# Sequence Comparison. mouse human

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1 Sequence Comparison

2 Sequence Comparison mouse human

3 Why Compare Sequences? The first fact of biological sequence analysis In biomolecular sequences (DNA, RNA, or amino acid sequences), high sequence similarity usually implies significant functional or structural similarity. Dan Gusfield in his book Algorithms on strings, trees, and sequences.

4 How to Measure The most often used distance on strings in computer science is Hamming distance. AGTTTAATCA AGTATAACGA There are other mutations during evolution Substitution ACAGT ACGGT Insertion/deletion (indel) ACAGT ACGT Inversion ACA GT AG ACT Translocation AC AG TAA AG TC AAA Duplication AC A AC A C A There are many formulations of sequence comparison and many algorithms by considering different combinations of these mutations. You are what you measure Harvard Business Review, June 2010.

5 The Most Popular Measure Edit operations: substitution, insertion, deletion. Edit distance: Minimum number of edit operations to convert one sequence to another. Example: A text editor.

6 Edit Distance vs. Alignment GAGTTTAATAC TAGTATAA-AG This is an alignment with score: 7*match + 3*mismatch + 1*indel Under correct score scheme, edit distance is equivalent to sequence alignment. Alignment is easier to show.

7 Levenshtein Edit distance or Levenshtein distance. Vladimir Iosifovich Levenshtein (Russian: Влади мир Ио сифович Левенште йн; born 1935) is a Russian scientist who has done research in information theory, error-correcting codes, and combinatorial design. V.I. Levenshtein. Binary codes capable of correcting deletions, insertions, and reversals. Soviet Physics Doklady (1966). Volume: 10, Issue: 8, Pages: Cited by In error correction coding. Not computational biology. IEEE Richard W. Hamming Medal Recipient 2006

8 Needleman-Wunsch Two western researchers independently proposed this distance in computational biology. SB Needleman, CD Wunsch. A general method applicable to the search for similarities in the amino acid sequence of two proteins. Journal of molecular biology (1970) 48, Cited by 6758.

9 Longest Common Subsequence Needleman-Wunsch actually used the term maximum match that is essentially the longest common subsequence. Let M(i,j) be the LCS of S[1..i] and T[1..j]. The algorithm is essentially the following: M ( i, j) max The statistical significance is also briefly discussed. This is important! M ( i 1, j 1) ( S[ i], T[ M ( i 1, M ( i, j) j 1) j])

10 Backtracking T M ( i, j) M max ( i 1, j 1) ( S[ i], T[ j]) M ( i 1, j) M ( i, j 1) S

11 In Terms of Edit Distance D(i,j) := edit distance between S[1..i] and T[1..j]. Then D( i, j) min D( i 1, j 1) ( S[ i], T[ D( i 1, j) 1 D( i, j 1) 1 j]) Time Complexity: O(mn)

12 In Terms of Alignment Edit distance Alignment D( i, j) D( i min 1, j 1) ( S[ i], T[ j]) D( i 1, j) 1 D( i, j 1) 1 M ( i, j) M max ( i 1, j 1) score( S[ i], T[ j]) M ( i 1, M ( i, j) indel j 1) indel LCS, Edit Distance, Alignments are closely related.

13

14 Linear Space 20 bits addressing space = 1MB memory. 16 Bits linear space = 64KB. 640KB limit for DOS programming. Special technique needed to use > 640KB.

15 D.S. Hirschberg, A linear space algorithm for computing longest common subsequences, Comm. ACM 18 (1975) Cited by 847.

16 First Trick Compute column by column and only keep two recent columns. O(m) space. Drawback: can only know the score of one (or two) columns. S T

17 The Algorithm S k Divide and Conquer. In O mn time and O m + n space, find k such that LCS(S[1.. k], T[1.. n ]) + LCS(S[k m], 2 T[n n]) 2 is maximized. Then recursively solve the two smaller problems. T n/2 T(m, n) = mn + T k, n 2 + T m k, n 2 = O mn

18 How to Find k? LCS(S[1.. k], T[1.. n 2 ]) LCS(S[k m], T[n n]) 2

19 Gaps Are not Welcomed Think of deleting a consecutive row of letters during editing. It s cheaper than scattered deleting. Evolution is somewhat similar. So we want to minimum number of gaps (not necessarily number of indels) AGT--AATCA AGTTCAACGA

20 David Sankoff David Sankoff first proposed a way to restrict gap. Longest common subsequence. Restrict the number of gaps to be K. Cited 245 times.

21 What Is a Gap in LCS AGT--AATCA AGTTCAACGA

22 LCS with No More than K Gaps V q (i,j) = LCS of S[1..i] to T[1..j] with at most q gaps, AND last match is on the same diagonal of i vs. j. If S[i]=T[j], Else, V q ( i, V j) 1 maxmaxk maxk V q ( i 1, ( i k, ( i 1, A straightforward implementation takes O(n 3 K). q 0 0 V V q1 q1 ( i, j) V ( i 1, j 1) q j 1) j 1) j k)

23 More Efficient Algorithm Sankoff introduced another matrix W q (i,j) := LCS of S[1..i] to T[1..j] with at most q gaps. Same as V, except that no same diagonal restriction. W Now V and W can be computed simultaneously O(n 2 K) time. This is like magic q ( i, j) max{ W ( i 1, j), W ( i, j 1), V ( i, j)} for i from 1 to n for j from 1 to n for q from 0 to K q q V ( i, j) ( S[ i], T[ j]) max{ V ( i 1, j 1), W 1( i 1, j 1)} q W ( i, j) max{ W ( i 1, j), W ( i, j 1), V ( i, j)} q q q q q q q

24 A few notes about this particular research 1. Small number of citations. 2. Statistics 3. Use of abstract notations (V,W).

25 Gap Penalty Instead of limiting # of gaps, Waterman, Smith and Beyer proposed to penalize them. Gap penalty: g(k) is the cost of k-consecutive deletions. Normally g(k) < k*g(1).

26 When There s a Gap Penalty D(i 1, j 1) (S[i],T[ j]) D(i, j) max max k D(i k, j) g(k) max k D(i, j k) g(k) Time complexity: O(mnL) L is maximum length of a gap.

27 Local Alignment Biologists do not necessarily know the start and end of the comparison. E.g. Proteins have domains. To find a substring of S and a substring of T, so that their alignment score is maximized. Question: Why not local edit distance?

28 Smith-Waterman Smith, Temple F.; and Waterman, Michael S. (1981). "Identification of Common Molecular Subsequences". Journal of Molecular Biology 147: Michael Waterman Temple Smith

29 indel j i M indel j i M j T i S score j i M j i M 1), ( ) 1, ( ]) [ ], [ ( 1) 1, ( 0 max ), ( indel j i M indel j i M j T i S score j i M j i M 1), ( ) 1, ( ]) [ ], [ ( 1) 1, ( max ), ( Cited 6035 times This simple change from Needleman-Wunsch made a big difference.

30 Affine Gap Penalty Recall that when Waterman et al. introduced the gap penalty g(k), time was cubic. Osamu Gotoh noticed that when the gap penalty is affine: g(k)=a+b*(k-1), the time can be quadratic. a: gap open b: gap extension

31 Affine Gap Penalty In a paper 1986, Altschul gave an example where Gotoh s algorithm may fail due to a glitch, and proposed a new algorithm. Stephen Altschul

32 Affine Gap Penalty 1) 1, ( 1) 1, ( 1) 1, ( max ]) [ ], [ ( ), ( j i M j i M j i M j T i S score j i M M0[i,j]: best alignment score of S[1..i], T[1..j], such that S[i] aligns with T[j]. M1: T[j] aligns with - M2: S[i] aligns with - M0 M1 M2 a j i M b j i M a j i M j i M 1), ( 1), ( 1), ( max ), ( M2 is similarly computed.

33 Linear Space Affine Gap Penalty The goal of this paper is to give Hirschberg s idea the visibility it deserves by developing a linear-space version of Gotoh s algorithm.

34 Speaking of History Question: Why 350kb?

35 History Fact Screenshot of floppydisk.com

36 Amino Acid Matrix Earlier justifications of the sequence alignment algorithms are more about protein sequences. Dayhoff developed the first amino acid substitution matrix. PAM. Atlas of protein sequence and structure (1978) Volume: 5, Issue: Suppl 3, Publisher: National Biomedical Research Foundation,Pages: Cited 5257 times. Margaret Oakley Dayhoff

37 1 PAM: evolution distance of about 1 substitution per 100 amino acids.

38

39 N PAM The 1 PAM matrix can multiply itself N times to get the N PAM matrix.

40 BLOSUM S Henikoff and J G Henikoff. Amino acid substitution matrices from protein blocks. PNAS vol That is when his wife, a mathematician by training, got involved. They started by constructing a database of conserved protein motifs, called BLOCKS. The Henikoffs then developed a technique to extract alignment scores from the BLOCKS database to determine how related two proteins might be. They called their technique BLOSUM, for BLOcks of Amino Acid SUbstitution Matrix.

41 BLOSUM They first estimated probabilities that two amino acids occur in the same column of a pair of alignment P x, y. To avoid over-sampling of some proteins, they clustered the proteins too close (e.g. 62% or higher identity) into one group and count them with weight 1. P x,y Then log is the log likelihood ratio or P x P y sometimes log odds are calculated as the similarity score.

42 More Precisely score( x, y) 2log 2 P xy 2P P x y, if x y score( x, x) 2log 2 P x xx P P x In BLOSUM matrices these values are rounded to the nearest integer.

43 Practical Programs Computational biology was initially regarded as a branch of theoretical computer science. It provides 20 years of problems to work on. But from late 1980s to 1990, two practical programs started to change this

44 FASTP Pearson

45 Computer History for

46 FASTA Pearson WR. Rapid and sensitive sequence comparison with FASTP and FASTA. Methods in Enzymology 1990, 183: The FASTA program can search the NBRF protein sequence library (2.5 million residues) in less than 20 min on an IBM-PC microcomputer. FASTA is also known as a sequence file format.

47 BLAST blast blast Cited by 40501

48 Computer History in 1990

49 BLAST finds hits then extends GCNTACACGTCACCATCTGTGCCACCACNCATGTCTCTAGTGATCCCTCATAAGTTCCAACAAAGTTTGC GCCTACACACCGCCAGTTGTG-TTCCTGCTATGTCTCTAGTGATCCCTGAAAAGTTCCAGCGTATTTTGC 1 m seq1 1 n seq2 Time complexity becomes O(4-11 mnt) The homology grows from the 11 consecutive matches therefore they are called the seed More precisely these are called hits. A seed often is used to refer to the way these 11 positions are selected.

50 For Protein Sequence A hit is the approximate match of two 3-mers, so that the total score (under PAM) is above a threshold. Use query sequence s hitting 3-mers to build a DFA (Deterministic Finite Automata). Use the DFA to scan the database.

51 Gapped BLAST and PSI-BLAST Cited by blast psi-blast

52 New Ideas in Second BLAST Paper Two-hits: 1 m seq1 1 n seq2 Position-Specific Iterated (PSI): Multiple sequence alignment of returned proteins. Calculate position-specific scoring matrix (instead of using BLOSUM). Search again with the new matrix.

53 Computer History for 1997

54 Example of missing a target Fail: GAGTACTCAACACCAACATTAGTGGGCAATGGAAAAT GAATACTCAACAGCAACATCAATGGGCAGCAGAAAAT Two objectives Sensitivity (success rate of finding a homology) needs a shorter seed Speed (the fewer hits, the faster) needs a longer seed But we really want both!

55

56 Small change We now use eleven spaced matches as a hit compare to consecutive matches Match locations given by a pre-defined pattern Eleven required positions (weight=11) Seven don t care positions GAGTACTCAACACCAACATTAGTGGCAATGGAAAAT GAATACTCAACAGCAACACTAATGGCAGCAGAAAAT

57 Difference Speed Random hit probability is still 4-11 Weight of the seed determines the hit probability Sensitivity Spaced seed longer, so fewer positions to hit Intuitively lower. 1 L

58 Simulated sensitivity curves

59 Why spaced seeds are better? TTGACCTCACC?? TTGACCTCACC? CAA?A??A?C??TA?TGG????????? CAA?A??A?C??TA?TGG? BLAST s seed usually uses more than one hits to detect one homology (redundant) Spaced seeds uses fewer hits to detect one homology (efficient)

60

61 Seed shape is important PH s seed not overlap much when slides: The hits at different positions are independent.

62 2004 M. Li, B. Ma, D. Kisman, and B. Ma. PatternHunter II: Highly Sensitive and Fast Homology Search. Journal of Bioinformatics and Computational Biology 2(3):

63 Multiple Spaced Seeds Different spaced seeds detect different homologies. Use k seeds simultaneously! Slows down k times. Is this worth? Decreasing the seed weight can also increase the sensitivity. Slows down 4 times.

64 Simulated sensitivity curves: Solid curves: Multiple (1, 2, 4, 8, 16) weight-12 spaced seeds. Dashed curves: Optimal spaced seeds with weight = 11, 10, 9, 8. Two weight-12 One weight-11 Typically, Doubling the seed number gains better sensitivity than decreasing the weight by 1. One weight-12

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