8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats1 BCB 444/544 Lecture 6 Finish Dynamic Programming Scoring Matrices Alignment Statistics #6_Aug31

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats2 Mon Aug 27 - for Lecture #4 Pairwise Sequence Alignment Chp 3 - pp Wed Aug 29 - for Lecture #5 Dynamic Programming Eddy: What is Dynamic Programming? 2004 Nature Biotechnol 22:909 Thurs Aug 30 - Lab #2: Databases, ISU Resources & Pairwise Sequence Alignment Fri Aug 31 - for Lecture #6 Scoring Matrices & Alignment Statistics Chp 3 - pp Required Reading (before lecture)

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats3 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 to Pete Zaback (HW#2 assignment will be posted online) Fri Sept 14 - HW#2 Due by 5 PM (or sooner!) Fri Sept 21 - Exam #1

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats4 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.

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats5 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats6 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats7 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats8 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats9 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!

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats10 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)

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats11 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)

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats12 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats13 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?

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats14 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!

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats15 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)

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats16 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats17 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats18 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats19 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!

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats20 Global Alignment: Scoring C T G T C G – C T G C - T G C – C G – T G 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!

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats21 Alignment Algorithms Global: Needleman-Wunsch Local: Smith-Waterman Both NW and SW use dynamic programming Variations: Gap penalty functions Scoring matrices

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats22 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats23 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats24 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats25 Initial conditions: Recursive definition: For 1  i  N, 1  j  M: 1- Define Score of Optimum Alignment using Recursion Define:

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats26 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:

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats27 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).

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats28 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:

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats29 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats30 λ C T C G C A G C A C T T C A C λ +10 for match, -2 for mismatch, -5 for space Fill in the matrix

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats for match, -2 for mismatch, -5 for space Calculate score of optimum alignment λ C T C G C A G C C A C T T C A λ

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats32 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats33 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats35 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats36 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 -

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats37 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats39 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]

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats40 "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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats41 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)

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats42 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

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats43 Statistical Significance of Sequence Alignment

8/31/07BCB 444/544 F07 ISU Dobbs #6 - Scoring Matrices & Alignment Stats44 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