Sequence Alignment (chapter 6)

Transcription

1 Sequence lignment (chapter 6) he biological problem lobal alignment Local alignment Multiple alignment Introduction to bioinformatics, utumn 6

2 Background: comparative genomics Basic question in biology: what properties are shared among organisms? enome sequencing allows comparison of organisms at DN and protein levels Comparisons can be used to Find evolutionary relationships between organisms Identify functionally conserved sequences Identify corresponding genes in human and model organisms: develop models for human diseases Introduction to bioinformatics, utumn 6 3

3 Homologs wo genes or characters g B and g C evolved from the same ancestor g are called homologs Homologs usually exhibit conserved functions g = agtgtccgttaagtgcgttc g B = agtgccgttaaagttgtacgtc g C = ctgactgtttgtggttc Close evolutionary relationship => expect a high number of homologs Introduction to bioinformatics, utumn 6 4

4 Sequence similarity Intuitively, similarity of two sequences refers to the degree of match between corresponding positions in sequence agtgccgttaaagttgtacgtc ctgactgtttgtggttc What about sequences that differ in length? Introduction to bioinformatics, utumn 6 5

5 Similarity vs homology Sequence similarity is not sequence homology If the two sequences g B and g C have accumulated enough mutations, the similarity between them is likely to be low #mutations agtgtccgttaagtgcgttc agtgtccgttatagtgcgttc agtgtccgcttatagtgcgttc 4 agtgtccgcttaagggcgttc 8 agtgtccgcttcaaggggcgt 6 gggccgttcatgggggt 3 gcagggcgtcactgagggct #mutations 64 acagtccgttcgggctattg 8 cagagcactaccgc 56 cacgagtaagatatagct 5 taatcgtgata 4 acccttatctacttcctggagtt 48 agcgacctgcccaa 496 caaac Homology is more difficult to detect over greater evolutionary distances. Introduction to bioinformatics, utumn 6 6

6 Similarity vs homology () Sequence similarity can occur by chance Similarity does not imply homology Similarity is an expected consequence of homology Introduction to bioinformatics, utumn 6 7

7 Orthologs and paralogs We distinguish between two types of homology Orthologs: homologs from two different species Paralogs: homologs within a species Organism g g g g ene is copied within organism g B Organism B g C Organism C g B g C Introduction to bioinformatics, utumn 6 8

8 Orthologs and paralogs () Orthologs typically retain the original function In paralogs, one copy is free to mutate and acquire new function (no selective pressure) g Organism g g g ene is copied within organism g B Organism B g C Organism C g B g C Introduction to bioinformatics, utumn 6 9

9 Sequence alignment lignment specifies which positions in two sequences match acgtctag actctag acgtctag actctag acgtctag actctag matches 5 mismatches not aligned 5 matches mismatches not aligned 7 matches mismatches not aligned Introduction to bioinformatics, utumn 6 3

10 Mutations: Insertions, deletions and substitutions Indel: insertion or deletion of a base with respect to the ancestor sequence acgtctag actctag Mismatch: substitution (point mutation) of a single base Insertions and/or deletions are called indels We can t tell whether the ancestor sequence had a base or not at indel position Introduction to bioinformatics, utumn 6 3

11 Problems What sorts of alignments should be considered? How to score alignments? How to find optimal or good scoring alignments? How to evaluate the statistical significance of scores? In this course, we discuss the first three problems. Course Biological sequence analysis tackles all four indepth. Introduction to bioinformatics, utumn 6 3

12 Sequence lignment (chapter 6) he biological problem lobal alignment Local alignment Multiple alignment Introduction to bioinformatics, utumn 6 33

13 lobal alignment Problem: find optimal scoring alignment between two sequences (Needleman & Wunsch 97) We give score for each position in alignment Identity (match) + Substitution (mismatch) µ Indel WH WHY S(WH/WHY) = + µ Introduction to bioinformatics, utumn 6 34

14 Representing alignments and scores WH W H WHY W X H X X Y X Introduction to bioinformatics, utumn 6 35

15 Representing alignments and scores WH W H WHY W lobal alignment score S 3,4 = µ H Y µ Introduction to bioinformatics, utumn 6 36

16 Dynamic programming How to find the optimal alignment? We use previous solutions for optimal alignments of smaller subsequences his general approach is known as dynamic programming Introduction to bioinformatics, utumn 6 37

17 Filling the alignment matrix W H Y W Case Case 3 H Case Consider the alignment process at shaded square. Case. lign H against H (match or substitution). Case. lign H in WHY against (indel) in WH. Case 3. lign H in WH against (indel) in WHY. Introduction to bioinformatics, utumn 6 38

18 Filling the alignment matrix () W H Scoring the alternatives. Case. S, = S, + s(, ) Case. S, = S, W H Y Case Case 3 Case Case 3. S, = S, s(i, j) = for matching positions, s(i, j) = µ for substitutions. Choose the case (path) that yields the maximum score. Keep track of path choices. Introduction to bioinformatics, utumn 6 39

19 lobal alignment: formal development = a a a 3 a n, 3 4 B = b b b 3 b m b b b 3 b 4 b b b 3 b 4 a a a 3 ny alignment can be written as a unique path through the matrix Score for aligning and B up to positions i and j: S i,j = S(a a a 3 a i, b b b 3 b j ) 3 a a a 3 Introduction to bioinformatics, utumn 6 4

20 Scoring partial alignments lignment of = a a a 3 a n with B = b b b 3 b m can end in three ways Case : (a a a i ) a i (b b b j ) b j Case : (a a a i ) a i (b b b j ) Case 3: (a a a i ) (b b b j ) b j Introduction to bioinformatics, utumn 6 4

21 Scoring alignments Scores for each case: Case : (a a a i ) a i (b b b j ) b j Case : (a a a i ) a i s(a i, b j ) = + ifa { i = b j µ otherwise (b b b j ) Case 3: (a a a i ) s(a i, ) = s(, b j ) = (b b b j ) b j Introduction to bioinformatics, utumn 6 4

22 Scoring alignments () First row and first column correspond to initial alignment against indels: S(i, ) = i b b 3 b 3 4 b 4 S(, j) = j 3 4 Optimal global alignment score S(, B) = S n,m a a 3 a 3 3 Introduction to bioinformatics, utumn 6 43

23 lgorithm for global alignment Input sequences, B, n =, m = B Set S i, := i for all i Set S,j := j for all j for i := to n for j := to m S i,j := max{s i,j, S i,j + s(a i,b j ), S i,j } end end lgorithm takes O(nm) time and space. Introduction to bioinformatics, utumn 6 44

24 lobal alignment: example µ = = 4 C 6 8? Introduction to bioinformatics, utumn 6 45

25 lobal alignment: example () µ = = C C Introduction to bioinformatics, utumn 6 46

26 Sequence lignment (chapter 6) he biological problem lobal alignment Local alignment Multiple alignment Introduction to bioinformatics, utumn 6 47

27 Local alignment: rationale Otherwise dissimilar proteins may have local regions of similarity > Proteins may share a function Human bone morphogenic protein receptor type II precursor (left) has a 3 aa region that resembles 9 aa region in F receptor (right). he shared function here is protein kinase. Introduction to bioinformatics, utumn 6 48

28 Local alignment: rationale B Regions of similarity lobal alignment would be inadequate Problem: find the highest scoring local alignment between two sequences Previous algorithm with minor modifications solves this problem (Smith & Waterman 98) Introduction to bioinformatics, utumn 6 49

29 From global to local alignment Modifications to the global alignment algorithm Look for the highestscoring path in the alignment matrix (not necessarily through the matrix) llow preceding and trailing indels without penalty Introduction to bioinformatics, utumn 6 5

30 Scoring local alignments = a a a 3 a n, B = b b b 3 b m Let I and J be intervals (substrings) of and B, respectively:, Best local alignment score: where S(I, J) is the score for substrings I and J. Introduction to bioinformatics, utumn 6 5

31 llowing preceding and trailing indels First row and column initialised to zero: M i, = M,j = b b 3 b 3 4 b 4 a b b b3 a a 3 a 3 Introduction to bioinformatics, utumn 6 5

32 Introduction to bioinformatics, utumn 6 53 Recursion for local alignment M i,j = max { M i,j + s(a i, b i ), M i,j, M i,j, } C

33 Introduction to bioinformatics, utumn 6 54 Finding best local alignment Optimal score is the highest value in the matrix = max i,j M i,j Best local alignment can be found by backtracking from the highest value in M C

34 Introduction to bioinformatics, utumn 6 55 Local alignment: example C 3 C C C C

35 Introduction to bioinformatics, utumn 6 56 Local alignment: example C 3 C C C C Scoring Match: + Mismatch: Indel: C C C

36 Nonuniform mismatch penalties We used uniform penalty for mismatches: s(, C ) = s(, ) = = s(, ) = µ ransition mutations (>, >, C>, >C) are approximately twice as frequent than transversions ( >, >, >C, >) use nonuniform mismatch C penalties C Introduction to bioinformatics, utumn 6 57

37 aps in alignment ap is a succession of indels in alignment C C C C Previous model scored a length k gap as w(k) = k Replication processes may produce longer stretches of insertions or deletions In coding regions, insertions or deletions of codons may preserve functionality Introduction to bioinformatics, utumn 6 58

38 ap open and extension penalties () We can design a score that allows the penalty opening gap to be larger than extending the gap: w(k) = (k ) ap open cost, ap extension cost Our previous algorithm can be extended to use w(k) (not discussed on this course) Introduction to bioinformatics, utumn 6 59

39 Sequence lignment (chapter 6) he biological problem lobal alignment Local alignment Multiple alignment Introduction to bioinformatics, utumn 6 6

40 Multiple alignment Consider a set of n sequences on the right Orthologous sequences from different organisms Paralogs from multiple duplications How can we study relationships between these sequences? aggcgagctgcgagtgcta cgttagattgacgctgac ttccggctgcgac gacacggcgaacgga agtgtgcccgacgagcgaggac gcgggctgtgagcgcta aagcggcctgtgtgcccta atgctgctgccagtgta agtcgagccccgagtgc agtccgagtcc actcggtgc Introduction to bioinformatics, utumn 6 6

41 Optimal alignment of three sequences lignment of = a a a i and B = b b b j can end either in (, b j ), (a i, b j ) or (a i, ) = 3 alternatives lignment of, B and C = c c c k can end in 3 ways: (a i,, ), (, b j, ), (,, c k ), (, b j, c k ), (a i,, c k ), (a i, b j, ) or (a i, b j, c k ) Solve the recursion using threedimensional dynamic programming matrix: O(n 3 ) time and space eneralizes to n sequences but impractical with moderate number of sequences Introduction to bioinformatics, utumn 6 6

42 Multiple alignment in practice In practice, realworld multiple alignment problems are usually solved with heuristics Progressive multiple alignment Choose two sequences and align them Choose third sequence w.r.t. two previous sequences and align the third against them Repeat until all sequences have been aligned Different options how to choose sequences and score alignments Introduction to bioinformatics, utumn 6 63

43 Multiple alignment in practice Profilebased progressive multiple alignment: CLUSLW Construct a distance matrix of all pairs of sequences using dynamic programming Progressively align pairs in order of decreasing similarity CLUSLW uses various heuristics to contribute to accuracy Introduction to bioinformatics, utumn 6 64

44 dditional material R. Durbin, S. Eddy,. Krogh,. Mitchison: Biological sequence analysis Course Biological sequence analysis in Spring 7 Introduction to bioinformatics, utumn 6 65