1. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment1 BCB 444/544 Lecture 6 Try to Finish Dynamic Programming Global & Local Alignment Next lecture: Scoring Matrices Alignment Statistics #6_Aug31

2. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment2 Mon Aug 27 - for Lecture #4 Pairwise Sequence Alignment Chp 3 - pp 31-41 Wed Aug 29 - for Lecture #5 Dynamic Programming Eddy: What is Dynamic Programming? 2004 Nature Biotechnol 22:909 http://www.nature.com/nbt/journal/v22/n7/abs/nbt0704-909.html Thurs Aug 30 - Lab #2: Databases, ISU Resources & Pairwise Sequence Alignment Fri Aug 31 - for Lecture #6 Scoring Matrices & Alignment Statistics Chp 3 - pp 41-49 Required Reading (before lecture)

3. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment3 Announcements Fri Aug 31 - Revised notes for Lecture 5 posted online Changes? mainly re-ordering, symbols, color "coding" Mon Sept 3 - NO CLASSES AT ISU (Labor Day)!! - Enjoy!! Tues Sept 4 - Lab #2 Exercise Writeup Due by 5 PM (or sooner!) Send via email to Pete Zaback petez@iastate.edupetez@iastate.edu (HW#2 assignment will be posted online) Fri Sept 14 - HW#2 Due by 5 PM (or sooner!) Fri Sept 21 - Exam #1

4. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment4 Chp 3- Sequence Alignment SECTION II SEQUENCE ALIGNMENT Xiong: Chp 3 Pairwise Sequence Alignment √Evolutionary Basis √Sequence Homology versus Sequence Similarity √Sequence Similarity versus Sequence Identity Methods - cont Scoring Matrices Statistical Significance of Sequence Alignment Adapted from Brown and Caragea, 2007, with some slides from: Altman, Fernandez-Baca, Batzoglou, Craven, Hunter, Page.

5. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment5 Methods √Global and Local Alignment √Alignment Algorithms √Dot Matrix Method Dynamic Programming Method - cont Gap penalities DP for Global Alignment DP for Local Alignment Scoring Matrices Amino acid scoring matrices PAM BLOSUM Comparisons between PAM & BLOSUM Statistical Significance of Sequence Alignment

6. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment6 Sequence Homology vs Similarity Homologous sequences - sequences that share a common evolutionary ancestry Similar sequences - sequences that have a high percentage of aligned residues with similar physicochemical properties (e.g., size, hydrophobicity, charge) IMPORTANT: Sequence homology: An inference about a common ancestral relationship, drawn when two sequences share a high enough degree of sequence similarity Homology is qualitative Sequence similarity: The direct result of observation from a sequence alignment Similarity is quantitative; can be described using percentages

7. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment7 Goal of Sequence Alignment Find the best pairing of 2 sequences, such that there is maximum correspondence between residues DNA 4 letter alphabet (+ gap) TTGACAC TTTACAC Proteins 20 letter alphabet (+ gap) RKVA-GMA RKIAVAMA

8. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment8 Statement of Problem Given: 2 sequences Scoring system for evaluating match (or mismatch) of two characters Penalty function for gaps in sequences Find: Optimal pairing of sequences that: Retains the order of characters Introduces gaps where needed Maximizes total score

9. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment9 Avoiding Random Alignments with a Scoring Function Introducing too many gaps generates nonsense alignments: s--e-----qu---en--ce sometimesquipsentice Need to distinguish between alignments that occur due to homology and those that occur by chance Define a scoring function that rewards matches (+) and penalizes mismatches (-) and gaps (-) Scoring Function (S): e.g. Match:  1 Mismatch:  1 Gap:  0 S =  (#matches) -  (#mismatches) -  (#gaps) Note: I changed symbols & colors on this slide!

10. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment10 Not All Mismatches are the Same Some amino acids are more "exchangeable" than others (physicochemical properties are similar) e.g., Ser & Thr are more similar than Trp & Ala Substitution matrix can be used to introduce "mismatch costs" for handling different types of substitutions Mismatch costs are not usually used in aligning DNA or RNA sequences, because no substitution is "better" than any other (in general)

11. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment11 Substitution Matrix s(a,b) corresponds to score of aligning character a with character b Match scores are often calculated based on frequency of mutations in very similar sequences (more details later)

12. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment12 Global vs Local Alignment Local alignment Finds local regions with highest similarity between 2 sequences Aligns these without regard for rest of sequence Sequences are not assumed to be similar over entire length Global alignment Finds best possible alignment across entire length of 2 sequences Aligned sequences assumed to be generally similar over entire length

13. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment13 Global vs Local Alignment - example 1 = CTGTCGCTGCACG 2 = TGCCGTG CTGTCGCTGCACG -TGCCG-T----G Global alignment CTGTCGCTGCACG -TG-C-C-G--TG CTGTCGCTGCACG -TGCCG-TG---- Local alignment Which is better?

14. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment14 Global vs Local Alignment Which should be used when? It is critical to choose correct method! Global Alignment vs Local Alignment? Shout out the answers!! Which should we use for? 1.Searching for conserved motifs in DNA or protein sequences? 2.Aligning two closely related sequences with similar lengths? 3.Aligning highly divergent sequences? 4.Generating an extended alignment of closely related sequences? 5.Generating an extended alignment of closely related sequences with very different lengths? Hmmm - we'll work on that Excellent!

15. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment15 Alignment Algorithms 3 major methods for pairwise sequence alignment: 1.Dot matrix analysis 2.Dynamic programming 3.Word or k-tuple methods (later, in Chp 4)

16. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment16 Dot Matrix Method (Dot Plots) Place 1 sequence along top row of matrix Place 2nd sequence along left column of matrix Plot a dot each time there is a match between an element of row sequence and an element of column sequence For proteins, usually use more sophisticated scoring schemes than "identical match" Diagonal lines indicate areas of match Contiguous diagonal lines reveal alignment; "breaks" = gaps (indels) A C A C G AC CGG

17. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment17 Interpretation of Dot Plots When comparing 2 sequences: Diagonal lines of dots indicate regions of similarity between 2 sequences Reverse diagonals (perpendicular to diagonal) indicate inversions What do such patterns mean when comparing a sequence with itself (or its reverse complement)? e.g.: Reverse diagonals crossing diagonals (X's) indicate palindromes Exploring Dot Plots

18. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment18 Dynamic Programming C A T - T C A - C | | | | | C - T C G C A G C Idea: Display one sequence above another with spaces inserted in both to reveal similarity For Pairwise sequence alignment

19. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment19 Global Alignment: Scoring CTGTCG- CTGCACG -TGC-CG-TG---- Reward for matches:  Mismatch penalty:  Space/gap penalty:  Score =  w –  x -  y w = #matches x = #mismatches y = #spaces Note: I changed symbols & colors on this slide!

20. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment20 Global Alignment: Scoring C T G T C G – C T G C - T G C – C G – T G - -5 10 10 -2 -5 -2 -5 -5 10 10 -5 Total = 11 Reward for matches:10 Mismatch penalty: -2 Space/gap penalty:-5 We could have done better!! Note: I changed symbols & colors on this slide!

21. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment21 Alignment Algorithms Global: Needleman-Wunsch Local: Smith-Waterman Both NW and SW use dynamic programming Variations: Gap penalty functions Scoring matrices

22. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment22 Dynamic Programming - Key Idea: The score of the best possible alignment that ends at a given pair of positions (i, j) is equal to: the score of best alignment ending just previous to those two positions (i.e., ending at i-1, j-1) PLUS the score for aligning x i and y j

23. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment23 Global Alignment: DP Problem Formulation & Notations Given two sequences (strings) X = x 1 x 2 …x N of length N x = AGC N = 3 Y = y 1 y 2 …y M of length M y = AAAC M = 4 Construct a matrix with (N+1) x (M+1) elements, where S(i,j) = Score of best alignment of x[1..i]=x 1 x 2 …x i with y[1..j]=y 1 y 2 …y j S(2,3) = score of best alignment of AG ( x 1 x 2 ) to AAA ( y 1 y 2 y 3 ) x1x1 x2x2 x3x3 y1y1 y2y2 y3y3 y4y4 Which means: Score of best alignment of a prefix of X and a prefix of Y

24. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment24 Dynamic Programming - 4 Steps: 1.Define score of optimum alignment, using recursion 2.Initialize and fill in a DP matrix for storing optimal scores of subproblems, by solving smallest subproblems first (bottom-up approach) 3.Calculate score of optimum alignment(s) 4.Trace back through matrix to recover optimum alignment(s) that generated optimal score

25. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment25 Initial conditions: Recursive definition: For 1  i  N, 1  j  M: 1- Define Score of Optimum Alignment using Recursion Define:

26. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment26 2- Initialize & Fill in DP Matrix for Storing Optimal Scores of Subproblems S(N,M) S(0,0)=0 S(i,j) S(i-1,j) S(i-1,j-1) S(i,j-1) 0 01N 1 M Initialization Recursion Construct sequence vs sequence matrix:

27. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment27 2- cont Fill in DP Matrix S(N,M) S(0,0)=0 S(i,j) S(i-1,j)S(i-1,j-1) S(i,j-1) 0 01N 1 M Fill in from [0,0] to [N,M] (row by row), calculating best possible score for each alignment including residues at [i,j] Keep track of dependencies of scores (in a pointer matrix).

28. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment28 x 1 x 2... x i-1 x i y 1 y 2... y j-1 y j S(i-1,j-1) +  (x i,y j ) x 1 x 2... x i-1 x i y 1 y 2... y j — S(i-1,j) -  x 1 x 2... x i — y 1 y 2... y j-1 y j S(i,j-1) -  x i aligns to y j x i aligns to a gapy j aligns to a gap 3- Calculate Score S(N,M) of Optimum Alignment - for Global Alignment What happens in last step in alignment of x[1..i] to y[1..j]? 1 of 3 cases applies:

29. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment29 Example Case 1: Line up x i with y j x: C A T T C A C y: C - T T C A G i - 1 i j j -1 x: C A T T C A - C y: C - T T C A G - Case 2: Line up x i with space i - 1i j x: C A T T C A C - y: C - T T C A - G Case 3: Line up y j with space i jj -1

30. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment30 λ C T C G C A G C A C T T C A C 0 -5 -10 -15 -20 -25 -30 -35 -40 -5 -10 -15 -20 -25 -30 -35 10 5 λ +10 for match, -2 for mismatch, -5 for space Fill in the matrix

31. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment31 +10 for match, -2 for mismatch, -5 for space Calculate score of optimum alignment 0-5-10-15-20-25-30-35-40 -51050-5-10-15-20-25 -10583-2-70-5-10 -150151050-5-2-7 -20-5101383-2-7-4 -25-1052015181383 -30-150151813282318 -35-20-5101328232633 λ C T C G C A G C C A C T T C A λ

32. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment32 4- Trace back through matrix to recover optimum alignment(s) that generated the optimal score How? "Repeat" alignment calculations in reverse order, starting at from position with highest score and following path, position by position, back through matrix Result? Optimal alignment(s) of sequences

33. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment33 Traceback - for Global Alignment Start in lower right corner & trace back to upper left Each arrow introduces one character at end of sequence alignment: A horizontal move puts a gap in left sequence A vertical move puts a gap in top sequence A diagonal move uses one character from each sequence

34. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment34 0-5-10-15-20-25-30-35-40 -51050-5-10-15-20-25 -10583-2-70-5-10 -150151050-5-2-7 -20-5101383-2-7-4 -25-1052015181383 -30-150151813282318 -35-20-5101328232633 λ C T C G C A G C C A C T T C A λ * * Can have >1 optimum alignment; this example has 2 Traceback to Recover Alignment

35. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment35 C T C G C A G C C A T T C A C What are the 2 Alignments with Optimum Score = 33? C T C G C A G C C T C G C A G C 1: 2:

36. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment36 Local Alignment: Motivation To "ignore" stretches of non-coding DNA: Non-coding regions (if "non-functional") are more likely to contain mutations than coding regions Local alignment between two protein-encoding sequences is likely to be between two exons To locate protein domains or motifs: Proteins with similar structures and/or similar functions but from different species (for example), often exhibit local sequence similarities Local sequence similarities may indicate ”functional modules” Non-coding - "not encoding protein" Exons - "protein-encoding" parts of genes vs Introns = "intervening sequences" - segments of eukaryotic genes that "interrupt" exons Introns are transcribed into RNA, but are later removed by RNA processing & are not translated into protein

37. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment37 Local Alignment: Example Best local alignment: Match: +2Mismatch or space: -1 Score = 5 g g t c t g a g a a a c g a g g t c t g a g a a a c – g a -

38. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment38 Local Alignment: Algorithm S [i, j] = Score for optimally aligning a suffix of X with a suffix of Y Initialize top row & leftmost column of matrix with "0" Recall: for Global Alignment, S [i, j] = Score for optimally aligning a prefix of X with a prefix of Y Initialize top row & leftmost column of with gap penalty

39. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment39 000000000 010101001 000000200 001000010 001000000 010201001 000010200 010102011 λ C T C G C A G C A C T T C A C λ +1 for a match, -1 for a mismatch, -5 for a space Traceback - for Local Alignment

40. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment40 Some Results re: Alignment Algorithms (for ComS, CprE & Math types!) Most pairwise sequence alignment problems can be solved in O(mn) time Space requirement can be reduced to O(m+n), while keeping run-time fixed [Myers88] Highly similar sequences can be aligned in O (dn) time, where d measures the distance between the sequences [Landau86]

41. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment41 "Scoring" or "Substitution" Matrices 2 Major types for Amino Acids: PAM & BLOSUM PAM = Point Accepted Mutation relies on "evolutionary model" based on observed differences in alignments of closely related proteins BLOSUM = BLOck SUbstitution Matrix based on % aa substitutions observed in blocks of conserved sequences within evolutionarily divergent proteins

42. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment42 PAM Matrix PAM = Point Accepted Mutation relies on "evolutionary model" based on observed differnces in closely related proteins Model includes defined rate for each type of sequence change Suffix number (n) reflects amount of "time" passed: rate of expected mutation if n% of amino acids had changed PAM1 - for less divergent sequences (shorter time) PAM250 - for more divergent sequences (longer time)

43. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment43 BLOSUM Matrix BLOSUM = BLOck SUbstitution Matrix based on % aa substitutions observed in blocks of conserved sequences within evolutionarily divergent proteins Doesn't rely on a specific evolutionary model Suffix number (n) reflects expected similarity: average % aa identity in the MSA from which the matrix was generated BLOSUM45 - for more divergent sequences BLOSUM62 - for less divergent sequences

44. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment44 Statistical Significance of Sequence Alignment

45. 8/31/07BCB 444/544 F07 ISU Dobbs #6 - More DP: Global vs Local Alignment45 Affine Gap Penalty Functions Gap penalty = h + gk where k = length of gap h = gap opening penalty g = gap extension penalty Can also be solved in O(nm) time using dynamic programming