1. 1 Omics Achim Tresch UoC / MPIPZ Cologne treschgroup.de/OmicsModule1415.html tresch@mpipz.mpg.de

2. Mapping of Sequence Reads Today‘s topics: Hash tables Suffix arrays Burrows-Wheeler transform

3. RNA-seq, ChIP-seq, Methyl-seq, ClIP-seq …CCA TAGGCTATATGCGCCCTATCGGCAATTTGCGGTATAC… GCGCCCTA GCCCTATCG CCTATCGGA CTATCGGAAA AAATTTGC TTTGCGGT TTGCGGTA GCGGTATA GTATAC… TCGGAAATT CGGAAATTT CGGTATAC TAGGCTATA GCCCTATCG CCTATCGGA CTATCGGAAA AAATTTGC TTTGCGGT TCGGAAATT CGGAAATTT AGGCTATAT GGCTATATG CTATATGCG …CC …CCA …CCAT ATAC… C… …CCAT …CCATAGTATGCGCCC GGTATAC… CGGTATAC GGAAATTTG …CCATAGGCTATATGCGCCCTATCGGCAATTTGCGGTATAC… ATAC… …CC GAAATTTGC Goal: identify variations Goal: classify, measure significant peaks Genotyping Reference genome Short reads Short Read Applications Mapping of Sequence Reads

4. Genomes and reads are too large for direct approaches like dynamic programming Indexing is required Choice of index is key to performance Suffix tree Suffix array Seed hash tables Many variants, incl. spaced seeds Indexing of the reference genome

5. Genome indices can be big. For human: Large indices necessitate painful compromises 1.Require big-memory machine 2.Use secondary storage > 35 GBs > 12 GBs 3.Build new index each run 4.Subindex and do multiple passes Indexing of the reference genome

6. Slides taken from Michael Main University of Colorado Hash tables

7. The simplest kind of hash table is an array of records. This example has 701 records. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] An array of records... [ 700] Hash tables

8. Each record has a special field, called its key. In this example, the key is a long integer number [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ]... [ 700] [ 4 ] Key 506643548 Hash tables

9. The number might be a person's identification number, and the rest of the record has information about the person. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ]... [ 700] [ 4 ] Hash tables Key 506643548

10. When a hash table is in use, some spots contain valid records, and other spots are "empty". [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322... Hash tables

11. In order to insert a new record, the key must somehow be converted to an index. The function which does this is the hash function. The index is also called the hash value of the key. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322... Key 580625685 In our case: The keys are short sequences, and the records contain their location in the genome Inserting a new record

12. Typical hash function: Take the integer division rest of the key mod the array size: [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322... Key mod 701 Inserting a new record Key 580625685

13. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322... 3 Inserting a new record Key 580625685 Typical hash function: Take the integer division rest of the key mod the array size: Key mod 701 = 580625685 mod 701 = 3

14. The hash value is used for the location of the new record. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322... [3] Inserting a new record Key 580625685

15. The hash value is used for the location of the new record. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322... Number 580625685 Inserting a new record

16. Here is another new record to insert, with a hash value of 2. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322... Number 580625685 My hash value is [2]. Collisions Key 701466868

17. This is called a collision, because there is already another valid record at [2]. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322... Number 580625685 Key 701466868 When a collision occurs, move forward until you find an empty spot. Collisions

18. This is called a collision, because there is already another valid record at [2]. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322... Number 580625685 Number 701466868 When a collision occurs, move forward until you find an empty spot. Collisions

19. This is called a collision, because there is already another valid record at [2]. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322... Number 580625685 Number 701466868 When a collision occurs, move forward until you find an empty spot. Collisions

20. This is called a collision, because there is already another valid record at [2]. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322... Number 580625685 Number 701466868 The new record goes in the empty spot. Collisions

21. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322 Number 580625685 Number 701466868... If the keys were short sequences, can you think of a hash function for generating index values? ATACCG? A Quiz

22. The data that's attached to a key can be found quickly. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322... Number 580625685 Number 701466868 Searching for a Key Key 701466868

23. Calculate the hash value of the key. Check that location of the array for the key. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322... Number 580625685 Number 701466868 Key 701466868 My hash value is [2]. Not me. Searching for a Key

24. Keep moving forward until you find the key, or you reach an empty spot. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322... Number 580625685 Number 701466868 My hash value is [2]. Not me. Searching for a Key Key 701466868

25. Keep moving forward until you find the key, or you reach an empty spot. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322... Number 580625685 Number 701466868 My hash value is [2]. Not me. Searching for a Key Key 701466868

26. Keep moving forward until you find the key, or you reach an empty spot. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322... Number 580625685 Number 701466868 My hash value is [2]. Yes! Searching for a Key Key 701466868

27. When the item is found, the information can be copied to the necessary location. [ 0 ][ 1 ][ 2 ][ 3 ][ 4 ][ 5 ] [ 700] Number 506643548 Number 233667136 Number 281942902 Number 155778322... Number 580625685 Number 701466868 My hash value is [2]. Yes! Searching for a Key Key 701466868

28. Hash tables store a collection of records with keys. The location of a record depends on the hash value of the record's key. When a collision occurs, the next available location is used. Searching for a particular key is generally quick. Summary How can hash tables be used for mapping?

29. Preprocessing of the target genome: Cut the genome into short sequences of fixed length L Use these sequences as keys to create a hash table (this takes time, but only once!)... Key: ACTAGGTCTT GAGAATCTTA Matches: Chr II, 304938 Chr V, 2053723 Mapping by hash tables Key: ACTAGGTCTT GAGAATCTTA Content: Starting position Chr V, 2053723 Key: ACTAGGTCTT GAGAATCTTA Content: Starting position Chr V, 2053723 Key: ACTAGGTCTT GAGAATCTTA Content: Starting position Chr V, 2053723 Key: ACTAGGTCTT GAGAATCTTA Content: Starting position Chr V, 2053723 For all such sequences, store all matching positions in the genome as data in the hash table

30. Mapping of short reads from a sequencing experiment: For every read, use a substring of length L and check its occurrence in the hash table Given the few (possibly none) matching positions, try to extend the alignment to the whole short read.... Key: ACTAGGTCTT GAGAATCTTA Matches: Chr II, 304938 Chr V, 2053723 Mapping by hash tables Key: ACTAGGTCTT GAGAATCTTA Content: Starting position Chr V, 2053723 Key: ACTAGGTCTT GAGAATCTTA Content: Starting position Chr V, 2053723 Key: ACTAGGTCTT GAGAATCTTA Content: Starting position Chr V, 2053723 Key: ACTAGGTCTT GAGAATCTTA Content: Starting position Chr V, 2053723

32. Suffix Arrays Suffix arrays were introduced by Manber and Myers in 1993 More space efficient than suffix trees A suffix array for a string x of length m is an array of size m that specifies the lexicographic ordering of the suffixes of x. Idea: Every substring is a prefix of a suffix

33. Example of a suffix array for acaaacatat$ 3 4 1 5 7 9 2 6 8 10 11 Starting position of that suffix in the search string Suffix Arrays

34. Naive construction – Similar to insertion sort – Insert all the suffixes into the array one by one making sure that the newly inserted suffix is in its correct place – Running time complexity: O(m 2 ) where m is the length of the string Manber and Myers give a O(m log m) construction in their 1993 paper. Suffix Array Construction

35. There exists a memory efficient O(n) space where n is the size of the database string However in this case query time increases Lookup query – Binary search – O(m log n) time; m is the size of the query – Can reduce time to O(m + log n) using a more efficient implementation Suffix Array Construction

36. find(Pattern P in SuffixArray A): lo = 0, hi = length(A) for i in 0:length(P) Binary search for x,y such that P[i]=S[A[j]+i] for all j=x,x+1,…,y lo = x, hi = y return {lo,hi} Suffix Array Search

37. Search ‘is’ in mississippi$ 011i$ 18ippi$ 25issippi$ 32ississippi$ 41mississippi$ 510pi$ 69ppi$ 77sippi$ 84sissippi$ 96ssippi$ 103ssissippi$ 1112$ Examine the pattern letter by letter, reducing the range of occurrence each time. - First letter i: occurs in indices from 0 to 3 - Second letter s: occurs in indices from 2 to 3 Done. Output: issippi$ and ississippi$ Suffix Array Search

38. It can be built very fast. It can answer queries very fast: – How many times does ‘ATG’ appear? Disadvantages: – Can’t do approximate matching – Hard to insert new sequences / modify sequences dynamically (need to rebuild the array) Summary

39. http://pauillac.inria.fr/~quercia/documents-info/Luminy- 98/albert/JAVA+html/SuffixTreeGrow.html http://home.in.tum.de/~maass/suffix.html http://homepage.usask.ca/~ctl271/857/suffix_tree.shtml http://homepage.usask.ca/~ctl271/810/approximate_matchin g.shtml http://www.cs.mcgill.ca/~cs251/OldCourses/1997/topic7/ http://dogma.net/markn/articles/suffixt/suffixt.htm http://www.csse.monash.edu.au/~lloyd/tildeAlgDS/Tree/Suffi x/ Links

41. Bowtie: A Highly Scalable Tool for Post-Genomic Datasets (Slides by Ben Langmead)

42. Short Read Alignment Given a reference and a set of reads, report at least one “good” local alignment for each read if one exists –Approximate answer to: where in genome did read originate? …TGATCATA… GATCAA …TGATCATA… GAGAAT better than What is “good”? For now, we concentrate on: …TGATATTA… GATcaT …TGATcaTA… GTACAT better than –Fewer mismatches is better –Failing to align a low-quality base is better than failing to align a high-quality base

43. Burrows-Wheeler Transform Burrows Wheeler Matrix Last column contains the characters preceding the characters in the first column BWT(T) a c a a c g $ $ a c a a c g g $ a c a a c a c g $ a c a a a c g $ a c c a a c g $ a a c a a c g $ Rotate string one by one in each row Sort suffixes lexicographically Text T

44. Burrows-Wheeler Transform Reversible permutation used originally in compression Once BWT(T) is built, all else shown here is discarded –Matrix will be shown for illustration only In long texts, BWT(T) contains more repeated character occurrences than the original text  easier to compress! Burrows Wheeler Matrix Last column BWT(T) T

45. Burrows-Wheeler Transform Property that makes BWT(T) reversible is “LF Mapping” –i th occurrence of a character in Last column is same text occurrence as the i th occurrence in First column BWT(T) Burrows Wheeler Matrix Rank: 2 (sexond ‘a’) Burrows M, Wheeler DJ: A block sorting lossless data compression algorithm. Digital Equipment Corporation, Palo Alto, CA 1994, Technical Report 124; 1994 Rank: 2 (sexond ‘a’)

46. Burrows-Wheeler Transform To recreate T from BWT(T), repeatedly apply rule: T  BWT[ LF(i) ] + T; i = LF(i) –Where LF(i) maps row i to row whose first character corresponds to i’s last per LF Mapping Could be called “unpermute” or “walk-left” algorithm Final T

47. BWT in Bioinformatics Oligomer counting –Healy J et al: Annotating large genomes with exact word matches. Genome Res 2003, 13(10):2306-2315. Whole-genome alignment –Lippert RA: Space-efficient whole genome comparisons with Burrows-Wheeler transforms. J Comp Bio 2005, 12(4):407-415. Smith-Waterman alignment to large reference –Lam TW et al: Compressed indexing and local alignment of DNA. Bioinformatics 2008, 24(6):791-797.

48. TopHat: Bowtie for RNA-seq TopHat is a fast splice junction mapper for RNA-Seq reads. It aligns RNA-Seq reads using Bowtie, and then analyzes the mapping results to identify splice junctions between exons. –Contact: Cole Trapnell (cole@cs.umd.edu) –http://tophat.cbcb.umd.edu

49. Nicolas Delhomme, EMBL Heidelberg University of Umeå Acknowledgements NGS Exercises were designed by

50. Comparison to Maq & SOAP PC: 2.4 GHz Intel Core 2, 2 GB RAM Server: 2.4 GHz AMD Opteron, 32 GB RAM Bowtie v0.9.6, Maq v0.6.6, SOAP v1.10 SOAP not run on PC due to memory constraints Reads: FASTQ 8.84 M reads from 1000 Genomes (Acc: SRR001115) Reference: Human (NCBI 36.3, contigs) CPU time Wall clock time Reads per hour Peak virtual memory footprint Bowtie speedup Reads aligned (%) Bowtie –v 2 (server)15m:07s15m:41s33.8 M1,149 MB-67.4 SOAP (server)91h:57m:35s91h:47m:46s0.08 M13,619 MB351x67.3 Bowtie (PC)16m:41s17m:57s29.5 M1,353 MB-71.9 Maq (PC)17h:46m:35s17h:53m:07s0.49 M804 MB59.8x74.7 Bowtie (server)17m:58s18m:26s28.8 M1,353 MB-71.9 Maq (server)32h:56m:53s32h:58m:39s0.27 M804 MB107x74.7 Bowtie delivers about 30 million alignments per CPU hour