Sequence Alignment

1. Sequence Alignment Motivation: • Storing,retrieving and comparing DNA sequences in Databases. • Comparing two or more sequences for similarities. • Searching databases for related sequences and subsequences. • Exploring frequently occurring patterns of nucleotides. • Finding informative elements in protein and DNA sequences. • Various experimental applications (reconstruction of DNA, etc.)

2. ? Similar 3D structure ? Similar sequences produce similar proteins Seq.Align. Protein Function Protein1 Protein2 More than 25% sequence identity ? Similar function

3. Exact Pattern Matching • Given a pattern P of length m and a (longer) string T of length n, find all the occurrences of P in T. • Naïve algorithm: O(m*n) • Boyer-Moore, Knuth-Pratt-Morris: O(n+m)

4. Alignment - inexact matching • Substitution - replacing a sequence base by another. • Insertion - an insertion of a base (letter) or several bases to the sequence. • Deletion - deleting a base (or more) from the sequence. • (Insertion and deletion are the reverse of one another)

5. Seq. Align. Score Commonly used matrices: PAM250, BLOSUM64

6. Global Alignment Global Alignment INPUT:Two sequences S and T of roughly the same length. QUESTION:What is the maximum similarity between them? Find one of the best alignments.

7. The IDEA s[1…n] t[1…m] To aligns[1...i]witht[1…j]we have three choices: * align s[1…i-1] with t[1…j-1] and match s[i] with t[j] * align s[1…i] with t[1…j-1] and match a space with t[j] * align s[1…i-1] with t[1…j] and match s[i] with a space s[1…i-1] i t[1…j-1] j s[1… i ] - t[1…j-1] j s[1…i-1] i t[1… j ] -

8. Recursive Relation Define: scoring matrix m(a,b) a,b ∈ ∑ U {-} Define: Hij the best score of alignment between s[1…i] and t[1…j] for 1 <= i <= n, 1 <= j <= m Hi-1j-1 + m(si,tj) Hij = max Hij-1 + m(-,tj)Hi-1j + m(si,-) Hi0 = ∑0,k m(sk,-) H0j = ∑0,k m(-,tk) Optimal alignment score = Hnm Needleman-Wunsch 1970

9. t s3 t4 I T s3 - I - - t4 - T s

11. Local Alignment Local Alignment INPUT:Two sequences S and T . QUESTION:What is the maximum similarity between a subsequence of S and a subsequence of T ? Find most similar subsequences.

12. Recursive Relation for 1 <= i <= n, 1 <= j <= m Hi-1j-1 + m(si,tj) Hij-1 + m(-,tj)Hi-1j + m(si,-) 0 Hi0 = 0 H0j = 0 Hij = max Optimal alignment score = maxijHij Smith-Waterman 1981 *Penalties should be negative*

13. Sequence Alignment Complexity: Time O(n*m) Space O(n*m) (exist algorithm with O(min(n,m)))

14. Ends free alignment Ends free alignmentINPUT:Two equences S and T (possibly of different length).QUESTION:Find one of the best alignments betweensubsequences ofS and Twhen at least one of these subsequences is a prefix of theoriginal sequence and one (not necessarily theother) is a suffix. or

15. Gap Alignment Definition:A gap is the maximal contiguous run of spaces in a single sequence within a given alignment.The length of a gap is the number of indel operations on it. A gap penalty function is a function that measure the cost of a gap as a (nonlinear)function of its length. Gap penaltyINPUT:Two sequences S and T (possibly of differentlength).QUESTION:Find one of the best alignments between the two sequencesusing the gap penalty function. Affine Gap: Wtotal = Wg + qWs Wg – weight to open the gap Ws – weight to extend the gap

16. What Kind of Alignment to Use? • The same protein from the different organisms. • Two different proteins sharing the same function. • Protein domain against a database of complete proteins. • Protein against a database of small patterns (functional units) • ...

17. Sequence Alignment vs. Database • Task: Given a query sequence and millions of database records, find the optimal alignment between the query and a record ACTTTTGGTGACTGTAC

18. Sequence Alignment vs. Database • Tool: Given two sequences,there exists an algorithm tofind the best alignment. • Naïve Solution: Apply algorithm to each of the records, one by one

19. Sequence Alignment vs. Database • Problem: An exact algorithm is too slowto run millions of times (even linear time algorithm will run slowly on a huge DB) • Solution: • Run in parallel (expensive). • Use a fast (heuristic) method to discard irrelevant records. Then apply the exact algorithm to the remaining few.

20. Sequence Alignment vs. Database • General Strategy of Heuristic Algorithms: • Homologous sequences are expected to contain un-gapped (at least) short segments (probably with substitutions, but without ins/dels) • Preprocess DB into some fast access data structure of short segments.

21. FASTA Idea • Idea: a good alignment probably matches some identical ‘words’ (ktups) • Example: Database record: ACTTGTAGATACAAAATGTG Aligned query sequence: A-TTGTCG-TACAA-ATCTGT Matching words of size 4

22. Dictionaries of Words ACTTGTAGATAC Is translated to the dictionary: ACTT, CTTG, TTGT, TGTA… Dictionaries of well aligned sequences share words.

23. FASTA Stage I • Prepare dictionary for db sequence (in advance) • Upon query: • Prepare dictionary for query sequence • For each DB record: • Find matching words • Search for long diagonal runs of matching words • Init-1 score: longest run • Discard record if low score *= matching word * * * * * * * * * * * * Position in DB record Position in query

24. FASTA stage II • Good alignment – path through many runs, withshort connections • Assign weights to runs(+)and connections(-) • Find a path of max weight • Init-n score – total path weight • Discard record if low score

25. FASTA Stage III • Improve Init-1. Apply an exact algorithm around Init-1 diagonal within a given width band. • Init-1 Opt-score – new weight • Discard record if low score

26. FASTA final stage • Apply an exact algorithm to surviving records, computing the final alignment score.

27. BLAST(Basic Local Alignment Search Tool) Approximate Matches BLAST: Words are allowed to contain inexact matching. Example: In the polypeptide sequence IHAVEADREAM The 4-long word HAVE starting at position 2 may match HAVE,RAVE,HIVE,HALE,…

28. Approximate Matches For each wordof length w from a Data Base generate all similar words. ‘Similar’ means: score( word, word’ ) > T Store all similar words in a look-up table.

29. DB search 1) For each wordof length w from a query sequence generate all similar words. 2) Access DB. 3) Each hit extend as much as possible -> High-scoring Segment Pair (HSP) score(HSP) > V THEFIRSTLINIHAVEADREAMESIRPATRICKREAD INVIEIAMDEADMEATTNAMHEWASNINETEEN

30. DB search (2) 4) Around HSP perform DP. At each step alignment score should be > T s-db starting point (seed pair) s-query

31. Homework • Write a cgi script (using Perl) that performs pairwise Local/Global Alignment for DNA sequences. All I/O is via HTML only. • Input: • Choice for Local/Global alignment. • Two sequences – text boxes. • Values for match, mismatch, ins/dels. • Number of iterations for computing random scores. • Output: • Alignment score. • z-score value (z= (score-average)/standard deviation.) Remarks: 1) you are allowed to use only linear space. 2)To compute z-score perform random shuffling: srand(time| $$); #init, $$-proc.id int(rand($i)); #returns rand. number between [0,$i]. 3)Shuffling is done in windows (non-overlapping) of 10 bases length. Number of shuffling for each window is random [0,10].