Tse BMC Bioinformatics 13) Given a genome s log(# of `-repeats) GREEDY DEBRUIJN lower bound Lcritical repeat length Human Chr 19 Build 37 SIMPLEBRIDGING MULTIBRIDGING Lander-Waterman coverage GAGE Benchmark Datasets http://gage.cbcb.umd.edu/ Rhodobacter sphaeroides lower bound Staphylococcus aureus Human Chromosome14 G = 2,903,081 G = 88,289,540 G = 4,603,060 MULTIBRIDGING lower bound MULTIBRIDGING lower bound MULTIBRIDGING Lower bound: Interleaved repeats Necessary condition: all interleaved repeats are bridged. L m n m n In particular: L > longest interleaved repeat length (Ukkonen) Lower bound: Triple repeats Necessary condition: all triple repeats are bridged L In particular: L > longest triple repeat length (Ukkonen) Individual sequence performance bounds (Bresler, Bresler, T. BMC Bioinformatics 13) log(# of `-repeats) lower bound length Human Chr 19 Build 37 Lander-Waterman coverage Greedy algorithm (TIGR Assembler, phrap, CAP3...) Input: the set of N reads of length L 1. Set the initial set of contigs as the reads 2. Find two contigs with largest overlap and merge them into a new contig 3. Repeat step 2 until only one contig remains Greedy algorithm: first error at overlap repeat contigs bridging read already merged A sufficient condition for reconstruction: all repeats are bridged L Back to chromosome 19 lower bound greedy algorithm log(# of `-repeats) 15 10 longest interleaved repeats at length 2248 non-interleaved repeats are resolvable! 5 0 0 1000 2000 GRCh37 Chr 19 (G = 55M) 3000 4000 longest repeat at Dense Read Model • As the number of reads N increases, one can recover exactly the L-spectrum of the genome. • If there is at least one non-repeating L-mer on the genome, this is equivalent information to having a read at every starting position on the genome. • Key question: What is the minimum read length L for which the genome is uniquely reconstructible from its L-spectrum? de Bruijn graph CCCT CCTA GCCC (L = 5) ATAGACCCTAGACGAT AGCC CTAG TAGA ATAG AGAC AGCG GCGA CGAT 1. Add a node for each (L-1)-mer on the genome. 2. Add k edges between two (L-1)-mers if their overlap has length L-2 and the corresponding L-mer appears k times in genome. Eulerian path CCCT CCTA GCCC (L = 5) ATAGACCCTAGACGAT AGCC CTAG TAGA ATAG AGAC AGCG GCGA CGAT Theorem (Pevzner 95) : If L > max(linterleaved, ltriple) , then the de Bruijn graph has a unique Eulerian path which is the original genome. Resolving non-interleaved repeats Condensed sequence graph non-interleaved repeat Unique Eulerian path. From dense reads to shotgun reads [Idury-Waterman 95] [Pevzner et al 01] Idea: mimic the dense read scenario by looking at K-mers of the length L reads Construct the K-mer graph and find an Eulerian path. Success if we have K-coverage of the genome and K > Lcritical De Bruijn algorithm: performance Loss of info. from the reads! GREEDY DEBRUIJN lower bound length Human Chr 19 Build 37 Lander-Waterman coverage Resolving bridged interleaved repeats bridging read interleaved repeat Bridging read resolves one repeat and the unique Eulerian path resolves the other. Simple bridging: performance GREEDY DEBRUIJN lower bound SIMPLEBRIDGING length Human Chr 19 Build 37 Lander-Waterman coverage Resolving triple repeats all copies bridged neighborhood of triple repeat triple repeat all copies bridged resolve repeat locally Triple Repeats: subtleties Multibridging De-Brujin Theorem: (Bresler,Bresler, Tse 13) Original sequence is reconstructible if: 1. triple repeats are all-bridged 2. interleaved repeats are (single) bridged 3. coverage Necessary conditions for ANY algorithm: 1. triple repeats are (single) bridged 1. interleaved repeats are (single) bridged. 2. coverage. Multibridging: near optimality for Chr 19 GREEDY DEBRUIJN lower bound SIMPLEBRIDGING length MULTIBRIDGING Human Chr 19 Build 37 Lander-Waterman coverage GAGE Benchmark Datasets http://gage.cbcb.umd.edu/ Rhodobacter sphaeroides Staphylococcus aureus Human Chromosome14 G = 2,903,081 G = 88,289,540 G = 4,603,060 Lcritical = length of the longest triple or interleaved repeat. Lcritical Lcritical Lcritical lower bound MULTIBRIDGING lower bound MULTIBRIDGING lower bound MULTIBRIDGING Gap Sulfolobus islandicus. G = 2,655,198 triple repeat lower bound interleaved repeat lower bound MULTIBRIDGING algorithm Complexity: Computational vs Informational • Complexity of MULTIBRIDGING – For a G length genome, O(G2) • Alternate formulations of Assembly – Shortest Common Superstring: NP-Hard – Greedy is O(G), but only a 4-approximation to SCS in the worst case – Maximum Likelihood: NP-Hard • Key differences – We are concerned only with instances when reads are informationally sufficient to reconstruct the genome. – Individual sequence formulation lets us focus on issues arising only in real genomes. Read Errors ACGTCCTATGCGTATGCGTAATGCCACATATTGCTATGCGTAATGCGT TATA CTTA Error rate and nature depends on sequencing technology: Examples: • Illumina: 0.1 – 2% substitution errors • PacBio: 10 – 15% indel errors We will focus on a simple substitution noise model with noise parameter p. Consistency Basic question: What is the impact of noise on Lcritical? This question is equivalent to whether the L-spectrum is exactly recoverable as the number of noisy reads N -> 1. Theorem (C.C. Wang 13): Yes, for all p except p = ¾. What about coverage depth? Theorem (Motahari, Ramchandran,Tse, Ma 13): Assume i.i.d. genome model. If read error rate p is less than a threshold, then Lander-Waterman coverage is sufficient for L > Lcritical For uniform distr. on {A,G,C,T}, threshold is 19%. A separation architecture is optimal: error correction assembly Why? noise averaging M • Coverage means most positions are covered by many reads. • Multiple aligning overlapping noisy reads is possible if • Assembly using noiseless reads is possible if From theory to practice Two issues: 1) Multiple alignment is performed by testing joint typicality of M sequences, computationally too expensive. Solution: use the technique of finger printing. 2) Real genomes are not i.i.d. Solution: replace greedy by multibridging. Lam, Khalak, T. Recomb-Seq 14 X-phased multibridging Prochlorococcus marinus Lcritical Substitution errors of rate 1.5 % More results Prochlorococcus marinus Lcritical Methanococcus maripaludis Lcritical Helicobacter pylori Lcritical Mycoplasma agalactiae Lcritical A more careful look Mycoplasma agalactiae Lcritical-approx Lcritical Approximate repeat example: Yersinia pestis exact triple repeat, length 1662 5608 approximate triple repeat length Acknowledgements DNA Assembly Abolfazl Motahari Sharif RNA Assembly Soheil Mohajer U. of Minnesota Guy Bresler MIT Sreeram Kannan Berkeley Lior Pachter Berkeley Ma’ayan Bresler Berkeley Ka Kit Lam Berkeley Eren Sasoglu Berkeley Asif Khalak Pacific Biosciences Joseph Hui Berkeley Kayvon Mazooji Berkeley